Volume of unit ball in an n-dimensional normed space and its asymptotic properties

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力学专业英语考试重点整理

学而不思则惘，思而不学则殆力学专业英语考试重点整理一、单词：英译汉、汉译英Centroid 质心，形心Elasticity 弹力，弹性Linear 线性的，直线的Prismatic 棱镜的，棱柱形的Strain 应变Stress 应力Tension 张力，拉力，拉紧Alloy 合金Aluminium 铝Ductile 易延展的，韧性的Failure 失败，破坏，失效Lateral 侧面的，横向的Necking 颈缩Couple 力偶Cylinder 圆筒，圆筒状物Inertia 惯性，惯量，惰性Shaft 轴，杆状物Torsion 扭矩Cantilever 悬臂梁，伸臂Neutral 中性的Statics 静力学，静止状态，静态Symmetry 对称Transverse 横向的，横断的Astronomer 天文学家Galaxy 天河，银河，星系Planet 行星Collinear 共线的，在同一直线上的Dimension 尺寸，大小，维数Equate 使相等，等同Parameter 参量，参数Visualize 想象，形象化，使看得见Acceleration 加速度Dynamics 动力学Stationary 不动的，稳定的，定常的Vector 矢量Velocity 速度Angular 角的，角度的Coordinate 坐标Radian 弧度Shaft 轴Symbol 符号Conservation 守恒，保存Differentiation 微分Integration 积分，集成，一体化Interval 间隔，间隙，空隙Linear 直线的，线性的，一次的Moment 力矩，瞬间，片刻Vector 矢量Velocity 速度Derivative 导数，派生的Frequency 频率Friction 摩擦Magnitude 大小，量级Power 力量，乘方，幂Viscous 黏性的Continuum 连续体，连续统Rectangular 矩形的，成直角的Resultant 合成的，合力，合量Torque 扭转力，扭矩Dilatation 膨胀，扩张Distortion 扭曲，变形Isotropic 各向同性的Tensor 张量Coordinate 坐标Crack 裂缝Curvature 曲率Ellipse 椭圆Formula 公式Function 函数，功能Buckle 屈曲，皱曲，弄弯，翘曲Deflection 挠曲，偏向Wrinkle 皱纹，皱褶，起皱Factor 因数，系数Flexural 弯曲的，挠曲的Notch 缺口，凹槽，刻痕Vibrate 振动（v）Vibration 振动（n）Detector 发现者，侦察器，探测器，检波器Vacuum 真空，空间，真空的，产生真空的Other than 除了二、句子：英译汉1、The concepts of stress and strain can be illustrated in an elementary way byconsidering the extension of a prismatic bar. As shown in Fig. 1, a prismatic bar is one that has constant cross section throughout its length and a straight axis. In this illustration the bar is assumed to be loaded at its ends by axial forces P that produce a uniform stretching, or tension, of the bar.翻译：应力和应变的概念可以通过考虑一个棱柱形杆的拉伸这样一个简单的方式来说明。

AP物理学实战练习题（2013年版）—— 电势潜能、电容性与相关基本微积分知识说明书

1µF6µF 5µF12Vdielectric-Q+Q +2Q (+r , 0)(-r , 0)(0, +r )OPart II. Free Response10.The electric potential diagram above shows equipotentials for a 2-dimensional region of space.a.At which point—A, B, C, D, or E—would an electron have the highest electric potentialenergy? Briefly explain your answer.b.In which general direction does the electric field point in this diagram? Briefly explain youranswer.c.Based on the equipotentials, draw a sketch on the diagram above of the electric field,including at least five field lines.d.At which point—A, B, C, D, or E—is the magnitude of the electric field the greatest? Brieflyjustify your answer.e. A proton is released from rest at point C. Qualitatively describe the proton’s subsequent:i.direction of motionii.speediii.accelerationf.For the proton in part e, calculate its velocity after having moved through a potentialdifference of 10 V.+q –q 0.01 m0.50 m0.50 m–q +qe Gauss’s Law to determine the magnitude of the electric field between the plates.c.Calculate the electric potential V between the two plates.d.Calculate the capacitance of this capacitor.AP Physics Practice Test: Potential, Capacitance κ=2.00A dielectric of is now inserted between the isolated plates while the same amount of charge Qremains on each plate.e.Calculate the new capacitance of the system with the dielectric between the plates.f.The electric field strength between the plates has (check one): ____ increased____ decreased____ remained the sameg.The electric potential between the plates has (check one): ____ increased____ decreased____ remained the sameh.The energy stored in the capacitor has (check one): ____ increased____ decreased____ remained the samei.How would your answers to f , g, and h change if the dielectric had been inserted while thevoltage supply was still connected to the capacitor? Explain.–Qba +Qc r +E –E c b ac.Calculate the magnitude of the difference in electric potential V between the two spheres.d.Calculate the capacitance of this conducting-sphere system.e.The spheres are discharged, and then connected to a source of electric potential of magnitude2V. Calculate how much Work must be done to fully charge the capacitor under these new conditions.-Q+Q +2Q (+r , 0) (-r , 0) (0, +r ) O9. The correct answer is a . The electric potential, or energy per unit charge, represents the amount ofenergy per unit charge it takes to move a test particle from infinitely far away to a given location. For apoint charge, the absolute potential is calculated using for each charge, and the electricpotential at a given location is simply the sum of the individual potentials for each charge in the vicinity:V =kQrV =V +Q +V +2Q +V −Q∑V =k (+Q )r +k (+2Q )r +k (−Q )r =2kQr. Field lines become more closely spaced there.The proton accelerates in the same direction of field, ie, towards upper left of diagram.The proton has a speed that increases over time; the electric field applies a force to it, causing it to accelerate.The proton’s acceleration increases as it moves into an area with an increasingly strong electricfield.This is a conservation of energy problem, with the field doing Work on the charge to increase its kinetic energy. Here, we can look at the change in electric potential energy and see how that converts to kinetic−Ki =12mv2−0=2(1.60e−19C)(10V)(1.67e−27kg)=4.38e4m/s– +– +–Q ba+Qcr +E –E c b aBecause only the magnitude of the potential was requested, is also acceptable.d. Using the definition of capacitance:Note that capacitance formula must use (b – a ) in denominator to produce positive result, because capacitance is always positive.e. Potential has doubled, and because Q = VC , the charge on the capacitor has doubled as well.kQ 1a −1b "#$%&'C =Q V =Q kQ 1a −1b #$&'=1k ab b −a "#$%&'U =12QV =122Q ()2kQ ab b −a "#$%&'=2kQ 2ab b −a "#$%&'。

2015国际青年物理学家锦标赛(IYPT)赛题翻译

Problems for the 28th IYPT 20151. PackingThe fraction of space occupied by granular particles depends on their shape. Pour non-spherical particles such as rice, matches, or M&M’s candies into a box. How do characteristics like coordination number, orientational order, or the random close packing fraction depend on the relevant parameters?1.堆积(Packing)被颗粒状物体(particles)占据的小部分空间取决于它们的形状。

将例如米、火柴或M&M糖果的非球状物体倾倒进一个盒子里，相关参量如何影响配位数(coordination number)、秩序性排列(orientational order)和随机紧密堆积分数(random close packing fraction)这样的特征？2. Plume of SmokeIf a burning candle is covered by a transparent glass, the flame extinguishes and a steady upward stream of smoke is produced. Investigate the plume of smoke at various magnifications.2.羽状的烟/烟羽(Plume of smoke)如果一支燃烧着的蜡烛被一块透明玻璃板覆盖，火焰会熄灭，并且产生一缕稳定的向上流动的轻烟。

研究在各种放大倍数下的羽状的烟。

选择性必修一Unit4ExploringPoetry夯基-新高考英语一轮复习教材为本夯基提能(译林版

选择性必修一Unit 4 Exploring Poetry 夯基全部单词过一遍和部分单词变一变重要短语览一览1.breathe vitality into给……注入活力2.break with sth.与某事终止关联，破除拓展：break into强行闯入break into tears/laughter突然大哭/笑起来break up分裂；解体；打碎break down使分解；出故障；垮掉；失败break off折断；中断break out爆发break through突破break away from逃脱，脱离3.be fascinated by被……迷住，被……深深吸引4.be inseparable from与……密不可分5.be recognized as被认为……6.be representative of是……的代表，是……的典型7.be rooted in根源在于；植根于e back to 回到……；返回……9.contribute to导致，促成，有助于10.dig up发现，搜集，查明11.distinguish ... from ...把……与……区分开拓展：tell...from把……与……区分开make a distinction between...and...把……与……区分开12.f13.find out 找出，查明；发现14.hold fast to dreams/ideals坚持梦想/理想15.make allowance for体谅，考虑到，估计到16.put together把……放在一起，组合，组装17.set...aside把……放一边18.s19.beyond one’s grasp无法理解20.in the end终于，最后核心词汇讲一讲核心词汇-【教材原句】Hold fast to dreamsFor when dreams goLife is a barren fieldFrozen with snow.(P43)【考点归纳】①词性/形变化frozen adj.结冰的，冰封的；冷冻的；冻僵的→freeze v.(使)冻结；冰冻→freezing adj.冰冻的；极冷的，冷冻机，冷冻柜②相关短语freeze(be frozen)with/in terror/horror/fright/fear吓呆freeze(be frozen)with/in shock惊呆freeze to death冻死freeze one’s blood=make one’s blood freeze使人恐怖万分；令人毛骨悚然freeze over(表面)封冻，结冰freeze up冻结，使……结冰freeze one’s blood/make one’s blood freeze使人恐怖万分；令人毛骨悚然【语境运用】用该词条恰当的形式填空①On such ________ weather, all the rivers were ________ and even fresh snow ________ instantly, whichmade it rather difficult for us to move about.【答案】freezing, frozen, froze【解析】第一空作定语修饰weather，表示“极冷的”，故填形容词freezing；第二空作表语，表示“结冰的”，故填形容词frozen；第三空作谓语表示“冻结”，由句中的were和made可知，空处应用一般过去时；句意：在这样一个极冷的天气里，所有河流都结冰了，甚至连新雪都瞬间结冰，这让我们很难四处走动。

n维球sphereVolume

Volume of the n-sphereJason D.M.Rennie*****************November22,2005AbstractWe derive the volume of an n-sphere,using argumentation given by Weisstein[3].We use the geometers’nomenclature for n-sphere,n referring to the number of the underlying dimension[3].Let V n(R)be the volume of an n-sphere of radius R.Let S n be the surface area of the unit n-sphere.Consider a small patch of area on the surface of the unit n-sphere.We can approximate such a patch with an(n−1)-cube;let the cube have edge-length l.Then,the cube’s “area”is l n−1.Now,consider the same patch projected onto the n-sphere of radius R.It’s“area”is now(lR)n−1,or R n−1times the area of the cube on the unit n-sphere.Thus,the surface area of an n-sphere of radius R is S n R n−;the volume of an n-sphere of radius R isV n(R)= R0S n r n−1dr=S n R nZ= ∞−∞exp(−x2)dx.Also,note that the Gamma function[2] can be written in a form similar to the Polar coordinate version,Γ(n)=2 ∞0exp(−r2)r2n−1dr.(3) Thus,2Z=S nΓ(n/2)=2Γ(1/2)n=2πn/2.Solving for S n,we get2πn/2S n=For integer n,we can writeΓ(n/2)=(n−2)!!√2(n−1)/2,where n!!is a double factorial[1].For even n,this simpliﬁes toΓ(n/2)=(n/2−1)!.Thus,the volume of a radius R n-sphere isV n(R)= 2(n+1)/2π(n−1)/2R nn(n/2−1)!for n even.(5)References[1]E.W.Weisstein.Double factorial./DoubleFactorial.html.From MathWorld–A Wolfram Web Resource.[2]E.W.Weisstein.Gamma function./GammaFunction.html.From MathWorld–A Wolfram Web Resource.[3]E.W.Weisstein.Hypersphere./Hypersphere.html.From MathWorld–A Wolfram Web Resource.2。

