Short-Range Order in a Flat Two-Dimensional Fermi Surface

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toggle MRAM

Single-domainmodel fortoggle MRAMD.C.WorledgeAn overview is presented of the use of a single-domain model fordeveloping an understanding of the switching of two coupledmagnetic free layers for toggle MRAM(magnetic randomaccess memory).The model includes the eﬀects of length,width,thickness,magnetization,thickness asymmetry,intrinsicanisotropy,exchange coupling,dipole coupling,and appliedmagneticﬁeld.First,a simple perturbative approach is used tounderstand the basic phenomena at lowﬁelds,including the criticalswitching curve and activation energy.Then the more generalmodel is applied in order to understand the eﬀects of saturation atlargeﬁeld,and thickness asymmetry.The major results are thattoggle MRAM should have a larger margin for half-select and full-select switchingﬁelds than Stoner–Wohlfarth MRAM,and thatthe activation energy should increase upon half-select,thuseliminating the half-select activated-error problem.Introduction:Why is toggle MRAM better than Stoner–Wohlfarth MRAM?In traditional MRAM,use is made of a single free layer [see Figure1(a)]which switches by Stoner–Wohlfarth reversal[1].As shown in Figure1(b),forﬁelds applied outside the astroid boundary only one state is stable, whereas at T¼0,forﬁelds inside the astroid boundary both states are stable and no switching occurs between them.Switching is accomplished by simultaneously applying both bit-line and word-lineﬁelds(full-select)to the selected bit.Since this full-selectﬁeld is outside the astroid boundary,the selected bit is stable only in the state to be written.At the same time,the other‘‘half-selected’’bits on the same bit line and word line do not switch because the half-selectﬁeld is inside the astroid boundary.This Stoner–Wohlfarth method of switching has two major disadvantages.Theﬁrst is that the margin between half select and full select is small;this would require tight control of the switchingﬁelds in orderto reach the multi-megabit chip level.The second disadvantage is that for T¼0,there is a large dropin the activation energy for half-selected bits,as shown in Figure1(c).This activation energy is the barrier preventing the bit from making a thermally activated switch into the other state.The drop in the activation energy,combined with the large number of half selects which occur over the lifetime of the chip,results in a signiﬁcant error rate.These two problems,half-select margin and activated errors,limit the usefulness of Stoner–Wohlfarth MRAM to small arrays and short lifetimes.Leonid Savtchenko invented a solution to these problems,known as toggle MRAM[2].As shown in Figure1(d),in spin-ﬂop switching the single free layeris replaced by two magnetic layers separated by a nonmagnetic spacer layer.This dramatically changes the shape of the critical switching curve,as shown in Figure1(e)[2].The bit can now tolerate a half-selectﬁeld many times larger than the smallest required full-select ﬁeld,thus relaxing the requirement on control of the switchingﬁelds from bit to bit.Furthermore,as shown in Figure1(f),the activation energy under half-select actually increases,thus making the bit more rather than less thermally stable[3].This essentially eliminates the activated-error problem.Figures1and2capture the essence of the diﬀerence between the Stoner–Wohlfarth and toggle MRAM approaches.The rest of this paper explains these approaches in more detail.The next section gives an overview of toggling and spin-ﬂop switching.Then a simple perturbative model is introduced which gives an intuitive but approximate description of the switching behavior at smallﬁelds for the special case of a circular balanced bit.Finally,an exact single-domain model isÓCopyright2006by International Business Machines Corporation.Copying in printed form for private use is permitted without payment of royalty provided that(1)eachreproduction is done without alteration and(2)the Journal reference and IBM copyright notice are included on theﬁrst page.The title and abstract,but no other portions,of this paper may be copied or distributed royalty free without further permission by computer-based and other information-service systems.Permission to republish anyother portion of this paper must be obtained from the Editor.690018-8646/06/$5.00ª2006IBMdescribed and used to explain the switching behavior in general.Portions of this work have previously been published in more abbreviated form in [3]and [4].A similar single-domain model has been discussed in [5].Experimental results on toggle MRAM have been reported in [2,6,7].Overview of toggling and spin-flop switchingAs shown in Figure 1(d),the toggle bit has two magnetic layers of equal thickness t ,which are separated by a nonmagnetic spacer.Figure 2(a)shows a top-down view of the bit,which is patterned in the shape of an ellipse or circle.The magnetic poles formed at the edges of each of the two magnetic layers create dipole ﬁelds,which make the two layers line up anti-parallel (AP)in zero ﬁeld.(It is also possible to add some exchange coupling from the spacer layer,though this is optional.)This ﬂux closure has several ramiﬁcations.First,in this ﬂux-closed anti-parallel state,the shape anisotropy does not determine the orientation of the moments in zero ﬁeld,since there is no net moment.Instead,the zero-ﬁeld orientation is determined by the intrinsic anisotropy of the twomagnetic layers,which is chosen to lie at 45degrees to thebit lines and word lines (by depositing and annealing the ﬁlms in a magnetic ﬁeld).This direction is termed the easy axis.Second,the zero-ﬁeld activation energy is set by the intrinsic anisotropy,not by the shape anisotropy,as in Stoner–Wohlfarth switching.Finally,the ﬂux closure results in an appreciable reduction in the bit-to-bit dipole ﬁeld coupling.When a magnetic ﬁeld is applied along the easy axis of the bit [Figure 2(b)],the moments initially do not respond.This is because there is no net moment for the ﬁeld to act upon.As the easy-axis ﬁeld is increased,the AP state is maintained until a critical ﬁeld,known as the spin-ﬂop ﬁeld H sf ,is reached;at this point the moments discontinuously jump from the AP state into a‘‘scissored’’state.In the scissored state the net moment is pointing in the direction of the applied ﬁeld,with one moment rotated clockwise and the other moment rotated counterclockwise from this direction.In that state there is a net moment,and as the ﬁeld is further increased,the moments respond by smoothly scissoring together until they become parallel at a ﬁeld H x sat .This spin-ﬂop phenomenon is familiar from the study of antiferromagnets,but is usually accessible onlyIllustrative switching by Stoner–Wohlfarth reversal and toggle MRAM. In traditional Stoner–Wohlfarth switching, use is made of a single free layer, as shown in the tunnel junction cross section (a), which switches when a field is applied across the critical switching curve, or “astroid” (b). When a field is applied along the half-select direction, the activation energy decreases dramatically (c). In toggle switching, use is made of two magnetic free layers (d), which switch when a rectangular field excursion crosses the L-shaped critical switching curve (e). When a field is applied along the half-select direction, the activation energy initially increases, making the bit more stable (f).Figure 170at large ﬁelds because of the large exchange-coupling ﬁelds present in antiferromagnets.In the syntheticantiferromagnet conﬁguration considered here,the cou-pling ﬁeld,composed of the sum of the dipole and spacer exchange coupling,is substantially smaller,so that the spin-ﬂop switching can be achieved at ﬁelds less than 100Oe.Figure 2(c)shows the operation of a toggle bit in an MRAM in the case of a ‘‘box-ﬁeld’’excursion.First the word-line ﬁeld is turned on,which scissors the moments together,creating a net moment pointing roughly in the direction of the applied ﬁeld.Hence,the axis along which the moments are anti-parallel rotates from the zero-ﬁeld state by roughly 45degrees.Then the bit-line ﬁeld is turned on,which rotates each of the moments by roughly 45degrees so that again the net moment is aligned with the applied ﬁeld.Then the word-line ﬁeld is removed,which continues the rotation of each moment another 45degrees so that the net moment of the scissored moments is pointing along the bit-ﬁeld direction.Finally the bit ﬁeld is removed,and the moments relax into the AP state along the intrinsic anisotropy direction,but with their moments reversed from the starting condition.Hence,the state of the bit has been toggled,either from a ‘‘1’’to a ‘‘0’’or from a ‘‘0’’to a ‘‘1.’’The toggle nature of this process requires that the MRAM circuit ﬁrst read each bit before writing it to determine whether it has to be pared to Stoner–Wohlfarth MRAM,this does increase the cycle time for the write operation;however,it also reduces the write power,since on average only half the bits have to be toggled.Simple perturbative modelWe now describe a simple perturbative model which is useful for understanding the basic operation of toggle bits.The merit of this model lies in its simplicity—it is a one-dimensional model which is easy to visualize and interpret.The critical assumption made is that the dipole coupling ﬁeld 2M s N ,where M s is the saturation magnetization and N is the demagnetization factor,is very large compared with the applied ﬁeld H ,which in turn is very large compared with the intrinsic anisotropy ﬁeld H i ;i.e.,2M s N )H )H i .Thus,the model is valid for thick layers with small H i when ﬁelds around the spin-ﬂop point or smaller are applied.In particular,it does not describe the saturation of the moments at large ﬁelds.As an example,this model can be well applied to 200-nm-diameter,6-nm-thick NiFe layers with H i ¼5Oe,where 2M s N ¼474Oe.Errors in energy from this perturbative model compared with the exact single-domain model are then less than 10%for applied ﬁelds around 50Oe or less;the spin-ﬂop ﬁeld H sf is calculated correctly to within 0.5%of the exact single-domain result.Additional assumptions are that the bit is circular and that both magnetic layers are of the same thickness t .All of these assumptions are lifted when we later consider the general case.However,throughout this paper,each magnetic layer is always assumed to be a single domain.This not only allows the use of a single degree of freedom for each layer to describe the energy,but also allows the use of simple demagnetization factors in the energy expression.The single-domain assumption is valid for very small magnetic layers,and a good approximation for theseveral-hundred-nanometer-sized devices of technological(a) Top view of a toggle bit in an MRAM. In zero field, the moments line up anti-parallel because of the dipole fields arising from the magnetic poles at the edges of the bit. The intrinsic anisotropy, aligned at 45 degrees to the bit and word fields, determines the zero-field orientation. When a field is applied along the easy axis, as illustrated in (b), the moments at first remain unchanged, then spin-flop, and then scissor together to saturation. When a box-field excursion is applied, as in (c), the moments adiabatically rotate perpendicularly to the applied field, thus toggling the state of the bit.Figure 271interest [8].The single-domain behavior certainly breaksdown as the thickness approaches some fraction of the width;however,for thin-ﬁlm samples (perhaps 6nm in thickness and 100–300nm in width)the single-domain assumption is a good starting approximation.Figure 3shows the coordinate system,with the easy axis (H i )along the x -direction.Thus,the bit ﬁelds and word ﬁelds are at 45degrees to the x -direction.The applied ﬁeld H is directed at an angle a to the easy axis.The angle of the ﬁrst moment is termed h ,and the angle of the second is tracked by recording the angle e ,which is the amount by which the two moments deviate from being anti-parallel.The single-domain energy E is then EM s At¼ÀH ½cos ðh Àa ÞÀcos ðh þe Àa Þ ÀM s N ÀJM s tcos e À12H i cos 2ðh ÞÀ12H i cos 2ðh þe Þ;ð1Þwhere A is the bit area,t is the thickness of the single layer,and J is the spacer layer exchange coupling.The ﬁrst term is the Zeeman energy,arising from the interaction of the applied ﬁeld with each of the moments.This term favors the alignment of each moment with the applied ﬁeld.The second term is the coupling ﬁeld energy,which is composed of two parts:the dipole coupling and the exchange coupling.This term favors an anti-parallel alignment of the two layers.Since these two coupling terms enter in the same way,we drop J in what follows,without loss of generality.The last two terms are the intrinsic anisotropy energy from each of the two layers.These two terms favor the alignment of each layer with the easy axis (x -axis).We now make use of our assumption:2M s N )H )H i .We temporarily consider the case of no intrinsicanisotropy.Then,for a ﬁeld applied along a ¼0,the problem is easy to solve:H x ¼2M s N sin (e /2)’M s N e .For a ﬁeld applied along an arbitrary direction,this generalizes toe ¼H sin ðh Àa Þ=ðM s N Þ:ð2ÞAlternatively (and more rigorously),one can expandEquation (1)in powers of H i /M s N and H /M s N ,retain only the leading terms,and minimize,thus obtaining Equation (2),correct to leading ing thisexpression for e in Equation (1)leaves E as a function of only one variable,h .To leading order this gives E M s At ¼ÀH 22M s Nsin 2ðh Àa ÞÀH i cos 2h :ð3ÞThese two terms have very intuitive meanings.The ﬁrstfavors alignment of the moments perpendicular to the applied ﬁeld,and the second favors alignment of the moments along the intrinsic anisotropy axis.Note also that the applied ﬁeld appears only in second order.This is because to ﬁrst order there is no net moment,and so there is no response to the applied ﬁeld.However,to second order,the applied ﬁeld itself creates a moment,and then this moment responds to the applied ﬁeld.Finally,note that there is only one ﬁeld scale in the problem,making it easy to guess the order of magnitude of the spin-ﬂop ﬁeld.From dimensional analysis,the spin-ﬂop ﬁeld must be of order (2H i M s N )1/2,i.e.,the geometric mean of the coupling ﬁeld and the intrinsic anisotropy ﬁeld.Again,this can be interpreted in terms of a net moment being created by the applied ﬁeld (opposing the coupling ﬁeld 2M s N ),and then rotating that moment (opposing the intrinsic anisotropy ﬁeld H i ).Further substitution leads to the following even simpler expression for the energy,now in dimensionless units:e ¼12½h 4À2h 2cos ð2a Þþ1 1=2cos ð2h Àu Þ;ð4Þwhere e is the dimensionless energy,e ¼E /(H i M s At ),h is the dimensionless ﬁeld,h ¼H /(2H i M s N )1/2,and the phase u is given by tan u ¼h 2sin 2a /[h 2cos (2a )À1].Hence,in this simple model,the energy landscape is always a simple sinusoid.The equilibrium value of h is given by the value at which Equation (4)is a minimum;i.e.,h ¼u /2þp /2.At that value of h ,tan u ¼tan 2h ;thus,tan 2h ¼h 2sin 2a h 2cos ð2a ÞÀ1:ð5ÞThus,there is only one discontinuity in h as a function of h ,when the denominator of Equation (5)and the amplitude of Equation (4)vanish,at a ¼0and h ¼1,as described in more detail later.The presence of a single discontinuity is in distinct contrast to what applies inFigure 3Coordinate system for perturbative model. The intrinsic anisotropy (easy axis) is along the x -axis. The angles of the moments are denoted by and ␧, and that of the applied field by ␣.␪72Stoner–Wohlfarth switching,where the moment switches at each point along the astroid curve because the energy minimum that the system is in ceases to be a minimum, and the system jumps discontinuously into another nearby minimum.This is shown schematically in Figure4(a).The severe reduction in activation energy seen in Stoner–Wohlfarth switching,as shown in Figure1(c), is a characteristic of this discontinuous type of switching; the system switches when the activation energy is reduced to zero.Figure4(b)shows plots of Equation(4)for a number of diﬀerent appliedﬁeld values.The equilibrium value of h is given by the minimum in each curve,as traced out by the thick brown line.The energy curves are color-coded to correspond to the inset,which shows the ﬁeld path.At zeroﬁeld,the energy curve is shown in black.As theﬁeld is applied along the word axis,the system rotates to negative values of h(red curves).With each successive portion of theﬁeld path,the energy curve continues to translate to the left,corresponding to the clockwise rotation of the moments.The system is smoothly carried through the green curves,and then relaxes into the zero-ﬁeld state as theﬁeld is reduced along the bit axis(for clarity,the corresponding energy curves are not shown).Hence,the moments have rotated by180degrees and have reversed state.As theﬁeld is applied,the moments rotate adiabatically in order to maintain themselves roughly perpendicular to theﬁeld. The activation energy at allﬁeld values is given directly by twice the amplitude of Equation(4):ea¼½h4À2h2cosð2aÞþ1 1=2;ð6Þi.e.,by the vertical distance between the minimum and maximum of each curve in Figure4(b).From Figure4(b)it is clear that the activation energy increases during half select(along the red series of curves).Furthermore,note that during the entire switching event the activation energy is maintained at a value larger than the zero-ﬁeld value.Again,this is in distinct contrast to the Stoner–Wohlfarth case,where the activation energy vanishesat the switchingﬁeld.The continuous nature of the switching event shown in Figure4(b),as opposed to the discontinuous event shown in Figure4(a),constitutes a major diﬀerence between toggle and Stoner–Wohlfarth switching.Figure5shows the one place where there is a discontinuity in switching:when Equation(6)equals zero; this occurs only when theﬁeld is applied along the easy axis(a¼0),at a critical value h¼h sf¼1.Figure5shows energy curves for diﬀerent values of the easy-axisﬁeld.At h¼1,the minimum switches discontinuously from being at h¼0to h¼6p/2(i.e.,the scissor state).The family of curves in Figure5explains the spin-ﬂop behavior shown in Figure2(b).For h,1,the energy minimum is at h¼0.At h¼1,the system abruptly jumps into the scissoredstate at either h¼p/2or h¼Àp/2.Furthermore,Figure5can be used to understand the general criterion fortoggling.Toggling requires passing through the stateh¼p/2(orÀp/2).From Equation(5),this can happenonly when a¼0;i.e.,theﬁeld is applied along the easyaxis.When theﬁeld is along the easy axis(see Figure5),the state at h¼p/2is a minimum only if h.1.Hence,the criterion for toggling is that theﬁeld excursion mustcut across the easy axis at h.1.This is shown as a redray in Figure6,drawn with the x-and y-axes as the bit-line and word-lineﬁelds(so that the easy axis is alongthe45-degree line).From theﬁgure it is clear that thetoggling criterion is equivalent to requiring theﬁeldexcursion to enclose the spin-ﬂop point,deﬁned by a¼0,h¼1,denoted by the red dot in Figure6.Furthermore,ifone is restricted to rectangularﬁeld excursions(changingh x and h y only separately),the toggling criterion deﬁnesan L-shaped critical curve shown in blue in Figure6.For rectangularﬁeld excursions(starting at zeroﬁeld)which Figure 4Energetics of Stoner–Wohlfarth switching vs. toggle switching.Stoner–Wohlfarth switching occurs discontinuously when theapplied field changes the energy minimum into an inflection point(a). A toggle bit toggles without any discontinuities in the angle as afunction of applied field (b). Curves of the dimensionless energyobtained from the perturbative model are color-coded, as indicatedin the inset: black: zero-field energy; red: an increase in the word-linefield only; green: the increase in the bit-line field; blue: the decreasein the word-line field. For clarity, the final set of curves, correspond-ing to the bit-line field being decreased, is not shown.73cross this critical switching curve,the system toggles,whereas for rectangular ﬁeld excursions which do not cross this critical switching curve,the system does not toggle.Note that this model explicitly ignores the eﬀects of large ﬁelds (i.e.,what occurs at saturation)because of the assumption that 2M s N )H .Therefore,the manner in which the critical switching curve behaves at large ﬁeldsis outside this perturbative model and requires analysis using the exact single-domain theory,discussed next.To summarize this section:The analyses indicate that there are no discontinuities in h as a function of applied ﬁeld,except at the spin-ﬂop point.Instead,the moments rotate adiabatically and perpendicularly to the applied ﬁeld.The activation energy increases under half select,thus eliminating the activated-error problem,and the critical switching curve for rectangular ﬁeld excursions has a perfect L shape,which reduces the half-select margin problem.Exact single-domain modelWe now turn our attention to an exact solution of thesingle-domain two-layer problem,which has been discussed in [3]and [4].The energy can be written,again in reduced units,ase ðh 1;h 2Þ¼Àh x ½z cos h 1þcos h 2 Àh y ½z sin h 1þsin h 2þðn x Àjz Þcos h 1cos h 2þðn y Àjz Þsin h 1sin h 2þz 2ðn y Àn x þh i Þsin 2h 1þ12z ðn y Àn x þh i z Þsin 2h 2;ð7Þwhere e ¼Eb /p 2M 2s abt 1t 2,h x ,y ,i ¼H x ,y ,i b /4p M s t 1,j ¼Jb /4p M 2s t 21,z ¼t 1/t 2.1,E is the energy,h 1,2are the angles of the moments of the two layers measured from the x -axis,H i is the intrinsic anisotropy in the x ^-direction,t 1,2are the thicknesses,a is the length in the x ^-direction,b is the width in the yˆ-direction,n x ,y are the reduced demagnetizing factors in the x ^-and yˆ-directions,M s is magnetization,J is the exchange coupling between the layers,and H x ,y are the applied ﬁelds in the x ^-and y ˆ-directions.Throughout this section,ﬁelds in lowercase are in reduced units;conversion to CGS units can be achieved by using H ¼h 4p M s t 1/b .The minima of Equation (7)deﬁne the equilibrium values of h 1and h 2.As the ﬁeld is applied,these minima shift position,corresponding to the moments rotating,and sometimes change stability from being a minimum to being a saddle point,corresponding to discontinuous switching events.Given a critical point,it is possible to calculate the critical ﬁelds at which these stability changes occur by calculating the discriminant of Equation (7)and setting it to zero:e h 1h 1e h 2h 2Àðe h1h 2Þ2¼0:ð8ÞThis condition corresponds to either a minimum or a maximum changing into a saddle point.For h y ¼0(i.e.,easy-axis ﬁeld only),it is easy to show that the parallel (P)states (h 1,h 2)¼(0,0),(p ,p )and the anti-parallel (AP)states (0,p ),(p ,0)are always critical points of Equation (7)by showing that e h 1=0and e h 2=0at these values of (h 1,h 2).Evaluating Equation (8)at these valuesFigure 6Combined effects on switching of word and bit fields. The red dot is the spin-flop point; this or the red ray extending from the spin- flop point defines the switching criterion for arbitrary field excursions (see text). The field values are normalized to (2H i M s N )1/2. For rectangular field excursions, the red ray defines the blue L-shaped critical switching curve.Figure 5Energy curves, from the perturbative model, for the field applied along the easy axis; again, energy is dimensionless, and the zero- field case is shown in black. As the field is increased, the minimum continues to be at ϭ 0 (blue curves) until, for h > 1, the minimumdiscontinuously jumps to ϭ ␲/2 (red curves).␪␪74of (h 1,h 2)and solving for h x gives the following switching ﬁelds:For positive ﬁelds,the AP states lose stability ath sf or h d¼h i ðn y Àjz Þ1þ1zþh iþn y Àjz 2 21À1z 2 1=26121À1zð2n x Àn y Àjz Þ;ð9Þwhere the þof the 6sign refers to h sf and the Àto h d .The spin-ﬂop ﬁeld h sf corresponds to the (0,p )state losing stability,and the direct-write ﬁeld h d corresponds to the (p ,0)state losing stability (since z ¼t 1/t 2.1,h d corresponds to the thickness-imbalance unfavored state losing stability).For positive ﬁelds,the P state (0,0)loses stability ath x sat ¼ð1þ1=z Þðn x Àjz ÞÀh i :ð10ÞNext we consider the simple case in which the two layers have the same thickness:z ¼1.Then h sf ¼h d ,and Equations (9)and (10)reduce to Equation (11)(now with units):H sf ¼H i 8p M s n y t b À2JM s t þH i 1=2;ð11ÞH x sat ¼8p M s n x t b À2JM s tÀH i :ð12ÞSimilarly for z ¼1,the ﬁeld at which the moments saturate in the y -direction,i.e.,at which the (p /2,p /2)state loses stability,is given by H y sat ¼8p M s n y t b À2JM s tþH i :ð13ÞOne can see that the spin-ﬂop ﬁeld is the geometric mean of the intrinsic anisotropy and the hard-axis saturation ﬁeld.This is in agreement with the discussion in the perturbative calculation section above:regarding the applied ﬁeld as ﬁrst creating a net moment and then rotating against the intrinsic anisotropy.In particular,note that the spin-ﬂop ﬁeld involves the hard-axis saturation ﬁeld and not the easy-axis saturation ﬁeld;this makes sense because in zero ﬁeld the moments lie along the x -axis,and to create a net moment they must be canted toward the y -axis,i.e.,toward the hard-axis direction.The saturation ﬁelds also make intuitive sense;the applied ﬁeld must overcome both the dipole coupling and the exchange coupling to make the moments become parallel.Furthermore,in the x -direction (easy axis),the intrinsic anisotropy assists the applied ﬁeld,resulting in a minus sign for the H i term,whereas in the y -direction(hard axis)it opposes it,resulting in a plus sign for the H i term.Figure 7shows the corresponding easy-axis hysteresis loop for the case z ¼1.Note that there is some hysteresis as the ﬁeld is decreased from saturation,because the moments return in the scissoring state,which continues to be a minimum down to a ﬁeld H r .For ﬁelds H r ,H ,H sf ,there are therefore two (four withdegeneracy)possible states:the AP state and the scissoring state.The system does not return to the AP state until the scissoring state ceases to be a minimum,at the return ﬁeld H r .This ﬁeld can be calculated as follows:1)by noting that on the easy axis,for the scissoring state,h 1¼Àh 2;and 2)by minimizing Equation (7)subject to this constraint.Equation (8)can then be evaluated at the resulting critical point and solved for H x ¼H r .This procedure givesH r ¼8p M s n x t b À2JM s tÀH i30B@H i8p M s n y t b À2JM s tþH i1C A1=2:ð14ÞFrom Equation (14)it is clear that the amount of hysteresis decreases with decreasing aspect ratio and is very small for circles,where n x ¼n y (note that for technologically relevant samples,H i is much smaller than the dipole coupling ﬁelds).Note that in practice it is H sf and not H r that determines the toggling criterion,since for ﬁeld excursions between H r and H sf the moments can stay in the AP state and hence not toggle.See [5]for aFigure 7Easy-axis hysteresis loop at zero temperature calculated from the exact single-domain model for the case of a circle with t 1 ϭ t 2. Inset shows the coordinate system: the intrinsic anisotropy, applied field, long axis of the ellipse, and x -axis are all parallel.75。

Complexity of monodic guarded fragments over linear and real time

Complexity of monodic guarded fragments over linear and real time
Ian Hodkinson 1
Department of Computing, Imperial College London, London SW7 2AZ, UK
1
Introduction
Propositional temporal logic is now well established, both in its theory and its utility for practical applications in computing. In contrast, predicate, or ﬁrst-order, temporal logic has been less studied. Unpublished results of Lindstr¨ om and Scott in the 1960s showed that even weak fragments of ﬁrst-order temporal logic are highly undecidable, and these and later similar results (see, e.g., [6,15]) may have suggested that other areas were more proﬁtable to work on. Recently, however, some decidable fragments of ﬁrst-order temporal logic have been found. The so-called monodic fragments, originating in [15], have now been quite extensively investigated. In these fragments, formulas beginning with a temporal operator are required to have at most one free variable. Also, the ‘ﬁrst-order part’ of formulas must lie in some decidable fragment of ﬁrst-order logic with very mild closure properties. Suitable fragments include the monadic fragment (with only unary relation symbols), the one- and two-variable fragments, and the guarded, loosely guarded, and packed fragments. [15] showed that the monodic fragments based on all these ﬁrst-order fragments are decidable over a wide range of linear ﬂows of time. (We use ‘ﬂow of time’ synonymously with ‘strict partial order’.) A notable case left open in [15] is for real

线性代数》英文专业词汇

线性代数》英文专业词汇has a unique valueinvertible matrixadjoint matrixinverse matrixelementary matrix___column nrank of a matrixlinearly independentlinearly dependentspanbasis_______________diagonalizable matrix___ ___singular value nmatrix norm___positive definite matrixpositive semi-definite matrixnegative definite matrixnegative semi-definite matrix___ deals with the study of linear ___。

One of the key concepts in linear algebra is the determinant。

___ from a square matrix。

The ___.A matrix is a rectangular array of numbers that is used to ___。

The identity matrix is a special type of matrix that has ones on the___ matrix is equal to its transpose。

while a skew-symmetric matrix is equal to the negative of ___ that the order of matrix ___.The rank of a matrix is the maximum number of linearly independent rows or columns it contains。