Exact solution of the one-dimensional ballistic aggregation

a r X i v :c o n d -m a t /9808077v 1 7 A u g 1998Exact solution of the one-dimensional ballistic aggregationL.FrachebourgInstitut de Physique Th´e orique Ecole Polytechnique F´e d´e rale de LausanneCH-1015Lausanne,SwitzerlandAbstractAn exact expression for the mass distribution ρ(M,t )of the ballistic ag-gregation model in one dimension is derived in the long time regime.It is shown that it obeys scaling ρ(M,t )=t −4/3F (M/t 2/3)with a scaling function F (z )∼z −1/2for z ≪1and F (z )∼exp(−z 3/12)for z ≫1.Relevance of these results to Burgers turbulence is discussed.Ballistic aggregation provides a simple model of nonequilibrium statistical physics which is a natural version of a dissipative gas of hard spheres where particles follow the basic laws of mechanics.It consists in a one-dimensional gas of point-like massive particles which move freely until they collide.The perfectly inelastic collision of two masses conserves the total mass and momentum,while dissipation occurs as kinetic energy is loss in each collision.One can anticipate the formation of more and more massive while slower and slower aggregates.This model was introduced by Carnevale,Pomeau and Young [1]where they conjectured,based on scaling arguments and numerical simulations,an asymptotic scaling regime for the mass distribution ρ(M,t )=F (M/ M t )/ M 2t .The average mass per aggregate was supposed to grow algebraically with time as M t ∼t 2/3and the scaling function had a simple universal exponential form F (z )=exp(−z )independent of the initial ter,this conjecture was reinforced by Piasecki [2]where he solved the hierarchy of dynamicalequations governing the system inside a mean-ﬁeld approximation scheme.This system,in its continuous limit,was also studied as a simpliﬁed astronomical model for the agglomeration of cosmic dust into macroscopic objects[3].In the ballistic aggregation model,the aggregates interact only through their collisions.An aggregation model where gravitational interactions are present has been studied in[4].It is important to mention the connection between this model and some solutions of the Burgers equation.At very high Reynolds number,the asymptotic solution of the Burgers equation consists of a train of shock waves.The laws of motion which govern the dynamics of these shock waves are found to be equivalent to a ballistic aggregation system(see[5]).In this letter,I verify the scaling hypothesis for the mass distribution andﬁnd in an exact calculation an explicit form for the scaling function.It happens to be diﬀerent from the conjectured simple exponential.Rather than solving the set of partial diﬀerential equations governing the evolution of the system,I exploit the fact that,once the initial state of the system is given,the dynamics is completely deterministic.Our approach will thus be based on a statistical study of the initial conditions and is largely inspired by the work of Martin and Piasecki[6].Initially,particles having all the same mass m are regularly placed on a line with the same inter-particle distance a.Initial mass density is thusρ0=m/a.The initial momentum of the thermalized particles are not correlated and are distributed according to the same Gaussian distributionφ(p)=can be determined from the initial state.I label the location of the CM at time t of the r particles located initially at(j+1)a,(j+2)a,...,(j+r)a byX r j+1(t):=12a+tt1/3ρm′(M′,P′)(3) with M′=M/t2/3,P′=P/t1/3and m′=m/t2/3.Note that,due to translational invariance, the mass distribution does not depend on X.Owing to the uncorrelated initial Gaussian distribution of the momentum,one can com-pute the densityρusing an analogy with a Brownian motion in the momentum space under particular constraints[6,7],(see Fig.(1)).Oneﬁndsρm′(M′,P′)=J m′ −M′−P′M′ (4) where J m′(Z)is the probability for a Brownian motion P(τ)to start from P(0)=0and pass above the discrete points P(rm′)>Zrm′−(rm′)2(r≥1),and I m′(M′,P′)is the probability for a Brownian motion to start at P(0)=0,end at P(M′)=P′and over-passing the discrete points P(rm′)>(M′+P′/M′)rm′−(rm′)2(1≥r≥n).FIGURESFIG.1.The Brownian motion used in the construction of our solution.I will derive below an expression for the mass distribution in the limit m′=m/t2/3→0 which is reached either when t→∞for aﬁxed m(asymptotic long time limit)or for any ﬁxed time t when m→0(continuous limit).In this limit,one keeps M′and P′of order O(1).In terms of the Brownian motion introduced above,the space m′between the discrete points barrier shrinks to zero and approaches a continuous barrier which makes the problem tractable analytically.Nevertheless,the functions I and J are identically null for m′=0. One should thus keeps track of theﬁrst space m′(the Brownian motion will be unrestricted up to theﬁrst point of the barrier)and willﬁnd a mass distribution which is an expansion in power of m′.From now on,I drop the subscript′and setρ0=1/2without loss of generality.Oneﬁnds the dominant contribution in m:¯Im(M,P)=e−P2πe−P2∂P1∂P2K M(m,P1,M−m,P2) P1=P2=0+O(m2)(5)and¯Jm(Y)= ∞Y m−m2dP1φ(P1)lim N→∞ ∞Y Nm−(Nm)2dP2K Y(P1,m,P2,Nm) = πlim N→∞ ∞Y Nm−(Nm)2dP2∂2(Q1f′(τ1)−Q2f′(τ2)−1∂τ2−∂22f′′(τ2) G(Q1,τ1,Q2,τ2)=0(8)with G(Q1,τ,Q2,τ)=δ(Q1−Q2)and G(0,τ1,Q2,τ2)=G(Q1,τ1,0,τ2)=0.In our problem f′′(τ)=2.The equation(8)can be solved(see[7]for details)and oneﬁndsG(Q1,τ1,Q2,τ2)= k≥1e−ωk(τ2−τ1)Ai(Q1−ωk)Ai(Q2−ωk)πe−M3/12I(M)+O(m2)(10) withI(M)= k≥1e−ωk M.(11) In the same way,I use Eqs.(6,7,9)and obtain¯Jm(Y)= πlim M→∞e(Y/2−M)3/3−(Y/2)3/3 ∞0dx e−x(Y/2−M) k≥1e−ωk M Ai(x−ωk)Using the integral representation of the sum in(12)[9],k≥1e−ωk M Ai(x−ωk)Ai(z)(13) with c>−ω1,one can exchange the integration andﬁnd after a tedious analytical calculation[7]¯Jm(Y)= πe−(Y/2)3/3J(Y)+O(m3/2)(14) withJ(Y)=1Ai(z)(15) where c>−ω1.Now,inserting the expression for I and J in Eq.(4),one has in the original variablesρ(M,P;t)=m2t2/3 J−M M J −M M +≀ m2P2 t∼t1/3,E(t)∼t−2/3.(17)A careful integration over P[7]leads to the mass distribution,which is the main result of this letter,ρ(M,t)=1t2/3 +≀m2π2M′I(M′)H(M′)(19)whereI(M′)= k≥1e−ωk M′,H(M′)=1Ai2(z)(20)with c >−ω1.The scaling function F (M ′)is plotted on Fig.2.0.0 1.02.03.04.0M/t2/30.000.050.100.150.20t 4/3ρ(M /t 2/3)FIG.2.The rescaled mass distribution t 4/3ρ(M,t )as a function of M/t 2/3.One can compare the obtained scaling function with the conjectured one (F conj .(M ′)=exp(−M ′))[1].In particular small and large arguments present strong diﬀerences.Indeed,for M ′≪1,one get H (M ′)=1+O (M ′)while one can estimate I (M ′)using the asymptotic properties of the zeroes of the Airy function ωk =[(3πk )/2]2/3+O (k −1/3)and ﬁnd I (M ′)∼(2√π5/21M′+O (√of small masses M <M 0≪t 2/3at time t is well underestimated by the conjectured formwhich leads to N (M 0,t )∼M 0/t ,while the exact solution gives N (M 0,t )∼√πM ′3/2exp(−M ′3/12).On the other end,one has I (M ′)∼exp(−ω1z )andﬁnallyF (M ′)=2M 1−P 2M 1−P 2M ′1−M ′1I m ′(M ′1,P ′1)I m ′(M ′2,P ′2)J m ′P ′2tπ3FM 1t 2/3(24)withF (M ′1,M ′2)=(M ′1+M ′2)M ′1M ′2I (M ′1)I (M ′2)H (M ′1+M ′2)(25)and I and H as above.This collision frequency clearly does not factorize in a product of functions of M 1and M 2,respectively.This fact invalidates the assumption on which the mass distribution was computed in[2].One can inquire about the universality of these results with respect to other initial conditions.Let usﬁrst consider a Poissonian distribution of the particles initial positions with an average interparticle distance a.The discrete points over which the Brownian motion should pass in the construction of our solution are still distributed on the same parabola but with irregular spacing.In the long time limit and after rescaling,the spacing between points of average a′=a/t2/3become smaller and smaller up to be,inﬁrst order in m′, a continuum.The diﬀerence between irregular and regular spacing is thus asymptotically erased and the result Eq.(18)should be recovered in this case.A bimodal momentum distributionφ(p)=(δ(p−p0)+δ(p+p0))/2is used in the initial state in[1].I believe that this should not aﬀect the form of the mass distribution(18)as the random walk initiated by this distribution is well approximated,in the long time limit, by the considered Brownian motion.One can deﬁne a distribution where momentum are initially correlated.In this case,one expects the scaling function to be diﬀerent,at least for small M′[12].In summary,I found an exact asymptotic solution for the mass distribution of the ballistic aggregation in one dimension.Such an exact solution is not frequent in a nonequilibrium system and has permitted to verify scaling hypothesis for this system.While the average mass per aggregate was proved to behave with time as M t∼t2/3for t≫1,as expected from previous studies,the scaling function is shown here to be diﬀerent from the conjectured one.This distribution also solve the shock strength distribution of the one dimensional Burgers equation in the inviscid limit with a white noise initial condition.I gratefully acknowledge numerous useful discussions with P.Martin and J.Piasecki and ﬁnancial support from the Swiss National Foundation.REFERENCES[1]G.F.Carnevale,Y.Pomeau and W.R.Young,Phys.Rev.Lett.64,2913(1990).[2]J.Piasecki,Physica A190,90(1992).[3]S.F.Shandarin and Ya.B.Zeldovich,Rev.Mod.Phys.61,185(1989).[4]P.A.Martin and J.Piasecki,J.Stat.Phys.84,837(1996).[5]J.M.Burgers,The nonlinear diﬀusion equation,Reidel,Dordrecht(1974).[6]P.A.Martin and J.Piasecki,J.Stat.Phys.76,447(1994).[7]L.Frachebourg,P.A.Martin and J.Piasecki,in preparation.[8]M.Abramowitz and I.A.Stegun,Handbook of Mathematical Functions,Dover,New-York(1965).[9]P.Groeneboom,Probab.Th.Rel.Fields81,79(1989).[10]M.Avellaneda and W.E,Comm.Math.Phys.172,13(1995);M.Avellaneda,Comm.Math.Phys.169,45(1995).[11]S.Kida,J.Fluid Mech.93,337(1979).[12]Ya.G.Sinai,Comm.Math.Phys.148,601(1992);Z.-S.She,E.Aurell and U.Frisch,Comm.Math.Phys.148,623(1992).11。

数学专业英语第2章课后答案

2.12.比:ratio 比例:proportion 利率:interest rate 速率:speed 除:divide 除法:division 商:quotient 同类量:like quantity 项:term 线段:line segment 角:angle 长度:length 宽:width高度:height 维数:dimension 单位:unit 分数:fraction 百分数:percentage3.(1)一条线段和一个角的比没有意义,他们不是相同类型的量.(2)比较式通过说明一个量是另一个量的多少倍做出的,并且这两个量必须依据相同的单位.(5)为了解一个方程,我们必须移项,直到未知项独自处在方程的一边,这样就可以使它等于另一边的某量.4.(1)Measuring the length of a desk, is actually comparing the length of the desk to that of a ruler.(3)Ratio is different from the measurement, it has no units. The ratio of the length and the width of the same book does not vary when the measurement unit changes.(5)60 percent of students in a school are female students, which mean that 60 students out of every 100 students are female students.2.22.初等几何:elementary geometry 三角学:trigonometry 余弦定理:Law of cosines 勾股定理/毕达哥拉斯定理:Gou-Gu theorem/Pythagoras theorem 角:angle 锐角:acute angle 直角:right angle 同终边的角:conterminal angles 仰角:angle of elevation 俯角:angle of depression 全等:congruence 夹角:included angle 三角形:triangle 三角函数:trigonometric function直角边:leg 斜边:hypotenuse 对边:opposite side 临边:adjacent side 始边:initial side 解三角形:solve a triangle 互相依赖:mutually dependent 表示成:be denoted as 定义为:be defined as3.(1)Trigonometric function of the acute angle shows the mutually dependent relations between each sides and acute angle of the right triangle.(3)If two sides and the included angle of an oblique triangle areknown, then the unknown sides and angles can be found by using the law of cosines.(5)Knowing the length of two sides and the measure of the included angle can determine the shape and size of the triangle. In other words, the two triangles made by these data are congruent.4.(1)如果一个角的顶点在一个笛卡尔坐标系的原点并且它的始边沿着x轴正方向，这个角被称为处于标准位置.(3)仰角和俯角是以一条以水平线为参考位置来测量的,如果正被观测的物体在观测者的上方,那么由水平线和视线所形成的角叫做仰角.如果正被观测的物体在观测者的下方,那么由水平线和视线所形成的的角叫做俯角.(5)如果我们知道一个三角形的两条边的长度和对着其中一条边的角度,我们如何解这个三角形呢?这个问题有一点困难来回答,因为所给的信息可能确定两个三角形,一个三角形或者一个也确定不了.2.32.素数:prime 合数:composite 质因数:prime factor/prime divisor 公倍数:common multiple 正素因子: positive prime divisor 除法算式:division equation 最大公因数:greatest common divisor(G.C.D) 最小公倍数: lowest common multiple(L.C.M) 整除:divide by 整除性:divisibility 过程:process 证明:proof 分类:classification 剩余:remainder辗转相除法:Euclidean algorithm 有限集:finite set 无限的:infinitely 可数的countable 终止:terminate 与矛盾:contrary to3.(1)We need to study by which integers an integer is divisible, that is , what factor it has. Specially, it is sometime required that an integer is expressed as the product of its prime factors.(3)The number 1 is neither a prime nor a composite number;A composite number in addition to being divisible by 1 and itself, can also be divisible by some prime number.(5)The number of the primes bounded above by any given finite integer N can be found by using the method of the sieve Eratosthenes.4.(1)数论中一个重要的问题是哥德巴赫猜想,它是关于偶数作为两个奇素数和的表示.(3)一个数,形如2p-1的素数被称为梅森素数.求出5个这样的数.(5)任意给定的整数m和素数p,p的仅有的正因子是p和1,因此仅有的可能的p和m的正公因子是p和1.因此,我们有结论:如果p是一个素数,m是任意整数,那么p整除m,要么(p,m)=1.2.42.集:set 子集:subset 真子集:proper subset 全集:universe 补集:complement 抽象集:abstract set 并集:union 交集:intersection 元素:element/member 组成:comprise/constitute包含:contain 术语:terminology 概念:concept 上有界:bounded above 上界:upper bound 最小的上界:least upper bound 完备性公理:completeness axiom3.(1)Set theory has become one of the common theoretical foundation and the important tools in many branches of mathematics.(3)Set S itself is the improper subset of S; if set T is a subset of S but not S, then T is called a proper subset of S.(5)The subset T of set S can often be denoted by {x}, that is, T consists of those elements x for which P(x) holds.(7)This example makes the following question become clear, that is, why may two straight lines in the space neither intersect nor parallel.4.(1)设N是所有自然数的集合,如果S是所有偶数的集合,那么它在N中的补集是所有奇数的集合.(3)一个非空集合S称为由上界的,如果存在一个数c具有属性:x<=c对于所有S中的x.这样一个数字c被称为S的上界.(5)从任意两个对象x和y，我们可以形成序列（x，y），它被称为一个有序对，除非x=y，否则它当然不同于（y，x）.如果S和T是任意集合，我们用S*T表示所有有序对（x,y),其中x术语S，y属于T.在R.笛卡尔展示了如何通过实轴和它自己的笛卡尔积来描述平面的点之后，集合S*T被称为S和T的笛卡尔积.2.52.竖直线:vertical line 水平线:horizontal line 数对:pairs of numbers 有序对:ordered pairs 纵坐标:ordinate 横坐标:abscissas 一一对应:one-to-one 对应点:corresponding points圆锥曲线:conic sections 非空图形:non vacuous graph 直立圆锥:right circular cone 定值角:constant angle 母线:generating line 双曲线:hyperbola 抛物线:parabola 椭圆:ellipse退化的:degenerate 非退化的:nondegenerate任意的:arbitrarily 相容的:consistent 在几何上:geometrically 二次方程:quadratic equation 判别式:discriminant 行列式:determinant3.(1)In the planar rectangular coordinate system, one can set up aone-to-one correspondence between points and ordered pairs of numbers and also a one-to-one correspondence between conic sections and quadratic equation.(3)The symbol can be used to denote the set of ordered pairs（x，y）such that the ordinate is equal to the cube of the abscissa.（5）According to the values of the discriminate，the non-degenerate graph of Equation （iii） maybe known to be a parabola， a hyperbolaor an ellipse.4.（1）在例1，我们既用了图形，也用了代数的代入法解一个方程组（其中一个方程式二次的，另一个是线性的）。