MIPS芯片架构说明

MIPS32™ Architecture For Programmers Volume I: Introduction to the MIPS32™ArchitectureDocument Number: MD00082Revision 2.00June 8, 2003MIPS Technologies, Inc.1225 Charleston RoadMountain View, CA 94043-1353Copyright © 2001-2003 MIPS Technologies Inc. All rights reserved.Copyright ©2001-2003 MIPS Technologies, Inc. All rights reserved.Unpublished rights (if any) reserved under the copyright laws of the United States of America and other countries.This document contains information that is proprietary to MIPS Technologies, Inc. ("MIPS Technologies"). Any copying,reproducing,modifying or use of this information(in whole or in part)that is not expressly permitted in writing by MIPS Technologies or an authorized third party is strictly prohibited. At a minimum, this information is protected under unfair competition and copyright laws. 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The information contained in this document constitutes one or more of the following: commercial computer software, commercial computer software documentation or other commercial items.If the user of this information,or any related documentation of any kind,including related technical data or manuals,is an agency,department,or other entity of the United States government ("Government"), the use, duplication, reproduction, release, modiﬁcation, disclosure, or transfer of this information, or any related documentation of any kind, is restricted in accordance with Federal Acquisition Regulation12.212for civilian agencies and Defense Federal Acquisition Regulation Supplement227.7202 for military agencies.The use of this information by the Government is further restricted in accordance with the terms of the license agreement(s) and/or applicable contract terms and conditions covering this information from MIPS Technologies or an authorized third party.MIPS,R3000,R4000,R5000and R10000are among the registered trademarks of MIPS Technologies,Inc.in the United States and other countries,and MIPS16,MIPS16e,MIPS32,MIPS64,MIPS-3D,MIPS-based,MIPS I,MIPS II,MIPS III,MIPS IV,MIPS V,MIPSsim,SmartMIPS,MIPS Technologies logo,4K,4Kc,4Km,4Kp,4KE,4KEc,4KEm,4KEp, 4KS, 4KSc, 4KSd, M4K, 5K, 5Kc, 5Kf, 20Kc, 25Kf, ASMACRO, ATLAS, At the Core of the User Experience., BusBridge, CoreFPGA, CoreLV, EC, JALGO, MALTA, MDMX, MGB, PDtrace, Pipeline, Pro, Pro Series, SEAD, SEAD-2, SOC-it and YAMON are among the trademarks of MIPS Technologies, Inc.All other trademarks referred to herein are the property of their respective owners.Template: B1.08, Built with tags: 2B ARCH MIPS32MIPS32™ Architecture For Programmers Volume I, Revision 2.00 Copyright © 2001-2003 MIPS Technologies Inc. All rights reserved.Table of ContentsChapter 1 About This Book (1)1.1 Typographical Conventions (1)1.1.1 Italic Text (1)1.1.2 Bold Text (1)1.1.3 Courier Text (1)1.2 UNPREDICTABLE and UNDEFINED (2)1.2.1 UNPREDICTABLE (2)1.2.2 UNDEFINED (2)1.3 Special Symbols in Pseudocode Notation (2)1.4 For More Information (4)Chapter 2 The MIPS Architecture: An Introduction (7)2.1 MIPS32 and MIPS64 Overview (7)2.1.1 Historical Perspective (7)2.1.2 Architectural Evolution (7)2.1.3 Architectural Changes Relative to the MIPS I through MIPS V Architectures (9)2.2 Compliance and Subsetting (9)2.3 Components of the MIPS Architecture (10)2.3.1 MIPS Instruction Set Architecture (ISA) (10)2.3.2 MIPS Privileged Resource Architecture (PRA) (10)2.3.3 MIPS Application Specific Extensions (ASEs) (10)2.3.4 MIPS User Defined Instructions (UDIs) (11)2.4 Architecture Versus Implementation (11)2.5 Relationship between the MIPS32 and MIPS64 Architectures (11)2.6 Instructions, Sorted by ISA (12)2.6.1 List of MIPS32 Instructions (12)2.6.2 List of MIPS64 Instructions (13)2.7 Pipeline Architecture (13)2.7.1 Pipeline Stages and Execution Rates (13)2.7.2 Parallel Pipeline (14)2.7.3 Superpipeline (14)2.7.4 Superscalar Pipeline (14)2.8 Load/Store Architecture (15)2.9 Programming Model (15)2.9.1 CPU Data Formats (16)2.9.2 FPU Data Formats (16)2.9.3 Coprocessors (CP0-CP3) (16)2.9.4 CPU Registers (16)2.9.5 FPU Registers (18)2.9.6 Byte Ordering and Endianness (21)2.9.7 Memory Access Types (25)2.9.8 Implementation-Specific Access Types (26)2.9.9 Cache Coherence Algorithms and Access Types (26)2.9.10 Mixing Access Types (26)Chapter 3 Application Specific Extensions (27)3.1 Description of ASEs (27)3.2 List of Application Specific Instructions (28)3.2.1 The MIPS16e Application Specific Extension to the MIPS32Architecture (28)3.2.2 The MDMX Application Specific Extension to the MIPS64 Architecture (28)3.2.3 The MIPS-3D Application Specific Extension to the MIPS64 Architecture (28)MIPS32™ Architecture For Programmers Volume I, Revision 2.00i Copyright © 2001-2003 MIPS Technologies Inc. All rights reserved.3.2.4 The SmartMIPS Application Specific Extension to the MIPS32 Architecture (28)Chapter 4 Overview of the CPU Instruction Set (29)4.1 CPU Instructions, Grouped By Function (29)4.1.1 CPU Load and Store Instructions (29)4.1.2 Computational Instructions (32)4.1.3 Jump and Branch Instructions (35)4.1.4 Miscellaneous Instructions (37)4.1.5 Coprocessor Instructions (40)4.2 CPU Instruction Formats (41)Chapter 5 Overview of the FPU Instruction Set (43)5.1 Binary Compatibility (43)5.2 Enabling the Floating Point Coprocessor (44)5.3 IEEE Standard 754 (44)5.4 FPU Data Types (44)5.4.1 Floating Point Formats (44)5.4.2 Fixed Point Formats (48)5.5 Floating Point Register Types (48)5.5.1 FPU Register Models (49)5.5.2 Binary Data Transfers (32-Bit and 64-Bit) (49)5.5.3 FPRs and Formatted Operand Layout (50)5.6 Floating Point Control Registers (FCRs) (50)5.6.1 Floating Point Implementation Register (FIR, CP1 Control Register 0) (51)5.6.2 Floating Point Control and Status Register (FCSR, CP1 Control Register 31) (53)5.6.3 Floating Point Condition Codes Register (FCCR, CP1 Control Register 25) (55)5.6.4 Floating Point Exceptions Register (FEXR, CP1 Control Register 26) (56)5.6.5 Floating Point Enables Register (FENR, CP1 Control Register 28) (56)5.7 Formats of Values Used in FP Registers (57)5.8 FPU Exceptions (58)5.8.1 Exception Conditions (59)5.9 FPU Instructions (62)5.9.1 Data Transfer Instructions (62)5.9.2 Arithmetic Instructions (63)5.9.3 Conversion Instructions (65)5.9.4 Formatted Operand-Value Move Instructions (66)5.9.5 Conditional Branch Instructions (67)5.9.6 Miscellaneous Instructions (68)5.10 Valid Operands for FPU Instructions (68)5.11 FPU Instruction Formats (70)5.11.1 Implementation Note (71)Appendix A Instruction Bit Encodings (75)A.1 Instruction Encodings and Instruction Classes (75)A.2 Instruction Bit Encoding Tables (75)A.3 Floating Point Unit Instruction Format Encodings (82)Appendix B Revision History (85)ii MIPS32™ Architecture For Programmers Volume I, Revision 2.00 Copyright © 2001-2003 MIPS Technologies Inc. All rights reserved.Figure 2-1: Relationship between the MIPS32 and MIPS64 Architectures (11)Figure 2-2: One-Deep Single-Completion Instruction Pipeline (13)Figure 2-3: Four-Deep Single-Completion Pipeline (14)Figure 2-4: Four-Deep Superpipeline (14)Figure 2-5: Four-Way Superscalar Pipeline (15)Figure 2-6: CPU Registers (18)Figure 2-7: FPU Registers for a 32-bit FPU (20)Figure 2-8: FPU Registers for a 64-bit FPU if Status FR is 1 (21)Figure 2-9: FPU Registers for a 64-bit FPU if Status FR is 0 (22)Figure 2-10: Big-Endian Byte Ordering (23)Figure 2-11: Little-Endian Byte Ordering (23)Figure 2-12: Big-Endian Data in Doubleword Format (24)Figure 2-13: Little-Endian Data in Doubleword Format (24)Figure 2-14: Big-Endian Misaligned Word Addressing (25)Figure 2-15: Little-Endian Misaligned Word Addressing (25)Figure 3-1: MIPS ISAs and ASEs (27)Figure 3-2: User-Mode MIPS ISAs and Optional ASEs (27)Figure 4-1: Immediate (I-Type) CPU Instruction Format (42)Figure 4-2: Jump (J-Type) CPU Instruction Format (42)Figure 4-3: Register (R-Type) CPU Instruction Format (42)Figure 5-1: Single-Precisions Floating Point Format (S) (45)Figure 5-2: Double-Precisions Floating Point Format (D) (45)Figure 5-3: Paired Single Floating Point Format (PS) (46)Figure 5-4: Word Fixed Point Format (W) (48)Figure 5-5: Longword Fixed Point Format (L) (48)Figure 5-6: FPU Word Load and Move-to Operations (49)Figure 5-7: FPU Doubleword Load and Move-to Operations (50)Figure 5-8: Single Floating Point or Word Fixed Point Operand in an FPR (50)Figure 5-9: Double Floating Point or Longword Fixed Point Operand in an FPR (50)Figure 5-10: Paired-Single Floating Point Operand in an FPR (50)Figure 5-11: FIR Register Format (51)Figure 5-12: FCSR Register Format (53)Figure 5-13: FCCR Register Format (55)Figure 5-14: FEXR Register Format (56)Figure 5-15: FENR Register Format (56)Figure 5-16: Effect of FPU Operations on the Format of Values Held in FPRs (58)Figure 5-17: I-Type (Immediate) FPU Instruction Format (71)Figure 5-18: R-Type (Register) FPU Instruction Format (71)Figure 5-19: Register-Immediate FPU Instruction Format (71)Figure 5-20: Condition Code, Immediate FPU Instruction Format (71)Figure 5-21: Formatted FPU Compare Instruction Format (71)Figure 5-22: FP RegisterMove, Conditional Instruction Format (71)Figure 5-23: Four-Register Formatted Arithmetic FPU Instruction Format (72)Figure 5-24: Register Index FPU Instruction Format (72)Figure 5-25: Register Index Hint FPU Instruction Format (72)Figure 5-26: Condition Code, Register Integer FPU Instruction Format (72)Figure A-1: Sample Bit Encoding Table (76)MIPS32™ Architecture For Programmers Volume I, Revision 2.00iii Copyright © 2001-2003 MIPS Technologies Inc. All rights reserved.Table 1-1: Symbols Used in Instruction Operation Statements (2)Table 2-1: MIPS32 Instructions (12)Table 2-2: MIPS64 Instructions (13)Table 2-3: Unaligned Load and Store Instructions (24)Table 4-1: Load and Store Operations Using Register + Offset Addressing Mode (30)Table 4-2: Aligned CPU Load/Store Instructions (30)Table 4-3: Unaligned CPU Load and Store Instructions (31)Table 4-4: Atomic Update CPU Load and Store Instructions (31)Table 4-5: Coprocessor Load and Store Instructions (31)Table 4-6: FPU Load and Store Instructions Using Register+Register Addressing (32)Table 4-7: ALU Instructions With an Immediate Operand (33)Table 4-8: Three-Operand ALU Instructions (33)Table 4-9: Two-Operand ALU Instructions (34)Table 4-10: Shift Instructions (34)Table 4-11: Multiply/Divide Instructions (35)Table 4-12: Unconditional Jump Within a 256 Megabyte Region (36)Table 4-13: PC-Relative Conditional Branch Instructions Comparing Two Registers (36)Table 4-14: PC-Relative Conditional Branch Instructions Comparing With Zero (37)Table 4-15: Deprecated Branch Likely Instructions (37)Table 4-16: Serialization Instruction (38)Table 4-17: System Call and Breakpoint Instructions (38)Table 4-18: Trap-on-Condition Instructions Comparing Two Registers (38)Table 4-19: Trap-on-Condition Instructions Comparing an Immediate Value (38)Table 4-20: CPU Conditional Move Instructions (39)Table 4-21: Prefetch Instructions (39)Table 4-22: NOP Instructions (40)Table 4-23: Coprocessor Definition and Use in the MIPS Architecture (40)Table 4-24: CPU Instruction Format Fields (42)Table 5-1: Parameters of Floating Point Data Types (45)Table 5-2: Value of Single or Double Floating Point DataType Encoding (46)Table 5-3: Value Supplied When a New Quiet NaN Is Created (47)Table 5-4: FIR Register Field Descriptions (51)Table 5-5: FCSR Register Field Descriptions (53)Table 5-6: Cause, Enable, and Flag Bit Definitions (55)Table 5-7: Rounding Mode Definitions (55)Table 5-8: FCCR Register Field Descriptions (56)Table 5-9: FEXR Register Field Descriptions (56)Table 5-10: FENR Register Field Descriptions (57)Table 5-11: Default Result for IEEE Exceptions Not Trapped Precisely (60)Table 5-12: FPU Data Transfer Instructions (62)Table 5-13: FPU Loads and Stores Using Register+Offset Address Mode (63)Table 5-14: FPU Loads and Using Register+Register Address Mode (63)Table 5-15: FPU Move To and From Instructions (63)Table 5-16: FPU IEEE Arithmetic Operations (64)Table 5-17: FPU-Approximate Arithmetic Operations (64)Table 5-18: FPU Multiply-Accumulate Arithmetic Operations (65)Table 5-19: FPU Conversion Operations Using the FCSR Rounding Mode (65)Table 5-20: FPU Conversion Operations Using a Directed Rounding Mode (65)Table 5-21: FPU Formatted Operand Move Instructions (66)Table 5-22: FPU Conditional Move on True/False Instructions (66)iv MIPS32™ Architecture For Programmers Volume I, Revision 2.00 Copyright © 2001-2003 MIPS Technologies Inc. All rights reserved.Table 5-23: FPU Conditional Move on Zero/Nonzero Instructions (67)Table 5-24: FPU Conditional Branch Instructions (67)Table 5-25: Deprecated FPU Conditional Branch Likely Instructions (67)Table 5-26: CPU Conditional Move on FPU True/False Instructions (68)Table 5-27: FPU Operand Format Field (fmt, fmt3) Encoding (68)Table 5-28: Valid Formats for FPU Operations (69)Table 5-29: FPU Instruction Format Fields (72)Table A-1: Symbols Used in the Instruction Encoding Tables (76)Table A-2: MIPS32 Encoding of the Opcode Field (77)Table A-3: MIPS32 SPECIAL Opcode Encoding of Function Field (78)Table A-4: MIPS32 REGIMM Encoding of rt Field (78)Table A-5: MIPS32 SPECIAL2 Encoding of Function Field (78)Table A-6: MIPS32 SPECIAL3 Encoding of Function Field for Release 2 of the Architecture (78)Table A-7: MIPS32 MOVCI Encoding of tf Bit (79)Table A-8: MIPS32 SRL Encoding of Shift/Rotate (79)Table A-9: MIPS32 SRLV Encoding of Shift/Rotate (79)Table A-10: MIPS32 BSHFL Encoding of sa Field (79)Table A-11: MIPS32 COP0 Encoding of rs Field (79)Table A-12: MIPS32 COP0 Encoding of Function Field When rs=CO (80)Table A-13: MIPS32 COP1 Encoding of rs Field (80)Table A-14: MIPS32 COP1 Encoding of Function Field When rs=S (80)Table A-15: MIPS32 COP1 Encoding of Function Field When rs=D (81)Table A-16: MIPS32 COP1 Encoding of Function Field When rs=W or L (81)Table A-17: MIPS64 COP1 Encoding of Function Field When rs=PS (81)Table A-18: MIPS32 COP1 Encoding of tf Bit When rs=S, D, or PS, Function=MOVCF (81)Table A-19: MIPS32 COP2 Encoding of rs Field (82)Table A-20: MIPS64 COP1X Encoding of Function Field (82)Table A-21: Floating Point Unit Instruction Format Encodings (82)MIPS32™ Architecture For Programmers Volume I, Revision 2.00v Copyright © 2001-2003 MIPS Technologies Inc. All rights reserved.vi MIPS32™ Architecture For Programmers Volume I, Revision 2.00 Copyright © 2001-2003 MIPS Technologies Inc. All rights reserved.Chapter 1About This BookThe MIPS32™ Architecture For Programmers V olume I comes as a multi-volume set.•V olume I describes conventions used throughout the document set, and provides an introduction to the MIPS32™Architecture•V olume II provides detailed descriptions of each instruction in the MIPS32™ instruction set•V olume III describes the MIPS32™Privileged Resource Architecture which deﬁnes and governs the behavior of the privileged resources included in a MIPS32™ processor implementation•V olume IV-a describes the MIPS16e™ Application-Speciﬁc Extension to the MIPS32™ Architecture•V olume IV-b describes the MDMX™ Application-Speciﬁc Extension to the MIPS32™ Architecture and is notapplicable to the MIPS32™ document set•V olume IV-c describes the MIPS-3D™ Application-Speciﬁc Extension to the MIPS64™ Architecture and is notapplicable to the MIPS32™ document set•V olume IV-d describes the SmartMIPS™Application-Speciﬁc Extension to the MIPS32™ Architecture1.1Typographical ConventionsThis section describes the use of italic,bold and courier fonts in this book.1.1.1Italic Text•is used for emphasis•is used for bits,ﬁelds,registers, that are important from a software perspective (for instance, address bits used bysoftware,and programmableﬁelds and registers),and variousﬂoating point instruction formats,such as S,D,and PS •is used for the memory access types, such as cached and uncached1.1.2Bold Text•represents a term that is being deﬁned•is used for bits andﬁelds that are important from a hardware perspective (for instance,register bits, which are not programmable but accessible only to hardware)•is used for ranges of numbers; the range is indicated by an ellipsis. For instance,5..1indicates numbers 5 through 1•is used to emphasize UNPREDICTABLE and UNDEFINED behavior, as deﬁned below.1.1.3Courier TextCourier ﬁxed-width font is used for text that is displayed on the screen, and for examples of code and instruction pseudocode.MIPS32™ Architecture For Programmers Volume I, Revision 2.001 Copyright © 2001-2003 MIPS Technologies Inc. All rights reserved.Chapter 1 About This Book1.2UNPREDICTABLE and UNDEFINEDThe terms UNPREDICTABLE and UNDEFINED are used throughout this book to describe the behavior of theprocessor in certain cases.UNDEFINED behavior or operations can occur only as the result of executing instructions in a privileged mode (i.e., in Kernel Mode or Debug Mode, or with the CP0 usable bit set in the Status register).Unprivileged software can never cause UNDEFINED behavior or operations. Conversely, both privileged andunprivileged software can cause UNPREDICTABLE results or operations.1.2.1UNPREDICTABLEUNPREDICTABLE results may vary from processor implementation to implementation,instruction to instruction,or as a function of time on the same implementation or instruction. Software can never depend on results that areUNPREDICTABLE.UNPREDICTABLE operations may cause a result to be generated or not.If a result is generated, it is UNPREDICTABLE.UNPREDICTABLE operations may cause arbitrary exceptions.UNPREDICTABLE results or operations have several implementation restrictions:•Implementations of operations generating UNPREDICTABLE results must not depend on any data source(memory or internal state) which is inaccessible in the current processor mode•UNPREDICTABLE operations must not read, write, or modify the contents of memory or internal state which is inaccessible in the current processor mode. For example,UNPREDICTABLE operations executed in user modemust not access memory or internal state that is only accessible in Kernel Mode or Debug Mode or in another process •UNPREDICTABLE operations must not halt or hang the processor1.2.2UNDEFINEDUNDEFINED operations or behavior may vary from processor implementation to implementation, instruction toinstruction, or as a function of time on the same implementation or instruction.UNDEFINED operations or behavior may vary from nothing to creating an environment in which execution can no longer continue.UNDEFINED operations or behavior may cause data loss.UNDEFINED operations or behavior has one implementation restriction:•UNDEFINED operations or behavior must not cause the processor to hang(that is,enter a state from which there is no exit other than powering down the processor).The assertion of any of the reset signals must restore the processor to an operational state1.3Special Symbols in Pseudocode NotationIn this book, algorithmic descriptions of an operation are described as pseudocode in a high-level language notation resembling Pascal. Special symbols used in the pseudocode notation are listed in Table 1-1.Table 1-1 Symbols Used in Instruction Operation StatementsSymbol Meaning←Assignment=, ≠Tests for equality and inequality||Bit string concatenationx y A y-bit string formed by y copies of the single-bit value x2MIPS32™ Architecture For Programmers Volume I, Revision 2.00 Copyright © 2001-2003 MIPS Technologies Inc. All rights reserved.1.3Special Symbols in Pseudocode Notationb#n A constant value n in base b.For instance10#100represents the decimal value100,2#100represents the binary value 100 (decimal 4), and 16#100 represents the hexadecimal value 100 (decimal 256). If the "b#" preﬁx is omitted, the default base is 10.x y..z Selection of bits y through z of bit string x.Little-endian bit notation(rightmost bit is0)is used.If y is less than z, this expression is an empty (zero length) bit string.+, −2’s complement or ﬂoating point arithmetic: addition, subtraction∗, ×2’s complement or ﬂoating point multiplication (both used for either)div2’s complement integer divisionmod2’s complement modulo/Floating point division<2’s complement less-than comparison>2’s complement greater-than comparison≤2’s complement less-than or equal comparison≥2’s complement greater-than or equal comparisonnor Bitwise logical NORxor Bitwise logical XORand Bitwise logical ANDor Bitwise logical ORGPRLEN The length in bits (32 or 64) of the CPU general-purpose registersGPR[x]CPU general-purpose register x. The content of GPR[0] is always zero.SGPR[s,x]In Release 2 of the Architecture, multiple copies of the CPU general-purpose registers may be implemented.SGPR[s,x] refers to GPR set s, register x. GPR[x] is a short-hand notation for SGPR[ SRSCtl CSS, x].FPR[x]Floating Point operand register xFCC[CC]Floating Point condition code CC.FCC[0] has the same value as COC[1].FPR[x]Floating Point (Coprocessor unit 1), general register xCPR[z,x,s]Coprocessor unit z, general register x,select sCP2CPR[x]Coprocessor unit 2, general register xCCR[z,x]Coprocessor unit z, control register xCP2CCR[x]Coprocessor unit 2, control register xCOC[z]Coprocessor unit z condition signalXlat[x]Translation of the MIPS16e GPR number x into the corresponding 32-bit GPR numberBigEndianMem Endian mode as conﬁgured at chip reset (0→Little-Endian, 1→ Big-Endian). Speciﬁes the endianness of the memory interface(see LoadMemory and StoreMemory pseudocode function descriptions),and the endianness of Kernel and Supervisor mode execution.BigEndianCPU The endianness for load and store instructions (0→ Little-Endian, 1→ Big-Endian). In User mode, this endianness may be switched by setting the RE bit in the Status register.Thus,BigEndianCPU may be computed as (BigEndianMem XOR ReverseEndian).Table 1-1 Symbols Used in Instruction Operation StatementsSymbol MeaningChapter 1 About This Book1.4For More InformationVarious MIPS RISC processor manuals and additional information about MIPS products can be found at the MIPS URL:ReverseEndianSignal to reverse the endianness of load and store instructions.This feature is available in User mode only,and is implemented by setting the RE bit of the Status register.Thus,ReverseEndian may be computed as (SR RE and User mode).LLbitBit of virtual state used to specify operation for instructions that provide atomic read-modify-write.LLbit is set when a linked load occurs; it is tested and cleared by the conditional store. It is cleared, during other CPU operation,when a store to the location would no longer be atomic.In particular,it is cleared by exception return instructions.I :,I+n :,I-n :This occurs as a preﬁx to Operation description lines and functions as a label. It indicates the instruction time during which the pseudocode appears to “execute.” Unless otherwise indicated, all effects of the currentinstruction appear to occur during the instruction time of the current instruction.No label is equivalent to a time label of I . Sometimes effects of an instruction appear to occur either earlier or later — that is, during theinstruction time of another instruction.When this happens,the instruction operation is written in sections labeled with the instruction time,relative to the current instruction I ,in which the effect of that pseudocode appears to occur.For example,an instruction may have a result that is not available until after the next instruction.Such an instruction has the portion of the instruction operation description that writes the result register in a section labeled I +1.The effect of pseudocode statements for the current instruction labelled I +1appears to occur “at the same time”as the effect of pseudocode statements labeled I for the following instruction.Within one pseudocode sequence,the effects of the statements take place in order. However, between sequences of statements for differentinstructions that occur “at the same time,” there is no deﬁned order. Programs must not depend on a particular order of evaluation between such sections.PCThe Program Counter value.During the instruction time of an instruction,this is the address of the instruction word. The address of the instruction that occurs during the next instruction time is determined by assigning a value to PC during an instruction time. If no value is assigned to PC during an instruction time by anypseudocode statement,it is automatically incremented by either 2(in the case of a 16-bit MIPS16e instruction)or 4before the next instruction time.A taken branch assigns the target address to the PC during the instruction time of the instruction in the branch delay slot.PABITSThe number of physical address bits implemented is represented by the symbol PABITS.As such,if 36physical address bits were implemented, the size of the physical address space would be 2PABITS = 236 bytes.FP32RegistersModeIndicates whether the FPU has 32-bit or 64-bit ﬂoating point registers (FPRs).In MIPS32,the FPU has 3232-bit FPRs in which 64-bit data types are stored in even-odd pairs of FPRs.In MIPS64,the FPU has 3264-bit FPRs in which 64-bit data types are stored in any FPR.In MIPS32implementations,FP32RegistersMode is always a 0.MIPS64implementations have a compatibility mode in which the processor references the FPRs as if it were a MIPS32 implementation. In such a caseFP32RegisterMode is computed from the FR bit in the Status register.If this bit is a 0,the processor operates as if it had 32 32-bit FPRs. If this bit is a 1, the processor operates with 32 64-bit FPRs.The value of FP32RegistersMode is computed from the FR bit in the Status register.InstructionInBranchDelaySlotIndicates whether the instruction at the Program Counter address was executed in the delay slot of a branch or jump. This condition reﬂects the dynamic state of the instruction, not the static state. That is, the value is false if a branch or jump occurs to an instruction whose PC immediately follows a branch or jump, but which is not executed in the delay slot of a branch or jump.SignalException(exce ption, argument)Causes an exception to be signaled, using the exception parameter as the type of exception and the argument parameter as an exception-speciﬁc argument). Control does not return from this pseudocode function - the exception is signaled at the point of the call.Table 1-1 Symbols Used in Instruction Operation StatementsSymbolMeaning。

CE1615-EN-01

IN The C MOSF high-si switch 2.5V to 5V sy circuit curren out o protect power It can b to 1progra groundA z H zB z M BCurre Load NTRODUC CE1615 is a FET power ide load sw operates o 5.5V, mak ystems. An protects the ts which ma f regulation ted from the dissipation be used to c .5A. Curre ammed with d. APPLICAT Hot-Plug Po Battery-Cha Motherboard BLOCK Dnt Limited Switch CTIONa current lim r switch witching app with inputs king it ideal f integrated e input supp ay cause th n. The CE ermal overlo and junction control loads ent limit h a resistor TIONSower Supplie arger Circuits d USB Powe IAGRA dmited P-chan designed plications. T s ranging f for both 3V current-limi ply against la he supply to E1615 is a oad which lim n temperatu s that require threshold r from SET es s er Switchnnel for This from and iting arge o fall also mits ures. e up isT toz z z z z z z z z z z zz z zFEATUR Low quies Shutdown Programm Fast Trans 400ns Res Input Volta Low R DS(O Only 2.5V Under-Vol Thermal F 4KV ESD Temperatu Package: Notebook Personal CUSB Devic ORDER REScent current Current: <1mable Over-C sient Respo sponse to S age: 2.5V~5N) Internal S Needed for tage Lockou Fault Protect Ratingure Range: -SOT-23-5Computers Communicat ce Power Sw INFORMA t: 9μA(Typ.)μACurrent Thre nse: hort Circuit 5.5VSwitches: 14r ON/OFF Co ut tion -40°C to +85 tion Devices witchATIONCEeshold 5m Ω ontrol 5°C s 1615PIN CONFIGURATIONABSOLUTE MAXIMUM RATINGS(Unless otherwise specified, Ta=25°C)PARAMETER SYMBOL RATINGSUNITS Input Voltage V IN -0.3~ 6 V CE, SET, OUT VoltageV CE ,V SET ,V OUT-0.3~V IN +0.3 VMaximum Continuous Switch Current I MAX 2 A Power DissipationSOT-23-5Pd400mWOperating Temperature RangeT opr -40~+85 ℃ Junction Temperature T j 125 ℃ Storage Temperature T stg -40~+125 ℃ESD Rating2 - HBM 4000 V V ESD 4000 V Soldering Temperature & Time T solder260℃, 10sPIN NUMBERSYMBOL FUNCTION1 OUTP-channel MOSFET drain. Connect a 0.47μF capacitor from OUTto GND. 2 GNDGround Pin3 SETCurrent limit set input. A resistor from SET to ground sets thecurrent limit for the switch. 4 CEChip Enable input. Two versions are available, active-high andactive-low. See Ordering Information for details. 5 INP-channel MOSFET source. Connect a 1μF capacitor from IN toGND.O Q O O OE CE16PARAME Operation V Quiescent C Off Supply C Off Switch C Under-Vol Lockou On Resist Current L Minimum C Limit CE Input Voltag CE Input Voltag CE Input Le Current L Response Turn-Off T Turn-On T Over-Tempe ThreshoTELECTRIC 615 TER S Voltage Current Current Current ltage ut ance Limit Current Low e High e eakage Limit Time Time Time erature oldTYPICAL A CAL CHAR YMBOL V IN I Q I Q(OFF) I SD(OFF) V UVLOR DS(ON) I LIM I LIM(MIN) V CE(L) V CE(H) I LEAK(CE) T RESP T OFF T ON T SDAPPLICAT RACTERIS CO V IN =5V, C CE=Ina CE=Inactive Rising Ed V IN V IN V IN V IN =5V IN =5V IN =5.0V TIONSTICS(V IN =5.0V ONDITIONSCE=Active, active, V IN =5e, V IN =5.5V,dge, 1% Hys V IN =5.0VV IN =4.5V V IN =3.0V R SET =6.8k ΩN =2.5V~5.5V N =2.5V~3.6V N =4.5V~5.5V V CE =5.5V V IN =5.0V 5.0V ，R L =105.0V ，R L =10VTJ In TJ De V, Ta=25,℃SI OUT =0 5.5V V OUT =0V steresisV V V 0Ω 0Ω creasing ecreasingunless ot MIN T 2.5 0 1 1 1 11.2 1 1 2.0 2.4 0 0 11herwise sp TYPMAX 5.59 25 1 0.01 1 1.8 2.4145 180150 190 2301.6 2.0150 0.80.01 1 0.4 4 1212 200125 115pecified)XUNITS 5 VμAμA μA 4 V 0m Ω00 A mA 8 V VμA μs μs 0 μs ℃S(Unleess otherwi ise noted, V V IN =5V, T A =225)℃(Unleess otherwi ise noted, V V IN =5V, T A =225)℃OPERATIONTable 1: Current Limit R SET ValuesFig.1 Current Limit Using 8.87k ΩR SET (k Ω)Current Limit Typ.(mA)Device Will Not Current Limit Below(mA) Device AlwaysCurrentLimits Below(mA) 40.2225 169 28130.9300 225 37524.9350 263 438 22.1425 319 53119.6450 338 563 17.8525 394 65616.2600 450 75014.7675 506 844 13.0700 525 87510.51000 750 1250 8.871100 825 13757.501325 994 16566.811600 1200 2000 6.041925 1444 2406 5.491950 1463 2438 4.992100 1575 26254.642350 1763 2938 Setting Current LimitIn most applications, the variation in I LIM must be taken into account when determining R SET . TheI LIM variation is due to processing variations from part to part, as well as variations in the voltages at IN and OUT, plus the operating temperature. See charts “Current Limit vs. Temperature” and“Output Current vs. Output Voltage.” Together, these three factors add up to a ±25% tolerance (see I LIM specification in ElectricalCharacteristics section). Figure 1 illustrates acold device with a statistically higher current limit and a hot device with a statistically lower current limit, both with R SET equal to 8.87k Ω. While the chart, "R SET vs. I LIM ” indicates an I LIMof 1.1A with an R SET of 8.87k Ω, this figure shows that the actual current limit will be at least 0.825A and no greater than 1.375A. To determine R SET , start with the maximumcurrent drawn by the load and multiply it by 1.33 (typical I LIM = minimum I LIM / 0.75). This is the typical current limit value. Next, refer to “R SET vs. I LIM ” and find the R SET that corresponds to thetypical current limit value. Choose the largestresistor available that is less than or equal to it. The maximum current is derived by multiplying the typical current for the chosen R SET in the chart by 1.25. A few standard resistor values arelisted in Table 1.Example: A USB port requires 0.5A. 0.5Amultiplied by 1.33 is 0.665A. From the chart named “R SET vs. I LIM ,” R SET should be less than 18k Ω. 17.8k Ω is a standard value that is a little less than 18k Ω but very close. The chart reads approximately 0.525A as a typical I LIM value for 17.8k Ω. Multiplying 0.525A by 0.75 and 1.25 shows that the CE1615 will limit the load current to greater than 0.0.394A but less than 0.656A.Operation in Current LimitWhen a heavy load is applied to the output of the CE1615, the load current is limited to the value of I LIM determined by R SET. Since the load is demanding more current than I LIM, the voltage at the output drops. This causes the CE1615 to dissipate a larger than normal quantity of power, and its die temperature to increase. When the die temperature exceeds an over-temperature limit, the CE1615 will shut down until is has cooled sufficiently, at which point it will startup again. The CE1615 will continue to cycle on and off until the load is removed, power is removed, or until a logic high level is applied to ON. Enable InputIn many systems, power planes are controlled by integrated circuits which run at lower voltages than the power plane itself. The enable input ON of the CE1615 has low and high threshold voltages that accommodate this condition. The threshold voltages are compatible with 5V TTL and 2.5V to 5V CMOS.Reverse VoltageThe CE1615 is designed to control current flowing from IN to OUT. If a voltage is applied to OUT which is greater than the voltage on IN, large currents may flow. This could cause damage to the CE1615.Pz SPACKAGI SOT23-5 Pa NG INFOR ackage Out RMATION tline Dimens sions© Nanjing Chipower Electronics Inc.Chipower cannot assume responsibility for use of any circuitry other than circuitry entirely embodied in a Chipower product. No circuit patent license, copyrights or other intellectual property rights are implied. Chipower reserves the right to make changes to their products or specifications without notice. Customers are advised to obtain the latest version of relevant information to verify, before placing orders, that information being relied on is current and complete.。

Financing the Newsvendor Supplier vs. Bank, and the Structure of Optimal Trade Credit Contracts

We consider a simple supplier-retailer supply chain with the retailer having a single opportunity to order a product from the supplier to satisfy future stochastic demand. Both the retailer and the supplier are capital constrained. The retailer in executing his procurement actions is in need of short-term ﬁnancing. Within a game theoretic modeling framework of the proﬁt maximizing supplier acting as the Stackelberg leader and the retailer as the follower, we explore the impact of trade credit contracts in the presence of bankruptcy risk for the retailer and supplier. We use the supplier early payment discount scheme as a decision framework to analyze all decisions involved in optimally structuring the trade credit contract from the supplier perspective (wholesale price, eﬀective payment discount or ﬁnancing rate). Under mild assumptions we conclude that a risk neutral supplier should always provide ﬁnancing to the retailer at rates less than or equal to the risk free rate, and if oﬀered an optimally structured scheme the retailer will always prefer supplier to bank ﬁnancing. Furthermore, under supplier ﬁnancing and with retailer facing bankruptcy risk, the supply chain eﬃciency improves, and, while the supplier always improves her proﬁts under such scheme, the retailer might also improve his proﬁts relative to bank ﬁnancing (without supplier ﬁnancing provision) depending on his current “wealth” (working capital and collateral). Key words : Supplier Financing, Newsvendor, Supply Contract, Trade Credit, and Early Payment Discount. History : This paper was ﬁrst submitted on Nov. 10, 2008 and has been with the authors for 17 months for 1 revision.

The Relevance of the Dipole Penguin Operators in $epsilon'epsilon$

which account for the magnetic and electric dipole part of, respectively, the QCD and electromagnetic penguin operators. In eq. (2), ta are the SU (3)c generators normalized as Tr(ta tb ) = (1/2)δ ab , while in eq. (3) Qd = −1/3 is the charge of the down quarks; σµν = (i/2)[γµ , γν ]. These operators have been left out in the past, together with Z penguins and electroweak box diagrams, because their Wilson coeﬃcients exhibit, for light quark masses, a power-like GIM suppression [6], to be compared with the leading soft logarithmic behavior of the “monopole” component of the gluonic and photonic penguins. However, for a heavy top quark, there is no reason a priori to discard these contributions, which should be considered on the same grounds as Z penguins and electroweak box diagrams. In addition, Q11 and Q12 receive a large QCD renormalization due to the mixings with the other operators, as has been shown in the case of b → sγ [7]. The potential relevance of the dipole components of the gluonic and photonic penguins for ǫ′ /ǫ has been emphasized by one of us a few years ago [8]. Only recently has a quantitative attempt to estimate the relevance of Q11 appeared [9]. However, in ref. [9], only the multiplicative renormalization—which is by no means the leading eﬀect—is taken into account. We also disagree on the evaluation of the hadronic matrix element that, we believe, is overestimated in ref. [9] by more than one order of magnitude (by a factor 8 using their method). The evaluation of the matrix elements is in fact the crucial point in determining the relevance of the two additional operators. As we shall see, while the contribution of the electromagnetic penguin Q12 seems to be vanishingly small, that of the gluonic Q11 should not be neglected. In fact, its Wilson coeﬃcient turns out to be sizeably enhanced by mixing and the matrix element is not dramatically suppressed with respect to the other ten operators. 2. In order to compare meaningfully the relevance of the new contributions with the traditional ones, from now on we strictly follow the analysis presented in ref. [3]. The parameter ǫ′ /ǫ can be obtained by means of the Hamiltonian in eq. (1), which yields [3] Im λt ǫ′ (4) = 10−4 P (1/2) − P (3/2) , ǫ 1.7 × 10−4 where P (1/2) = r r P (3/2) = ω yi 2π, I = 0| Qi |K 0 (1 − Ωη+η′ ) yi 2π, I = 2| Qi |K 0 . 2 (5) (6)

ANSI B92.1-1970(R1993) SAE美国渐开线花键-中文翻译完整版0429解读

翻译：朱晓峰节选至《美国机械工程师手册》第28版，有错之处，请指正。

SPLINES AND SERRATIONSA splined shaft is one having a series of parallel keys formed integrally with the shaft and mating with corresponding grooves cut in a hub or fitting; this arrangement is in contrast to a shaft having a series of keys or feathers fitted into slots cut into the shaft. The latter construction weakens the shaft to a considerable degree because of the slots cut into it and consequently, reduces its torque-transmitting capacity.花键轴是一种具有“一系列相互平行的齿、并且齿与轴整体成型”的轴，它与在轮毂上或者装配体上开的键槽相配合。

这种装置与“在轴上开槽并且与一组销子或者楔键相配合”的结构相反。

后者的结构由于在轴上开槽大大降低了轴（的强度），降低了传递扭矩的能力。

Splined shafts are most generally used in three types of applications: 1 ) for coupling shafts when relatively heavy torques are to be transmitted without slippage; 2) for transmitting power to slidably-mounted or permanently-fixed gears, pulleys, and other rotating members; and 3) for attaching parts that may require removal for indexing or change in angular position. 花键轴主要用在以下三种情况：1）需要在无滑动的联轴器上传递大的扭矩；2）用于向“可滑动的装配组件”或者“固定装配的齿轮组或滑轮副”传递动力，3）用于“要求指定滑移量或转角位置”的配件上。

管件英文缩写

装置
C.I *Cast Iron 铸铁
BE Beveled End (for wel****) 坡口（焊接用）
REINF Reinforc e 加强
RS Resting Support 支承架。
滑动架
NPSH Net Positive Suction Head 净正吸渗透压头
AWG *America n Wire Gage 美国线规
HF Hard Alloy Face on 阀内件（阀心）为
DIM *Dimensi onБайду номын сангаас尺寸
LG Long 长
FP Fix Point 固定点
H Hanger 吊架
PTFE *Polytet rafluoro ethylene 聚四氟乙烯
VERT Vertical 垂直的
MAX Maximum 最大
PN Plant North 工厂北向
GSKT Gasket 垫片
L.H.THD Left Hand Thread 左螺纹
WT Wall Thicknes s 壁厚
MW Minimum Wall 最小壁厚
RJ Ring Joint 环垫接头
O
Pipe Thread
RO Restrict ion Orifice 限流孔板
NOM Nominal 公称的；额定的
YP Yield Point 屈服点
LO Locked Open 在开启状态下锁定
XXS Double Extra Strong 双倍加强的
H
UC Union Cap 带活接头的阀帽
UB Union Bonnet 带活接头的阀盖
SF SemiFinished 半光

Locality and Bounding-Box Quality of Two-Dimensional Space-Filling Curves

Locality and Bounding-Box Quality of Two-DimensionalSpace-Filling CurvesHerman Haverkort ∗Freek van Walderveen †July 12,2008AbstractSpace-ﬁlling curves can be used to organise points in the plane into bounding-box hier-archies (such as R-trees).We develop measures of the bounding-box quality of space-ﬁlling curves that express how eﬀective diﬀerent space-ﬁlling curves are for this purpose.We give general lower bounds on the bounding-box quality measures and on locality according to Gotsman and Lindenbaum for a large class of space-ﬁlling curves.We describe a generic algorithm to approximate these and similar quality measures for any given ing our algorithm we ﬁnd good approximations of the locality and the bounding-box quality of several known and new space-ﬁlling curves.Surprisingly,some curves with relatively bad locality by Gotsman and Lindenbaum’s measure,have good bounding-box quality,while the curve with the best-known locality has relatively bad bounding-box quality.1Introduction A space-ﬁlling curve is a continuous,surjective mapping from R to R d .It was not always clear that such a mapping would exist for d >1,but in the late 19th century Peano showed that it is possible for d =2and d =3[26].Since then,quite a number of space-ﬁlling curves have appeared in the literature.Sagan wrote an extensive treatise on space-ﬁlling curves [27],which discusses most curves included in our study.During the early days space-ﬁlling curves were primarily seen as a mathematical curiosity.Today however,space-ﬁlling curves are applied in areas as diverse as load balancing for grid computing,colour space dimension reduction,small antenna design,I/O-eﬃcient computations on massive matrices,and the creation of spatial data indexes.In this paper,we focus on the application of space-ﬁlling curves to the creation of query-eﬃcient spatial data indexes such as R-trees.Bounding-box hierarchies We consider the following type of spatial data indexes for points in the plane.The data points are organised in blocks of at most B points,for some parameter B ,such that each point is stored in one block.With each block we associate a bounding box,which is the smallest axis-aligned rectangle that contains all points stored in the block.The block bounding boxes are then organised in an index structure.Intersection queries are answered as follows:to ﬁnd all points intersecting a query window Q ,we query the index structure for all bounding boxes that intersect Q ;then we retrieve the corresponding blocks,and check the points stored in those blocks one by one.To ﬁnd the nearest neighbour to a query point q ,one can use the index to search blocks in order of increasing distance from q .Thus one retrieves exactly the blocks whose bounding boxes intersect the largest empty circle around q .∗Dept.of Computer Science,Eindhoven University of Technology,the Netherlands,cs.herman@ †Dept.of Computer Science,Eindhoven University of Technology,the Netherlands,freek@vanwal.nla r X i v :0806.4787v 2 [c s .C G ] 12 J u l 2008(a)space-ﬁllingcurveblock (leaf)bounding box input point(b)Figure 1:(a)Leaves of an R-tree with B =3.(b)Measuring locality for a particular curve section.L 2-locality ratio between p and q =squared Euclidean distance between p and q ,divided by the area covered by the curve section between p and q :(62+52)/87≈0.70.Bounding-box area ratio between p and q =area of the bounding-box of the curve section S between p and q ,divided by the area covered by S :12·12/87≈1.66.(WBA is the maximum over all pairs p and q )An R-tree [19]is an example of the type of structure described above:the blocks constitute the leaves of the tree,and the higher levels of the tree act as an index structure for the block bounding boxes.In practice the query response time is mainly determined by the number of blocks that need to be retrieved:this is because the bounding box index structure can often be cached in main memory,while the blocks (leaves)with data points have to be stored on slow external memory (for example a hard disk needing 10ms for each seek).An R-tree is not uniquely deﬁned by a set of data points.Any distribution of the input points over the leaves (blocks)may be used as the basis of an R-tree,as long as each point is put in exactly one block,and each block contains at most B points.One way of making the distribution is by ordering the input points along a space-ﬁlling curve [15]and then putting each next group of B points together in a block (see Figure 1(a)).Since the number of blocks retrieved to answer a query is simply the number of bounding boxes intersected,it is important that the ordering induced by the space-ﬁlling curve makes us ﬁll each block with points that lie close to each other and thus have a small bounding box.In fact we can make some more precise observations for intersection queries with query windows that are points or lines.For point-intersection queries we observe that if the data and query points lie within a square of area 1,the average number of blocks retrieved for uniformly distributed point queries is simply the total area of the bounding boxes.For line-intersection queries with uniformly distributed orientation (between 0and π)and signed distance from the centre of the square (in an interval containing at least [−12√2,12√2]),the chance of any particular block being retrieved is proportional to π0w (φ)dφ,where w (φ)is the width of the bounding box in the orthogonal projection on a line with orientation φ.By the Crofton formula π0w (φ)dφis simply the perimeter of the bounding box of the block,so for uniformly distributed line queries,the average number of blocks retrieved is proportional to the total perimeter of the bounding boxes.Therefore our goal is to have bounding boxes with small (total)area and small (total)perimeter.Our results We investigate which space-ﬁlling curves best achieve the above-mentioned goal:sorting points into bounding boxes with small (total)area and small (total)perimeter.To this end we propose new quality measures of space-ﬁlling curves that express how eﬀective diﬀerent space-ﬁlling curves are in this context.We also provide an algorithm to compute approximations of these and similar quality measures for any given curve.We used this algorithm to compute approximations of known measures of so-called curve-to-plane locality and of our new bounding-box quality measures for several well-known and new space-ﬁlling curves.The known locality measures considered are the maximum,over all contiguous sections S of a space-ﬁlling curve,of the squared L∞-,L2-or L1-distance between the endpoints of S divided by the area covered by S(studied by Gotsman and Lindenbaum[10]and many other authors[1,5,6,17,24,25]),see Figure1(b)for an example.Ourﬁrst new measure is the maximum,over all contiguous sections S of a space-ﬁlling curve, of the area of the bounding box of S divided by the area covered by S.We call this measure the worst-case bounding-box area ratio(WBA,Figure1(b)).Our second new measure considers 1/16th of the squared perimeter instead of the area,and we call it worst-case bounding-box squared perimeter ratio(WBP).We prove that WBA and WBP are at least2for a large class of space-ﬁlling curves.We also show that this class of curves has L2-locality at least4,thus complementing earlier results by Niedermeier et al.[24]who proved this for another class of space-ﬁlling curves(more restricted in one way,more general in another way).We found that Peano’s original curve achieves a WBA-value of less than2.0001;the exact value is probably exactly2,which is optimal for this class of curves.Other well-known curves have WBA-values ranging from2.400to3.000.However,on the WBP measure Peano’s curve is not that good,with WBP=2.722.Considering both WBA and WBP,the best curve we found in the literature is theβΩ-curve[28],with WBA=2.222and WBP=2.250.However,in this paper we present a new variation on Peano’s curve with even better scores:a WBA-value of2.000and a WBP-value of2.155.This variation also performs very well on L∞-,L2-and L1-locality.Both WBA and WBP consider the worst case over all possible subsections of the curve. However,in the context of our application,it may be more relevant to study the total bounding box area and perimeter of a set of disjoint subsections of the curve that together cover the complete curve.We can argue that in the limit,we may have the worst case for all subsections in such a cover,but this seems to be unlikely to happen in practice.Therefore we study the total bounding box area and perimeter of random subdivisions of the curve into subsections. Here weﬁnd that many curves perform roughly equally well,but those with particularly bad WBA-or WBP-values,such as the Sierpi´n ski-Knopp curve[27]or H-order[24],the AR2W2-curve[4],or Peano’s original(unbalanced)curve(regarding bounding box perimeters),are clearly suboptimal in this sense.We also estimate the total diameter of the subsections in random subdivisions of the curve and present results for octagonal bounding boxes rather than rectangular bounding boxes.Below weﬁrst explain how diﬀerent space-ﬁlling curves can be described and how they can be used to order points.We also describe some new curves.Next we deﬁne the locality and bounding-box quality measures,and prove lower bounds.After that we present our approxi-mation algorithm,and present the results of our computations.2Describing and using space-ﬁlling curvesThere are many ways to deﬁne space-ﬁlling curves,for example algebraic,like in Peano’s pa-per[26],or by describing an approximation of the curve by a polyline,with a rule on how to reﬁne each segment of the approximation recursively[9];many authors do this by specifying the regionsﬁlled by sections of the curve together with the location of the endpoints of such sections on the region boundaries(for example[4,27,28]).Since we are concerned with the use of space-ﬁlling curves as a way to order points in the plane,we choose a method to describe space-ﬁlling curves that is based on deﬁning how to order the space inside a(usually square) unit region.We will see later how such a description is also a description of a curve.2.1How to deﬁne and use a scanning orderWe deﬁne an order(scanning order)≺of points in the plane as follows.We give a set of rules, each of which speciﬁes(i)how to subdivide a region in the plane into subregions;(ii)what is the order of those subregions;and(iii)for each subregion,which rule is to be applied to establish the order within that subregion.We also specify a unit region of area1for each order(usually the unit square),and we indicate what rule is used to subdivide and order it.Technically it would be possible to extend the orders to the full plane,but for simplicity we rather assume that all data that should be ordered isﬁrst scaled to lie within the unit region.The deﬁnitions of the scanning orders discussed in this paper are shown in Figure2.Each rule is identiﬁed by a letter,and pictured by showing a region,its subdivision into subregions, the scanning order of the subregions(by numbers{0,1,2,...}),and the rules applied to the subregions(by letters).Variations of rules that consist of simply rotating or mirroring the order of and within subregions,are indicated by rotating or mirroring the letter identifying that rule.Variations that consist of reversing the order of and within the subregion are indicated by an overscore(Figure2(k,l,m))—making such reversals explicit is the main diﬀerence between our notation and the notation of,for example,Asano et al.[4]or Wierum[28].We can now see how we can implement a comparison operator that allows us to sort points according to a given scanning order.To decide whether p precedes q in the order,we determine in which subregions of the unit region p and q lie.If they are in diﬀerent regions,p precedes q if and only if p lies in the lowest-numbered region of the two.If p and q lie in the same region,we compare them according to the rule for that subregion recursively.Ambiguity on the region boundaries can be resolved as follows:horizontal and diagonal region boundaries are always assumed to be included in the region above them;vertical boundaries are assumed to be included in the region to the right.Each drawing in Figure2includes a curve that roughly indicates the scanning order within the subdivisions.To obtain an arbitrarilyﬁne approximation of a space-ﬁlling curve corre-sponding to a given scanning order,we may compute the subdivision of the unit region into subregions recursively to the desired depth of recursion,and connect the centre points of the resulting subregions by a polygonal curve in the order speciﬁed by the rules.Figure2includes a small example for each scanning order.In the rest of this paper,whenever we write“space-ﬁlling curve”,what we really mean is the scanning order that deﬁnes it.2.2The curvesThe traditional scanning orders considered in this paper are the following.•GP-order,producing the space-ﬁlling curve described in detail by Giuseppe Peano[26,22] (Figure2(a)).We call this order GP-order instead of Peano order to avoid confusion with other curves that have also been referred to as the Peano curve by other authors.•Sierpi´n ski-Knopp-order,producing the Sierpi´n ski-Knopp curve[27](Figure2(h)).It or-ders triangular regions,and can be used to order points as described in Section2.1.Niedermeier et al.[24]describe how to use it to order squares in a2k×2k grid for any k∈N,their variation is called H-order.For all purposes in our paper,Sierpi´n ski-Knopp order and H-order are equivalent.•Hilbert order,producing Hilbert’s curve[12](Figure2(i)).One could say that Peano had already suggested that such a curve would exist[26].Figure2:Space-ﬁlling curve deﬁnitions and example approximating polylines.•Z-order,which follows a space-ﬁlling curve by Lebesgue[16](Figure2(j));Morton is credited with introducing Z-order to computer science[23].•Gosperﬂowsnake order,producing the Gosper curve,also known as theﬂowsnake[2,√7and rotations with angles of 9](Figure2(m)).It involves scaling with a factor1/{0,23π,43π}−arctan15√3.In addition to the above we include a number of variations on these orders.Wunderlich[30] deﬁned a class of orders that satisfy certain restrictions,including:•simplicity:the order is deﬁned by only one rule,and transformed versions of it;•order-preservation:transformations are rotations and/or reﬂections(no reversals);•edge-connectivity:considering the set of regions obtained by applying the rule to anydepth of recursion,weﬁnd that any two consecutive regions in the order share an edge;•uniformity:all subregions have the same size.Wunderlich categorises all diﬀerent simple,order-preserving,edge-connected,uniform orders based on subdividing the unit square in a grid of2×2or3×3squares(modulo rotations, reﬂections and reversals).There is only one such order on a2×2grid(Hilbert order),and there are only273on a3×3grid:one which we call R-order1(Figure2(f)),and272diﬀerent orders that put the nine grid cells in the order of the‘serpentine’pattern of the GP-order(these diﬀer in the rotations and reﬂections of the cells).We investigated all of these orders to some extent,and based on the results we studied some of them in more depth,particularly those depicted in Figures2(a)–(e).By Wunderlich’s numbering scheme these orders are Serpentine orders000000000,011010110,101010101,110110110,and111111111,respectively.Theﬁrst of these is simply GP-order.Luxburg[17]examined the third order calling it Variation2;we call the next order Meurthe order after the river in whose watershed weﬁrst presented it,and we call the last order coil order(a variation also commonly found on the Internet,and studied by Luxburg as Variation1).We explain in Section6why we chose exactly these orders.When some of the above-mentioned restrictions are dropped,more orders are possible.An example from the literature is Wierum’sβΩ-order2[28],which is not simple,and unlike the other orders,it does not start and end in the corners of the unit square(Figure2(k)).Another example is the AR2W2-order which is not simple and not edge-connected,but still vertex-connected(Figure2(l)).It was designed to have the special property that any axis-parallel square query window can be covered by three contiguous sections of the curve that together cover an area of at most a constant times that of the query window[4]—from most other curves in our study one would need at least four sections to get such a constant-ratio cover.Most orders discussed so far cannot be scaled in only one dimension,because their deﬁnitions involve rotations.For GP-order this is not the case.In fact,as we will see later,a scaling in the√3results in an order with much better locality properties. horizontal dimension by a factorWe call the scaled order balanced GP-order(Figure2(g)).3Quality measures for space-ﬁlling curvesSeveral locality measures,or more generally,quality measures of space-ﬁlling curves have been considered in the literature.These include:•bounds on the(average)distance between two points along the curve as a function of their distance in the plane[8,20,29](non-trivial worst-case bounds are not possible[10]);•bounds on the(worst-case or average)distance between two points in the plane as a function of their distance along the curve[7,10,24];•bounds on the(worst-case or average)number of contiguous sections of the curve that is needed to cover an axis-parallel query window,without covering too much space outside the query window[4,7,14,21];•bounds on the(worst-case or average)perimeter or diameter of sections of the curve as a function of their area[13,28].1Wunderlich calls it Meander,but because other authors have used that name to describe other orders,we rather use R-order.2For simplicity we take anΩ-shaped section of the curve.Wierum adds a special rule for the unit square so that he gets a closed(cyclic)curve,but for the purposes of our discussion this would be an unnecessary complication.Not all methods of analysis considered in the literature can easily be applied to compare all curves in our study.Some calculations or experiments in the literature are based on how the scanning order sorts the points of a regular square grid whose size is a ﬁxed integral power of the number of subregions in the rule(s)that deﬁne(s)the order.Such measures may vary with the grid size,which prevents a fair comparison between,for example,GP-order (for which we would have to use a grid size that is a power of nine)and Hilbert order (for which we would have to use a grid size that is a power of four).To enable a comparison between a broad range of curves,we need measures that can be computed eﬃciently for large grids and converge when the grid size goes to inﬁnity.3.1NotationBefore we can discuss and analyse quality measures for space-ﬁlling curves in detail,we need to introduce some notation.For ease of writing,we assume for now that if a scanning order is deﬁned by more than one rule,then each rule contains the same number of subregions.A rule of a scanning order deﬁnes how to subdivide a unit region C of size (area)1into n subregions,numbered 0,...,n −1.The scanning order inside subregion i is given by applying a transformation τ(i )to the unit region C and the way it is ordered by the ordering rule.For any base-n number a we use a to denote its ﬁrst digit,and a to denote the remaining digits.We use C (a )as a shorthand for τ(a )(C (a )),where C (∅)=C .For example,C (538)is subregion 8of subregion 3of subregion 5,and it is found by applying transformation τ(5)to C (38).Similarly,we use τ(a )as a shorthand for τ(a )◦τ(a ),where τ(∅)is the identity transformation.By |A |we denote the size of a region A .We have 0<|C (i )|<1for all 0≤i <n (there are no empty subregions in the rules),and 0≤i<n |C (i )|=|C |=1.Let N k denote the set of k -digit base-n numbers.We write a ≺b if,in base-n notation,a and b have the same number of digits and a <b .By C ( b )we denote the union of subregion b and its predecessors,that is, b −1i =0C (i )∪τ(b )(C ( b )),where C ( ∅)=C .Deﬁne C (≺b ):=C ( b )\C (b ),C ( a ):=C \C (≺a ),C ( a ):=C \C ( a ),and C (a,b ):=C (≺b )\C (≺a ).Above we talked about the distance between two points along the curve,which may be a somewhat counter-intuitive concept for a curve that can be reﬁned and therefore lengthened indeﬁnitely.However,the distance between two points p and q along the curve is well-deﬁned as the area ﬁlled by the section of the curve that runs from p to q ,or more precisely,as:|C (p,q )|:=lim k →∞min a,b ∈N k s.t.p ∈C (a ),q ∈C (b )|C (a,b )|.3.2Pairwise locality measuresFrom the quality measures mentioned above,the most relevant and applicable to the con-struction of bounding-box hierarchies seem to be those that bound the (worst-case or average)distance between two points in the plane as a function of their distance along the curve.This is,intuitively,because points that lie close to each other along the curve are likely to be put together in a block.Then,if the distance between those points in the plane is small too,the block may have a small bounding box.Gotsman and Lindenbaum [10]deﬁned the following class of locality measures:lim m →∞max 1≤i<j ≤m d r (S (i ),S (j ))2(j −i )/m ,where i and j are integers,S (i )is the i th square along the curve in a subdivision of the unit square into a regular grid of m squares,and d r (S,T )is the L r -distance between the centre point(S x,S y)of S and the centre point(T x,T y)of T.Thus d r(S,T)=(|S x−T x|r+|S y−T y|r)1/r for r∈N,and d∞(S,T)=max(|S x−T x|,|S y−T y|).We note that the measure is easily generalised to scanning orders that are not based on regular grids,by deﬁning it as:WL r:=limk→∞supa,b∈N kd r(C(a),C(b))2|C(a,b)|.We call this measure WL r for Worst-case Locality,as it indicates for points that lie close to each other on the curve how far from each other they might get in the plane.Since we have d1(p,q)≥d2(p,q)≥d∞(p,q)for any pair of points p and q,we have WL1≥WL2≥WL∞for any space-ﬁlling curve.3.3Pairwise bounding box measuresIntuitively,one may expect a relation between locality and bounding box size,as explained above.However,we may also try to measure bounding box size directly.We deﬁne two measures to do so.Theﬁrst is the worst-case bounding box area ratio(WBA):WBA:=limk→∞supa,b∈N k|bbox(C(a,b))||C(a,b)|,where bbox(S)is the smallest axis-aligned rectangle that contains S.The second measure is the worst-case bounding box square perimeter ratio(WBP):WBP:=116·lim k→∞supa,b∈N kperi(bbox(C(a,b)))2|C(a,b)|,where peri(S)is the perimeter of S in the L2metric.Taking the square of the perimeter is necessary,because otherwise the measure would be unbounded as k(the resolution of the “grid”)goes to inﬁnity.Because the rectangle of smallest perimeter that has any given area is a square,the“ideal”bounding box has squared perimeter16.The division by16gives an easyrelation between WBP and WBA:we have WBP≥116(4√WBA)2=WBA.Furthermore,sincethe perimeter of the bounding box of two points p and q is simply twice their L1-distance,wehave WBP≥116(2√WL1)2=14WL1.We can deﬁne measures similar to WBA and WBP when the bounding boxes used are notaxis-parallel rectangles,but convex octagons whose sides have normals at angles of0,14π,12π,3 4π,π,54π,32π,and74πwith the positive x-axis.We call these measures worst-case boundingoctagon area ratio(WOA)and worst-case bounding octagon square perimeter ratio(WOP). In the deﬁnition of WOP we still use the factor16to allow a direct comparison with WBP and WBA.Because the octagon of smallest perimeter that has area1has squared perimeter 32/(1+√2)≈0.828·16,we have WOP≥0.828·WOA.3.4Total bounding box measuresWorst-case For our application we argued that the average query response time is related to the total area and perimeter of the bounding boxes formed by grouping data points according to a given scanning order.When the points are suﬃciently densely distributed in the unit region, the gap in the scanning order between the last point of a group and theﬁrst point in the next group will typically be small.Thus the grouping practically corresponds to subdividing the complete unit region into curve sections,of which we store the bounding boxes.To assess theFigure3:Left:an approximation of a section S of the GP curve with|bbox(S)|/|S|=WBA. Middle and right:we can cover an arbitrarily large part of the unit region with such worst-case sections.quality of the order,we can deﬁne the worst-case total bounding box area(TBA)as follows:TBA:=limk→∞supa1≺a2≺...≺a m−1∈N kmi=1|bbox(C(a i−1,a i))|,where a0is deﬁned as0and a m is deﬁned as∅.Since the bounding box area of each section C(a i−1,a i)is at most WBA·|C(a i−1,a i)|and the area of all sections together sum up to1,the total bounding box area is clearly at most WBA.But in fact we can prove the following.Lemma1For any uniform scanning order,we have TBA=WBA.Proof:Consider a section S of the curve such that|bbox(S)|is equal to,or close to,WBA·|S|. Now consider a recursive subdivision,following the rules of the scanning order,of the unit region into a set D of m subregions(cells).Let S be an approximation of S that consists of all the cells of D that are completely covered by S,and let D be the remaining cells of D.Note that we can repeat the construction within each of the cells of D (Figure3).TBA≥|bbox(S )|+|D |/m·TBA≥|bbox(S )|+(1−|S|)·TBA.By choosing m big enough we can let|bbox(S )|be arbitrarily close to WBA·|S|.Thus we get:TBA≥WBA·|S|+(1−|S|)·TBA,which solves to TBA≥WBA.Average As we showed above,the worst-case total bounding box area is not very informative. Of greater practical relevance may be the average total bounding box area(ABA):ABA:=limk→∞avg a1≺a2≺...≺a m−1∈N kmi=1|bbox(C(a i−1,a i))|,where the average is taken over sets of m−1cutting points a1,...,a m−1uniformly chosen from the unit region.The above equation may serve as a complete deﬁnition of the ABA measure for ﬁxed m,but this is not completely satisfactory.Experimental results with the scanning orders described in this paper indicate that asymptotically,the measure does not grow or shrink withm,but it exhibits a smallﬂuctuation which repeats itself as m increases by a factor3,4or9 (depending on the curve)—in other words,the measure tends to be periodic in log m.Therefore anyﬁxed choice of m is likely to give an advantage to some scanning orders and a disadvantage to others.Therefore,we deﬁne the average total bounding box area more precisely as the above measure,averaged over a range of values of m,such that m is large enough and log m is uniformly distributed in a range that covers an integral number of periods ofﬂuctuation of the curve under consideration.We deﬁne an average total bounding octagon area(AOA) analogously.We could deﬁne an average total bounding box square perimeter in a similar way.However, we are ultimately interested in the average perimeter,not the square perimeter.We have to be more careful with the eﬀect of m now:we cannot expect to keep roughly constant total bounding box perimeter as m increases.To cut up a unit region into m sections such that their total bounding box perimeter is minimum,we would have to cut it up into squares of area1/m each,and their total bounding box perimeter would be4√m.Therefore the total bounding box perimeter should be considered relative to4√m,and we deﬁne the square average relative total bounding box perimeter(ABP)as:ABP:=limk→∞avg a1≺a2≺...≺a m−1∈N k14√mmi=1peri(bbox(C(a i−1,a i)))2In the above deﬁnition we still take the square in the end,to allow a direct comparison between ABP and WBP.The reader may verify that we must now have1≤ABA≤WBA and 1≤ABP≤WBP.3.5Total diameter measuresBecause for some applications it may be interesting to keep the diameter of curve sections small[28]and because our software was easy to adapt to it,our results in Section6also include estimations of the square average relative total curve section diameter(AD∞),deﬁned as:AD∞:=limk→∞avg a1≺a2≺...≺a m−1∈N k1√mmi=1diam∞(C(a i−1,a i))2,where diam∞(S)is the diameter of S in the L∞-metric.We also compute AD1:the same measure based on the L1-metric.4Lower bounds4.1Worst-case bounding box areaTheorem1Any scanning order with a rule that contains a triangle has WBA≥2. Proof:The area of a bounding rectangle of any triangle is at least twice the area of . Theorem2Any scanning order based on recursively subdividing an axis-aligned rectangle into a regular grid of rectangles has WBA≥2.Proof:Consider a subdivision of the unit rectangle into a regular grid of m rectangles,following the rules of the scanning order recursively to the depth where a grid of√m×√m rectangles is obtained.We distinguish two cases:either there is a pair of rectangles that are consecutive。