A Volume Product Representation and its Ramifications in lp,

A VOLUME PRODUCT REPRESENTATION AND ITSRAMIFICATIONS IN p l np ≤1,∞≤D.KARAYANNAKISp < ∞, is the volume of the unit p -ball in n R and q the Hölder conjugate exponent of p , we represent the product n p B nqB as a suitable function free of its gamma symbolism; this representation will allows us to confirm by use of basicclassical analysis tools, for the particular case ,1,∞≤≤=p B K np two conjectured and/or proved lower and upper bounds for the volume product of centrally symmetric convex bodies of the Euclidean n R that play a central role in convex geometric analysis.Part I: Notation, goals and main strategyOne of the key notions in convex analysis is the volume product )(K M = o K K where K is a (centrally symmetric) convex compact set of the Euclidean ()..,,n R with non-empty interior (or simply “body”) and }},1,:{K x y x R y K n o ∈∀≤∈=is the so- called polar set of KFor this product, one of the long standing conjectures stated by Mahler (who proved it forn 2=) , claims that )(!4K M n n≤for origin symmetric bodies K . This conjecture has beenconfirmed in many special cases of K and in particular for bodies symmetric with respect to the coordinate planes, which naturally include the p -balls, using advanced Banach spacetheory. On the other hand, for an upper bound, we have the inequality ≤)(K M )(2nB M proved in 1948 by Santaló (and much earlier for 2=n by Blashke). A survey of the above facts and other related results can be found e.g. in [4 ].We set forward in this short work to establish Mahler’s conjecture and the Blashke-Santaló inequality for the case ,1,∞≤≤=p B K np by using only basic special functions and classical analysis theory .It is clear that ,)(nq o n p B B =where 111=+qp , and also directly verifiable through multipleintegration(see e.g. [4] and [1]) that n p B = )1()11(2pn p nn +Γ+Γfor 1<p < ∞ and n B 1=n nB 2=∞.So we should be able to manipulate the expression )(np B M =)1()1()]11(11([4qn p n qp n n+Γ+Γ+Γ+Γ. (1)Mathemetics Subject Classification (2000): 33B15Thus, in Part II, we start with a suitable for our goals gamma functions ratio result (LemmaII.1) that will allow us to represent )(np B M as a suitable function ),,(p n M for 1<p < ∞, free of its gamma symbolism(Prop. II.1); in Part III, by establishing0),(≥dpp n dM for 1<2≤p (Lemma.III.1) and then using the evident facts that ),(),(q n M p n M = and1<2≤q iff ∞<≤p 2, and also by examining separately the case p =1, we will obtain the announced results (Prop.III.1).We also obtain, as byproducts of independent interest, two seemingly new closed formulae concerning infinite products(Corol.III.1 & Corol.III.2).Part II: A Lemma and a PropositionLemma II.1For 0>x and 1<a we have that ∏∞=−++−−+=Γ+Γ−Γ1)1)(()1()()()1(k a x k a k x k k x a x a . Proof :Let ),(a x P the above infinite product .One of the various classical definitions for thegamma function is =Γ)(z 1!lim()z k kk k z −→∞ , for any complex ,...2,1,0−−≠z , where by k z )(we have denoted the shifted factorial )1)....(1(−++k z z z .Substituting in the above limit respectively ,,1a x z a z +=−=and x z = and after simplifying we arrive atlimk →∞k k ka x a x k )()1()(!+− which is identical to ),(a x P .⁪Remark II.1(i)Independently of the above argumentation we can easily check that ),(a x P exists as a two-variable function over )1,0[),0(×∞ since evidently ≤0),(a x P and, by use of the inequality0,1log >−≤t t t , ∞<−++−−+≤∑∞=1)1)((1)1(),(log k a x k a k a x a a x P .(ii)Lemma II.1 was proved (formally and from “scratch”) in [3 ] where the scheme of the proof served different purposes concerning the numerical evaluation of the gamma and psi function).Proposition II. 1For ,1∞<<p =),(p n M )()1()1()(4221222222pqn nk k k pq k k p h k n n n n +++++∏∞=−−− (2) where )(p h =sin(ppq ππ.Proof :Evidently 1)1(=+h and so (2) is trivially true for 1=n .Thus we can consider .2≥nAt first let us rewrite (1) as ),(p n M =24n )]1()1([11qp n n ΓΓ−.2Based on Lemma II.1 for p a 1=and 1,...,,1,−==n m pmx we see that ∏−=−−ΓΓ=Γ1111,()1()1((n m n pp m n P qp p n (3) where ),(a x P was defined above in Lemma II.1.Working in a similar way we obtain theconjugate expression for (qnΓWe observe now that)1,(p p m n P −),1(),()()1()1(11,(122p m n r p m n r p g k m n m n pq q q m n P k k k k −+−+−+−=−∏∞= (4) where we have set pqj jk k p j r k 22),(++= and =)(p g k ),1(p r k . Combining (1), (3), and (4), and after “telescoping” inside the infinite product, we obtain the announced result.⁪Part III: One more Lemma and a conclusive PropositionLemma III.1Let 1<2≤p .Then0),(≥dpp n dM for all n with equality iff 2=p for 1≠n . Proof:n p M 4),1(=and so once more we can consider .2≥n By straightforward differentiation with respect to p and in the case of the infinite product of (2) by logarithmic differentiation (noticing that this product by construction is a real analytic function of p having as logarithm a uniformly converging series of differentiable functions of p ) we obtainsgn[]),(sgn[=dpp n dM )]2(1()22(21k k k r n g n h pq h n +−′+′−∑∞=. (5)In (5) )(p h h =as defined in (2) and ),(),(p n r r p g g k k k k ==as defined in (4); still for simplicity from now on we suppress any possible dependence from p and .nSince evidently the infinite sum in (5) and h are positive and 0)1()2()(2≤−−=′p p p pq (withequality iff 2=p ) it will suffice to show that 0≥′h (with equality iff 2=p ).Simple calculations show that sgn =′h -sgn ])sin([′ppq π=sgn )(ω, wherecos()1(sin()2()(pp pp p p πππωω−+−== (6)Now sgn =′)(ω sgn 0)]cos()22(sin()1([2<−++−pp p p p πππ , (7)and since 0)2(=ω we conclude that 0≥ω with equality iff 2=p .⁪We are now ready to prove the announced double inequality concerning ).,(p n MProposition III.1For ∞≤≤p 1and all positive integers ,n ),2,(),(!4n M p n M n n≤≤ with left (resp. right)equality iff 1=p (resp. ),2=p whenever .1≠nProof:Based on Lemma III.1 we can see immediately that for ∞<<<p t 1, <),(t n M ),2,(),(n M p n M ≤with equality iff .2=pWe only need to examine (2) whenever +→1p .It is clear that n n s n M 4)1,(=+, with)()1(11n k k k s k nn n ++=∏∞=−.Since 11=s and noticing that 111)(1(11+=++++=∏∞=+n n k n k k k s s k n n we see that !1n s n =and we are done.⁪Remark III.1Independently of the above approach one can easily verify that n s converges for all ,n by the logarithmic series test along the lines of Remark II.1(i): evidently 0>n s and also for 2≥n (by the crudest logarithmic inequality) log n n s σ<−,where 21().(1)n mnn n mnm k k k σ−∞===<∞+∑∑Thus we obtain the (crude but not obvious) inequality 1!n e n σ−<for 2.n ≥We conclude this work with two closed type formulae that are automatically true when we set2p = in (2).Exploiting the fact that (,2)M n =2n B 2224()2n n n π=Γ and the classical value of ()2nΓfor even and odd n (see e.g.[2]) we arrive, respectively, for m N ∈ at the following:Corollary III.11222114()(21)(22)(22)!m m m k k k m k m π−−∞−=++=+∏ .Corollary III.2121218()(21)(223).(22)(23)!!m m mk k k m k m π+−∞=+++=++∏Remark III.2It is clear that the above two formulae provide us in closed form the value of the seeminglyuntabulated infinite product 1(22)(22)(21)(223)k k k m k k m ∞=+++++∏.REFERENCES[1] G.Andrews, R.Askey &R.Roy, Special Functions,1999, Cambridge University Press[2] I.Gradshteyn & I.Ryzhik ( editor Alan Jeffrey), Tables of Integrals, Series and Products, 1980, Academic Press.[3] D.Karayannakis, An algorithm for the evaluation of the Gamma function and ramifications, ArXiv:07120292v1[math.CA] Nov.2007.[4] L.E.Lutwak, Selected affine isoperimetric inequalities, Handbook of Convex Geometry, 1993, North-Holland, Amsterdam.DEPARTMENT OF SCIENCES ,TEI OF CRETE, 71004 HERAKLION, GREECEE-mail address: dkar@stef.teiher.gr。