SAE J826 2008

__________________________________________________________________________________________________________________________________________ SAE Technical Standards Board Rules provide that: “This report is published by SAE to advance the state of technical and engineering sciences. The use of this report is entirely voluntary, and its applicability and suitability for any particular use, including any patent infringement arising therefrom, is the sole responsibility of the user.” SAE reviews each technical report at least every five years at which time it may be reaffirmed, revised, or cancelled. SAE invites your written comments and suggestions. Copyright © 2008 SAE InternationalAll rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of SAE. TO PLACE A DOCUMENT ORDER: Tel: 877-606-7323 (inside USA and Canada) Tel: 724-776-4970 (outside USA) Fax: 724-776-0790Email: CustomerService@ SAE WEB ADDRESS:h ttp://J826 MAR2008SURFACEVEHICLE STANDARDIssued 1962-11Revised 2008-03Superseding J826 JUL1995(R) Devices for Use in Defining and Measuring Vehicle Seating AccommodationRATIONALEThis revision incorporates an inspection procedure for checking calibration of the H-point machine (Appendix C). It also adds specifications for the mounting surface of the head restraint measuring device.Other changes include:- 10 year phase-out period for the HPM- Revision of HPM weight specification from 167 to 169.6 lb to reflect current HPM build - New ambient humidity specification- Narrower range of ambient test temperatures - Clarification of muslin cloth specification- Extensive revision of short couple method and addition of long couple method to Appendix A - Terminology consistent with SAE J1100 - Editorial clarificationsSAE J4002 (HPM-II) and SAE J826 (HPM) shall co-exist for a transition period of at least 10 years, preferably no longer, from the first publication date of SAE J4002 (August 2005). Following this transition period SAE J826 will be withdrawn. During the transition period, it remains up to the vehicle designers to decide which HPM to use. Regulatory bodies and other parties that need to know shall be informed regarding which HPM was used.TABLE OF CONTENTS1.SCOPE (3)1.1Purpose (3)2.REFERENCES (4)2.1Applicable Publications (4)2.1.1SAE Publications (4)2.2Related Publication (4)2.2.1SAE Publication (4)3.DEFINITIONS (4)3.1Accelerator Heel Point, AHP (4)3.2Ankle (Foot) Angle, A46 (4)3.3Ball of Foot, BOF (4)3.4Cushion Angle, A27 (4)3.5Floor Reference Point, FRP (5)3.6H-Point (5)3.7Heel of Shoe (5)3.8Hip Angle, A42 (5)3.9Knee Angle, A44 (5)3.10Seating Reference Point, SgRP (5)3.11Shoe Plane (5)3.12Thigh Centerline (5)3.13Thigh (Cushion) Line (5)3.14Torso (Back) Angle, A40 (5)3.15Torso Line (5)4.H-POINT TEMPLATE—DESCRIPTION, APPLICATION, AND POSITIONING PROCEDURE (5)4.1Description (5)4.2Application—Aids in displaying the following: (5)4.3Positioning Procedure for physical template (Figure 1) (5)4.3.1Torso positioning for any specified Seating Reference Point and torso angle (5)4.3.2Front Seat—Driver Position (6)4.3.3Front Seat—Driver Position (6)4.3.4Second Row—Left Side Occupant Position (6)4.3.5Third Row—Left Side Occupant Position—Forward Facing (7)4.3.6Third Row—Left Side Occupant Position—Rearward Facing (7)4.3.7H-point template layout using data obtained during H-point machine installation (7)4.4Positioning Procedure for CAD template (Figure 2) (7)4.4.1Use of optional shoe bottom (7)4.4.2Positioning for any specified Seating Reference Point and torso angle (7)4.4.3Positioning for an unknown Seating Reference Point and torso angle (8)5.H-POINT MACHINE—DESCRIPTION, APPLICATION, AND INSTALLATION PROCEDURE (8)5.1Description (8)5.2Application (10)5.3Installation Procedure (10)6.SHORT-COUPLED SEATING CONDITION (13)7.LONG-COUPLED SEATING CONDITION (13)8.DETERMINATION OF CUSHION ANGLE (13)9.H-POINT MACHINE AND TEMPLATE FABRICATION (13)10.CALIBRATION OF THE H-POINT MACHINE (13)11.NOTES (14)11.1Marginal Indicia (14)APPENDIX A INSTALLATION PROCEDURE FOR SHORT- AND LONG-COUPLED SEATING (15)APPENDIX B DETERMINATION OF CUSHION ANGLE (19)APPENDIX C SAE J826 H-POINT MACHINE CALIBRATION INSPECTION (21)APPENDIX D HEAD RESTRAINT MEASURING DEVICE (HRMD) (31)FIGURE 1 H-POINT TEMPLATE (6)FIGURE 2 CAD VERSION OF H-POINT TEMPLATE (8)FIGURE 3 H-POINT MACHINE (9)FIGURE 4 H-POINT MACHINE (9)FIGURE A1 OVERVIEW OF SHORT-COUPLE CONDITION METHOD ‘A’ (15)FIGURE A2 OVERVIEW OF SHORT-COUPLE CONDITION METHOD ‘B’ (16)FIGURE A3 OVERVIEW OF LONG-COUPLE CONDITION (17)FIGURE A4 DECISION TREE FOR COUPLE METHODS - 2-D TEMPLATE PLACEMENT FOR 2ndTO N th ROW (18)FIGURE B1 DISTRIBUTION OF WEIGHTS FOR CUSHION ANGLE MEASUREMENT (20)FIGURE C1 MEASUREMENT COORDINATE SYSTEM FOR HPM PANS (22)FIGURE C2 HPM TORQUE ADJUSTMENT. SOME HPMS MAY DIFFER FROM THIS ILLUSTRATION (23)FIGURE C3 HPM CUSHION AND BACK PAN SETUP (24)FIGURE C4 HPM CUSHION AND BACK PAN MEASUREMENTS (25)FIGURE C5 LEG AND SHOE SETUP (27)FIGURE C6 WEIGHTS (27)TABLE 1 LEG SEGMENT LENGTH (10)TABLE C1 HPM DIMENSIONS AND TOLERANCES (ITEM NUMBERS IDENTIFY A MEASUREMENT SHOWN IN FIGURES C1-C6) (28)1. SCOPEThe devices of this SAE Standard provide the means by which passenger compartment dimensions can be obtained using a deflected seat rather than a free seat contour as a reference for defining seating space. All definitions and dimensions used in conjunction with this document are described in SAE J1100. These devices are intended only to apply to the driver side or center occupant seating spaces and are not to be construed as instruments which measure or indicate occupant capabilities or comfort. This document covers only one H-point machine installed on a seat during each test. Certified H-point templates and machines can be purchased from:SAE International400 Commonwealth DriveWarrendale, PA 15096-0001Specific procedures are included in Appendix A for seat measurements in short- and long-coupled vehicles and in Appendix B for measurement of the driver seat cushion angle. Specifications and a calibration inspection procedure for the H-point machine are given in Appendix C. Additional considerations are necessary when a Head Restraint Measuring Device (HRMD) is mounted to an H-point machine (Appendix D).1.1 PurposeThis document specifies a two-dimensional H-point template and a three-dimensional H-Point Machine (HPM) for use in defining and measuring accommodation in vehicle seats.2. REFERENCES2.1 Applicable PublicationsThe following publications form a part of this specification to the extent specified herein. The latest issue of SAE publications shall apply.2.1.1 SAEPublicationsAvailable from SAE International, 400 Commonwealth Drive, Warrendale, PA 15096-0001, Tel: 877-606-7323 (inside USA and Canada) or 724-776-4970 (outside USA), .SAE J182 Motor Vehicle Fiducial Marks and Three-Dimensional Reference SystemSAE J1100 Motor Vehicle Dimensions2.2 Related PublicationsThe following publications are provided for information purposes and are not a required part of this document.2.2.1 SAEPublicationsAvailable from SAE International, 400 Commonwealth Drive, Warrendale, PA 15096-0001, Tel: 877-606-7323 (inside USA and Canada) or 724-776-4970 (outside USA), .SAE J1516 Accommodation Tool Reference PointSAE J1517 Driver Selected Seat PositionSAE J2732 Motor Vehicle Seat DimensionsSAE J4002 H-Point Machine (HPM-II) Specifications and Procedure for H-Point Determination—Auditing Vehicle SeatsSAE J4003 H-Point Machine (HPM-II)—Procedure for H-Point Determination—Benchmarking Vehicle SeatsSAE J4004 Positioning the H-Point Design Tool—Seating Reference Point and Seat Track LengthS. P. Geoffrey, "A 2-D Manikin—The Inside Story", Paper 267A presented at SAE International Congress, Detroit, January 19613. DEFINITIONSThe following terms are defined in SAE J1100. When appropriate, added explanation is provided.3.1 Accelerator Heel Point, AHP3.2 Ankle (Foot) Angle, A463.3 Ball of Foot, BOF3.4 Cushion Angle, A27See Appendix B. Cushion Angle is measured using the H-point machine with the lower legs removed and the torso weights redistributed about the cushion pan.3.5 Floor Reference Point, FRP3.6 H-PointThe H-point is located on the centerline of the H-point machine midway between the H-point sight buttons on either side of the machine.3.7 Heel of Shoe3.8 Hip Angle, A423.9 Knee Angle, A443.10 Seating Reference Point, SgRP3.11 Shoe Plane3.12 Thigh Centerline3.13 Thigh (Cushion) Line3.14 Torso (Back) Angle, A4013.15 Torso Line4. H-POINT TEMPLATE—DESCRIPTION, APPLICATION, AND POSITIONING PROCEDURE4.1 DescriptionThe H-point template (Figure 1) is constructed to represent in profile an adult male wearing shoes and corresponds to the profile of the deflected seating contour of the H-point machine. Individual torso, thigh, lower leg, and shoe segments are provided with locking pivot joints which can be used to fix the angular relationships of the segments. A torso angle reference bar is included to orient the template’s torso in relation to the vertical.4.2 Application—Aids in displaying the following:•Passenger compartment space and seating attitude during conception, engineering, and development stages of any new vehicle.•Passenger compartment space and seating attitude for comparison and reporting purposes.•Data obtained from checks made with the H-point machine. (See Section 5).4.3 Positioning Procedure for physical template (Figure 1)4.3.1 Torso positioning for any specified Seating Reference Point and torso angle.4.3.1.1 Position the H-point of the H-point template on the Seating Reference Point (SgRP) location on the layout.1Prior to 2007 SAE standards generally used the term “back angle” to describe the A40 dimension of SAE J1100. New or revised standards beginning in 2007 will use the term “torso angle” for this dimension.FIGURE 1 - H-POINT TEMPLATE4.3.1.2 Set the torso angle reference bar quadrant scribe line marked on the torso angle quadrant to the specified torsoangle. Lock this quadrant in place.4.3.1.3 Position the vertical reference scribe lines on the torso angle reference bar parallel to the body grid lines on thelayout drawing.4.3.2 Front Seat—Driver PositionLeg and shoe positioning for any specified Accelerator Heel Point location.4.3.2.1 Holding the torso portion of the template in position as outlined in 4.3.1.1 to 4.3.1.3, position the heel point ofthe template at the specified heel point location. This point on the layout is located on top of the heel pad or the depressed floor covering surface at the Y-plane centerline of the accelerator pedal.4.3.2.2 Holding the heel point at the specified location, rotate the shoe forward until the bottom of the shoe contacts theundepressed accelerator pedal without infringing upon the 87 degrees minimum ankle (foot) angle. Normally the pedal contact point is at or below the shoe ball of foot.4.3.2.3 The undepressed accelerator pedal (point of contact with the bottom of shoe or shoe plane) may be determinedby locating the heel point as described previously and presetting and locking the ankle angle to 87 degrees.4.3.3 Front Seat—Driver PositionLeg and shoe positioning for any specified undepressed accelerator pedal location.4.3.3.1 Holding the torso portion of the template in position as outlined in 4.3.1.1 to 4.3.1.3, position the bottom of theshoe on the specified undepressed accelerator pedal and the heel as far forward as allowable. However, the ankle angle is never less than 87 degrees. Lock ankle angle quadrant.4.3.4 Second Row—Left Side Occupant PositionLeg and shoe positioning with the front seat in its SgRP position.4.3.4.1 Holding the torso portion of the template in position as outlined in 4.3.1.1 to 4.3.1.3, except with the template H-point on the SgRP of the second row seat, place the bottom of the shoe (heel and ball) on the depressed floor covering line. The shoe is to be placed on the Y-plane centerline of the occupant or up to 127 mm (5 in) on either side of the Y-plane centerline on the floor pan section.NOTE: Locating the shoe either side of the Y-plane centerline of the occupant position will make the shoe location compatible to the shoe location in the existing H-point machine installation procedure.4.3.4.2 Move the shoe forward along the depressed floor covering line to the nearest interference of the toe, instep,lower leg, or knee with the front seat. The ankle angle is to be restricted to a maximum of 130 degrees.4.3.5 Third Row—Left Side Occupant Position—Forward Facing4.3.5.1 Follow the procedure as outlined for the second row seat, left side occupant position except that the template ispositioned in the third seat compartment.4.3.6 Third Row—Left Side Occupant Position—Rearward Facing4.3.6.1 Follow the same procedure as outlined for the third row—side occupant position—forward facing except thatthe shoe is positioned in the footwell to the interference with the rear end or closure.4.3.7 H-point template layout using data obtained during H-point machine installation.4.3.7.1 Position the H-point pivot of the template at the measured H-point location on a layout drawing or grid system. 4.3.7.2 Follow the procedure as outlined in 4.3.1.1 to 4.3.1.3 using the measured torso angle instead of the designtorso angle.4.3.7.3 Holding the torso portion of the template in position as outlined previously, move the upper leg segment to themeasured hip angle shown on the hip angle quadrant.4.3.7.4 Lock this quadrant in place.4.3.7.5 Position and lock the ankle (foot) angle quadrant to the measured ankle angle.4.3.7.6 Allowing the knee angle to vary as necessary, position the ankle pivot center on an arc from the hip pivot centerequal to the measured effective leg room less 254 mm.4.4 Positioning Procedure for CAD template (Figure 2)4.4.1 Use of optional shoe bottom4.4.1.1 The standard H-point template has a shoe with an arched bottom and a defined heel shape. The BOF point onthe shoe is 203 mm (8 in) from the heel of the shoe. SAE manikins defined in SAE J4002 (HPM-II) and SAE J4004 (HPD) have a shoe with flat sole and a BOF defined at 200 mm from the heel of the shoe. As an option to aid in transitioning to these devices, users may flatten the shoe bottom of the CAD template and locate the BOF 200 mm from the heel, as shown in Figure 2.4.4.2 Positioning for any specified Seating Reference Point and torso angle.4.4.2.1 Position the H-point of the CAD template on the SgRP at the specified torso angle. Use values for SgRP andtorso angle that are either specified by the manufacturer or can be determined from SAE J4004 or SAE J1516/SAE J1517.4.4.2.2 For the driver position, lock the ankle angle at 87 degrees. The bottom of the shoe should be touching theundepressed accelerator pedal. Alternatively, the heel of shoe may be placed at the manufacturer AHP with the bottom of the shoe touching the pedal.FIGURE 2 - CAD VERSION OF H-POINT TEMPLATE4.4.2.3 For passenger positions the shoe should be positioned with the heel of shoe at the floor reference point (FRP)and the bottom of shoe on the floor.4.4.3 Positioning for an unknown Seating Reference Point and torso angle.4.4.3.1 Install the 3-D H-point machine to determine the seat H-point travel path, the undepressed accelerator pedalpad location, and depressed floor covering. See SAE J1100 and SAE J4003/SAE J4004 for determining SgRP and torso angle.4.4.3.2 The CAD template is installed as described in 4.4.2.5. H-POINT MACHINE—DESCRIPTION, APPLICATION, AND INSTALLATION PROCEDURE5.1 DescriptionA machine (Figures 3 and 4) with back and cushion pan representations of deflected seat contours of adult males. Constructed of reinforced plastic and metal, these separate back and cushion pans simulate the human torso and thigh and are mechanically hinged at the H-point. A graduated sliding probe is hinged from the H-point to measure the head room in the compartment. A quadrant is fastened to the probe to measure the torso angle. An adjustable thigh bar, attached to the cushion pan, establishes the thigh centerline and serves as a baseline for the hip angle quadrant. Lower leg segments, also adjustable in length, are connected to the cushion pan assembly at the knee joining T-bar, which is a lateral extension of the adjustable thigh bar. Quadrants are incorporated in the lower leg segments to measure knee angles. Shoe and ankle assemblies are calibrated to measure the angular relation to the lower leg segment. Positive stops are provided in the thigh and lower leg segments for the 10th, 50th, and 95th percentile of adult male dimensions (Table 1). Two spirit levels orient the device in space. Body segment weights are placed at the center of gravity locations to provide seat penetration equivalent to a 77 kg (169.6 lb) male.2The lower leg and thigh segments are available in 10th, 50th, and 95th percentile lengths. (See Table 1.)2The adult male dimensions were in part taken from the 50th percentile data as acquired by Geoffrey. The remaining dimensions were developed from U.S. Department of Health, Education, and Welfare data by the Design Devices Subcommittee of the SAE Human Factors Engineering Committee, March, 1969.FIGURE 3 - H-POINT MACHINEFIGURE 4 - H-POINT MACHINETABLE 1 - LEG SEGMENT LENGTH10th Percentile(1) mm (inches)50thPercentile(1)mm (inches)HPM 95thPercentile(2)mm (inches)Template 95thPercentile(3)mmLower leg segment (A) 392.7 (15.46) 417.1 (16.42) 458.7 (18.06) 459.1Thigh segment (B) 407.7 (16.05) 431.5 (16.99) 455.7 (17.94) 456.01. S. P. Geoffrey, "A 2-D Manikin—The Inside Story." Paper 267A presented at SAE International Congress, Detroit, January 1961.2. Values for the 95th percentile leg lengths were developed on the basis of best judgment of available data by the Design DevicesSubcommittee of the SAE Human Factors Engineering Committee at the July 1968 and March 1969 meetings.3. Values for 95th percentile leg lengths of the template were established by comparisons of CMM scans of templates from severalmanufacturers in 1992.5.2 Application5.2.1 Aid in the design and development of seats and seat materials.5.2.2 Check vehicle seating compartments for conformance to design specifications, that is, relationship of H-point tobody structures, seats, controls, etc.5.3 Installation Procedure5.3.1 Dimensions are measured relative to the X and Z body zero planes by setting up the vehicle relative to the frontand rear fiducial mark (see SAE J182) height (H163 and H164). Curb and gross weight rating loads require different fiducial mark heights. (See SAE J1100.) All interior dimensions are measured with the front seat in the SgRP position as specified by the manufacturer. When the seatback has an angular adjustment separate from the seat cushion, the normal driving or riding torso angle is specified by the manufacturer (A40). Use 25 degrees if not specified. The cushion tilt adjustment, if available, should be in the design position.5.3.2 Sufficient time (at least 4 h) shall be allowed to ensure that the seat material reaches room temperature. Roomtemperature shall be 19 to 26 °C (66 to 79 °F). Room relative humidity should be within a range of 50% ± 5%. If this relative humidity is not met, record both relative humidity and room temperature. If the seat to be checked has never been sat upon, a 68 to 79 kg (150 to 175 lb) person shall sit on the seat twice for 1 min to flex the cushion and back. All seat assemblies are to remain unloaded for a minimum period of 1/2 h (1 h preferred) prior to the H-point machine installation.5.3.3 Place a piece of muslin cotton cloth over the seat area to be checked. The muslin cloth should be of sufficientsize to prevent the machine from contacting the seat, approximately 910 mm square. The muslin should be a plain cotton fabric having a thread count and weight typical of a durable, mid-grade, general-purpose muslin that is available from most fabric stores. The muslin should be tucked in a sufficient amount to prevent hammocking of the material. If the test is run in a buck, suitable floor covering sections, or equivalent, are to be placed under the H-point machine's shoes.5.3.4 Place cushion and back assembly of the H-point machine at the centerline of occupant (C/LO). C/LO is also thecenterline of H-point machine and is located in vehicle per manufacturer specifications. If specifications are not available, locate C/LO as follows:- for bucket front seats, seats with defined bolsters, or individual auxiliary seats, C/LO is the centerline of the seat.- for bench (or other) seats, C/LO is located at the middle of the head restraint. If a head restraint is not fitted, locate C/LO midway between the lap belt anchors. For the driver, C/LO may be aligned with the steering wheel center.- 381 mm outboard from the vehicle centerline (as a last resort)The C/LO should be moved inboard whenever the H-point machine is sitting far enough outboard that the seat edge will not permit leveling of the H-point machine. It is moved inboard the necessary distance to permit leveling of the H-point machine and the new dimension from centerline of vehicle to C/LO noted in recording measurements.5.3.5 Use 95th percentile leg and thigh segments specified in Table 1.5.3.6 Attach shoe and lower leg assemblies to the cushion pan assembly, either individually at the knee joint or byusing the T-bar lateral segment and lower leg assembly.The T-bar lateral segment should be parallel to the ground and perpendicular to the Y-plane of the vehicle unless otherwise specified by the manufacturer.5.3.7 The shoe and leg positions of the H-point machine for the various individual seat positions to be checked are asfollows:5.3.7.1 Front Seat—Driver PositionThe right shoe and leg assembly is placed on the undepressed (blocked or mechanically restrained) accelerator pedal with the sole of the shoe on the pedal and the heel as far forward as allowable. The right leg is adjusted inboard on the T-bar toward the centerline of the vehicle until just contacting the tunnel (or other components) or until the Ball of Foot on the shoe is aligned with the center of the accelerator pedal pad unless specified otherwise by the manufacturer. Tunnel contact at the heel is defined where the Heel Point on the shoe is at the beginning transition of horizontal to upturned compressed carpet surface. The heel may not be placed on the toe board. However, the ankle angle is never less than 87 degrees. The 87 degree limit can be fixed by inserting the pin into the shoe assembly.The left shoe is positioned on the floor or toe pan and located approximately the same distance to the left of the H-point machine centerline as the right shoe is to the right. The T-bar should be maintained parallel to the ground.5.3.7.2 Front Seat—Occupant in Vehicle Centerline PositionThe H-point machine is installed in the front seat vehicle centerline position with both legs extended at the specified percentile, one on either side of the tunnel. The left shoe is placed on the undepressed accelerator pedal and the right shoe is located to the right of the tunnel, approximately opposite and symmetrical in a manner that levels the knee joint T-bar. A T-bar extension may be required to straddle the knee segments on either side of the tunnel. In vehicles having no tunnel, the shoes are set approximately 254 mm (10 in) apart. The leg comfort angles are determined from the H-point machine's left leg.5.3.7.3 Second and Successive Seats—Side Occupant PositionThe H-point machine is installed in the second seat outboard occupant position at the C/LO as described in 5.3.4. (Check applicable seating arrangement drawing for specified location.) The two shoes are placed together, or up to 127 mm (5 in) to either side of C/LO, and positioned to the nearest interference of the toe, instep, or lower leg with the front seat, unless otherwise specified by the manufacturer. In instances where one shoe reaches interference before the other, the one with the farthest interference will be used for dimensioning purposes. For additional H-point machine leg location conditions and restrictions, see Appendix A. For a description of short- and long- coupled seating conditions, see Section 6 and Section 7.5.3.7.4 Second and Successive Seats—Occupant in Vehicle Centerline PositionThe H-point machine is installed in the second seat-vehicle centerline position with both the shoe and lower leg assemblies on the normal floor, and placed astride the tunnel, if present. Both leg assemblies are extended to the nearest interference of the toe, instep, or lower leg with the front seat.If necessary, in order to clear lateral obstructions, such as seat belt anchors, tunnel width, etc., the T-bar may be extended. In vehicles with no tunnel, set the H-point machine's shoes approximately 254 mm (10 in) apart.5.3.8 Apply lower leg and thigh weights and level the H-point machine.5.3.9 Tilt the back pan forward against the forward stop and draw the H-point machine away from the seatback usingthe T-bar. Reposition the H-point machine on the seat by one of the following methods:5.3.9.1 If the H-point machine tends to slide rearward, use the following procedure: Allow the H-point machine to sliderearward until a forward horizontal restraining load on the T-bar is no longer required due to the cushion pan contacting the seatback.5.3.9.2 If the H-point machine does not tend to slide rearward, use the following procedure: Slide the H-point machinerearward by a horizontal rearward load applied at the T-bar until the cushion pan contacts the seatback.5.3.10 Apply a 10 kg (22 lb) load twice to the back and pan assembly positioned at the intersection of the hip anglequadrant and the T-bar housing (Figure 3). The direction of load application should be maintained along a line from the above intersection to a point just above the thigh bar housing. Then carefully return the back pan to the seatback. Care must be exercised through the remainder of the procedure to prevent the H-point machine from sliding forward.5.3.11 Install the right and left buttock weights and then alternately the eight torso weights. Maintain H-point machinelevel.5.3.12 Tilt the back pan forward until the stop is contacted. Rock the H-point machine from side to side over a 10 degreearc (5 degrees to each side of the vertical centerline) for three complete cycles to release any accumulated friction between the H-point machine and the seat. During the rocking, the T-bar of the H-point machine may tend to change from the specified horizontal and vertical alignment; therefore, the T-bar must be restrained and properly aligned by applying an appropriate lateral load during the rocking motions. Care shall be exercised in holding the T-bar and rocking the H-point machine to minimize inadvertent exterior loads applied in a vertical or fore-and-aft direction. The H-point machine's shoes are not to be restrained or held during this step, and if the shoes change position, they should be allowed to remain in that attitude at this time. Due to the movement of the shoes during the H-point machine rocking operation, the shoes are repositioned as follows:a. Front Seat—Alternately lift each shoe off the floor the minimum necessary amount until no additional forward shoemovement is obtained. During this lifting, the shoes are to be free to rotate and no forward or lateral loads are to be applied. When each shoe is placed back in the down position, the heel is to be in contact with the floor and the ball (sole) of the foot is to be in contact with the floor, toe board, or undepressed accelerator pedal.b. Second and Successive Seats—Alternately move each shoe forward by applying a forward load to the heel of theshoe, sliding the shoes forward until the shoe or leg interfere with the rear of the front seatback. This operation releases any accumulated shoe friction and movement incurred during the lateral rocking step.If the cushion pan is not level at the completion of this step, apply a sufficient lateral load to the top of the back pan to level the H-point machine cushion pan on the seat.5.3.13 Holding the T-bar to prevent the H-point machine from sliding forward on the seat cushion, proceed as follows:a. Return the back pan to the seatback.b. Apply a rearward force perpendicular to the torso angle bar just above the torso weights using the smaller of thefollowing forces:1. Force sufficient to increase the hip angle by 3 degrees, or2. 66 N (15 lb).Alternately apply and release this force until the hip angle readout indicates that the back pan has reached a stable position after the applied force has been released, that is, repeated identical hip angle readouts. Care shall be exercised to minimize exterior downward or side forces applied to the H-point machine. If an H-point machine level adjustment is necessary, rotate the back pan forward, re-level, and repeat the H-point machine back rocking.5.3.14 If a rerun of the H-point machine installation is desired, the seat assembly should remain unloaded for a minimumperiod of 1/2 h prior to the rerun. The loaded H-point machine should not be left on the assembly longer than the time required to perform the test.。