模具术语中英文对照Mold

模具术语中英文对照Mold第一篇：模具术语中英文对照Mold模具专业术语中英文对照模具Mold模胚Mold Base 分模线Parting Base 母模线PartingLine 公模侧Core Side嵌板Mold Plate 嵌件Insert 滑块板Slider滑块板固定板Wear Plate 定位机构Inter Lock 吊圈Eye Bolt 日期转印Date Mark 前模Cavity 后模Core 型心Core Pin 出模编号Cavity Number 冷却管Cooling Channel 水嘴Hose Nipple 注塑Injection 树脂Resin 材料Material 等级/类型Grade 干燥Dry干燥不足Not Dried Enough 收缩率Shrinkage 充填Full Shot 比重Density斜针组装板第二固定板顶针板方铁定位圈导柱撑顶定位杆小拉杆导柱套水口针斜导柱锁定块回针垃圾针顶出板导柱弹簧支撑柱顶针板顶针顶块顶出顶板顶出司筒顶出中心针机嘴套直流道流道支流道Angular Ejector Back PlateRunner Stripper Plate Ejector Plate Spacer Block Locating Ring Guide Pin Support Pin Stop Bolt Pull Bolt Guide Bush Runner Lock Pin Angular Pin Heal Block Return Pin Stop Ring Ejector GuideCoil Spring Support Pillar Ejector Pin Blade Ejector Block Ejector Plate Ejector Sleeve Ejector Center Pin Spure Bush Sprue Runner Drop 冷却棒加热管O形圈逃气孔销针铣床加工放电加工线切割加工磨床加工孔位加工细加工省模加工配模塞规铜公筋骨加工脱模斜度倒扣钢材咬花雕刻加工电镀加工热处理氮化处理表面处理内六角螺钉热流道热流道结构热嘴Baffle Heat Pipe O RingAir Vent Dowel PinMilling MachiningEDM Machining Wire Cutting Grinding Drilling Deburring PolishingFitting ShimEDM Master Rib MachiningDraft Angle Under Cut Steel Texture Engraving Electro Plating Hardening Nitrding Surface Hardness Allen Bolt Hot Runner Manifold Hot Tip 调温机热可塑性热硬化性银条状喷流痕侠水纹披峰缩水烧焦充填不良光泽不良气泡难型不良弯曲变形光泽不均难物不良打痕顶白谬丝拉伤油污点裂化倒塌分模定位锁水口点水口侧水口潜伏水口Temp Cont Unit Thermo Plastis Thermo Set Silver Line Flow Mark Weld Line Burr Sink mark Burn Mark Short ShotGloss Not Enough Bloe Hole Sticking BendingWarpageUneven Gloss Black Spot Damage White Mark Hair Flash Scrtach Oil Dirt Crack DeformParting Lock Gate Pin Gate Side GateSubmarine Gate第二篇：模具常用术语中英文对照“Fudakin InsdustrialCo.,Ltd”模具常用术语中英文对照模芯Parting Core局部视图 Partial View 冷料# Cold Slag 线切割 WireE.D.M 轮廊Contour 螺纹孔 Tapping Hole 连接件 Fittings 斜针Angle Pin接合 Engage替换镶件Interchangeable MoldInserts 指定吨位的注塑机Specific Press水嘴接头Water Fittings 螺纹Eyebolt Thread 回针Stop Pin二级顶出针 Sub-Leaderd Pin 镶件 Mold Insert 加硬Harden唧嘴 Sprue 设计筒图 Design Preliminary 名称块表 Title Block 版本标识 Revision Level 材料清单 Stock List 制模 Build Mold 手动滑块 Hand Slide 漏水测试 Leak Test 流道排气Runner Vents抛光 Draw Polish 侧抽芯 Side Action 加强筋 Reinforcing 三角撑 Gusset 柱子 Bossed 出模斜度 Draft 外廊Contour落单会议Kick-Off Meeting 装卸孔HandlingHole 运输安全带Moldstrap 码模槽 Clamp Slot撑头 Support Pillar螺牙1/2-13 Eye Bolt 1/2-13Tap 导柱位 Leader Pin Location耐落胶 T eflon Paste 偏移量 Offset 水塞 Water Line Plug 撬模脚Ppy Slot 重新加工Reworked 配件Components 补偿Compensation平面度 Parallel倒角 Chamfer 模胚Mold Base热嘴 Hotnozzle 火花机 Edm 熔接线 Weildline 压机 Press 晒纹Texturing 梯形 Trapezoid 凸缘、法兰 Flange 方铁Spacer Block 顶针板Ejector Plate顶针底板Ejector RetainerPlate 垫板Retainer Plate 后模镶针Core Pin 拉圾钉Stop Pin有托顶针Shoulder Ejector Pin 顶针板导套Guided Ejection Bushing 针板导柱 Guided Ejection Leader Pin 唧嘴Sprue Bushing 三板模延伸式唧嘴Extension Nozzle Bushing 水口板导套Runner Stripper Plate Bushing 定位圈（法兰）Locating Ring 管钉（定位销）Dowel Pin 管状管钉Tubular Dowel 吊环Safety Hoist Ring 日期印Dating Insert环保印Recycling Insert气顶Air Poppet Valve截水口镶件 Runner Shut-Off Insert 早回Early Ejector Return加速项Accelerated Ejector 客户Client产品名Part Name 产品编号 Part No 缩水 Shrinkage 版本 Rev 模胚 Mold Base 下模镶件 Core Block 上模镶件Cavity Block小镶件 Sub-Insert下模小镶件 Core Sub-Insert 上模小镶件 Cavity Sub-Insert 行位Slide行位镶件SlideInsert压条 Gib压紧块（铲机）Jaw 硬片（摩擦片）Wear Plate 水口铁Runner Bar上模水口铁 Upper Runner Bar 下模水口铁 Lower Runner Bar 弹簧Spring 水口勾针Sprue Puller Pin 顶针Ejector Pin 撑头Support Pillar 直身锁 Side Lock 斜度锁 Interlock 锁模板Safety Bar‘O’令（密封圈）O'Ring喉塞 Plug隔水片 Baffle波子螺丝（行位定位螺丝）Ball-Catch 斜顶Lifter 控制开关Switch回针Return Pin 斜导柱Angle Pin推板Stripper Plate A’板A'Plate B’板B'Plate方铁（垫铁）Spacer Block 顶针板Ejector Plate顶针底板 Ejector Retainer Plate 垫板Retainer Plate 垃圾钉StopPin有托顶针Shoulder Ejector Pin 顶针板导套Guided Ejection Bushing 针板导柱 Guided Ejection Leader Pin唧嘴Sprue Bushing三板模延伸式唧嘴Extension Nozzle Bushing 水口板导套Runner Stripper Plate Bushing 定位圈（法兰）Locating Ring 管钉（定位销）Dowel Pin 管状管钉Tubular Dowel 吊环Safety Hoist Ring 日期印Dating Insert 环保印Recycling Insert 气顶Air Poppet Valve 截水口镶件 Runner Shut-Off Insert 早回Early Ejector Return 加速顶Accelerated Ejector 扁顶Blade出模斜波 Draft 手动滑块模具 Hand Slide-In Type Mold 回针板Backup 合模 Shutoff空隙槽 Clearance Slot导柱及导套 Leader Pin Bushing 水口拉钩 Spuer Puller 模框镶件 Pocket Insert成型热固性塑胶模具 Thermoset Mold 三板模 3-Plat Mold分型面 Parting Line 司筒 Ejector Sleeve 垫圈Washer熔接线（夹水纹）Weldline 吸针 Sucker Pin回针板 Retainer Plate顶出板 Knock-Out Plate电动安全开关Electrical-Safety Switch 脱开 Cut Of Position 预先决定 Preload 缓冲器 Bumper 衬垫 Cushion 公差Tolerance突然性动作 Slam 销针 Dowel 钩槽 Gib精磨Finished通框 Through Window粘后模 Sticking Core 粘水口 Sticking Sprue夹水纹Weld Line变形Warpage 走水不平均Filling Uneven 走不齐Short Shot 挂成品Part Hanging漏水Water Leakage 刮花（擦伤）Galling 漏电Ele Leakage 困气Air Trapping 温度Temperature 注塑模Injection Mold 入水Gate 试板Sampling 压力Pressure 倒圆Fillet 顶棍Ejector 顶白Stress Mark 粘前模Sticking Cav 名称块表Title Block 版本标识 Revision Level 材料清单Stock List斜导柱（斜边）Angle Pin A板A'plate B板B'plate 倒扣Under-Cut 披峰Flash缩水Sink Mark氮化Nitride 不规则四边形Trapezoid 缩水Shrinkage 连续的Consecutive 雕刻Engrave出模角Draft分模面Parting Surface 擦位Shut-Off(S/0)导套Bushing 回针Return Pin 加硬Harden 唧嘴Sprue设计筒图Design Preliminary 丝印Silkprint 不干胶Adhesive Sticker 导向针Guide Din 公差Tolerance线切割Wire-Cut 电火花Edm抛光Polishing 蚀纹Texture探热针Thermocouple三打螺丝毫（限螺丝）Stripper Bolt 盖板Cover Plate 齿轮Gear 油唧Hydraulic Cylinder 司筒Ejector Sleeve 导柱Leader Pin 冷料#Cold Slag 线切割Wire E.D.M.轮廓Contour 螺纹孔Tapping Hole 连接件Fittings斜针Angle Pin 接合Engage替换镶件Interchangeable Mold Inserts指定吨位的注塑机 Specific Press 水嘴接头 Water Fittings 螺纹Eyebolt Thread回针Stop Pin二级顶出针 Sub-Leader Pin 镶件Mold Insert锁定位Lock 楔子(铲鸡)Wedge高产量模量 High Volume Running Mold 剖面图Cross Section 模具结构Mold Construction 模芯Parting Core 局部视图Partial View 热流道Manifold 热嘴Hot Nozzle 型腔数Cav No 模号Mold No 胶料Material尺寸Dimension重要尺寸Critical Dimension雕刻Engrave托司EJ.GUIDE PIN第三篇：常用术语中英文对照十、常用术语中英文对照人生规划Life planning自我介绍Self-introduction 目标Target孔子Confucius《论语》The Analects of Confucius 修身养性cultivate one's moral character 儒家思想Confucianism诗歌Poem赏析Appreciation阅读理解Reading comprehension 意境Artistic conception意象Imagery情感Emotion朗诵Recite策划Consultant情景模拟Scenario simulation 记忆Memory贝多芬Beethoven命运交响曲Symphony of Destiny 古典音乐Classical music 莫扎特Mozart费加罗的婚礼The Marriage of Figaro 萧伯纳George Bernard Shaw 戏剧Drama理想主义Idealism人道精神Humanity反抗性Resistance辩论Debate演讲Speech主题Theme财富Wealth品格Character《红楼梦》Dream in Red Mansions 叶芝Yeats当你老了 when you are old 情景Scene道家Taoism无为而治Taoist Actionless Governance 消极避世Indifference 散文Prose小说Novel文学性Literary语言Language修辞Rhetoric敬畏生命Reverence for Life 抉择Choice普通话Mandarin个人简历Resume招聘求职Recruitment 求职信Cover letter自荐书Written submissions 岗位Post市场营销Marketing物流Logistics食品检测Food testing 高分子Macromolecule就业形势Employment situation 毕业论文Thesis摘要Abstract关键词Keyword答辩defense第四篇：模具常用专业术语中英文对照塑料模具常用专业术语中英文对照模胚（架）： mold base三板模（细水口）：3-plate mold二板模（大水口）：2-plate 定位圈（法栏）locating ring 浇口套（唧嘴）sprue bushing热流道： hot runner,hot manifold面板:cavity adaptor plate 水口板：runner stripper plate 上模板（A板）:cavity plate 下模板（B板）:core plate 上内模（型腔＼母模＼凹模）：cavity insert下内模（型芯＼公模＼凸模）：core insert 推板：stripper plate 模脚（方铁）spacer plate 顶针板：ejector retainner plate托板(顶针底板)： support plat垃圾钉：stop pin撑头: support pillar底板：coreadaptor plate 推杆：push bar 顶针： ejector pin 司筒：ejector sleeve司筒针：ejector pin 回针：push bake pin 导柱：leader pin/guide pin 导套：bushing/guide bushing中托司（顶针板导套）：shoulder guide bushing中托边(顶针板导柱)：guide pin滑块（行位）： slide 波子弹弓（定位珠）：ball catch 耐磨板/油板：wedge wear 压条：plate斜导边（斜导柱）：angle pin压座/铲鸡：wedge斜顶：angle from pin 斜顶杆：angle ejector rod 缩呵：movable core,return core core puller尼龙拉勾（扣机）：nylonlatch lock栓打螺丝：S.H.S.B 镶针：pin喉塞: pipe plug锁模块：lock plate挡板：stop plate螺丝： screw推板：stripper plate斜顶：lifterplate塑胶管：plastic tube快速接头：jiffy quick connector plug/sockermold内模管位：core/cavity inter-lockflash(塑件)毛边电极(铜公)：copper electrode五金模具常用专业术语中英文对照cutting die, blanking die冲裁模progressive die, follow(-on)die 连续模compound die复合模punched hole冲孔panel board镶块to cutedges=side cut=side scrap切边to bending折弯to pull, to stretch拉伸Line streching, line pulling线拉伸engraving, to engrave刻印 top plate上托板（顶板）top block 上垫脚punch set上模座punch pad上垫板punch holder上夹板stripper pad脱料背板up stripper上脱料板die pad下垫板die holder下夹板die set下模座bottom block下垫脚bottom plate 底板（下托板）stripping plate 脱料板（表里打）outer stripper外脱料板inner stripper内脱料板lower stripper 下脱料板上模座upper die set 成型公 form punch脱料板stripper 垫板subplate/backup plate下模座die plate垫脚parallel托板mounting plate 顶料销kick off初始管位first start pin 带肩螺丝shoulder screw两用销lifter pin弹簧护套spring cage 拔牙螺丝jack screw侧冲组件 cam sectionbites导导正装置 guide equipment 尺rail漏废料孔 slug hole限位块stop block送料板rail plate刀口trim line挡块stopper倒角chamfer入子insert 浮块lifter 销钉dowel 护套bushing压块keeper尖角sharp--angle整形公restrike forming 靠块heel 普通弹簧coil springpunch 对正块alignmentblock镶件insert止挡板stop plate闭合高度shuthight 插针pilot pin挂台head 上夹板/固定座顶杆lifter bolt扣位pocket of head导柱guide post导套guide bushing油嘴oil nipple接刀口mismatch/cookieholder/retainer下模座lower die set成刑母公formingdie码模槽mounting slot 球锁紧固定座ball-lock起吊孔handing hole垫片shim/wear-plate键槽key slot沉孔counter hole导正块thrustblock 第五篇：模具DFM常用中英文对照DFM常用中英文对照1、这个红色面在前模方向/后模方向/行位方向有倒扣。

The union of unit balls has quadratic complexity, even if they all contain the origin

a r X i v :c s /9907025v 1 [c s .C G ] 16 J u l 1999The union of unit balls has quadratic complexity,even if they allcontain the originHerv Br¨o nnimann and Olivier Devillers ∗June,1999AbstractWe provide a lower bound construction showing that the union of unit balls in R 3has quadratic complexity,even if they all contain the origin.This settles a conjecture of Sharir.1IntroductionThe union of a set of n balls in R 3has quadratic complexity Θ(n 2),even if they all have the same radius.All the already known constructions have balls scattered around,however,and Sharir posed the problem whether a quadratic complexity could be achieved if all the balls (of same radius)contained the origin.In this note,we show a construction of n unit balls,all containing the origin,whose union has complexity Θ(n 2).As a trivial observation,we observe that the centers are arbitrarily close to the origin in our construction.In fact,if the centers are forced to be at least pairwise εapart,for some constant ε>0,then no more than O (1ε3n )=O ε(n ).It is an interesting open question what a condition should beso that the union have subquadratic complexity and yet the balls have arbitrarily close centers.By contrast,the intersection of n balls can have quadratic complexity if their radii are not constrained,but the complexity is linear if all the radii are the same [2].Similarly,the convex hull of n balls can have also quadratic complexity [1],but that complexity is linear if they all have the same radius.2ConstructionLet m and k be any integers.We deﬁne two families of unit balls:the ﬁrst consists of k unit balls whose centers lie on a small vertical segment;the second consists of m unit balls whose centers lie on a small circle under the segment.(See Figure 3.)We show below that their union has quadratic O (km )complexity.The balls B 1...B k .We denote by B (p,r )the ball centered at p and of radius r .Let n =k +m and P i denote the point of coordinates (0,0,(i −1)/n 4),and B i =B (P i ,1),for i =1,...,k .It is clear that the boundary of ∪1≤i ≤k B i consists of two hemispheres belonging to B 1and B k linked by a narrow cylinder of height less than k/n 4≤1/n 3.This cylinder contains all the circles ∂B i ∩∂B i +1for i =1,...,k −1.(See Figure 1.)≤1n4,z=−2n2−4nin(2)below would do.)We deﬁneθas the rotation around the z-axis of angle2π/m,and for each j=1,...,m,R k+j=θj−1(R)and B k+j=B(R k+j,1).3AnalysisBy our choice of x and z,we prove below that the boundaries of B k+1and of the union∪k i=1B i depicted in Figure1meet along a curveγwhich satisﬁes the two claims below.The situation is depicted on Figure2.Claim1The curveγintersects all the balls B i for i=0,...,k,.Claim2The portion ofγwhich does not belong to B1(equivalently,which belongs to the union ∪k i=2B i)is contained in an angular sector of angle at most2π/m.From claim2,we conclude that the portion ofγwhich does not belong to B1is contained in the boundary of the union of the n=k+m balls,From claim1,we conclude that the portion of γwhich does not belong to B1has complexityΩ(k).From claim2,that it is contained in a small angular sector,hence appears completely on the boundary of the union of the n=k+m balls,and it is replicated m times,once for each of the balls B j,j=1,...,m.It follows that the union of all the balls B i for i=1,...,k+m has quadratic complexityΩ(km).Moreover,all the balls contain the origin.The union of the n balls is depicted on Figure3.The proofs involve only elementary geometry and trigonometry.The situation is depicted in Figure4and5.Figure4depicts a section in the xz-plane of the spheres∂B i and∂B k+1and the point M,the highest point of intersection of the bounding spheres.The point M is also depicted on Figure2.Proof of Claim1.It suﬃces to prove that M is higher than P k,since thenγextends higher than P k as well and passes through M by symmetry.The lowest point ofγbelongs to B1and is clearly below the origin.The two facts together prove thatγmust intersect all the balls between B1and B k.BRK =P k R22x,(1)where z k=k−1n4(n2−2)which is smaller than1for n≥2.Proof of Claim2.It is easy to see that the intersection ofγand a ball B i(2≤i≤k)consistsof at most two arcs of circle,any of which is monotone in angular coordinates around the z-axis, and that any such arc is entirely above the plane z=0.Hence the intersections ofγwith the xy-plane belong to B1and B k+1.It suﬃces to show that these intersections are at a distanceℓatmost2mfrom the x-axis.(See Figure5.)In the xy-plane section,B1is a unit circle,and B k+1is a circle of radius r=√1− z2+x2Figure3:The union∪1≤i≤k+m B i.On the right,a blow-up of thecenters.+1Figure4:Figure for Claim1.For our choice or x and z,this yieldsℓ= n8which is smaller than2/n for n≥2.Acknowledgments.Thanks to Micha Sharir for pointing out the problem the us.It was also pointed out that Alon Efrat might have a construction which leads to a quadratic lower bound as well.We have derived our construction independently.References[1]Jean-Daniel Boissonnat,Andr´e C´e r´e zo,Olivier Devillers,Jacqueline Duquesne,and MarietteYvinec.An algorithm for constructing the convex hull of a set of spheres in dimension d.Comput.Geom.Theory Appl.,6:123–130,1996.[2]A.Heppes.Beweis einer Vermutung von A.V´a zsonyi.Acta Math.Acad.Sci.Hungar.,7:463–466,1956.Figure5:Figure for Claim2.。

选修八unit2单词解析

( ) －Mom, I can’t see any point in working hard at all the subjects at school. －Come on, dear. Years of hard work will surely _____ in the future of your career. A. make sure B. pay off C. bring back D. pay back
辨析 altogether, all together 1.let’s all together sing. 全部，一起
7.object vi 反对(oppose/be opposed to ) object to sb/sth/doing sth I object to such treatment .
他强烈反对那么早起床 He has a strong objection to getting up that early. =He strongly objects to getting up that early object match was cancelled because most of the members ___ a match without a standard court. A.objected to having B. were objected to have C. objected to have D. were objected to having
4.There is a board by the road, which ____”parking__!”
9.in favour of=be for 赞成，支持你赞成这个计划还是反对这个计划？ Are you in favour of the plan or against the plan? favour n.帮助；恩惠；赞成；支持；偏袒；偏爱 favourable adj.有利的；支持的 favourite adj.& n.最喜欢的 in one’s favour 对某人有利 do sb a favour=do a favour for sb 帮助某人 owe sb a favour 欠某人情 [考例] My sister was against my suggestion while my brother was ______ it. (陕西2006) A. in favour of B. in memory of C. in honour of D. in search of

法布里珀罗基模共振英文

法布里珀罗基模共振英文The Fabryperot ResonanceOptics, the study of light and its properties, has been a subject of fascination for scientists and researchers for centuries. One of the fundamental phenomena in optics is the Fabry-Perot resonance, named after the French physicists Charles Fabry and Alfred Perot, who first described it in the late 19th century. This resonance effect has numerous applications in various fields, ranging from telecommunications to quantum physics, and its understanding is crucial in the development of advanced optical technologies.The Fabry-Perot resonance occurs when light is reflected multiple times between two parallel, partially reflective surfaces, known as mirrors. This creates a standing wave pattern within the cavity formed by the mirrors, where the light waves interfere constructively and destructively to produce a series of sharp peaks and valleys in the transmitted and reflected light intensity. The specific wavelengths at which the constructive interference occurs are known as the resonant wavelengths of the Fabry-Perot cavity.The resonant wavelengths of a Fabry-Perot cavity are determined bythe distance between the mirrors, the refractive index of the material within the cavity, and the wavelength of the incident light. When the optical path length, which is the product of the refractive index and the physical distance between the mirrors, is an integer multiple of the wavelength of the incident light, the light waves interfere constructively, resulting in a high-intensity transmission through the cavity. Conversely, when the optical path length is not an integer multiple of the wavelength, the light waves interfere destructively, leading to a low-intensity transmission.The sharpness of the resonant peaks in a Fabry-Perot cavity is determined by the reflectivity of the mirrors. Highly reflective mirrors result in a higher finesse, which is a measure of the ratio of the spacing between the resonant peaks to their width. This high finesse allows for the creation of narrow-linewidth, high-resolution optical filters and laser cavities, which are essential components in various optical systems.One of the key applications of the Fabry-Perot resonance is in the field of optical telecommunications. Fiber-optic communication systems often utilize Fabry-Perot filters to select specific wavelength channels for data transmission, enabling the efficient use of the available bandwidth in fiber-optic networks. These filters can be tuned by adjusting the mirror separation or the refractive index of the cavity, allowing for dynamic wavelength selection andreconfiguration of the communication system.Another important application of the Fabry-Perot resonance is in the field of laser technology. Fabry-Perot cavities are commonly used as the optical resonator in various types of lasers, providing the necessary feedback to sustain the lasing process. The high finesse of the Fabry-Perot cavity allows for the generation of highly monochromatic and coherent light, which is crucial for applications such as spectroscopy, interferometry, and precision metrology.In the realm of quantum physics, the Fabry-Perot resonance plays a crucial role in the study of cavity quantum electrodynamics (cQED). In cQED, atoms or other quantum systems are placed inside a Fabry-Perot cavity, where the strong interaction between the atoms and the confined electromagnetic field can lead to the observation of fascinating quantum phenomena, such as the Purcell effect, vacuum Rabi oscillations, and the generation of nonclassical states of light.Furthermore, the Fabry-Perot resonance has found applications in the field of optical sensing, where it is used to detect small changes in physical parameters, such as displacement, pressure, or temperature. The high sensitivity and stability of Fabry-Perot interferometers make them valuable tools in various sensing and measurement applications, ranging from seismic monitoring to the detection of gravitational waves.The Fabry-Perot resonance is a fundamental concept in optics that has enabled the development of numerous advanced optical technologies. Its versatility and importance in various fields of science and engineering have made it a subject of continuous research and innovation. As the field of optics continues to advance, the Fabry-Perot resonance will undoubtedly play an increasingly crucial role in shaping the future of optical systems and applications.。