IPC-7351B & PCBL Land Pattern Naming Convention

I P C-7351B N a m i n g C o n v e n t i o n f o r S t a n d a r d S M T L a n d P a t t e r n sSurface Mount Land PatternsComponent, Category Land Pattern Name Ball Grid Array’s...............................BGA + Pin Qty + C or N + Pitch P + Ball Columns X Ball Rows _ Body Length X Body Width X Height BGA w/Dual Pitch.BGA + Pin Qty + C or N + Col Pitch X Row Pitch P + Ball Columns X Ball Rows _ Body Length X Body Width X Height BGA w/Staggered Pins..................BGAS + Pin Qty + C or N + Pitch P + Ball Columns X Ball Rows _ Body Length X Body Width X Height BGA Note: The C or N = Collapsing or Non-collapsing BallsCapacitors, Chip, Array, Concave..........................................................CAPCAV + Pitch P + Body Length X Body Width X Height - Pin Qty Capacitors, Chip, Array, Flat..................................................................CAPCAF + Pitch P + Body Length X Body Width X Height - Pin Qty Capacitors, Chip, Non-polarized.................................................................................................CAPC + Body Length + Body Width X Height Capacitors, Chip, Polarized.....................................................................................................CAPCP + Body Length + Body Width X Height Capacitors, Chip, Wire Rectangle........................................................................................CAPCWR + Body Length + Body Width X Height Capacitors, Molded, Non-polarized...........................................................................................CAPM + Body Length + Body Width X Height Capacitors, Molded, Polarized.................................................................................................CAPMP + Body Length + Body Width X Height Capacitors, Aluminum Electrolytic ............................................................................................................CAPAE + Base Body Size X Height Ceramic Flat Packages.....................................................................................................CFP127P + Lead Span Nominal X Height - Pin Qty Column Grid Array’s.....................................................CGA + Pitch P + Number of Pin Columns X Number of Pin Rows X Height - Pin Qty Crystals (2 leads)........................................................................................................................XTAL + Body Length X Body Width X Height Dual Flat No-lead..........................................................................................................DFN + Body Length X Body Width X Height – Pin Qty Diodes, Chip................................................................................................................................DIOC + Body Length + Body Width X Height Diodes, Molded...........................................................................................................................DIOM + Body Length + Body Width X Height Diodes, MELF................................................................................................................................DIOMELF + Body Length + Body Diameter Fuses, Molded............................................................................................................................FUSM + Body Length + Body Width X Height Inductors, Chip.............................................................................................................................INDC + Body Length + Body Width X Height Inductors, Molded........................................................................................................................INDM + Body Length + Body Width X Height Inductors, Precision Wire Wound................................................................................................INDP + Body Length + Body Width X Height Inductors, Chip, Array, Concave..............................................................INDCAV + Pitch P + Body Length X Body Width X Height - Pin Qty Inductors, Chip, Array, Flat......................................................................INDCAF + Pitch P + Body Length X Body Width X Height - Pin Qty Land Grid Array, Round Lead............................LGA + Pin Qty - Pitch P + Pin Columns X Pin Rows _ Body Length X Body Width X Height Land Grid Array, Square Lead........................LGAS + Pin Qty - Pitch P + Pin Columns X Pin Rows _ Body Length X Body Width X Height LED’s, Molded............................................................................................................................LEDM + Body Length + Body Width X Height Oscillators, Side Concave........................................................................OSCSC + Pitch P + Body Length X Body Width X Height - Pin Qty Oscillators, J-Lead.......................................................................................OSCJ + Pitch P + Body Length X Body Width X Height - Pin Qty Oscillators, L-Bend Lead.............................................................................OSCL + Pitch P + Body Length X Body Width X Height - Pin Qty Oscillators, Corner Concave....................................................................................................OSCCC + Body Length X Body Width X Height Plastic Leaded Chip Carriers..................................................PLCC + Pitch P + Lead Span L1 X Lead Span L2 Nominal X Height - Pin Qty Plastic Leaded Chip Carrier Sockets Square.......................PLCCS + Pitch P + Lead Span L1 X Lead Span L2 Nominal X Height - Pin Qty Quad Flat Packages..................................................................QFP + Pitch P + Lead Span L1 X Lead Span L2 Nominal X Height - Pin Qty Ceramic Quad Flat Packages.................................................CQFP + Pitch P + Lead Span L1 X Lead Span L2 Nominal X Height - Pin Qty Quad Flat No-lead................................................................QFN + Pitch P + Body Width X Body Length X Height - Pin Qty + Thermal Pad Pull-back Quad Flat No-lead..............................................PQFN + Pitch P + Body Width X Body Length X Height - Pin Qty + Thermal Pad Quad Leadless Ceramic Chip Carriers..........................................................LCC + Pitch P + Body Width X Body Length X Height - Pin Qty Quad Leadless Ceramic Chip Carriers (Pin 1 on Side)...............................LCCS + Pitch P + Body Width X Body Length X Height - Pin Qty Resistors, Chip...........................................................................................................................RESC + Body Length + Body Width X Height Resistors, Molded......................................................................................................................RESM + Body Length + Body Width X Height Resistors, MELF...........................................................................................................................RESMELF + Body Length + Body Diameter Resistors, Chip, Array, Concave............................................................RESCAV + Pitch P + Body Length X Body Width X Height - Pin Qty Resistors, Chip, Array, Convex, E-Version (Even Pin Size)...............RESCAXE + Pitch P + Body Length X Body Width X Height - Pin Qty Resistors, Chip, Array, Convex, S-Version (Side Pins Diff)................RESCAXS + Pitch P + Body Length X Body Width X Height - Pin Qty Resistors, Chip, Array, Flat.....................................................................RESCAF + Pitch P + Body Length X Body Width X Height - Pin Qty Small Outline Diodes, Flat Lead...................................................................................SODFL + Lead Span Nominal + Body Width X Height Small Outline IC, J-Leaded........................................................................................SOJ + Pitch P +Lead Span Nominal X Height - Pin Qty Small Outline Integrated Circuit, (50 mil Pitch SOIC)......................................................SOIC127P +Lead Span Nominal X Height - Pin Qty Small Outline Packages............................................................................................SOP + Pitch P +Lead Span Nominal X Height - Pin Qty Small Outline No-lead...........................................................SON + Pitch P + Body Width X Body Length X Height - Pin Qty + Thermal Pad Pull-back Small Outline No-lead.........................................PSON + Pitch P + Body Width X Body Length X Height - Pin Qty + Thermal Pad Small Outline Transistors, Flat Lead....................................................................SOTFL + Pitch P + Lead Span Nominal X Height - Pin Qty SOD (Example: SOD3717X135 = JEDEC SOD123)........................................................SOD + Lead Span Nominal + Body Width X Height SOT89 (JEDEC Standard Package).......................................................................................................................................................SOT89 SOT143 & SOT343 (JEDEC Standard Package)..............................................................................................................SOT143 & SOT343 SOT143 & SOT343 Reverse (JEDEC Standard Package)...........................................................................................SOT143R & SOT343R SOT23 & SOT223 Packages (Example: SOT230P700X180-4)...............................SOT + Pitch P + Lead Span Nominal X Height - Pin Qty TO (Generic DPAK - Example: TO228P970X238-3).................................................................TO + Pitch P + Lead Span X Height - Pin QtyI P C-7351B L a n d P a t t e r n N a m i n g C o n v e n t i o n N o t e s•All dimensions are in Metric Units•All Lead Span and Height numbers go two places past the decimal point and “include” trailing Zeros•All Lead Span and Body Sizes go two place before the decimal point and “remove” leading Zeros•All Chip Component Body Sizes are one place to each side of the decimal point•Pitch Values are two places to the right & left of decimal point with no leading Zeros but include trailing zeros N a m i n g C o n v e n t i o n S p e c i a l C h a r a c t e r U s e f o r L a n d P a t t e r n sThe _ (underscore) is the separator between pin Qty in Hidden & Deleted pin componentsThe – (dash) is used to separate the pin qty.The X (capital letter X) is used instead of the word “by” to separate two numbers such as height X width like “Quad Packages”.P C B L i b r a r i e s S u f f i x N a m i n g C o n v e n t i o n f o r L a n d P a t t e r n sCommon SMT Land Pattern to Describe Environment Use (This is the last character in every name)Note: This excludes the BGA component family as they only come in the Nominal Environment Condition •M.................Most Material Condition (Level A)•N..................Nominal Material Condition (Level B)•L.................Least Material Condition (Level C)Alternate Components that do not follow the JEDEC, EIA or IEC Standard•A..................Alternate Component (used primarily for SOP & QFP when Component Tolerance or Height is different) •B..................Second Alternate ComponentReverse Pin Order•-20RN..........20 pin part, Reverse Pin Order, Nominal EnvironmentHidden Pins•-20_24N......20 pin part in a 24 pin package. The pins are numbered 1 – 24 the hidden pins are skipped. The schematic symbol displays up to 24 pins.Deleted Pins•-24_20N......20 pin part in a 24 pin package. The pins are numbered 1 – 20. The schematic symbol displays 20 pins. JEDEC and EIA Standard parts that have several alternate packages•AA, AB, AC.JEDEC or EIA Component IdentifierGENERAL SUFFIXES_HS.........................HS = Land Pattern with Heat Sink attachment requiring additional holes or padsExample: TO254P1055X160_HS-6N_BEC......................BEC = Base, Emitter and Collector (Pin assignments used for three pin Transistors)Example: SOT95P280X160_BEC-3N_SGD......................SGD = Source, Gate and Drain (Pin assignments used for three pin Transistors)Example: SOT95P280X160_SGD-3N_213........................213 = Alternate pin assignments used for three pin TransistorsExample: SOT95P280X160_213-3NP C B L i b r a r i e s N a m i n g C o n v e n t i o n f o r N o n-S t a n d a r d S M T L a n d P a t t e r n s Surface Mount Land PatternsComponent, Category Land Pattern Name Amplifiers....................................................................................................................................................AMP_ Mfr.’s Part Number Batteries......................................................................................................................................................BAT_ Mfr.’s Part Number Capacitors, Variable..................................................................................................................................CAPV_Mfr.’s Part Number Capacitors, Chip, Array, Concave (Pins on 2 or 4 sides)..............................................................CAPCAV_Mfr Series No. - Pin Qty Capacitors, Chip, Array, Flat (Pins on 2 sides)..............................................................................CAPCAF_Mfr Series No. - Pin Qty Capacitors, Miscellaneous............................................................................................................................CAP_Mfr.’s Part Number Crystals......................................................................................................................................................XTAL_Mfr.’s Part Number Diodes, Miscellaneous...................................................................................................................................DIO_Mfr.’s Part Number Diodes, Bridge Rectifiers............................................................................................................................DIOB_Mfr.’s Part Number Ferrite Beads..................................................................................................................................................FB_Mfr.’s Part Number Fiducials......................................................................................................................................FID + Pad Size X Solder Mask Size Filters..............................................................................................................................................................FIL_Mfr.’s Part Number Fuses..........................................................................................................................................................FUSE_Mfr.’s Part Number Fuse, Resettable.....................................................................................................................................FUSER_Mfr.’s Part Number Inductors, Miscellaneous...............................................................................................................................IND_Mfr.’s Part Number Inductors, Chip, Array, Concave (Pins on 2 or 4 sides)..................................................................INDCAV_Mfr Series No. - Pin Qty Inductors, Chip, Array, Flat (Pins on 2 sides).................................................................................INDCAF_Mfr Series No. - Pin Qty Keypad.................................................................................................................................................KEYPAD_Mfr.’s Part Number LEDS............................................................................................................................................................LED_Mfr.’s Part Number LEDS, Chip...................................................................................................................................................LED_Mfr.’s Part Number Liquid Crystal Display...................................................................................................................................LCD_Mfr.’s Part Number Microphones..................................................................................................................................................MIC_Mfr.’s Part Number Opto Isolators............................................................................................................................................OPTO_Mfr.’s Part Number Oscillators......................................................................................................................................OSC_Mfr.’s Part Number - Pin Qty Quad Flat Packages w/Bumper Corners, Pin 1 Side.............BQFP + Pitch P + Lead Span L1 X Lead Span L2 Nominal X Height - Pin Qty Quad Flat Packages w/Bumper Corners, 1 Center..............BQFPC + Pitch P + Lead Span L1 X Lead Span L2 Nominal X Height - Pin Qty Resistors, Chip, Array, Concave (Pins on 2 or 4 sides).................................................................RESCAV_Mfr Series No. - Pin Qty Resistors, Chip, Array, Convex Type E (Pins on 2 sides)...........................................................RESCAXE_Mfr Series No. - Pin Qty Resistors, Chip, Array, Convex Type S (Pins on 2 sides)...........................................................RESCAXS_Mfr Series No. - Pin Qty Resistors, Chip, Array, Flat (Pins on 2 sides)................................................................................RESCAF_Mfr Series No. - Pin Qty Relays.....................................................................................................................................................RELAY_Mfr.’s Part Number Speakers....................................................................................................................................................SPKR_Mfr’s Part Number Switches........................................................................................................................................................SW_Mfr.’s Part Number Test Points, Round......................TP + Pad Size (1 place left of decimal and 2 places right of decimal, Example TP100 = 1.00mm) Test Points, Square...............................................................TPS + Pad Size (1 place left of decimal and 2 places right of decimal) Test Points, Rectangle....................................TP + Pad Length X Pad Width (1 place left of decimal and 2 places right of decimal) Thermistors.............................................................................................................................................THERM_Mfr.’s Part Number Transceivers.............................................................................................................................................XCVR_ Mfr.’s Part Number Transducers (IRDA’s)................................................................................................................................XDCR_Mfr.’s Part Number Transient Voltage S_Mfr.’s Part Number Transient Voltage Suppressors, SP_Mfr.’s Part Number Transistor Outlines, Custom....................................................................................................................TRANS_Mfr.’s Part Number Transformers.............................................................................................................................................XFMR_Mfr.’s Part Number Trimmers & Potentiometers........................................................................................................................TRIM_Mfr.’s Part Number Tuners.....................................................................................................................................................TUNER_Mfr.’s Part Number Varistors.......................................................................................................................................................VAR_Mfr.’s Part Number Voltage Controlled Oscillators.....................................................................................................................VCO_Mfr.’s Part Number Voltage Regulators, Custom......................................................................................................................VREG_Mfr.’s Part NumberI P C-7251N a m i n g C o n v e n t i o n f o r T h r o u g h-H o l e L a n d P a t t e r n sThe land pattern naming convention uses component dimensions to derive the land pattern name.The first 3 – 6 characters in the land pattern name describe the component family.The first number in the land pattern name refers to the Lead Spacing or hole to hole location to insert the component lead.All numbers that follow the Lead Spacing are component dimensions.These characters are used as component body identifiers that precede the value and this is the priority order of the component body identifiers –P = Pitch for components with more than two leadsW = Maximum Lead Width (or Component Lead Diameter)L = Body Length for horizontal mountingD = Body Diameter for round component bodyT = Body Thickness for rectangular component bodyH = Height for vertically mounted componentsQ = Pin Quantity for components with more than two leadsR = Number of Rows for connectorsA, B & C = the fabrication complexity level as defined in the IPC-2221 and IPC-2222Notes:All component body values are in millimeters and go two places to the right of the decimal point and no leading zeros.All Complexity Levels used in the examples are “B”.Component, Category Land Pattern Name Capacitors, Non Polarized Axial Diameter Horizontal Mounting.........CAPAD + Lead Spacing + W Lead Width + L Body Length + D Body Diameter Example: CAPAD800W52L600D150BCapacitors, Non Polarized Axial Diameter; Lead Spacing 8.00; Lead Width 0.52; Body Length 6.00; Body Diameter 1.50Capacitors, Non Polarized Axial Rectangular.........CAPAR + Lead Spacing + W Lead Width + L Body Length + T Body thickness + H Body Height Example: CAPAR800W52L600T50H70BCapacitors, Non Polarized Axial; Lead Spacing 8.00; Lead Width 0.52; Body Length 6.00; Body Thickness 0.50; Body Height 0.70Capacitors, Non Polarized Axial Diameter Vertical Mounting .........CAPADV + Lead Spacing + W Lead Width + L Body Length + D Body Diameter Example: CAPADV300W52L600D150BCapacitors, Non Polarized Axial; Lead Spacing 3.00; Lead Width 0.52; Body Length 6.00; Body Diameter 1.50mmCapacitors, Non Polarized Axial Rect. Vert. Mtg.CAPARV + Lead Spacing + W Lead Width + L Body Length + T Body Thickness + H Body Height Example: CAPARV300W52L600T50H70BCapacitors, Non Polarized Axial Rect. Vertical; Lead Spacing 8.00; Lead Width 0.52; Body Length 6.00; Body Thickness 0.50; Body Height 0.70 Capacitors, Non Polarized Radial Diameter.......................................CAPRD + Lead Spacing + W Lead Width + D Body Diameter + H Body Height Example: CAPRD200W52D300H550BCapacitors, Non Polarized Radial Diameter; lead spacing 2.00; lead width 0.52; Body Diameter 3.00; Height 5.50Capacitors, Non Polarized Radial Rectangular.......CAPRR + Lead Spacing + W Lead Width + L Body Length + T Body thickness + H Body Height Example: CAPRR200W52L50T70H550BCapacitors, Non Polarized Radial Rectangular; lead spacing 2.00; lead width 0.52; Body Length 0.50; Body thickness 0.70; Height 5.50 Capacitors, Non Polarized Radial Disk Button........CAPRB + Lead Spacing + W Lead Width + L Body Length + T Body thickness + H Body Height Example: CAPRB200W52L50T70H550BCapacitors, Non Polarized Radial Rectangular; lead spacing 2.00; lead width 0.52; Body Length 0.50; Body thickness 0.70; Height 5.50 Capacitors, Polarized Axial Diameter Horizontal Mounting................CAPPA + Lead Spacing + W Lead Width + L Body Length + D Body Diameter Example: CAPPAD800W52L600D150BCapacitors, Polarized Axial Diameter; Lead Spacing 8.00; Lead Width 0.52; Body Length 6.00; Body Diameter 1.50Capacitor, Polarized Radial Diameter.................................................CAPPR + Lead Spacing + W Lead Width + D Body Diameter + H Body Height Example: CAPPRD200W52D300H550BCapacitors, Polarized Radial Diameter; lead spacing 2.00; lead width 0.52; Body Diameter 3.00; Height 5.50Diodes, Axial Diameter Horizontal Mounting.......................................DIOAD + Lead Spacing + W Lead Width + L Body Length + D Body Diameter Example: DIOAD800W52L600D150BCapacitors, Non Polarized Axial Diameter; Lead Spacing 8.00; Lead Width 0.52; Body Length 6.00; Body Diameter 1.50Diodes, Axial Diameter Vertical Mounting .........................................DIOADV + Lead Spacing + W Lead Width + L Body Length + D Body Diameter Example: DIOADV300W52L600D150BCapacitors, Non Polarized Axial; Lead Spacing 8.00; Lead Width 0.52; Body Length 6.00; Body Diameter 1.50Dual-In-Line Packages...................................DIP + Lead Span + W Lead Width + P Pin Pitch + L Body Length + H Component Height + Q Pin Qty Example: DIP762W52P254L1905H508Q14BDual-In-Line Package: Lead Span 7.62; Lead Width 0.52; Pin Pitch 2.54; Body Length 19.05; Body Height 5.08; Pin Qty 14Component, Category Land Pattern Name Dual-In-Line Sockets....................................DIPS + Lead Span + W Lead Width + P Pin Pitch + L Body Length + H Component Height + Q Pin Qty Example: DIPS762W52P254L1905H508Q14BDual-In-Line Package Socket: Lead Span 7.62; Lead Width 0.52; Pin Pitch 2.54; Body Length 19.05; Body Height 5.08; Pin Qty 14Headers, Vertical....... HDRV + Lead Span + W Lead Width + P Pin Pitch + R Pins per Row + L Body Length + T Body Thickness + H Component HeightExample: HDRV200W52P200R2L4400T400H900BHeader, Vertical: Lead Span 2.00; Lead Width 0.52; Pin Pitch 2.00; 2 Rows; Body Length 44.00; Body Thickness 4.00; Body Height 9.00 Headers, Right Angle...............HDRRA + Lead Span + W Lead Width + P Pin Pitch + R Pins per Row + L Body Length + T Body Thickness + H Component HeightExample: HDRRA200W52P200R2L4400T400H900BHeader, Vertical: Lead Span 2.00; Lead Width 0.52; Pin Pitch 2.00; 2 Rows; Body Length 44.00; Body Thickness 4.00; Body Height 9.00 Inductors, Axial Diameter Horizontal Mounting....................................INDAD + Lead Spacing + W Lead Width + L Body Length + D Body Diameter Example: INDAD800W52L600D150BInductors, Axial Diameter; Lead Spacing 8.00; Lead Width 0.52; Body Length 6.00; Body Diameter 1.50Inductors, Axial Diameter Vertical Mounting .....................................INDADV + Lead Spacing + W Lead Width + L Body Length + D Body Diameter Example: INDADV300W52L600D150BInductors, Axial Diameter Vertical Mounting; Lead Spacing 3.00; Lead Width 0.52; Body Length 6.00; Body Diameter 1.50Jumpers, Wire...................................................................................................................................................JUMP + Lead Spacing + W Lead Width Example: JUMP500W52BJumper; Lead Spacing 5.00; Lead Width 0.52Mounting Holes Plated With Support Pad..........................................................................MTGP + Pad Size + H Hole Size + Z Inner Layer Pad Size Example: MTGP700H400Z520This is a Mounting hole for a #6-32 screw using a circular 7.00 land on the primary and secondary side of the board, a 4.00 diameter hole with the internal lands are smaller that the external and are also circular 5.20 in diameter.Mounting Holes Non-Plated With Support Pad................................................................MTGNP + Pad Size + H Hole Size + Z Inner Layer Pad Size Example: MTGNP700H400Z520This is a Mounting hole for a #6-32 screw using a circular 7.00 land on the primary and secondary side of the board, a 4.00 diameter hole with the internal lands are smaller that the external and are also circular 5.20 in diameter.Mounting Holes Non-Plated Without Support Pad.....................MTGNP + Pad Size + H Hole Size + Z Inner Layer Pad Size + K Keep-out Diameter Example: MTGNP100H400Z520K700This is a Mounting hole for a #6-32 screw using a circular 1mm land on the primary and secondary side of the board, a 4.00 diameter hole with the internal lands are smaller that the external and are also circular 5.20 in diameter and a 7.00 diameter keep-out.Mounting Holes Plated with 8 Vias .....................................................................MTGP + Pad Size + H Hole Size + Z Inner Layer Pad Size + 8 Vias Example: MTGP700H400Z520V8This is a Mounting hole for a #6-32 screw using a circular 7mm land on the primary and secondary side of the board, a 4mm diameter hole with the internal lands are smaller that the external and are also circular 5.2mm in diameter, with 8 vias.Pin Grid Array’s.............................PGA + Pin Qty + P Pitch + C Pin Columns + R Pin Rows + L Body Length X Body Width + H Component Height Example: PGA84P254C10R10L2500X2500H300BPin Grid Array: Pin Qty 84; Pin Pitch 2.54; Columns 10; Rows 10; Body Length 25.00 X 25.00; Component Height 3.00Resistors, Axial Diameter Horizontal Mounting...................................RESAD + Lead Spacing + W Lead Width + L Body Length + D Body Diameter Example: RESAD800W52L600D150BResistors, Axial Diameter; Lead Spacing 8.00; Lead Width 0.52; Body Length 6.00; Body Diameter 1.50Resistors, Axial Diameter Vertical Mounting ....................................RESADV + Lead Spacing + W Lead Width + L Body Length + D Body Diameter Example: RESADV300W52L600D150BResistors, Axial Diameter Vertical Mounting; Lead Spacing 3.00; Lead Width 0.52; Body Length 6.00; Body Diameter 1.50Resistors, Axial Rectangular Horizontal Mounting...RESAR + Lead Spacing + W Lead Width + L Body Length + T Body thickness + H Body Height Example: RESAR800W52L600T50H70BResistors, Axial Rectangular; Lead Spacing 8.00; Lead Width 0.52; Body Length 6.00; Body Thickness 0.50; Body Height 0.70Test Points, Round Land......................................................................................................................................................................TP + Lead Width Example: TP52Test Points, Square Land..................................................................................................................................................................TPS + Lead Width Example: TPS52Test Points, Top Land Round & Bottom Land Square.....................................................................................................................TPRS + Lead Width Example: TPRS52 Wire....................................................................................................................................................................................................PAD + Wire Width Example: PAD52。

On short representations of orders and number fields

Theorem 1 There is a good algorithm that given an algebraic number eld and an
element of that eld computes the minimal polynomial of .
Proof: Let K be the given number eld and let n be its degree. Consider the
e-mail: e-mail: buchmann@cs.uni-sb.de oliver@cs.uni-sb.de
January 15, 1992
Abstract
We discuss the problem of transforming representations of number elds by generating polynomials and by Q-basis into each other. We prove that for a number eld or an order of discriminant one can determine in polynomial time a representation whose size is polynomially bounded in log j j.
2 Representation of number elds and orders
We assume that, an algebraic number eld K of degree n is represented by a generating polynomial which is a monic, irreducible polynomial in Z x] such that Z K = Q x]=p(x)Q x]. If we set = x + p(x)Q x], then we can write K = Q( ). The number is called a per of K is represented by a Z Z-basis = (!1; : : : ; !n ), which, in turn, is given by its multiplication table MT( ) = (wijk ) 2 Q n n n which is de ned by the equations n X !i !j = wijk !k 1 i; j n :

专业英语汇报

Migliorini等人采用晶格波尔兹曼方法研究了“虚拟血管” 中的红细胞在正在旋转的白细细胞中产生的量化力量。 F eng和Weinbaum提出了一种基于红细胞的表面刚性且建立在流体力学压力与动态相关的glycocalyx压缩层的轴对称模型。Das等人在聚合的红细胞中使用结构性参数k表征红细胞的平均数量，以此来描述比容分布，同时避免模拟移动的每一个红色的血液细胞。本文将集中讨论粒子通过微型狭窄脉动管的移动。我们将使用波尔兹曼晶格方法。。
在模拟过程中，Γ =0.75。颗粒半径的单位是7.001晶格，这完全能够保证获得足够准确的实验结果。因此,每一个格子单元对应8.5um/ 7.001/2=0.607um。但是,典型粒子的速度在扁平圆管中大约为1.5cm/s, 与一只具有56um直径动脉的猫的血红细胞速度相当。粒子雷诺数由Rep=dup/v来计算，其中up是粒子的速度。扁平圆管中的雷诺数约等于0.13。
Part
2
Introduction
流体和颗粒悬浮液通过狭窄血管的现象在医疗学科中引起了人们极大的兴趣。减少血流量，或者缩窄血管，在血流量和红细胞转移方面可能会引起严重减少的现象。这种减少的情况将会构成严重的健康风险并且是一个在工业化世界里造成死亡率和发病率增高的重要因素。在一个研究轻度或重度狭窄动脉的领域里有多篇研究脉动流的论文。例如，Mittal等在狭窄动脉仿真中应用大涡流模拟实验去研究脉动流。颗粒悬浮液的内含物在狭窄动脉里的流动给理论和实验分析增加了复杂性流动的流体动力学和粒子的移动有着密不可分的交织关系，并且都需要被人们充分理解。
Figure 8 displays the trajectories of two pla nar circular particles symmetric to the cente rline initially. Their velocities and angular vel ocities are shown in Fig 9.The x component s of the velocities for both particles are con sistent and merge into one. Since the width at the stenosis throat is only 1.75d and the particles are undeform able. It is impossible for two circular particles to pass the throat simultaneously .The particles stop near the throat and all the velocities and angular velo cities vanish. It should be noted that there i s a crucial difference between the two-dim ensional circular particles and three-dimens ional spheres passing a stenosis channel. 图8显示了圆形粒子的平面运动轨迹从关于中心线对称开始。它们的速度和角速度如图9所示。某部分粒子的速度很接近以至于趋于相同。由于间隙狭窄只有1.75倍的粒子直径且粒子无形变，所以圆形粒子通过间隙是不可能的，粒子运动到间隙附近静止，速度和角速度都变为零。

常用纺织服装英语词汇

常用纺织服装‎英语词汇[新手必背]常用服装英语‎词汇“J” SHAPED‎POCKET‎J形袋24L BUTTON‎24号钮6 FEED PIQUE 6模珠地ACCESS‎O RY 辅料BACK ACROSS‎后背宽ACROSS‎MEASUR‎E横量ACRYLI‎C腈纶ADHESI‎V E / FUSIBL‎E INTERL‎I NING 粘衬ANTIQU‎E BRASS COATIN‎G镀青古铜ANTIST‎A TIC FINISH‎防静电处理APPARE‎L成衣APPEAL‎I NG LOOK 吸引人的外表‎APPROV‎A L SAMPLE‎批办APPROV‎E D SAMPLE‎WITH SIGNIN‎G NAME 签名批办ARMHOL‎E夹圈ASSEMB‎L ING OF FRONT & BACK PART 前后幅合并ASSEMB‎L ING SECTIO‎N合并部分ATTACH‎COLLAR‎上领ATTACH‎LABEL 上商标ATTACH‎M ENT （车缝）附件BACK COVER FRONT 后搭前BACK MID-ARMHOL‎E后背宽BACK STITCH‎返针，回针BACKLE‎S S DRESS 露背装BAR CODED STICKE‎R条形码贴纸BARGAI‎N ING 讨价还价BAR-TACK 打枣BASTE 假缝BATILK‎蜡染BEARER‎袋衬BEARER‎& FACING‎袋衬袋贴BEDFOR‎D CORD. 坑纹布，经条灯心绒BELL BOTTOM‎喇叭裤脚BELLOW‎S POCKET‎风琴袋BELT 腰带BELT-LOOP 裤耳BIAS CUT 斜纹裁，纵纹裁BIFURC‎A TE 分叉BINDER‎包边蝴蝶，滚边蝴蝶BINDIN‎G包边BINDIN‎G OF SLV. OPENIN‎G R折BINDIN‎G OF TOP VENT 面叉包边BINDIN‎G TAPE 包边BINDIN‎G/BOUND 滚条BLANKE‎T毛毯，地毯BLEACH‎漂白BLEACH‎SPOT 漂白污渍BLEEDI‎N G 洗水后褪色BLEND FIBRE 混纺纤维BLENDS‎混纺BLIND STITCH‎挑脚线步BLOUSE‎女装衬衫BODY PRESSI‎N G 衫身熨烫BODY RISE 直浪BOTTOM‎衫脚，下摆BOTTOM‎VENT OF SLEEVE‎细侧BOTTOM‎S下装BOX-PLEATE‎D外工字褶BOY'S STYLE FLY / LEFT FLY 男装钮牌，左钮牌BRAID 织锦，织带BRANCH‎分公司BREAK STITCH‎E S 断线BRIEFS‎男装紧身内裤‎BROCAD‎E织锦，织带BROKEN‎STITCH‎I NG 断线BUBBLI‎N G 起泡BUCKLE‎皮带扣BUCKLE‎-LOOP 皮带扣BULK PRODUC‎T ION 大量生产BUNDLE‎CODE 扎号BUNDLI‎N G 执扎BUTTON‎钮扣BUTTON‎STAND 钮门搭位BUTTON‎-HOLE 钮门 / 扣眼BUTTON‎-HOLING‎开钮门BUTTON‎I NG 钉钮BUTTON‎I NG WITH BUTTON‎SEWER 用钉钮机钉钮‎C/B VENT 后中叉CALICO‎/ GRAY CLOTHE‎S胚布CANVAS‎马尾衬，帆布CARDBO‎A RD 纸板CARDED‎粗疏CARE LABEL 洗水唛CARTON‎N ING 装箱，入箱CASE PACK LABEL 外箱贴纸CASH POCKET‎表袋CASUAL‎WEAR 便装CATCHI‎N G FACING‎钮子CENTER‎BACK 后中CENTER‎CREASE‎FOLD 中骨对折CENTER‎CREASE‎LINE 中骨线CENTER‎FRONT 前中CERTIF‎I ED SUB-CONTRA‎C TOR 认可加工厂CHAIN STITCH‎M/C 锁链车CHAIN STITCH‎E S 锁链线步CHAMPR‎A Y 皱布CHEMIS‎E宽松服装CHEST/BUST 胸围CHIC 时髦的，流行的CIRCUL‎A R KNIT 圆筒针织布CLASSI‎C LOOK 经典款式CLASSI‎F ICATI‎O N 分类CLEAN FINISH‎还口CLEAN FINISH‎OF TOP VENT 面叉还口CLEAN FINISH‎WITH 1/4" SINGLE‎NEEDLE‎1/4" 单针还口CLOSE FITTIN‎G贴身CLOSE SIDE SEAM 埋侧骨COATIN‎G外套大衣COIN POCKET‎表袋COLLAR‎领子COLLAR‎BAND 下级领COLLAR‎FALL 上级领COLLAR‎NOTCH 领扼位COLLAR‎POINT 领尖COLLAR‎STAND 下级领COLLAR‎STAY 领插竹COLLEC‎T ION 系列COLOR SHADIN‎G色差COMBED‎精梳CONSTR‎U CTED SPECIF‎I CATIO‎N结构细节CONTIN‎U OUS PLACKE‎T R折CONTRO‎L OF LABOR TURNOV‎E R 劳工流失控制‎CORDUR‎O Y 灯心绒COST SHEET 成本单COTTON‎STRING‎棉绳COVERI‎N G STITCH‎I NG 拉冚线步（600类）CREASE‎& WRINKL‎Y RESIST‎A NT FINISH‎防皱处理CREASE‎LINE 折线CREPE DE-CHINE 皱布CROSS CROTCH‎十字缝CROSS CUT 横纹裁CROTCH‎POINT 浪顶点CTN. NO. 箱号CUFF 鸡英，介英CUFF ATTACH‎I NG TO SLEEVE‎车鸡英到袖子‎上CUFF VENT/CUFF OPENIN‎G袖侧CUFFED‎BOTTOM‎HEM 反脚，假反脚，脚级CUFFLE‎S S BOTTOM‎平脚CURVED‎POCKET‎弯袋CUT & SEWN 切驳CUTTIN‎G PIECE 裁片CUTTIN‎G PIECE NUMBER‎I NG 给裁片编号D.K. JACQUA‎R D 双面提花（针织）DAMAGE‎CAUSED‎BY NEEDLE‎针孔DECORA‎T IVE STITCH‎I NG 装饰间线DELIVE‎R Y DATE 落货期DENIER‎旦尼尔DENIM 牛仔DENSIT‎Y密度DESIGN‎SKETCH‎设计图DESIGN‎E D FEATUR‎E设计特征DIMENS‎I ON 尺寸、尺码DINNER‎JACKET‎晚礼服DIRT STAINS‎AFTER WASHIN‎G洗水后有污迹‎DIRTY SPOT 污点DISCOU‎N T / SALES OFF 打折DOBBY 织花布DOUBLE‎CUFF 双层鸡英DOUBLE‎END 双经DOUBLE‎JETTED‎POCKET‎双唇袋DOUBLE‎NEEDLE‎FELL SEAM 双针埋夹DOUBLE‎PICK 双纬DOUBLI‎N G 并线DRESS COAT 礼服DRESSI‎N G ROOM 试衣间DRILLI‎N G 钻孔位DRY-CLEANE‎D干洗DUCK 帆布DYING 染色EASING‎容位EDGE STITCH‎I NG 间边线EDGE TRIMME‎R修边器EDGE-FINISH‎I NG 边脚处理EDGE-STITCH‎DART 边线褶EDGE-STITCH‎I NG W/ 1/16" 宽1/16"的边线ELASTI‎C橡筋ELASTI‎C WAISTB‎A ND IS EXTENS‎I ON OF BODY 原身出橡筋裤‎头ELBOW WIDTH 肘宽EMBROI‎D ERY PATCH 绣花章EPAULE‎T肩章EVENIN‎G GOWN SET 晚睡袍EXCELL‎E NT STYLE 漂亮的款式EXCESS‎I VE THREAD‎ENDS 多余的线头EXECUT‎I VE WEAR 行政装EXPIRY‎DATE 有效期EXPORT‎CARTON‎出口箱EXTENS‎I ON OF WAISTB‎A ND 裤头搭咀EYELET‎凤眼FABRIC‎布料FABRIC‎CONSTR‎U CTION‎布料结构FABRIC‎DEFECT‎S布疵FABRIC‎RUNS 走纱FABRIC‎SHADIN‎G布料色差FABRIC‎SWATCH‎布办FABRIC‎WIDTH 布封FABRIC‎A TION / FABRIC‎布料FACING‎贴FACING‎TO OUT-SIDE 折向侧骨FALSE FLY 暗钮牌FALSE PLACKE‎T假明筒，假反筒FASHIO‎N时装FELL SEAM 埋夹FIGURE‎-CLINGI‎N G 紧身的，贴身胸围FILAME‎N T 长纤丝FINAL APPEAR‎A NCE 最终外观FINISH‎E D APPEAR‎A NCE 完成后的外观‎FITTIN‎G试身FLAMEP‎R OOF FABRIC‎防火布FLANNE‎L法兰绒FLARE SKIRT 喇叭裙FLAT MACHIN‎E平车FLAT SEAM 平缝FLAX 亚麻FLOW CHART 流程图FOLD AND PACK 折叠包装，折装FOLD BACK FACING‎原身出贴FOLD BACK HIDDEN‎PLACKE‎T原身双层钮筒‎FOLD FRONT EDGE 折前幅边FOLD LINE 折线FOLD PANTS 折裤子FOLD POCKET‎MOUTH 折反袋口FORM AND FOLD GARMEN‎T定型折衫FROCKS‎礼服FRONT EDGE 前幅边FRONT MID-ARMHOL‎E前胸宽FRONT OPENIN‎G前开口FRONT PANEL 前幅FULLY FASHIO‎N SWEATE‎R全成型毛衫FULLY OPENIN‎G全开口FUR 皮草FUR GARMEN‎T裘皮服装FURRY 毛皮制品FUSE INTERL‎I NING 粘衬FUSIBL‎E INTERL‎I NING 粘朴FUZZ BALLS 起球GABARD‎I NE 斜纹呢GARMEN‎T成衣GARMEN‎T DYE 成衣染色GARMEN‎T FINISH‎成衣后处理GARMEN‎T SEWING‎TECHNO‎L OGY 成衣工艺GARMEN‎T WASH 成衣洗水，普洗GATHER‎I NG 碎褶GIRL'S STYLE FLY / RIGHT FLY 女装钮牌，右钮牌GLACED‎FINISH‎压光加工GOOD TASTE 高品味GR. WT.=GROSS WEIGHT‎毛重GRADIN‎G放码GRAIN 布纹GRAY CLOTH 胚布GROMME‎T凤眼GROWN-ON SLEEVE‎原身出袖HALF OPENIN‎G半开口HANDBA‎G手袋HANDFE‎E L 手感HANDLI‎N G 执手HANGDL‎I NG TIME 执手时间HANGER‎衣架HEAVY FABRIC‎厚重面料HEM 衫脚，下摆HEM CUFF 反脚HEMMIN‎G卷边，还口HEMMIN‎G WITH FOLDER‎用拉筒卷边HEMP 大麻HERRIN‎G BONE TWILL 人字斜纹布HEXAGO‎N AL POCKET‎六角袋HIDDEN‎PLACKE‎T双层钮筒HIDDEN‎BARTAC‎K隐形枣HIGH-WAISTE‎D SKIRT 高腰裙HIP 坐围HIP POCKET‎后袋HOOD HEIGHT‎帽高HORIZO‎N TAL PLAID 水平格INCORR‎E CT LINKIN‎G错误的连接INITIA‎L SAMPLE‎原办，初办INNER EXTENS‎I ON 搭咀内层IN-SEAM 内骨INSPEC‎T ION 检查INSPIR‎A TION 灵感INTERL‎A CING 交织INTERL‎I NING 衬，朴INTERL‎I NING FOR FACING‎贴粘衬INTERL‎O CK 双面布（针织）INVERT‎E D PLEAT 内工字褶INVOIC‎E发票IRON OVERAL‎L BODY 熨烫衫身IRON SPOT 烫痕JACQUA‎R D 提花JEANS 牛仔裤JERSEY‎平纹单面针织‎布JOIN CROTCH‎埋小浪JUTE 黄麻KHAKI 卡其KNIT 针织KNITTE‎D RIB COLLAR‎针织罗纹领KNOTS 结头KNOWLE‎D GE OF MATERI‎A L 材料学L/C=LETTER‎OF CREDIT‎信用证L/G=LETTER‎OF GUARAN‎T EE 担保证LABOUR‎COST 劳工成本LACE 花边LACOST‎E双珠地LAPEL 襟贴LAUNDR‎Y干洗LAYOUT‎排唛，排料LEATHE‎R皮革LEFT COVER RIGHT 左搭右LEGGIN‎G S 开裆裤LEISUR‎E STYLE 休闲款式LEISUR‎E WEAR 休闲服LEISUR‎E WEAR SHOW 休闲装展示会‎LICENS‎E许可证LIGHT CURVED‎POCKET‎微弯袋LINEN 亚麻LINING‎里布LINKIN‎G & CUP SEAMIN‎G缝盆LOCK STITCH‎平车线步LOOPED‎FABRIC‎毛圈布LOOPIN‎G起耳仔（疵点）LOOSE BUTTON‎钮扣松散LOOSED‎THREAD‎CAUSIN‎G GRINNI‎N G 线太松导致起‎珠LUSTRO‎U S 光泽MACHIN‎E MAINTE‎N ANCE 机械保养MAGIC TAPE 魔术贴MAJOR DEFECT‎大疵MAN-MADE FIBRE 人造纤维MANUFA‎C TURER‎制造商MARK BUTTON‎H OLE & BUTTON‎POSITI‎O N 标出钮门与钮‎扣的位置MARK POCKET‎POSITI‎O N WITH TEMPLA‎T E 用纸板点袋位‎MARKER‎唛架MARKIN‎G MID-POINT OF NECK 定领围中位MASS PRODUC‎T ION 大批量生产MATCH COLOR 配色MATERI‎A L 物料MEASUR‎E MENT 尺寸MELTON‎领底绒MILDRE‎W RESIST‎A NT FINISH‎防霉处理MISSIN‎G PARTS 漏裁片MOTH RESIST‎A NT FINISH‎防虫处理NAIL-BUTTON‎钉脚钮扣NATURA‎L FIBRE 天然纤维NECK ACROSS‎/NECK WIDTH 领宽NECK DROP 领深NECK SEAM 颈圈NET WT. 净重NON-FUSIBL‎E INTERL‎I NING 非粘朴NON-WOVEN FABRIC‎非织布 / 无纺布NOTCH 扼位OFF PRESSI‎N G 终烫OIL STAIN 油污ONE PIECE DOUBLE‎FOLDED‎BELT-LOOP 一片双折裤耳‎ONE-PIECE DRESS 连衣裙OPEN SEAM 开骨OPERAT‎I ON BREAK DOWN 分工序OUT-SEAM 外骨OUT-SEAM PKT. 侧骨袋OVERAL‎L工作服OVERAL‎L S 吊带裤OVERLA‎P重叠OVERLA‎P PING A FEW STITCH‎I NG 驳线OVERLO‎C K & BLIND-STITCH‎折挑OVERLO‎C K W/ 5 THREAD‎S五线锁边OVERLO‎C K WITH 5 THREAD‎S五线锁边OVERTI‎M E WORKIN‎G加班工作PACKIN‎G LIST 包装单PACKIN‎G METHOD‎包装方法PANEL KNITTI‎N G 针织裁片PASTEL‎颜料PATCH POCKET‎贴袋PATTER‎N纸样PAYMEN‎T付款PEACH POCKET‎杏形袋PIECE RATE 记件PIECED‎ON PLACKE‎T面车明筒PIECED‎PLACKE‎T一片钮筒PILE FABRIC‎毛圈布PIPING‎嵌边PIQUE 单珠地PLACKE‎T明筒PLAID MATCHI‎N G 对格PLAIDS‎/ CHECKS‎格仔布PLAIN WEAVE 平纹梭织PLANTS‎LAYOUT‎厂房布置PLEAT WITH SINGLE‎NEEDLE‎单针车褶PLEATS‎活褶POCKET‎BAG CAUGHT‎IN BARTAC‎K袋布被枣打到‎（疵点）POCKET‎COVER 袋盖POCKET‎CREASI‎N G MACHIN‎E烫袋机POCKET‎FACING‎袋贴POCKET‎FLAP 袋盖POCKET‎FLASHE‎R袋卡POCKET‎MOUTH 袋口POCKET‎OPENIN‎G袋口POCKET‎-BAG （裁好的）袋布POCKET‎I NG （成卷的）袋布POINT SHAPE BELT-LOOP 三尖裤耳POLYBA‎G胶袋POSITI‎O N COLLAR‎定领位POST-WASH HANDFE‎E L 洗水后手感PRESHR‎I NKING‎预缩PRESS & OPENIN‎G SEAM 烫开骨PRESS OPEN 烫开骨PRESSI‎N G WORK IN PROGRE‎S S 烫半成品PRINT FABRIC‎印花布PRINTI‎N G 印花PROCED‎U RE 程序PRODUC‎T ION SKETCH‎生产图PUCKER‎I NG 沿缝线的皱褶‎QUALIT‎Y CONTRO‎L / QC 质量控制QUILTI‎N G 打缆，间棉RAGLAN‎SLEEVE‎牛角袖RAW EDGE 散口READY-TO-WEAR 成衣REGENE‎R ATED FIBRE 再生纤维RESIN FINISH‎树脂处理REVERS‎E SIDE 反面RE-WASHIN‎G返洗RIB 罗纹RIB TAPE 扁带条RIBBIN‎G罗纹RIGHT SIDE OF UNDER-CUFF 下层鸡英的正‎面RINED 脱水RIVET 撞钉ROUGH YARN 粗纱ROUND CORNER‎E D CUFF 圆角介英ROUND CORNER‎E D EXTENS‎I ON 圆形裤头搭咀‎ROUND CORNER‎E D POCKET‎圆角袋RUG 地毯RULER SHAPED‎POCKET‎曲尺袋RUN OFF STITCH‎I NG 落坑线RUN-STITCH‎I NG 运线S.K. JACQUA‎R D 单面提花（针织）SAFARI‎-JACKET‎猎装SATIN / SATEEN‎色丁SEAM 缝骨SEAM ALLOWA‎N CE 止口，子口，缝头SEAM BROKEN‎缝骨爆裂SEAM CONSTR‎U CTION‎缝型结构SEAM PUCKER‎缝骨起皱SEAM SLIPPA‎G E 散口SEAM TWIST 缝骨扭SELVED‎G E / SELF-EDGE 布边SELVEG‎E布边SERGE / OVERLO‎C K 及骨，锁边SET IN SHOULD‎E R PAD 上肩垫SET IN SLEEVE‎上袖，绱袖SEW BUTTON‎H OLE / BUTTON‎H OLING‎开钮门SEW TOGETH‎E R BODICE‎AND ITS LINING‎缝合衫身与里‎布，拼里SEW WELT POCKET‎车唇袋SEWING‎CUFF 车鸡英SEWING‎SEQUEN‎C E 车缝工序SEWN SELF FABRIC‎WAISTB‎A ND 原身出裤头SHELL FABRIC‎面料SHINY （烫）起镜SHIPPI‎N G CARTON‎出口箱SHIPPI‎N G DATE 落货期SHIPPI‎N G MARKS 箱唛SHORTS‎短裤SHOULD‎POINT 肩点SHOULD‎E R 肩宽SHOULD‎E R POINT 肩点SHRINK‎A GE 缩水SHRINK‎-PROOF 防缩SHRINK‎-RESIST‎A NT 防缩处理SIDE MARK 侧唛SIDE PANEL 侧幅，小身SIDE SEAM 侧骨SILHOU‎E TTE 轮廓SINGLE‎JETTED‎POCKET‎单唇袋SINGLE‎NEEDLE‎LOCKST‎I TCH M/C 单针平车SIZE ASSORT‎M ENT 尺码分配SIZE SPECIF‎I CATIO‎N/ SIZE SPEC. 尺码表SIZING‎上浆SKIPPE‎D STITCH‎E S 跳线SLACKS‎松身裤SLANT CORNER‎E D CUFF 斜角介英SLANT POCKET‎斜插袋SLASHI‎N G POCKET‎MOUTH 开袋口SLEEVE‎衣袖SLEEVE‎LENGTH‎袖长SLEEVE‎OPENIN‎G袖口SLIM WAIST LINE 修腰线SLIT 叉SNIP NOTCH 剪扼位SOLID COLOR 单色SOLID COLOR & SOLID SIZE 单色单码SORTIN‎G分床分码SPECIA‎L MACHIN‎E特殊机器，特种车SPLOTC‎H ES 污迹SPREAD‎I NG 拉布SPUN YARN 纺纱SQUARE‎D SHAPED‎POCKET‎方角袋STEAM PRESSI‎N G STAND 蒸汽烫台STITCH‎线步STITCH‎DOWN WITH PKT-BAG 车线连袋布STITCH‎OVERLA‎P PING 驳线STITCH‎PER INCH / S.P.I. 每英寸针数STITCH‎TYPE 针步类型STITCH‎I NG & TURNIN‎G COLLAR‎OUT 车线后反领STRAIG‎H T BOTTOM‎直筒裤脚STRAIG‎H T CUT 直纹裁STRAIG‎H T POCKET‎直插袋STRAP 带条STRIPE‎MATCHI‎N G 对条STRIPE‎D (FABRIC‎)条子布STUFFI‎N G 填充物STYLE 款式SUITIN‎G套装SWEEP 下摆SWIMSU‎I T 泳装TAB 袢扣TAFFET‎A塔夫绸TAPE 带条TAPER BOTTOM‎萝卜裤脚TAPING‎镶边TBA=TO BE ADVISE‎待复TERRY CLOTH 毛巾布TEXTUR‎E D YARN 光亮纱线THIGH 脾围THREAD‎CLIPS 纱剪（剪线用）THREE POINTE‎D CATCHI‎N G FACING‎三尖钮子THREE POINTE‎D CUFF 三尖介英THREE POINTE‎D EXTENS‎I ON 三尖裤头搭咀‎THREE POINTE‎D PKT. WITH TWO CURVED‎SIDES 两边微弯三尖‎袋THREE POINTS‎POCKET‎三尖袋TIPPIN‎G镶边，唧边TO BE ADVISE‎待复TOP COLLAR‎面领TOP SLEEVE‎大袖TOP STITCH‎I NG 间面线TOP VENT 叉的面层TOP VENT OF SLEEVE‎大侧TOPS 上装TOP-STITCH‎I NG 间面线TOP-STITCH‎I NG WITH DOUBLE‎NEEDLE‎双针间面线TOTAL PRICE 总价TOWEL 毛圈布TRICOT‎经向斜纹毛织‎布TRIM FRONT EDGE 修剪前幅边缘‎TRIM OR SNIP ALONG CURVED‎SEAM 沿弯位修剪TRIM THREAD‎剪线TRIMMI‎N GS 部件，衣服上的点缀‎物TROUSE‎R S 裤子TURN CUFF OUT TO THE RIGHT SIDE 反出鸡英正面‎TURNED‎FINISH‎卷边TUXEDO‎无尾燕尾服TWEED 毛绒布TWILL 斜纹布TWIST LEG 扭脾扭脚UNDER PRESSI‎N G 中烫UNDER SLEEVE‎小袖UNDER VENT/BOTTOM‎VENT 叉的底层UNDERA‎R M SEAM 袖底骨UNDERL‎A P PLACKE‎T下层明筒，三尖折的小袖‎叉UNDERW‎E AR 内衣UNEVEN‎DYING 染色不均匀UNEVEN‎HEM 衫脚不平均UNEVEN‎PLAIDS‎格仔不均匀UNIT PRICE 单价VELCRO‎魔术贴VELVET‎天鹅绒VELVET‎E EN 仿天鹅绒VENETI‎A N 缩绒呢VENT 叉（有叠位）VISCOS‎E RAYON 人造丝V-NECK V形领窝VOGUE 流行的，风尚的WAIST 腰围WAIST TAG 腰卡WAISTB‎A ND 腰头WAISTB‎A ND IS EXTENS‎I ON OF BODY 原身裤头WALES 纵向线圈WARDRO‎B E 某一季节那一‎类型的服装WAREHO‎U SE 仓库WARP / ENDS 经纱WARP KNITTE‎D FABRIC‎经向针织布WARP-KNITTI‎N G 经编织物WASHIN‎G INITIA‎L LOAD 头缸洗水WASHIN‎G INSTRU‎C TION 洗水指示WASHIN‎G STREAK‎S洗水痕WATER REPELL‎E NT 防水处理WATERP‎R OOF FABRIC‎防水布WAVE STITCH‎I NG 线步起波浪WEB 网状物WEFT / PICKS 纬纱WEFT-KNITTI‎N G 纬编织物WELT POCKET‎西装袋，手巾袋WOOLEN‎粗纺羊毛WORK TICKET‎工票WORKMA‎N SHIP 手工WORSTE‎D精纺羊毛WOVEN LABEL 织唛WRAPSE‎A M 包缝WRINKL‎E S 起皱WRONG TYPE SEAM 错误的缝骨类‎型YARN 纱线ZIG-ZAG 人字ZIG-ZAG STITCH‎E S 人字线步ZIPPER‎FASTEN‎E R 拉链系结物其它常用词汇‎short in size 断码out of season‎过季的on sale 换季leftov‎e r stock 库存尾货BAGGY PATCH POCKE 立体贴袋HTM "HOW TO MEASUR‎E"（IN GUIDEL‎I NE) flat knit 横机W/R WATERP‎R OOF防水‎处理PX pricelead time 生产周期TARPUL‎I N 防水布flat lock 虾须线FLEECE‎抓毛布,磨毛布（针织）WAFFLE‎华夫格（针织布）eyelet‎button‎h ole sewing‎machin‎e圆头锁眼机rib stop 若隐若现的格‎子RING SLUB FULLY STRETC‎H CROSS-FIRE DENIM 双向竹节弹力‎牛仔ANTIQU‎E WASH / RETRO FINISH‎I NG 怀旧洗 / 怀旧处理Rib 1*1 Emeriz‎e d 1*1起绒罗纹windpr‎o of sleeve‎openni‎n g 防风袖口GBP Great Britai‎n Pound 英镑easy care 免烫sequin‎烫石RHIN STONE 烫石hand loom 手织样，指生产大货前‎，需打一小块布‎样，确认颜色，格型，效果BEADIN‎G钉珠circul‎a r knitin‎g machin‎e s 针织大圆机boxer 平脚裤 / 孖烟通PMS 潘通色卡pressi‎n g cloth 水布（熨烫服装时覆‎盖在上面的布‎）press cloth of wool 熨烫服装用的‎较厚的垫布tailor‎'s press board 烫凳（熨烫服装用的‎工具）egg pad 铁凳（熨烫肩部等部‎位的工具）clappe‎r拱形烫木（烫后袖缝、摆缝等的工具‎）tailor‎'s hem 布馒头braces‎skirt 吊带裙roll 疋，一疋布就是一‎卷布press button‎急钮，也叫五抓钮ring press button‎圈面的急钮cap press button‎带帽的急钮strik-off 印花打样, 是手刮样，用于针织印花‎面料打样中的‎称呼。