流体力学专业英语词汇

流体力学专业词汇(V ocabulary of Fluid Mechanics )CHAPTER-1acceleration 加速度average velocity 平均速度Bernoulli 伯努力boundary layer 边界层calculus 微积分coefficient of viscosity 粘性系数compressible(incompressible) (不)可压的conservation of mass(momentum, energy) 质量(动量,能量)守恒continuum 连续介质control-volume 控制体density(mass per unit volume) 密度differential 微分dimension 量刚尺度dynamics 动力学Euler 欧拉eulerian (lagrangian) method of description欧拉(拉格郎日)观点，方法field of flow 流场flow pattern 流型（谱）fluid mechanics 流体力学function 函数inertia 惯性, 惯量integral 积分kinematics 运动学kinetic (potential, internal) energy 动(势,内)能Lagrange 拉格郎日liquid 流体Newtonian fluids 牛顿流体(non)linear (非)线性(non)uniform （非）均匀one-dimensional 一维pathline 迹线perfect-gas law 理想气体定律pressure 压力压强Reynolds 雷诺shear(normal) stress 剪(正)应力solution 解答statics 静力学steady(unsteady) (非)定常strain 应变streamline(tube) 流线(管)thermal conductivity 热传导thermodynamics 热力学variable 变量vector 矢量velocity distribution 速度分布velocity field 速度场velocity gradient 速度梯度viscous(inviscid) (无)粘性的volume rate of flow 体积流量CHAPTER -2absolute (gage,vacuum) pressure 绝对（表，真空）压力area moment of inertia 惯性面积矩atmospheric pressure 大气压力barometer 气压计body force 体力Cartesian [rectangular] coordinates 直角坐标（系）centroid 质心elliptic 椭圆的equilibrium 平衡horizontal 水平的hydrostatic 水静力学，流体静力学hyperbolic 双曲线的mercury 水银moment 矩parabolic 抛物线plane (curved) surface 平（曲）面plate 板pressure center 压力中心pressure distribution(gradient) 压力分布（梯度）reservoir 水库rigid-body 刚体scalar 标量specific weight 比重surface force 表面力vertical 垂直的, 直立的CHAPTER -3Bernoulli equation 伯努力方程Boundaries 边界Conservation of mass 质量Control volume 控制体Energy(hydraulic) grade line 能级线Flux 流率Free body 隔离体Heat transfer 热传到Imaginary 假想Inlet, outlet 进、出口Integrand 被积函数Jet flow 射流Linear(Angular)-momentum relation 线（角）动量关系式Momentum(energy)-flux 动量（能量）流量Net force 合力No slip 无滑移Nozzle 喷嘴Rate of work 功率Reynolds transport theorem 雷诺输运定理Shaft work 轴功Stagnation enthalpy 制止焓Surroundings 外围System 体系Time derivative 时间导数Vector sum 矢量合Venturi tube 文图里管V olume(mass) flow 体积（质量）流量V olume(mass) rate of flow体积（质量）流率CHAPTER -4Soomth 平滑Laminar 层流Transition 转捩Roughness 粗糙度Random fluctuations 随机脉动Reynolds number 雷诺数（Re）Instability 不稳定性Breakdown 崩溃Mean value 平均值Drag 阻力Osborne ReynoldsDye filament 染色丝Internal (external) flow 内(外)流Cartesian 笛卡坐标Infinitesimal 无限小local acceleration 当地加速度dot product 点乘total derivative 全导数convective acceleration 对流加速度substantial(material) derivative 随体(物质)导数operator 算子partial differential equation 偏微分方程Newtonian fluid 牛顿流体Navier-Stokes Equations N-S方程Second-order 二阶Similarity 相似Nondimensionalization 无量纲化Flat-plate boundary layer 平板边界层Thermal conductivity 热传导Heat flow 热流量Fourier’s law 傅立叶定律Couette Flow 库塔流动Channel 槽道Parallel plates 平行平板Pressure gradient 压力梯度No-slip condition 无滑移条件Poiseuille flow 伯肖叶流动Parabola 抛物线Wall shear stress 壁面剪应力Prandtl 普朗特Karman 卡门Momentum-integral relation 动量积分关系Momentum thickness 动量厚度Skin-friction coefficient 壁面摩擦系数Displacement thickness 排移厚度Blasius equation 布拉修斯方程Coordinate transformation 坐标变换Composite dimensionless variable 组合无量纲变量Shape factor 形状因子Velocity profile 速度剖面流体动力学fluid dynamics连续介质力学mechanics of continuous media介质medium流体质点fluid particle无粘性流体nonviscous fluid, inviscid fluid连续介质假设continuous medium hypothesis流体运动学fluid kinematics水静力学hydrostatics液体静力学hydrostatics支配方程governing equation伯努利方程Bernoulli equation伯努利定理Bernonlli theorem毕奥-萨伐尔定律Biot-Savart law欧拉方程Euler equation亥姆霍兹定理Helmholtz theorem开尔文定理Kelvin theorem涡片vortex sheet库塔-茹可夫斯基条件Kutta-Zhoukowski condition 布拉休斯解Blasius solution达朗贝尔佯廖d'Alembert paradox雷诺数Reynolds number施特鲁哈尔数Strouhal number随体导数material derivative不可压缩流体incompressible fluid质量守恒conservation of mass动量守恒conservation of momentum 能量守恒conservation of energy动量方程momentum equation能量方程energy equation控制体积control volume液体静压hydrostatic pressure涡量拟能enstrophy压差differential pressure流[动] flow流线stream line流面stream surface流管stream tube迹线path, path line流场flow field流态flow regime流动参量flow parameter流量flow rate, flow discharge涡旋vortex涡量vorticity涡丝vortex filament涡线vortex line涡面vortex surface涡层vortex layer涡环vortex ring涡对vortex pair涡管vortex tube涡街vortex street卡门涡街Karman vortex street马蹄涡horseshoe vortex对流涡胞convective cell卷筒涡胞roll cell涡eddy涡粘性eddy viscosity环流circulation环量circulation速度环量velocity circulation偶极子doublet, dipole驻点stagnation point总压[力] total pressure总压头total head静压头static head总焓total enthalpy能量输运energy transport速度剖面velocity profile库埃特流Couette flow单相流single phase flow单组份流single-component flow均匀流uniform flow非均匀流nonuniform flow二维流two-dimensional flow三维流three-dimensional flow准定常流quasi-steady flow非定常流unsteady flow, non-steady flow 暂态流transient flow周期流periodic flow振荡流oscillatory flow分层流stratified flow无旋流irrotational flow有旋流rotational flow轴对称流axisymmetric flow不可压缩性incompressibility不可压缩流[动] incompressible flow浮体floating body定倾中心metacenter阻力drag, resistance减阻drag reduction表面力surface force表面张力surface tension毛细[管]作用capillarity来流incoming flow自由流free stream自由流线free stream line外流external flow进口entrance, inlet出口exit, outlet扰动disturbance, perturbation分布distribution传播propagation色散dispersion弥散dispersion附加质量added mass ,associated mass 收缩contraction镜象法image method无量纲参数dimensionless parameter几何相似geometric similarity运动相似kinematic similarity动力相似[性] dynamic similarity平面流plane flow势potential势流potential flow速度势velocity potential复势complex potential复速度complex velocity流函数stream function源source汇sink速度[水]头velocity head拐角流corner flow空泡流cavity flow超空泡supercavity超空泡流supercavity flow空气动力学aerodynamics低速空气动力学low-speed aerodynamics 高速空气动力学high-speed aerodynamics 气动热力学aerothermodynamics亚声速流[动] subsonic flow跨声速流[动] transonic flow超声速流[动] supersonic flow锥形流conical flow楔流wedge flow叶栅流cascade flow非平衡流[动] non-equilibrium flow细长体slender body细长度slenderness钝头体bluff body钝体blunt body翼型airfoil翼弦chord薄翼理论thin-airfoil theory构型configuration后缘trailing edge迎角angle of attack失速stall脱体激波detached shock wave波阻wave drag诱导阻力induced drag诱导速度induced velocity临界雷诺数critical Reynolds number 前缘涡leading edge vortex附着涡bound vortex约束涡confined vortex气动中心aerodynamic center气动力aerodynamic force气动噪声aerodynamic noise气动加热aerodynamic heating离解dissociation地面效应ground effect气体动力学gas dynamics稀疏波rarefaction wave热状态方程thermal equation of state 喷管Nozzle普朗特-迈耶流Prandtl-Meyer flow瑞利流Rayleigh flow可压缩流[动] compressible flow可压缩流体compressible fluid绝热流adiabatic flow非绝热流diabatic flow未扰动流undisturbed flow等熵流isentropic flow匀熵流homoentropic flow兰金-于戈尼奥条件Rankine-Hugoniot condition 状态方程equation of state量热状态方程caloric equation of state完全气体perfect gas拉瓦尔喷管Laval nozzle马赫角Mach angle马赫锥Mach cone马赫线Mach line马赫数Mach number马赫波Mach wave当地马赫数local Mach number冲击波shock wave激波shock wave正激波normal shock wave斜激波oblique shock wave头波bow wave附体激波attached shock wave激波阵面shock front激波层shock layer压缩波compression wave反射reflection折射refraction散射scattering衍射diffraction绕射diffraction出口压力exit pressure超压[强] over pressure反压back pressure爆炸explosion爆轰detonation缓燃deflagration水动力学hydrodynamics液体动力学hydrodynamics泰勒不稳定性Taylor instability盖斯特纳波Gerstner wave斯托克斯波Stokes wave瑞利数Rayleigh number自由面free surface波速wave speed, wave velocity 波高wave height波列wave train波群wave group波能wave energy表面波surface wave表面张力波capillary wave规则波regular wave不规则波irregular wave浅水波shallow water wave深水波deep water wave重力波gravity wave椭圆余弦波cnoidal wave潮波tidal wave涌波surge wave破碎波breaking wave船波ship wave非线性波nonlinear wave孤立子soliton水动[力]噪声hydrodynamic noise 水击water hammer空化cavitation空化数cavitation number空蚀cavitation damage超空化流supercavitating flow水翼hydrofoil水力学hydraulics洪水波flood wave涟漪ripple消能energy dissipation海洋水动力学marine hydrodynamics谢齐公式Chezy formula欧拉数Euler number弗劳德数Froude number水力半径hydraulic radius水力坡度hvdraulic slope高度水头elevating head水头损失head loss水位water level水跃hydraulic jump含水层aquifer排水drainage排放量discharge壅水曲线back water curve压[强水]头pressure head过水断面flow cross-section明槽流open channel flow孔流orifice flow无压流free surface flow有压流pressure flow缓流subcritical flow急流supercritical flow渐变流gradually varied flow急变流rapidly varied flow临界流critical flow异重流density current, gravity flow堰流weir flow掺气流aerated flow含沙流sediment-laden stream降水曲线dropdown curve沉积物sediment, deposit沉[降堆]积sedimentation, deposition沉降速度settling velocity流动稳定性flow stability不稳定性instability奥尔-索末菲方程Orr-Sommerfeld equation涡量方程vorticity equation泊肃叶流Poiseuille flow奥辛流Oseen flow剪切流shear flow粘性流[动] viscous flow层流laminar flow分离流separated flow二次流secondary flow近场流near field flow远场流far field flow滞止流stagnation flow尾流wake [flow]回流back flow反流reverse flow射流jet自由射流free jet管流pipe flow, tube flow内流internal flow拟序结构coherent structure 猝发过程bursting process表观粘度apparent viscosity 运动粘性kinematic viscosity 动力粘性dynamic viscosity 泊poise厘泊centipoise厘沱centistoke剪切层shear layer次层sublayer流动分离flow separation层流分离laminar separation 湍流分离turbulent separation 分离点separation point附着点attachment point再附reattachment再层流化relaminarization起动涡starting vortex驻涡standing vortex涡旋破碎vortex breakdown涡旋脱落vortex shedding压[力]降pressure drop压差阻力pressure drag压力能pressure energy型阻profile drag滑移速度slip velocity无滑移条件non-slip condition壁剪应力skin friction, frictional drag壁剪切速度friction velocity磨擦损失friction loss磨擦因子friction factor耗散dissipation滞后lag相似性解similar solution局域相似local similarity气体润滑gas lubrication液体动力润滑hydrodynamic lubrication浆体slurry泰勒数Taylor number纳维-斯托克斯方程Navier-Stokes equation 牛顿流体Newtonian fluid边界层理论boundary later theory边界层方程boundary layer equation边界层boundary layer附面层boundary layer层流边界层laminar boundary layer湍流边界层turbulent boundary layer温度边界层thermal boundary layer边界层转捩boundary layer transition边界层分离boundary layer separation边界层厚度boundary layer thickness位移厚度displacement thickness动量厚度momentum thickness能量厚度energy thickness焓厚度enthalpy thickness注入injection吸出suction泰勒涡Taylor vortex速度亏损律velocity defect law形状因子shape factor测速法anemometry粘度测定法visco[si] metry流动显示flow visualization油烟显示oil smoke visualization孔板流量计orifice meter频率响应frequency response油膜显示oil film visualization阴影法shadow method纹影法schlieren method烟丝法smoke wire method丝线法tuft method氢泡法nydrogen bubble method相似理论similarity theory相似律similarity law部分相似partial similarity定理pi theorem, Buckingham theorem 静[态]校准static calibration动态校准dynamic calibration风洞wind tunnel激波管shock tube激波管风洞shock tube wind tunnel水洞water tunnel拖曳水池towing tank旋臂水池rotating arm basin扩散段diffuser测压孔pressure tap皮托管pitot tube普雷斯顿管preston tube斯坦顿管Stanton tube文丘里管Venturi tubeU形管U-tube压强计manometer微压计micromanometer多管压强计multiple manometer静压管static [pressure]tube流速计anemometer风速管Pitot- static tube激光多普勒测速计laser Doppler anemometer, laser Doppler velocimeter热线流速计hot-wire anemometer热膜流速计hot- film anemometer流量计flow meter粘度计visco[si] meter涡量计vorticity meter传感器transducer, sensor压强传感器pressure transducer热敏电阻thermistor示踪物tracer时间线time line脉线streak line尺度效应scale effect壁效应wall effect堵塞blockage堵寒效应blockage effect动态响应dynamic response响应频率response frequency底压base pressure菲克定律Fick law巴塞特力Basset force埃克特数Eckert number格拉斯霍夫数Grashof number努塞特数Nusselt number普朗特数prandtl number雷诺比拟Reynolds analogy施密特数schmidt number斯坦顿数Stanton number对流convection自由对流natural convection, free convec-tion强迫对流forced convection热对流heat convection质量传递mass transfer传质系数mass transfer coefficient热量传递heat transfer传热系数heat transfer coefficient对流传热convective heat transfer辐射传热radiative heat transfer动量交换momentum transfer能量传递energy transfer传导conduction热传导conductive heat transfer热交换heat exchange临界热通量critical heat flux浓度concentration扩散diffusion扩散性diffusivity扩散率diffusivity扩散速度diffusion velocity分子扩散molecular diffusion沸腾boiling蒸发evaporation气化gasification凝结condensation成核nucleation计算流体力学computational fluid mechanics多重尺度问题multiple scale problem伯格斯方程Burgers equation对流扩散方程convection diffusion equationKDU方程KDV equation修正微分方程modified differential equation拉克斯等价定理Lax equivalence theorem数值模拟numerical simulation大涡模拟large eddy simulation数值粘性numerical viscosity非线性不稳定性nonlinear instability希尔特稳定性分析Hirt stability analysis相容条件consistency conditionCFL条件Courant- Friedrichs- Lewy condition ,CFL condition狄里克雷边界条件Dirichlet boundary condition熵条件entropy condition远场边界条件far field boundary condition流入边界条件inflow boundary condition无反射边界条件nonreflecting boundary condition 数值边界条件numerical boundary condition流出边界条件outflow boundary condition冯.诺伊曼条件von Neumann condition近似因子分解法approximate factorization method 人工压缩artificial compression人工粘性artificial viscosity边界元法boundary element method配置方法collocation method能量法energy method有限体积法finite volume method流体网格法fluid in cell method, FLIC method通量校正传输法flux-corrected transport method通量矢量分解法flux vector splitting method伽辽金法Galerkin method积分方法integral method标记网格法marker and cell method, MAC method 特征线法method of characteristics直线法method of lines矩量法moment method多重网格法multi- grid method板块法panel method质点网格法particle in cell method, PIC method质点法particle method预估校正法predictor-corrector method投影法projection method准谱法pseudo-spectral method随机选取法random choice method激波捕捉法shock-capturing method激波拟合法shock-fitting method谱方法spectral method稀疏矩阵分解法split coefficient matrix method不定常法time-dependent method时间分步法time splitting method变分法variational method涡方法vortex method隐格式implicit scheme显格式explicit scheme交替方向隐格式alternating direction implicit scheme, ADI scheme 反扩散差分格式anti-diffusion difference scheme紧差分格式compact difference scheme守恒差分格式conservation difference scheme克兰克-尼科尔森格式Crank-Nicolson scheme杜福特-弗兰克尔格式Dufort-Frankel scheme指数格式exponential scheme戈本诺夫格式Godunov scheme高分辨率格式high resolution scheme拉克斯-温德罗夫格式Lax-Wendroff scheme蛙跳格式leap-frog scheme单调差分格式monotone difference scheme保单调差分格式monotonicity preserving difference scheme穆曼-科尔格式Murman-Cole scheme半隐格式semi-implicit scheme斜迎风格式skew-upstream scheme全变差下降格式total variation decreasing scheme TVD scheme 迎风格式upstream scheme , upwind scheme计算区域computational domain物理区域physical domain影响域domain of influence依赖域domain of dependence区域分解domain decomposition维数分解dimensional split物理解physical solution弱解weak solution黎曼解算子Riemann solver守恒型conservation form弱守恒型weak conservation form强守恒型strong conservation form散度型divergence form贴体曲线坐标body- fitted curvilinear coordi-nates[自]适应网格[self-] adaptive mesh适应网格生成adaptive grid generation自动网格生成automatic grid generation数值网格生成numerical grid generation交错网格staggered mesh网格雷诺数cell Reynolds number数植扩散numerical diffusion数值耗散numerical dissipation数值色散numerical dispersion数值通量numerical flux放大因子amplification factor放大矩阵amplification matrix阻尼误差damping error离散涡discrete vortex熵通量entropy flux熵函数entropy function分步法fractional step method广义连续统力学generalized continuum mechanics 简单物质simple material纯力学物质purely mechanical material微分型物质material of differential type积分型物质material of integral type混合物组份constituents of a mixture非协调理论incompatibility theory微极理论micropolar theory决定性原理principle of determinism等存在原理principle of equipresence局部作用原理principle of objectivity客观性原理principle of objectivity电磁连续统理论theory of electromagnetic continuum 内时理论endochronic theory非局部理论nonlocal theory混合物理论theory of mixtures里夫林-矣里克森张量Rivlin-Ericksen tensor声张量acoustic tensor半向同性张量hemitropic tensor各向同性张量isotropic tensor应变张量strain tensor伸缩张量stretch tensor连续旋错continuous dislination连续位错continuous dislocation动量矩平衡angular momentum balance余本构关系complementary constitutive relations共旋导数co-rotational derivative, Jaumann derivative 非完整分量anholonomic component爬升效应climbing effect协调条件compatibility condition错综度complexity当时构形current configuration能量平衡energy balance变形梯度deformation gradient有限弹性finite elasticity熵增entropy production标架无差异性frame indifference弹性势elastic potential熵不等式entropy inequality极分解polar decomposition低弹性hypoelasticity参考构形reference configuration响应泛函response functional动量平衡momentum balance奇异面singular surface贮能函数stored-energy function内部约束internal constraint物理分量physical components本原元primitive element普适变形universal deformation速度梯度velocity gradient测粘流动viscometric flow当地导数local derivative岩石力学rock mechanics原始岩体应力virgin rock stress构造应力tectonic stress三轴压缩试验three-axial compression test三轴拉伸试验three-axial tensile test 三轴试验triaxial test岩层静态应力lithostatic stress吕荣lugeon地压强geostatic pressure水力劈裂hydraulic fracture咬合[作用] interlocking内禀抗剪强度intrinsic shear strength 循环抗剪强度cyclic shear strength 残余抗剪强度residual shear strength 土力学soil mechanics孔隙比void ratio内磨擦角angle of internal friction休止角angle of repose孔隙率porosity围压ambient pressure渗透系数coefficient of permeability [抗]剪切角angle of shear resistance 渗流力seepage force表观粘聚力apparent cohesion粘聚力cohesion稠度consistency固结consolidation主固结primary consolidation次固结secondary consolidation固结仪consolidometer浮升力uplift扩容dilatancy有效应力effective stress絮凝[作用] flocculation主动土压力active earth pressure被动土压力passive earth pressure 土动力学soil dynamics应力解除stress relief次时间效应secondary time effect贯入阻力penetration resistance沙土液化liquefaction of sand泥流mud flow多相流multiphase flow马格努斯效应Magnus effect韦伯数Weber number环状流annular flow泡状流bubble flow层状流stratified flow平衡流equilibrium flow二组份流two-component flow冻结流frozen flow均质流homogeneous flow二相流two-phase flow气-液流gas-liquid flow气-固流gas-solid flow液-气流liquid-gas flow液-固流liquid-solid flow液体-蒸气流liquid-vapor flow浓相dense phase稀相dilute phase连续相continuous phase离散相dispersed phase悬浮suspension气力输运pneumatic transport气泡形成bubble formation体密度bulk density壅塞choking微滴droplet挟带entrainment流型flow pattern流[态]化fluidization界面interface跃动速度saltation velocity非牛顿流体力学non-Newtonian fluid mechanics 非牛顿流体non-Newtonian fluid幂律流体power law fluid拟塑性流体pseudoplastic fluid触稠流体rheopectic fluid触变流体thixotropic fluid粘弹性流体viscoelastic fluid流变测量学rheometry震凝性rheopexy体[积]粘性bulk viscosity魏森贝格效应Weissenberg effect流变仪rheometer稀薄气体动力学rarefied gas dynamics物理化学流体力学physico-chemical hydrodynamics 空气热化学aerothermochemistry绝对压强absolute pressure绝对反应速率absolute reaction rate绝对温度absolute temperature吸收系数absorption coefficient活化分子activated molecule活化能activation energy绝热压缩adiabatic compression绝热膨胀adiabatic expansion绝热火焰温度adiabatic flame temperature电弧风洞arc tunnel原子热atomic heat雾化atomization自燃auto-ignition自动氧化auto-oxidation可用能量available energy缓冲作用buffer action松密度bulk density燃烧率burning rate燃烧速度burning velocity接触面contact surface烧蚀ablation。