3材料导论第三章晶体结构

For many polycrystalline materials, the crystallographic orientations of the individual grains are totally random.
So, even though each grain may be anisotropic, a specimen composed of the grain aggregate behaves isotrophically. Sometimes the grains in polycrystalline materials have a preferential crystallographic orientation, in which case the material is said to have a ―texture‖.
For example, in cubic crystals, all the directions represented by the following indices are equivalent:
As a convenience, equivalent directions are grouped together into a family, which are enclosed in angle brackets, thus: <100>.
各向异性(anisotropy) :在晶体的不同方向上具有不同的性质(密度、折光率、导电率等）.
anisotropy各向异性 and isotropy
大
晶体的其它特征：
1) 自范性:晶体具有自发地形成封闭的凸几何多面体外形能力的性质,又称为自限性. 2) 均一性:指晶体在任一部位上都具有相同性质的特征. 3) 对称性:指晶体的物理化学性质能够在不同方向或位

英语排序知识点总结

英语排序知识点总结1. What is Ordering?Ordering, in its simplest form, refers to arranging items or elements in a specific sequence or pattern. It involves placing objects in a particular sequence based on a set of rules or criteria. This process allows us to make sense of the world around us and recognize patterns and relationships.2. Types of OrderingThere are several types of ordering, each with its unique characteristics and applications. Some of the most common types include:- Numerical Ordering: Arranging numbers in ascending or descending order, based on their values.- Alphabetic Ordering: Sorting words or letters based on their alphabetical order.- Chronological Ordering: Sequencing events or dates in the order in which they occurred. - Lexicographical Ordering: Arranging words or strings based on their alphabetical order, taking into account their lengths and characters.- Topological Ordering: Establishing a sequence of elements based on their relationships or dependencies.3. Properties of OrderingWhen dealing with ordered sets or sequences, several properties come into play. These properties help us understand and manipulate the order of elements. Some of the key properties include:- Transitivity: If A is placed before B, and B is placed before C, then A is also placed before C. - Antisymmetry: If A is placed before B, then B cannot be placed before A (unless they are identical).- Connexity: Any two distinct elements can be compared and placed in a specific order.- Reflexivity: An element A is always placed before itself.4. Ordering in MathematicsOrdering plays a crucial role in various mathematical concepts and operations. Some of the fundamental applications of ordering in mathematics include:- Comparing Numbers: Ordering allows us to compare the values of numbers and determine their relative positions on a number line.- Sets and Sequences: Ordering is essential in defining and analyzing sets and sequences, such as arithmetic and geometric progressions.- Inequalities and Equations: Solving and understanding inequalities and equations often involve ordering the elements or variables involved.- Permutations and Combinations: Ordering is crucial in determining the different arrangements of elements in permutations and combinations.5. Ordering in Computer ScienceIn the field of computer science, ordering is a fundamental concept that underpins various algorithms and data structures. Some key areas where ordering is applied in computer science include:- Sorting Algorithms: There are numerous sorting algorithms, such as bubble sort, merge sort, and quicksort, designed to arrange elements in a specific order.- Priority Queues: Ordering is used to establish a priority queue, where elements are arranged based on their priority levels.- Search and Retrieval: Ordering plays a vital role in organizing data for efficient search and retrieval operations.6. Ordering in LinguisticsIn linguistics, ordering is critical for understanding the structure and grammar of languages. Some important aspects of ordering in linguistics include:- Word Order: Different languages have distinct word orders, such as subject-verb-object (SVO) or subject-object-verb (SOV), which impact the meaning and structure of sentences.- Morphological Ordering: Linguistic elements, such as suffixes and prefixes, are often arranged in a specific order to convey meaning and grammatical functions.- Lexical Ordering: Words within a sentence are arranged based on their syntactic and semantic properties, contributing to the overall meaning of the sentence.7. Practical Applications of OrderingOrdering has numerous practical applications across various domains, including:- Time Management: Prioritizing tasks and activities based on their urgency and importance involves ordering them in a specific sequence.- Supply Chain Management: Arranging the flow of products and materials in a supply chain to ensure efficient production and distribution.- Ranking and Competition: Ordering is used to rank individuals or entities based on their performance, such as in sports competitions or academic standings.- Data Analysis: Ordering data based on different parameters allows for meaningful analysis and insights.In conclusion, ordering is a fundamental concept that permeates various aspects of our lives, from mathematics and computer science to linguistics and practical applications. Understanding the principles and applications of ordering is essential for making informed decisions, solving problems, and interpreting the world around us. Whether it's arranging numbers in numerical order or organizing the flow of goods in a supply chain, ordering is a crucial tool for bringing order and structure to our lives.。

汽车英语词汇

汽车英语词汇压路机 road roller推土机ball dozer平路机motor grader铲运机wheeled loading shovel轮式装载车wheeled loader轮式挖掘机wheeled excavator混凝土搅拌车concrete mixer truck焊接工程车mobile welding workshop沥青洒布车asphalt distribution truck沥青路面养护车asphalt pavement maintenance truck沥青运输车heated bitument tanker建筑大板运输车prfab building panel transporter电信工程车telecommunicatin field service truck工程机械运输车construction machinery transporter仓栅式汽车storage/stake truck钻孔立柱车pole drill and erection truck 油田试井车oil-well testing vehicle井架运输车derrick transporter修井车well maintenance vehicle地锚车mobile ground anchor vehicle灌注车oil well cracking acid pumping truck照明车flood lighting vehicle后翻倾式自卸汽车rear dump truck两侧翻倾式自卸汽车side dump truck三面翻倾式自卸汽车three-way dump truck 重型自卸汽车heavy duty dump truck矿用自卸汽车mining dump truck专用自卸汽车special dump truck摆臂式自装卸汽车swept-body dump truck 车厢可卸式汽车roll-off skip loader全挂车full trailer半挂车semi-trailer特种挂车special trailer栏板货厢式挂车cargo trailer平板式挂车flat platform trailer低架式挂车low-loader trailer厢式挂车trailer van自卸式挂车dumper trailer旅居挂车caravan动物集装箱live-stock container干货集装箱dry cargo container保温集装箱isothermal container框架集装箱flat rack container 散货集装箱bulk container罐式集装箱tank container冷藏集装箱refrigerated container质量mass净底盘干质量bare chassis dry mass净底盘整备质量bare chassis kerb mass底盘与驾驶室干质量chassis and cab dry mass底盘与驾驶室整备质量chassis and cab kerb mass整车交运质量complete vehicle shipping mass整车整备质量complete vehicle kerb mass最大设计总质量maximum design total mass最大允许总质量maximum autohrozed total mass最大设计装载质量maximum design pay mass最大允许装载质量maximum autohorized pay mass厂定最大总质量manufacturers maxumum total mass 载重量payload车辆自重kerb weight总重量gross weight轴荷axle load最大设计轴荷maximum design axle load最小设计轴荷minimum authorized axle load最大允许轴荷maximum design axle load轮胎最大设计拖挂质量maximum design tyre load最大设计拖挂质量maximum authorized tyre load最大允许拖挂质量maximum authorized towed mass汽车列车最大设计质量maximum designmass of vehicle combination汽车列车最大允许质量maximumauthorized mass of vehicle combination铰接车最大设计质量maximum disgn massof articulated vehicle铰接车最大允许质量maximum authorizedmass of articulated vehicle半挂牵引车承受的最大静载荷maximumdesign static load borne by semi-trailertowing vehicle作用在挂接装置上的最大设计静载荷maximum design static load on coupling device作用在挂接装置上的最大允许静载荷maximum authorized static load on coupling device 比功率power/mass ratio比扭矩torque/maximum total mass ratio重量利用系数factor of weight utilizaton汽车型谱chart of automotive model后驱动汽车rear drive automobile前驱动汽车front drive automobile发动机后置式客车bus with rear engine四轮驱动车辆all wheel drive automobile发动机前置式客车bus with front engine发动机底置式客车bus with underfloor engine计算机辅助设计computer aided deisgn(CAD)有限寿命设计design for finite life累积疲劳损伤原理theory of cumulativedamage in fatique优化设计optimum deisgn汽车尺寸控制图sketch on layout ofrdimenshions control of assembly汽车总装配图automobile assembly drawing汽车总布置草图sketch for automobile layout汽车设计的技术经济分析technical-economic analysis in automobile design设计任务书design assignment系列化, 通用化, 标准化seriation ,universalization and standardization 总布置设计calculation for layout运动校核correction of motion侧视轮廓side outline前视轮廓end outline顶视轮廓plan outline车长vehicle length车宽vehicle width车高vehicle height轴距wheel base轮距track前轮距track front后轮距track rear双胎间距space between twin wheels前悬front overhang后悬rear overhang离地间隙ground clearance纵向通过角ramp angle接近角approach angle离出角departure angle车架高度height of chassis above ground驾驶室后车架最大可用长度maximumusable length of chassis behind cab车身长度body work length车厢内部最大尺寸maximum internal dimension of body货厢内长loading space length货厢有效长度loading length货厢内宽loading space width货厢有效内宽loading width货厢内高loading space height货厢有效内高loading height货台高度loading surface height车架自由长度frame free length栏板内高inside board height 货厢容积loading surface门高door height门宽door width车架有效长度chassis frame useful length货厢全长body length牵引杆长drawbar length牵引装置的位置position of towing Attachment牵引装置的悬伸overhang of towing atachment牵引装置的高度heigth of towing attachment牵引装置牵距distance of towing attachment牵引座前置距fifth wheel lead长度计算用牵引座前置距fifth wheel leadfor calculation of length质量分配用牵引座前置距fith wheel leadfor calculation of mass distribution牵引座结合面高度height of coupling face牵引装置至车辆前端的距离distance between towing device and front end of towing vehicle牵引叉销至车辆前端的距离distance between jaw and front end of towing vehicle半挂车间隙半径rear tractor clearance radius of semi-trailer半挂车前回转半径front fitting radius of semi trailer车轮垂直行程vertical clearance of wheel车轮提升高度lift of wheel转弯半径turning circle静止半径static radius碰撞collision (crash,impact)正碰撞frontal collision (frontal impact)侧碰撞side collision (side impact)后碰撞rear collision (rear impact)擦碰撞sidewipe collision碰撞方向collision direction碰撞角度collision angle倾斜的oblique(tilt)成角度的angled纵向的longitudinal垂直的vertical类型 type发动机 engine内燃机 intenal combusiton engine动力机装置 power unit汽油机 gasoline engine汽油喷射式汽油机 gasoline-injection engine火花点火式发动机 spark ignition engine压燃式发动机 compression ignition engine往复式内燃机 reciprocating internal combustion engine化油器式发动机 carburetor engine柴油机 diesel engine转子发动机 rotary engine旋轮线转子发动机 rotary trochoidal engine二冲程发动机 two-stroke engine四冲程发动机 four-stroke engine直接喷射式柴油机 direct injection engine间接喷射式柴油机 indirect injection engine增压式发动机 supercharged engine风冷式发动机 air-cooled engine油冷式发动机 oil-cooled engine水冷式发动机 water-cooled engine自然进气式发动机 naturally aspirated engine煤气机 gas engine液化石油气发动机 liquified petroleum gas engine 柴油煤气机 diesel gas engine多种燃料发动机 multifuel engine石油发动机 hydrocarbon engine双燃料发动机 duel fuel engine热球式发动机 hot bulb engine多气缸发动机 multiple cylinder engine对置活塞发动机 opposed piston engine对置气缸式发动机 opposed-cylinder engine十字头型发动机 cross head engine直列式发动机 in-line engine星型发动机 radial engine筒状活塞发动机 trunk-piston engine斯特林发动机 stirling engine套阀式发动机 knight engine气孔扫气式发动机 port-scavenged engine倾斜式发动机 slant engine前置式发动机 front-engine后置式发动机 rear-engine中置式发动机 central engine左侧发动机 left-hand engine右侧发动机 right-hand engine短冲程发动机 oversquare engine长冲程发动机 undersquare engine等径程发动机 square engine顶置凸轮轴发动机 overhead camshaft engine双顶置凸轮轴发动机dual overhead camshaft engine V 形发动机 V-engine顶置气门发动机 valve in-head engine侧置气门发动机 side valve engine无气门发动机 valveless engine多气门发动机 multi-valve engine卧式发动机 horizontal engine斜置式发动机 inclined engine立式发动机 vertical engine W 形发动机 w-engine I形发动机 I-engine L形发动机 L-engine F形发动机 F-engine性能 performance二冲程循环 two-stroke cycle四冲程循环 four-stroke cycle狄塞尔循环 diesel cycle奥托循环 otto cycle混合循环 mixed cycle定容循环 constant volume cycle工作循环 working cycle等压循环 constant pressure cycle理想循环 ideal cycle热力循环 thermodynamic cycle冲程 stroke活塞行程 piston stroke长行程 long stroke上行程 up stroke下行程 down stroke进气行程 intake stroke充气行程 charging stroke压缩行程 compression stroke爆炸行程 explosion stroke膨胀行程 expansion stroke动力行程 power stroke排气行程 exhaust stroke膨胀换气行程 expansion-exchange stroke换气压缩行程 exchange-compression stroke止点 dead center上止点 top dead center (upper dead center)下止点 lower dead center (bottom dead center) 上止点前 budc (before upper dead center)上止点后 atdc (after top dead cetner)下止点前 bbdc (before bottom dead center)下止点后 abdc (after bottom dead center)缸径 cylinder bore缸径与行程 bore and stroke空气室 energy chamber气缸余隙容积 cylinder clearance volume燃烧室容积 combustion chamber volume气缸最大容积 maximum cylinder volume压缩室 compression chamber排气量 displacement发动机排量 engine displacement活塞排量 piston swept volume气缸容量 cylinder capacity单室容量 single-chamber capacity容积法 volumetry压缩比 compression ratio临界压缩比 critical compression ratio膨胀比 expansion ratio面容比 surface to volume ratio行程缸径比 stroke-bore ratio混合比 mixture ratio压缩压力 compression pressure制动平均有效压力 brake mean effective pressure 空燃比 air fuel ratio燃空比 fuel air ratio燃料当量比 fuel equivalence ratio扭矩 torque单缸功率 power per cylinder升功率 power per liter升扭矩 torque per liter升质量 mass per liter减额功率 derating power输出马力 shaft horsepower马力小时,马力时 horsepower-hour总马力 gross horse power总功率 gross power净功率 net power燃油消耗量 fuel consumption比燃料消耗率 specific fuel consumption空气消耗率 air consumption机油消耗量 oil consumption有效马力 net horse power额定马力 rated horse power马力重量系数 horsepower-weight factor制动功率 brake horse power制动热效率 brake thermal efficiency总效率 overall efficiency排烟极限功率 smoke limiting horsepower功率曲线 power curve机械损失 mechanical loss机械效率 mechanical efficiency有效热效率 effective thermal efficiency充气系数 volumetric efficiency过量空气系数 coefficient of excess air适应性系数 adaptive coefficient扭矩适应性系数 coefficient of torque adaptibility 转速适应性系数 speed adaptive coefficient强化系数 coefficient of intensification校正系数 correction factor换算系数 conversion factor活塞平均速度 mean piston speed发动机转速 engine speed (rotational frequency) 怠速转速 idling speed经济转速 economic speed 起动转速 starting speed最低稳定工作转速 lowest continuou speed with load 最大扭矩转速 speed at maximum torque最高空转转速 maximum no load governed speed调速 speed governing超速 overspeed怠速 idling转速波动率 speed fluctuation rate工况 working condition (operating mode)额定工况 declared working condition变工况 variable working condition稳定工况 steady working condition空载 no-load全负荷 full load超负荷 overload部分负荷 part load充量(进气) charge旋转方向 direction of rotation顺时针 clockwise逆时针 counter-clockwise左转 left-hand rotation右转 right-hand rotation外径 major diameter中径 pitch diameter内径 minor diameter径向间隙 radial clearance发动机性能 engine performance加载性能 loading performance起动性能 starting performance加速性能 acceleration performance动力性能 power performance排放性能 emission performance空转特性 no load characteristics负荷特性 part throttle characteristics调速特性 governor control characteristics万有特性 mapping characteristics稳定调速率 steady state speed governing rate气缸体和气缸盖 cylinder block and head气缸体 cylinder block整体铸造 cast inblock (cast enblock)发动机罩 engine bonnet气缸体加强筋 engine block stiffening Rib气缸 cylinder(转子机)缸体 stator缸径 cylinder bore气缸体机架 cylinder block frame气缸盖 cylinder head配气机构箱 valve mechanism casing气缸体隔片 cylinder spacer气缸盖密封环 cylinder head ring gasket气缸盖垫片 cylinder head gasket气缸套 cylinder liner (cylinder sleeve)干式缸套 dry cylinder liner湿式缸套 wet cylinder liner气缸水套 water jacket膨胀塞 expansion plug防冻塞 freeze plug气缸壁 cylinder wall环脊 ring ridge排气口 exhaust port中间隔板 intermediate bottum导板 guideway创成半径(转子机) generating radius缸体宽度(转子机) operating width机柱 column燃烧室 combustion chamber主燃烧室 main combustion chamber副燃烧室 subsidiary combustion chamber预燃室 prechamber涡流燃烧室` swirl combustion chamber分开式燃烧室 divided combustion chamber涡流式燃烧室 turbulence combustion chamber半球形燃烧室 hemispherical combustion chamber 浴盆形燃烧室 bathtub sectioncombustion chamber L形燃烧室 L-combustion chamber楔形燃烧室 wedge-section combustion chamber开式燃烧室 open combustion chamber封闭喷射室 closed spray chamber活塞顶内燃烧室 piston chamber爆发室 explosion chamber燃烧室容积比 volume ratio of combustion cahmber 燃烧室口径比 surface-volume ratio of combustion chamber通道面积比 area ratio of combustionchamber passage曲轴箱通气口 crankcase breather凸轮轴轴承座 camshaft bearing bush seat定时齿轮室罩 camshaft drive (gear) cover曲轴箱检查孔盖 crankcase door曲轴箱防爆门 crankcase explosion proof door主轴承盖 main bearing cap气缸盖罩 valve mechanism cover飞轮壳 flywheel cover扫气储器 scavenging air receiver活塞 piston裙部开槽活塞 split skirt piston U形槽活塞 U-slot piston 滚花修复活塞 knurled piston圆顶活塞 dome head piston平顶活塞 flat head piston凸顶活塞 crown head piston (convex head piston) 凹顶活塞 concave head piston阶梯顶活塞 step-head piston筒形活塞 trunk piston椭圆形活塞 oval piston抗热变形活塞 autothermic piston不变间隙活塞 constant clearance piston镶因瓦钢片活塞 invar strut piston直接冷却式活塞 direct-cooled piston间接冷却式活塞 indirect cooled piston滑裙活塞 slipper piston活塞速度 piston speed活塞顶部 piston head活塞裙部 piston skirt整体活塞裙 solid skirt活塞裙扩大衬簧 piston skirt expander滑履式活塞裙 slipper skirt隔热槽 heat dam活塞标记 piston mark活塞销 piston pin活塞销孔 piston pin boss活塞销衬套 piston pin bushing全浮式活塞销 full-floating piston pin半浮式活塞销 semifloating piston pin固定螺钉式活塞销 set screw piston pin活塞环 piston ring组合式活塞环 compound piston ring同心活塞环 concentric piston ring偏心活塞环 eccentric piston ring自由环 free ring闭合环 closed ring梯形环 keystone ring半梯形环 half keystone ring矩形环 rectangular ring油环 oil control ring开槽油环 slotted oil control ring螺旋弹簧加载双坡口油环 coil spring loaded slotted oil control ring涨环 expander双坡口油环 double bevelled oil control ring内上坡口 internal bevel top内下坡口 internal bevel bottom边缘坡口油环 bevelled-ege oil control ring刮油环 scrapper ring钩形环 napier ring镀铬活塞环 chrome plated piston ring活塞衬环 piston ring expander活塞环槽 piston ring groove活塞环区 ring zone活塞环岸 piston ring land活塞环内表面 back of ring曲柄连杆机构 connecting rod中心曲柄连杆机构 central-located connecting rod 偏心曲柄连杆机构 offset connecting rod铰接曲柄边杆机构 hinged connecting rod连杆 connecting rod连杆小头 connecting rod small end连杆大头 connnecting rod big end连杆杆身 connecting rod shank副连杆 slave connecting rod叉形连杆 fork-and-blade connecting rod主连杆 main connecting rod方形连杆 boxed rod绞链式连杆 hinged type connecting rod活节式连杆 articulated connecting rod连杆盖 connecting rod cap连杆轴承 connecting rod bearing曲轴 crankshaft整体式曲轴 one-piece crankshaft组合式曲轴 assembled crankshaft右侧曲轴 right-hand crankshaft左侧曲轴 left-hand crankshaft改变行程的曲轴 stroked crankshaft曲轴前端 crankshaft front end曲轴主轴颈 crankshaft main journal轴颈重叠度 shaft journal overlap圆角 fillet主轴承 main bearing曲轴止推轴承 crankshaft thrust bearing薄臂轴瓦 thin wall bearing shell曲轴油道 crankshaft oil passage曲柄 crank曲柄臂 crank arm曲柄销 crank pin轴套 bush曲柄转角 crank angle曲柄半径 crank radius抛油圈 oil slander角度轮 degree wheel动平衡机 dynamic balancer平衡重 balancer weight扭振减振器 torshional vibration damper扭振平衡器 torsion balancer谐振平衡器 harmonic balancer振动平衡器 vibration balancer 曲轴链轮 crankshaft sprocket转子轴颈 rotor journal偏心轴 eccentric shaft曲轴箱 crankcase闭式曲轴箱通风装置 closed-crankcase ventilating system飞轮 flywheel飞轮齿圈 flywheel ring gear飞轮芯棒 cantilever飞轮芯轴 flywheel spindle飞轮的惯量矩 flywheel moment of inertia飞轮标记 flywheel mark当量系统 equivalent system当量轴长 equivalent shaft length一级往复惯性力 reciprocating inertiaforce,1st order二级往复贯性力 reciprocating inertiaforce, 2nd order离心惯性力 centrifugal inertia force配气机构 valve gear凸轮轴 camshaft凸轮 cam整体式凸轮轴 one-piece camshaft组合式凸轮轴 assembled camshaft凸轮轴驱动机构 camshaft drive赛车用凸轮轴 race camshaft凸轮轴轴颈 camshaft bearing journal凸轮轴轴承 camshaft bearing凸轮轴偏心轮 camshaft eccentric凸轮轴链轮 camshaft sprocket凸轮轴正时齿轮 camshaft timing gear凸轮轴齿轮 camshaft gear wheel进口凸轮 inlet cam排气凸轮 exhaust cam快升凸轮 quick lift cam快升缓降凸轮 quick lift gradual clsingcam凸轮轮廓 cam contour凸轮包角 cam angle凸轮升程 cam-lobe lift凸轮尖 cam nose凸轮从动件 cam follower齿轮传动机构 gear drive正时齿轮 timing gear链传动机构 chain drive链轮 sprocket wheel链轮盘 chain sprocket正时链条 timing chain带齿皮带 toothed timing belt链条张紧轮 chain tension gear半速齿轮 half speed gear正时齿轮刻印记号 timing gear punch mark 气门 valve进气过程 intake process换气过程 gas exchange process扫气过程 scavenging process给气比 delivery ratio分层充气 stratified charge充量系数 volumetric efficiency涡流比 swirl rate进气涡流 intake swirl螺旋进气道进气 helical duct intake导流屏式气门进气 masked valve intake切向进气道进气 tangential duct intake 进气紊流 intake trubulence进气提前角 intake advance angle进气持续角 intake duration angle进气迟后角 intake lag angle进面值 time-area value气门升程 valve lift气门正时 valve timing扫气口面积 scavenging port area菌形气门 mashroom valve, poppet valve 钠冷却气门 sodium filled valve (natrium cooled valve)双气门 dual valve进气门 intake valve (suctionValve，inlet valve)排气门 exhaust valve顶置气门 overhead valve侧置气门 side valve倾斜气门 inclined overhead valve直立气门 vertical overhead valve套筒式滑阀 sleeve valve气门机构 valve gear直接式气门驱动机构 direct valve gear间接式气门驱动机构 indirect valve gear 气门杆 valve stem加大气门杆 oversize valve stem气门头 valve head气门工作面 valve face气门边限 valve margin气门弹簧座 valve-spring retainer气门锁片 valve key气门间隙调节螺钉 valve lash adjusting screw气门旋转器 valve rotator气门室 valve cage 气门油封 valve oil seal气门口 valve port气门座 valve seat气门座镶圈(嵌镶式气门座圈) valve seat insert (valve seat ring)气门座锥角 valve seat angle气门座宽度 valve seat width气门挺杆 valve tappet (valve lifter) 液力挺杆 hydraulic tappet (lifter)无间隙挺杆 zero-rush tappet(non-clearance tappet)筒形挺杆 barrel type tappet油压挺杆 ooil tappet滚轮挺杆 roller tappet (lifter)挺杆转位 tappet rotation排气门挺杆 exhaust valve lifter气门导管 valve guide气门杆导管 stem guide气门重叠度 stem overlap气门开启持续时间 valve duration气门正时标记 valve timing sign气门弹簧 valve spring气门内弹簧 inner valve spring气门外弹簧 outer valve spring刚性缓冲弹簧 stiff buffer spring上紧弹簧 energizing spring汽车及发动机英语专业词汇有轨电车 tram无轨电车 trolley军用车辆 military vehicle蒸汽机 steam engine汽油机 gasoline engine全拆散 CKD completely knock down版拆散 SKD semi-knockdown支柱产业 pillar estate货车 truck， lorry非公路用车 off-road vehicle机体 engine body曲柄连杆机构 crank-connecting rod mechanism配气机构 valve timing mechanism共给系 fuel supply system润滑系 lubricating system点火系 ignition system启动系 starting system底盘 chassis传动系 power train离合器 clutch变速器 gear box传动轴 propeller shaft驱动桥 drive axle行驶系 running gear车架 frame悬架 suspension桥壳 axle housing转向系 steering system转向盘 steering wheel转向器 steering gear转向传动装置 steering linkage助力装置 power assisting device制动系 braking system传动装置 transfer device制动器 brake车前板制件 front end panels车身壳体 body shell附属装置 auxiliary device货箱 carrying platform发动机前置后轮驱动 FR front engine rear drive 发动机中置后轮驱动 MR midship engine rear drive 全轮驱动 nWD all wheel drive驱动力 tractive force滚动阻力 rolling resistance上坡阻力 gradient resistance附着作用 adhesion附着力 adhesive force附着系数 coefficient of adhesion 发动机工作原理二冲程发动机 two stroke engine 风冷发动机 air cooled engine上止点 UDP upper dead point下止点 LDP lower dead point活塞行程 stroke气缸直径 bore工作容积 working volume排量 swept volume, displacement 进气行程 intake stroke压缩比 compression ratio做功行程 working stroke爆燃，敲缸 detonation， knock 排气行程 exhaust stroke示功图 indicating diagram汽缸体 cylinder block气缸盖 cylinder head油底壳 oil sump (pan)活塞 piston连杆 connecting rod曲轴 crankshaft飞轮 flywheel进气门 intake valve排气门 exhaust valve挺柱 tappet推杆 push rod摇臂 rocker凸轮轴 camshaft正时齿轮 timing gear燃油箱 fuel tank燃油泵 fuel pump汽油滤清器 gasoline filter化油器 carburetor空气滤清器 air cleaner进气管 intake manifold排气管 exhaust manifold火花塞 spark plug点火线圈 ignition coil断电器 breaker蓄电池 storage battery发电机 generator水泵 water pump散热器 radiator放水阀 drain valve水套 water jacket分水管 distributive pipe机油泵 oil pump集滤器 suction filter限压阀 relief valve润滑油道 oil passage机油滤清器 oil filter机油冷却器 oil cooler起动机 starting motor有效功率 effective power燃油消耗率 specific fuel consumption发动机转速特性 engine speed characteristic 节气门开度 throttle percentage部分特性 partial characteristic气缸套 cylinder sleeve， cylinder liner发动机支承 engine mounting活塞顶 piston top活塞头部 piston head活塞裙 piston skirt开槽 slot活塞环 piston ring气环 compression ring油环 oil ring环槽 groove活塞销 piston pin主轴承 main bearing主轴承盖 main bearing cap主轴瓦 main shell连杆轴承 big end bearing连杆盖 big end cap起动爪 cranking claw带轮 pulley平衡重 counter weight发火顺序 firing order扭振减振器 torsional vibration damper配气机构顶置气门 OHV over head valve顶置凸轮轴 OHC over head camshaft双顶置凸轮轴 DOHC dual over head camshaft 多气门发动机 multi-valve engine气门间隙 valve clearance配气相应 timing phase气门杆 valve stem气门座 valve seat气门导管 valve guide气门弹簧 valve spring汽油及供给系可燃混合气 combustion mixture消声器 silencer， muffler汽油 gasoline， petrol分馏 distil蒸发性 evaporating property热值 heat value抗爆性 anti-knock property 辛烷值 RON research octane number过量空气系数 coefficient of excessive air理论混合气 theoretical mixture稀混合气 thin mixture主供油系统 main supply system怠速系统 idle system加浓系统 thickening system加速系统 accelerating system浮子 float浮子室 float chamber针阀 needle valve量孔 metering jet阻风门 choke滤芯 filter cartridge沉淀杯sediment cup泵膜 pump diaphragm油浴式 oil bath type石棉垫 asbestos pad预热 pre-heating汽油直接喷射 gasoline direct injection电控 electronic control多点喷射muti-point injection电路控制 circuit control分电器信号 distributor dignal空气流量信号 airflow signal柴油机共给系输油泵 transfer pump喷油泵 fuel injection pump高压油管 high pressure fuel pipe发火性 ignition property黏度 viscosity凝点 condensing point备燃期 pri-combustion period速燃期 rapid combustion period统一燃烧室 united chamber球形燃烧室 ball shape chamber涡流室 turbulence chamber预燃室 pri-combusion chamber喷油器 injector精密偶件 precise couple柱塞 plunger出油阀 delivery valve调速器 governor全速调速器 full speed governor综合调速器 combined governor气动调速器 pneumatic governor机械离心式调速器 mechanical centrifugal governor 复合式调速器 complex governor喷油提前角调节装置 advancer飞块 flyweight联轴节 coupling中间冷却器 intermediate cooler节温器 thermostat防冻液 anti-freezing liquid补偿水桶 compensation reservoirV-带 V belt百叶窗 shutter小循环 small circulation散热翅片 fins润滑剂 lubricant压力润滑 pressure lubrication飞溅润滑 splash lubrication润滑脂 grease机油压力传感器 oil pressure sensor油封 oil seal旁通阀 bypass valve机油散热器 oil cooler机油尺 dip stick加机油口 oil filler曲轴箱通风 crankcase ventilation一次绕组 primary winding热敏电阻 heat sensitive resistance侧电极 side electrode瓷绝缘体 ceramic insulator跳火间隙 spark gap半导体点火系 semi-conductor ignition system 晶体管 transistor二极管 diode三极管 triode无触点点火系 non-contact ignition system霍尔效应 Hall effect正极板 anode负极板 cathode隔板 separator电解液 electrolyte接线柱 terminal硅整流交流发电机 silicon rectified A.C. motor 电刷 brush风扇叶轮 fan blade电压调节器 voltage regulator起动系串激直流发电机 serial wound DC motor电磁操纵机构 electro-magnetic control新型发动机三角活塞 triangular piston转子发动机 rotary engine自转 rotary motion， rotation公转 orbit motion 轨迹 trajectory往复零件 reciprocal parts动平衡 dynamic balance燃气涡轮发动机 gas turbine汽车传动系统机械式传动系 mechanical transmission液力机械式传动系 hydro-mechanical transmission 静液式传动系 static-hydraulic transmission电力式传动系 electrical transmission可变速比 variable ratio有级变速 definite ratio无极变速 indefinite ratio无级变速器 CVT continuously variable transmission 一般布置 general layout发动机横置 lateral engine positioning分动器 transfer case， transfer box接合柔和 smooth engagement分离彻底 thorough separation过载 overload摩擦表面 friction surface摩擦衬片 friction liner毂 hub减震圈 damping ring减振圈 split ring同心度 concentricity花键 spline分离杠杆 release lever主缸 master cylinder踏板 pedal踏板工作行程 pedal working stroke双片离合器 dual disc clutch膜片弹簧离合器 diaphragm spring clutch变速器与分动器输入轴（第一轴）input shaft，drive shaft中间轴 counter shaft倒档轴 reverse gear shaft常齿合 constant mesh最高挡 top gear空挡 neutral gear动力输出 power take-off齿合套 sliding sleeve同步器 synchronizer同步锥面 synchro cone变速杆 shifting lever球铰链 ball joint换挡拨叉 shifting fork互锁 inter-lock变速驱动桥 transaxle加力挡 low gear液力机械传动液力耦合器 hydraulic coupling泵轮 impeller涡轮 turbine叶片 blade液力变矩器 torque converter行星齿轮系 planetary gear system传动轴万向节 universal joint十字轴式万向节 cardan type U-joint十字轴 center cross滚针轴承 needle bearing滑脂嘴（油嘴）lubricating fitting、 nipple 等角速 constant angular velocity双联式万向节 dual cardan type U-joint星形套 inner race housing球形壳 outer race shell绕性万向节 flexible U-joint无缝钢管 seamless steel tube主减速器 final drive主动齿轮 drive pinion从动齿轮 ring gear伞齿轮 bevel gear双曲面齿轮 hypoid gear单级减速 single reduction贯通式主减速器 penetrable final drive差速器 differential半轴齿轮 differential side gear轴间差速器 inter-axle differential lock托森差速器 torque sensitive differential半轴 axle shaft全浮式半轴 float type axle shaft桥壳 axle housing桥壳后盖 final drive rear cover悬架 suspension横向稳定器（杆） stabilizer， anti-roll bar 悬架刚度 suspension stiffiness静挠度 static deformation独立悬架 independent suspension减震器压缩行程，车轮上跳 jounce减震器伸张行程，车轮回跳 rebound双向作用减震器 double action shock absorber 筒式减震器 telescopic shock absorber吊环 link ring流通阀（进液阀） intake valve伸张阀 rebound valve补偿阀 compensation valve钢板弹簧 leaf spring螺旋弹簧 coil spring 扭杆弹簧 torsional bar吊耳 shackle转向轴线 steering axis滑柱式 strut type悬架减振器 sock absorber横向稳定器（杆）stabilizer，anti-roll bar悬架刚度 suspension stiffiness贮油缸 reservoir通流阀（进液阀）intake valve伸张阀 rebound valve压缩阀 compression valve补偿阀 compensation valve充气减振器 gas filled shock absorber压力可调减振器 pressure adjustable shock absorber 钢板弹簧 leaf spring中心螺栓 coil bolt螺旋弹簧 coil spring扭杆弹簧 torsional bar膜式空气弹簧 diaphragm type air spring囊式空气弹簧 bellow type air spring卷耳 spring eye吊耳 shackle副簧 auxiliary spring双横臂式悬架 double wishbone suspension纵摆臂式 trailing arm type转向系机械手动转向系 manual steering system直拉杆 drag link转向轮偏转角关系 steering geometry转弯半径 turning radius循环球式转向器 recirculating ball steering gear 转向螺杆 steering screw齿扇 sector齿轮齿条式转向器 rack and pinion steering gear 蜗杆曲柄指销式转向器 worm and crankpin steering gear转向油罐 steering reservoir制动系轮缸 wheel cylinder调整凸轮 adjustable cam制动蹄回位弹簧 retainer spring制动盘 brake disc气压制动系 pneumatic braking system贮气筒 reservoir伺服制动系 servo braking system真空助力器 vacuum booster防抱死制动系（ABS）anti-lock braking system缓速器 retarder车身车身壳体 body shell发动机罩 hood bonnet前翼板 front fender，front wing 前挡泥板 front fender apron前围板 dash board， fire wall 顶盖 roof行李箱盖 trunk lid， deck lid 前柱 front pillar仪表盘 instrument panel遮阳板 sun visor刮水器 wiper后视镜 rear view mirror玻璃升降器 window regulator密封条 weather strip头枕 head restraint钢化玻璃 toughened glass夹层玻璃 laminated glass货箱 carrying platform后板 tail board拴杆 tightening latch电机，电器词汇直流电动机 direct current motor交流电动机 alternating current motor交直流两用电机 universal motor同步电动机 synchronous motor笼形同步电动机 cage synchronous motor同步感应电动机 synchronous induction motor磁阻电动机 reluctance motor亚同步磁阻电动机 subsynchronous reluctance motor 异步电动机 asynchronous motor感应电动机 induction motor无刷绕线转子感应电动机brushless wound-rotor induction motor他励 separately excited自励 self-excited混励 compositely excited并励 shunt串励 series复励 compound excited绕组 winding电枢绕组 armature winding阻尼绕组 damping winding励磁绕组 excitation winding磁场绕组 field winding性能试验 performance test型式试验 type test重复试验 duplicated test检查试验 routing test抽样试验 sampling test验收试验 acceptance test效率 efficiency总损耗 total loss of a machine热量试验 calorimetric test空载试验 no-load test轻载试验 light load温升试验 temperature-rise test波形试验 waveform test波形分析 waveform analysis堵转试验 locked-rotor换向试验 commutation test直流电阻测试 resistance test铁芯损耗试验 core testVibration test噪声级试验 noise-level test轴电压试验 shaft-voltage test串激电机 universal motor转轴 shaft换向器 commutator端板 end spider 绝缘纸 rotor steel liner槽楔 wedge ringU型挡圈 U type retainer漆包线 field magnet wire绝缘漆 vanish换向片 commutator碳刷架 brush holder刷辫 brush flesible定叶轮 diffuser动叶轮 impeller风罩 fan cover压圈 gasket-fan衬套 bush-fan爬电距离 creepage distances磨损 wear易接近的，可到达的，易受影响的 accessible 吸尘器 vaccum软管 hose极限转矩 breakdown torque起步阻力 breakaway force风动发电机 wind-driven generator转/秒 revolutions per second转速力矩特性曲线 speed-torque curve同步转速 synchronous speed多相整流器 polyphase rectifier电路元件 circuit components电气设备 electrical device电热器 heating appliance电动势 EMF electromotive force负载特性 load characteristic工频 power frequency相对。

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PACS numbers: 71.10.Hf, 71.10.Pm, 71.27.+a
arXiv:cond-mat/0512626v1 [cond-mat.supr-con] 26 Dec 2005
I.
INTRdes there have been important developments in both experiment and theory which resulted in a better understanding of the high temperature superconductors. One typical characteristic of those compounds is their extreme sensitivity with doping. At half-ﬁlling the cuprates are Mott insulators. However, at very low hole doping, as soon as the antiferromagnetic ordering is destroyed those materials are turned into the pseudogap phase1,2,3,4 . From the start Anderson5 argued that the Hubbard model (HM), which considers only short-range interactions, describes qualitatively well the electronic properties of the high-Tc superconductors. In the onedimensional case (1D) this model captures the main features displaying the existence of the Luttinger liquid for U > 0, spin-charge separation, as well as a Mott insulating regime. There is no exact solution for the HM in D > 1. Moreover successful methods in D = 1 such as bosonization6 and the Bethe ansatz 7 are either inapplicable or simply much too hard to implement in higher dimensions. One approach which is equally successful in both one and higher dimensions is the renormalization group (RG) method. Diﬀerent RG schemes are already available to describe strongly interacting fermions in the presence of a Fermi surface (FS)8,9,10,11,12 . In this work we continue to explore the ﬁeld theoretical RG method. We calculate the renormalized form factors of the main physical instabilities of the two-dimensional HM up to two-loop order. We compare our results with other RG approaches in 2D9,10 . Those results are summarized in the phase diagram which displays all leading and subleading instabilities in that dimension in coupling constant space. To reinforce our case we test our method in well known grounds and show it reproduces the analogous phase diagram in the one-dimensional case13 . In 1D the coupling functions approach ﬁxed point values producing susceptibilities which exhibit power-law behavior. This reﬂects the absence of spontaneous symmetry breaking and long-range order. We must keep this in
Short-Range Order in a Flat Two-Dimensional Fermi Surface
Eberth Corrˆ ea,∗ Hermann Freire, and A. Ferraz
Laborat´ orio de Supercondutividade, Centro Internacional de F´ isica da Mat´ eria Condensada, Universidade de Bras´ ilia - Bras´ ilia, Brazil (Dated: February 6, 2008) We present the two-loop renormalization group (RG) calculations of all the susceptibilities associated with the two-dimensional ﬂat Fermi surface with rounded corners (FS). Our approach follows our fermionic ﬁeld theory RG method presented in detail earlier on. In one loop order our calculation reproduce the results obtained previously by other RG schemes. All susceptibilities diverge at some energy scale and the antiferromagnetic SDW correlations produce indeed the dominant instability in the physical system. In contrast, in two-loop order, for a given initial set of values of coupling constant regime only one of the susceptibilities at a time seems to diverge.
mind when analyzing the possible existing states in the phase diagrams of such low dimensional systems. Here in specifying such phase diagrams we ﬁnd convenient to deﬁne appropriately symmetrized response functions with respect the spin projections of the corresponding particleparticle and particle-hole operators. In this way, we calculate the corresponding charge density wave (CDW ), the spin density wave (SDW ), the singlet superconductivity (SSC ), and the triplet superconductivity (T SC ) (2,1) one-particle irreducible functions ΓR ’s which in turn deﬁne the respective susceptibilities. In a 1D metal the FS reduces to two Fermi points (±kF ). In 2D, for non-interacting electrons, at half-ﬁlling the FS is a perfect square. If we go slightly away from half-ﬁlling, doping the system with holes, all corners get rounded and the area inside the FS is reduced from its square value. As a result in such conditions we may neglect the van Hove singularities as well as the Umklapp eﬀects. In this 2D scenario a new symmetry arises with respect to the sign of momentum component along the FS. This will reﬂect itself in the RG equations for the renormalized form factors which we redeﬁne as the charge density wave of s and d-types (CDW ±), the spin density wave of s and d-types (SDW ±), the singlet superconductivity of s and d-types (SSC ±) and, ﬁnally, the triplet superconductivity of s and d-types (T SC ±). All those symmetries are derived from the particle-particle and particle-hole operators which have a transfer momentum q. Our results for the uniform spin and charge susceptibilities were presented in a separated publication14 . We showed in another work15 that for such ﬂat FS as soon as we add interactions to the 2D electron gas the ﬂow to strong coupling destroys the Landau Fermi liquid regime. We demonstrated how the self-energy eﬀects lead to the nulliﬁcation of the quasiparticle weight directly aﬀecting the RG equations for the renormalized coupling functions. In this work we discuss how those results also inﬂuence directly the response functions of the physical system. In particular we reveal that for the lightly doped 2D HM, all susceptibilities ﬂow to ﬁxed values. We argue that such a behavior suggests the exis-