大学物理英语词汇

Chapter 1 Introduction（引言）§1.1 Space and Time（空间与时间）universe宇宙object物体measurement 测量kinematics运动学motion of objects 物体的运动mass point/particle质点center of mass 质心space and time 时空rotation 旋转subject研究的对象phenomena 现象intergalactic星系间的submicroscopic 亚微观的dimension尺度uniform均匀的isotropic各向同性的continuous连续的direction方向graininess 颗粒性location位置frame of reference 参考系specify确定、规定simultaneously 同时地inconsistent with与…不一致define/definition 定义platinum-iridium铂铱合金atomic standard 原子标准transition 跃迁meridian子午线general conference on weights and measures 国际计量大会vacuum真空former standard of length米原器atomic energy level原子能级isotope cesium 铯同位素krypton 氪angstrom埃§1.2 Coordinate Systems and Frames of Reference（坐标系与参考系）frame of reference 参考系coordinate system坐标系rectangular Cartesian coordinates直角笛卡儿坐标系axis / axes (pl.)（坐标）轴origin坐标原点at rest静止dimension维mutually perpendicular 互相垂直intersection 交点§1.3 Idealized Models（理想模型）idealized model 理想模型simplified version简化方式neglect忽略particle质点air resistance 空气阻力vacuum真空in terms of 利用rigid body刚体insulator绝缘体§1.4 Vectors（矢量）vector矢量scalar标量magnitude大小velocity速度acceleration 加速度momentum动量proportional to正比于parallel平行position vector位置矢量§1.5 Properties of Vectors（矢量的特点）resultant/net vectoradditionsubtractionequivalenttranslatehead-to-tail methodparallelogram method diagonalcommutative lawscalar productdot productdistributive lawmultiplicationcross product vector productarearight-hand ruleparallelmultiplyfunctionsome variable§1.6 Components of a Vector（矢量的分量）component分量absolute value绝对值projection投影perpendicular 垂线rectangular component正交分量§1.7 Unit Vectors（单位矢量）unit vector单位矢量dimensionless 无量纲的unit magnitude单位大小respectively分别地Chapter 2 Kinematics: Motion in Two and Three Dimensions （运动学：二维与三维运动）§2.1 Kinematical Function of a Point（质点的运动函数）position vector位置矢量trigonometry 三角学§2.2 Displacement and Velocity（位移与速度）trajectory轨迹displacement vector位移矢量velocity速度ratio比值，比率straight line直线approach趋近、接近limit极限average velocity 平均速度instantaneous velocity瞬时速度slope斜率chord弦limiting process 求极限过程curved path弯曲路径derivative导数magnitude and direction大小和方向speed速率scalar components标量分量limiting value极限值limiting process 求极限过程tangent相切、切线change增量、改变量differential n.微分differentiate v. 微分、求导integrate v.积分integration n.积分coefficient系数module (矢量的)模successively 连续地square root 平方根§2.3 Acceleration（加速度）acceleration 加速度average acceleration 平均加速度instantaneous acceleration 瞬时加速度second derivative二阶导数positive正的negative负的respectively 分别地one-dimensional motion一维运动uniform circular motion匀速圆周运动projectile motion抛体运动§2.4 Motion with Constant Acceleration（匀加速运动）无§2.5 Linear Motion with Constant Acceleration（匀加速直线运动）linear线性的one-dimensional一维的corresponding对应的eliminate消去freely falling bodies自由落体air resistance 空气阻力acceleration due to gravity 重力加速度altitude高度vertical direction 竖直方向negative sign 负号latitude经度regardless of与.无关maximum value最大值minimum value最小值§2.6 Projectile Motion （抛体运动）projectile抛体trajectory轨迹assumption 假设negligible可忽略的rotation 转动air friction 空气摩擦parabola抛物线parabolic trajectory 抛物线轨迹initial初始的horizontal水平的independent 独立的superposition叠加flight time飞行时间horizontal range射程maximum height最大高度horizontal surface水平面a body projected horizontally平抛物体vertical竖直的firing angle抛射角§2.7 Circular Motion（圆周运动）circular motion 圆周运动uniform circular motion匀速圆周运动circular motion with varying speed变速圆周运动centripetal向心的arc length 弧长angular displacement 角位移instantaneous angular velocity（瞬时）角速度radian(s) 弧度dimensional有量纲的counterclockwise 逆时针clockwise顺时针circle圆center of a circle圆心vectorially矢量地angular acceleration 角加速度tangential acceleration 切向加速度center-seeking 向心resolve （矢量）分解centripetal acceleration 向心加速度normal acceleration 法向加速度perpendicular to垂直于radial径向的radius半径§2.8 Relative Motion（相对运动）relative velocity相对速度relative acceleration 相对加速度observer观察者outcome结果measurement 测量stationary 静止的differentiate求微分Galilean transformation equation伽利略变换valid有效的special theory of relativity狭义相对论as it turns out结果是relative to相对于heading due north头朝北right triangle直角三角形upstream逆流hypotenuse直角三角形的斜边Chapter 3 Newton’s Laws of Motion（牛顿运动定律）§3.1 Newton’s First Law（牛顿第一定律）at rest静止net external force/ resultant force合外力inertial frame of reference 惯性参考系inertia惯性act on = exert（力）作用于approximation近似inertial mass 惯性质量interact (n. interaction)相互作用resultant external force合外力momentum动量unless stated otherwise 除非另有说明§3.2 Newton’s Second Law（牛顿第二定律）nonzero非零的mass质量momentum动量rate of change变化率directly proportional to正比于inversely proportional to反比于§3.3 Newton’s Third Law（牛顿第三定律）interact相互作用opposite相反、相对isolated 孤立的action force 作用力reaction force反作用力§3.4 Applications of Newton’s Laws（牛顿运动定律的应用）tension 张力diagram示意图isolate 隔离free-body diagram受力图unknown未知量Atwood’s Machine阿特伍德机light string轻绳vertically 竖直地frictionless 无摩擦的incline斜面pulley滑轮balanced平衡的block 木块、滑块wedge楔、斜铁plane 平面horizontal surface水平面§3.5 International Units and Dimensions（国际单位制与量纲）physical quantity物理量fundamental unit基本单位universally普遍scientific community科学界luminous intensity光强度abbreviation缩写lowercase小写的uppercase大写的rectangle矩形§3.6 Introduction to Some Common Forces（几种常见力）electromagnetic电磁的lean against 倚靠compress 压mattress spring 床垫弹簧normal force 法向力、支持力stiffness倔强性stretch 拉伸frictional force / force of friction 摩擦力viscous medium粘滞媒质（介质）resistance 阻力force of static friction 静摩擦力maximum force of static friction最大静摩擦力is proportional to正比于proportionality constant比例常数coefficient of static friction 静摩擦系数coefficient of kinetic friction 滑动摩擦系数variation变化§3.7 The Four Fundamental Forces（四种基本力）gravitational force 引力universal gravitational constant万有引力常数electromagnetic force电磁力bind约束Coulomb’s law库仑定律charged particle带电粒子strong nuclear force 强力hydrogen氢nucleus (pl. nuclei or nucleuses)原子核neutron 中子proton质子counteract抵抗repulsive排斥的strength强度weak nuclear force弱力short-range force 短程力radioactivity放射性radioactive decay 放射性衰变nucleons核子massless 无质量的action at a distance远程作用hypothesis 假设field场Chapter 4Linear Momentum and Angular Momentum （动量与角动量）§4.1 Linear Momentum and Impulse（动量与冲量）(linear) momentum动量impulse 冲量impulse-momentum theorem动量定理time-average force 平均冲力§4.2 Impulse-momentum Theorem for Particles System（质点系的动量定理）particles system 质点系internal forces 内力external forces 外力§4.3 Conservation of Linear Momentum（动量守恒定律）momenta（pl.）动量§4.4 Center of Mass（质心）vector notation矢量表示continuous object连续物体element of mass 质元§4.5 Motion of the Center of Mass（质心的运动）conserved 守恒的isolated system 孤立系统§4.6 Angular Momentum of a Particle（质点的角动量）conserved 守恒的isolated system 孤立系统§4.7 Conservation Law of Angular Momentum（角动量守恒定律）Kepler 开普勒ellipse椭圆Chapter 6 Rotation of a Rigid Body about a Fixed Axis （刚体的定轴转动）§6.1 Motion of a Rigid Body（刚体的运动）rigid body刚体parallelogram rule 平行四边形法则translation 平动an extended body 空间实体rotation 转动nondeformable 不变形的resultant motion 合运动parallel平行fixed axis 固定轴counterclockwise motion 逆时针运动angular acceleration 角加速度clockwise motion顺时针运动separation 间隔translation 平动angular velocity 角速度trajectory 轨迹§6.2 Law of Rotation of a Rigid Body about a Fixed Axis（刚体定轴转动定律）moment of inertia 转动惯量rotation axis 旋转轴torque 力矩proportionality constant比例常数element of mass 质元line of action of force 力的作用线analogue 类似；相似perpendicular distance垂直距离distribution of mass 质量分布pivot about 围绕…旋转；以…为轴旋转moment arm 力臂is proportional to与…成正比§6.3 Calculation of Moments of Inertia for Rigid Bodies（转动惯量的计算）an extended body 延续实体hoop圆环spherical shell薄球壳solid sphere实心球spherical cavity球腔linear density线密度§6.4 Application of Law of Rotation of a Rigid Body about a Fixed Axis（刚体定轴转动定律应用）orientation 方向；方位atwood’s machine伍德机brake制动器，刹车pedal踏板sprocket链轮齿bearing轴承pulley滑轮nonslip 无滑动§6.5 Conservation of Angular Momentum with Respect to the Fixed Axis（对定轴角动量守恒）resultant external torque合外力矩isolated隔离的valid 有效；适用pin 销；轴hapter 7Electric Fields of Stationary Electric Charges（静止电荷的电场）§7.1 Charge（电荷）Electricity电学magnetism磁学accelerator 加速器interatomic原子间的amber琥珀magnetite磁铁矿electrification充电magnet磁铁charge 电荷quantized量子化的quantization量子化proton质子electrically charged带电的charged body带电体conservation守恒uncharged不带电的§7.2 Coulomb’s Law（库仑定律）Coulomb’s Law库仑定律inversely proportional to相反地separating 分开的permittivity介电常数hydrogen氢opposite sign符号相反§7.3 The Electric Field（电场）electric field 电场test charge检验电荷distribution分布X-ray X-射线lightning闪电electronic电子的intermolecular分子间的rub摩擦magnesia氧化镁electromagnetism电磁学plastic rod塑料棒repel排斥attract 吸引suspend悬挂neutron中子electron电子neutral中性的integer整数integral multiple整数倍proportional to正比于square平方product乘积repulsive排斥Coulomb constant库仑常数superposition principle叠加原理electric field (intensity) 电场强度source charge场源电荷radio waves无线电波atmosphere大气thundercloud 雷雨云§7.4 Calculation of Electric Field（电场的计算）stationarydenominatorelectric dipoleelectric dipole moment spherically symmetriccontinuous charge distributioncharge elementstrategy静止的分母电偶极子电偶极矩球对称电荷连续分布元电荷策略bisector平分线manipulation处理linear charge density电荷线密度surface charge density 电荷面密度volume charge density电荷体密度ring charge带电圆环charged disk带电圆盘infinite plate of charge无限大带电平面§7.5 Electric Field Lines and Electric Flux（电场线和电通量）electric field lines电场线electric flux电通量infinity无穷远visualize形象化strength强度penetrate穿过qualitative定量的closed surface闭合曲面align排列thread线intersection 相交cross交叉§7.6 Gauss’s Law（高斯定理）Gauss’s law 高斯定理arbitrary shape 任意形状gaussian surface 高斯面electric flux电通量principle 原理practice实际§7.7 Application of Gauss’s Law（高斯定理的应用）algebraic代数的rearrange重新整理charge distribution电荷分布spherical symmetry 球对称cylindrical symmetry 柱对称plane symmetry 平面对称symmetric对称的spherical shell球壳infinite length无限长infinite plane无限大平面Chapter 8 Electric Potential（电势）§8.1 Conservativity of Electrostatic Field（静电场的保守性）line integral线积分conservative force field 保守力场closed path闭合路径conservative保守的circuital theorem for electrostatic field静电场环路定理§8.2 Potential Difference and Electric Potential（电势差和电势）potential difference电势差electric potential电势infinity无穷远electrostatic potential energy 静电势能volt伏特voltage电压electron volt电子伏特battery电池§8.3 Calculation of Electric Potential（电势的计算）equipotential surface等势面broken lines虚线semicircular半圆的insulating绝缘的infinite无限的dashed lines虚线extend延伸solid lines实线finite有限的arbitrary任意的function函数curved surface曲面§8.4 Electric Potential Gradient（电势梯度）gradient梯度notation符号potential Gradient电势梯度maximum最大值right angle 直角sketch勾画§8.5 Electrostatic Potential Energy（静电势能）electrostatic potential energy 静电势能vicinity附近Chapter 9 Conductor in Electrostatic Field（静电场中的导体）§9.1 Conductors in Electrostatic Equilibrium（导体的静电平衡）isolated conductor 孤立导体electrostatic equilibrium静电平衡equipotential body等势体radius of curvature曲率半径electrostatic shielding静电屏蔽neutralize电中和sharp point discharge尖端放电lightning rod 避雷针cosmic rays 宇宙射线lightning stroke雷击glow discharge 辉光放电ion离子corona discharge电晕放电shrink收缩cavity 空腔grounding接地curved surface 曲面conducting wire导线collision碰撞thunderstorm雷暴induced charge 感应电荷insert插入guarantee保证contradiction 矛盾§9.2 Calculation of Electrostatic Field with Conductors Nearby （有导体存在时静电场的分析与计算）conducting slab 导电板lateral area侧面uncharged conductor不带电导体edge effect边缘效应redistribute 重新分配external外部Chapter 10 Capacitors and Dielectrics in Electrostatic Field （电容器和静电场中的电介质）§10.1 Capacitance and Capacitors（电容和电容器）Leyden jar 莱顿瓶flash 闪光灯capacitance电容coaxial同轴的capacitor电容器coaxial cable同轴电缆parallel-plate capacitor 平行平板电容器concentric同心的cylindrical capacitor圆柱形电容器parallel combination 并联spherical capacitor 球形电容器series combination串联submultiple因数farad 法拉microfarad 微法拉picofarad 皮法拉rectify 调整inductance 自感应ignition 点火sparking打火花metallic金属(性)的combination联合、组合equivalent相当的§10.2 Dielectrics and Electric Field（电介质与电场）dielectric电介质relative dielectric constant 相对介电常数voltmeter 伏特计insulating绝缘的dielectric breakdown介质击穿dielectric strength介电强度§10.3 Polarization of Dielectrics（电介质的极化）polarize极化polar molecules极性分子polarization 极化nonpolar molecules非极性分子induced dipole moments 感应电矩permanent electric dipole moments 固有电矩surface charge表面电荷align排成一线orient取向bound charge束缚电荷homogeneous 均匀的free charge 自由电荷microwave 微波oven 烤箱vibrate 振动tune 调整resonate 共振oscillate 振荡§10.4 Gauss’s Law for Electric Displacement Vector （高斯定律）electric displacement 电位移dielectric constant介电常数deliberately故意地the flux of D(r) D(r) 的通量permittivity电容率§10.5 Energy Stored in a Charged Capacitor（电容器的能量）transfer转移electrostatic potential energy 静电势能battery电池electrostatic field energy 静电场能increment 增量energy density能量密度transformation转化maximum operating voltage 最大工作电压terminal 终端deliver递送dissipate消散pathway路径Chapter 11 Magnetic Force (磁力)§11.1 Nature of Magnetic Force(磁力的本质)magnetite磁铁矿石bar magnet条形磁铁interaction 相互作用magnetic pole磁极electric current loops of molecules分子环形电流§11.2 Magnetic Field and Magnetic Field Vector(磁场和磁感应强度)magnetic field磁场magnetic field vector=magnetic induction =magnetic flux density磁感应强度magnetic force 磁场力Lorentz force 洛仑兹力B-line磁感(应)线magnetic flux磁通量tesla(T)特（斯拉）weber韦伯§11.3 Motion of a Charged Particle in a Magnetic Field(带电粒子在磁场中的运动)cyclotron period回旋周期magnetic focusing磁聚焦helix螺旋线pitch螺距magnetic lens磁镜magnetic confinement 磁约束a magnetic bottle磁瓶the mass spectrometer 质谱仪schematic drawing示意图ion离子precision 精确度proton质子deuteron 氘核bombard 轰击cyclotron 加速器dees D型盒evacuate抽成真空shield屏蔽oscillate 振动plasma等离子体nuclear fusion核聚变Van Allen belts范阿仑辐射带§11.4 The Hall Effect(霍尔效应)the Hall voltage 霍尔电压the drift velocity漂移速度§11.5 Magnetic Force on a Current-carrying Conductor(载流导体在磁场中受力—安培力)current-carrying conductor/wire载流导体/导线current loop in a uniform magnetic field匀强磁场中的载流线圈linear element 线元current element vector 电流元矢量loop 环, 回路magnetic moment of a current loop载流线圈磁矩rectangular loop矩形回路a wire segment 一段导线strip 条；带Chapter 12 Source of Magnetic Field（磁场的源）§12.1 The Magnetic Field of Moving Point Charges（运动点电荷的磁场）permeability of free space真空磁导率§12.2 The Biot-Savart Law（毕奥-萨伐尔定律）the Biot-Savart Law毕奥-萨伐尔定律permeability of free space真空磁导率Gauss’law in magnetism磁场的高斯定律magnetic monopoles磁单极solenoid螺线管turn匝current-carrying wire 载流导线encircle环绕current element电流元diverge发散converge聚合magnetic pole磁极magnet磁铁magnetic flux磁通量§12.3 Ampere Circuital Theorem （安培环路定理）penetrate穿过bounded by以…为边界finite point 有限点line integral线积分§12.4 Application of Ampere Circuital Theorem（安培环路定理的应用）current-carrying wire 载流导线circumference 周长cylindrical shell圆柱形壳toroid螺绕环inner radius 内径outer radius外径spherical conductor 球形导体§12.5 Magnetic Field due to Varying Electric Field（与变化的电场相联系的磁场）displacement current位移电流generalized Ampere’s Law广义安培环路定理conduction current传导电流magnetic monopole磁单级postulate假设total current全电流steady current恒定电流§12.6 The Magnetic Force Between Two Parallel Current-carryingWires（平行电流间的相互作用力）antiparallel反平行Chapter 13 Magnetic Media in Magnetic Field（磁场中的磁介质）§13.1 Effect on Magnetic Field Caused by Magnetic Media（磁介质对磁场的影响）magnetic medium磁介质diamagnetic medium抗磁质paramagnetic medium顺磁质ferromagnetic material 铁磁质magnetic moment 磁矩paramagnetism 顺磁性partial alignment部分取向electron spin 电子自旋magnetic dipole 磁偶极子ferromagnetism 铁磁性diamagnetism抗磁性induced magnetic moment感生磁矩permanent magnetic moment固有磁矩§13.2 Atomic Magnetic Dipole Moments（原子磁矩）magnetization磁化atomic原子的magnetic dipole moment磁矩orbital magnetic moment 轨道磁矩quantum theory量子理论intrinsic spin angular momentum内禀自旋角动量§13.3 Magnetization（磁介质的磁化）magnetization n.磁化、磁化强度magnetize . 磁化atomic current loopamperian currentcross-sectional area分子环流v安培电流横截面积induced magnetic dipole moments感生磁矩surface magnetization current/ bound current 面磁化电流(面束缚电流)applied magnetic field外加磁场magnetic susceptibility磁化率relative permeability相对磁导率bismuth 铋Bohr magneton玻尔磁子superconductor超导体emf电动势§13.4 Ferromagnetic Materials（铁磁质）iron铁cobalt钴nickel镍alloy 合金ferromagnetism 铁磁性magnetic domain磁畴critical temperature临界温度Curie temperature居里温度thermal agitation热扰动end effect边界效应magnetic saturation磁饱和reversible 可逆的magnetic hysteresis磁滞效应hysteresis loop 磁滞回线magnetization curve磁化曲线initial magnetization curve起始磁化曲线remnant magnetization剩磁coercive force矫顽力memory 记忆能力magnetize磁化demagnetize去磁，退磁transformer 变压器motor 电动机secondary coil副线圈cycle循环irreversible process 不可逆过程hard ferromagnetic materials硬磁性材料soft ferromagnetic materials软磁性材料hysteresis loss磁滞损耗（铁损）Curie point居里点permanent magnet永久磁体, magnetic tape磁带，memory unit记忆元件iron cores铁芯galvanometer 电流计rr§13.5 Circuital Theorem for H （H 的环路定理）magnetic intensity磁场强度magnetization current 磁化电流free current自由电流isotropic各向同性的permeability磁导率relative permeability相对磁导率Chapter 14 Electromagnetic Induction（电磁感应）§14.1 Faraday Law of Electromagnetic Induction（法拉第电磁感应定律）electromagnetic induction 电磁感应induction current感应电流emf (electromotive force) 电动势induction emf 感生电动势weber韦伯Lenz Law楞次定律polarity极性§14.2 Motional emf（动生电动势）motional emf 动生电动势§14.3 Induced emf and Induced Electric Field（感生电动势和感生电场）nonelectrostatic force非静电力induced emf 感生电动势induced electric field感生电场vortex field涡旋场eddy currents 涡流nonconservative field 非保守场time-varying field时变场alternate变化alternative 交流电的，交变的laminated叠片（组成）的§14.4 Mutual Induction（互感现象）mutual induction互感现象mutual inductance互感系数emf by mutual induction互感电动势orientation 方位§14.5 Self-induction（自感现象）self-induction自感现象self-inductance 自感系数inductor电感self-induced emf 自感电动势is proportional to正比于§14.6 Energy of Magnetic Field（磁场的能量）magnetic energy density磁场能量密度energy due to mutual induction互感磁能Chapter 15 Maxwell’s Equations and Electromagnetic Waves （麦克斯韦方程组组与电磁波波）§15-1 Maxwell’s Equations（麦克斯韦方程组）§15-2 Electromagnetic Waves（电磁波）propagation传播in phase同相、同步transverse waves横波wavelength波长visible spectrum可见光谱infrared waves 红外波radiation 辐射ultraviolet ray紫外线Poynging vector 坡印亭矢量§15-3 The Wave Equation for Electromagnetic Waves（电磁波的方程）wave function波函数wave equation波的方程wave number 波数angular frequency 角频率plane wave平面波Chapter 16 Temperature and the Kinetic Theory of Gases（温度与气体运动论）§16.1 Thermal Equilibrium and Temperature （热平衡及温度）temperature 温度hotness热coldness冷thermometric property热力学特性thermal contact热接触the average internal molecular kinetic energy 分子内平均动能thermal equilibrium热平衡electrical conductor 导电器the zeroth law of thermodynamics热力学第零定律temperature scale温标§16.2 The Celsius and Fahrenheit Temperature Scales（摄氏温标与华氏温标）thermometer温度计temperature scale温标the ice-point temperature冰点温度freezing point冰点steam-point沸点normal boiling point标准沸点the steam-point temperature 气化点温度the Celsius temperature scale摄氏温标the Fahrenheit temperature scale华氏温标§16.3 Gas Thermometers and the Absolute Temperature Scale（气体温度计和绝对温标）calibrate 校对、校准discrepancy差异volume 体积density密度sufficiently low 足够低sulfur硫a constant-volume gas thermometer等容气体温度计triple point of water 水的三相点ideal-gas temperature scale理想气体温标absolute temperature scale绝对温标nitrogen氮hydrogen氢oxygen氧recalibrate再校准extrapolate外推，向外延长triple point 三相点coexist共存helium氦liquefy液化in terms of 利用rigid body刚体insulator绝缘体Kelvin scale 开尔文温标§16.4 The Ideal-Gas Law（理想气体定律）Boyle’s law玻意耳定律constant volume 等体Boltzmann’s constant玻耳兹曼常量mole摩尔Avogadro’s number 阿伏伽德罗常量carbon atom碳原子universal gas constant普适气体常量ideal gas理想气体equation of state状态方程state variable状态参量standard condition标准条件subscript 下标§16.5 The Kinetic Theory of Gases（气体分子运动论）macroscopic state variable宏观状态变量microscopic quantity微观量walls of a container容器壁translational kinetic energy平动动能root mean square (rms) speed方均根速率order of magnitude量级piston活塞redistribute 再分布partition 分配equipartition theorem（能）均分定理classical statistical mechanics经典统计力学degree of freedom自由度monatomic 单原子的bond键diatomic 双原子的polyatomic 多原子的vibration振动mean free path平均自由程air current 气流convection 对流diffuse扩散reciprocal倒数frequency频率§16.6 Maxwell Speed Distribution Function（麦克斯韦速率分布函数）probability概率abscissa横坐标normalization condition 归一化条件most probable distribution最概然分布Chapter 17 Heat and the First Law of Thermodynamics （热及热力学第一定律）§17.1 Heat Capacity and Specific Heat（热容与比热）atomist 原子学家thermal energy 热能manifestation 表现形式molecular motion 分子运动thermal contact热接触caloric a.热的n.热（质）internal energy 内能heat capacity热容量phase相heat conduction热传导calorie卡（路里）molar mass摩尔质量Law of conservation of energy能量守恒定律The first law of thermodynamics 热力学第一定律be proportional to和…成正比molar specific heat摩尔比热solar heating system太阳能热系统coolant冷却液§17.2 Change of Phase and Latent Heat（相变与潜热）heat capacity热容量phase change相变vaporization汽化，蒸发fusion 熔化melting融化condensation 凝聚sublimation升华carbon dioxide二氧化碳crystalline a. 结晶的、晶状的n.结晶体average translational kinetic energy平均平动动能latent heat潜热§17.3 Joule’s Experiment（焦耳实验）thermally insulated绝热的mechanical equivalence of heat热功当量§17.4 The Internal Energy of an Ideal Gas（理想气体内能）internal energy 内能real gas实际气体§17.5 Work and the PV Diagram for a Gas（功与气体PV图）quasi-static process准静态过程piston活塞isobaric等压的isothermal 等温的§17.6 The First Law of Thermodynamics（热力学第一定律）§17.7 Heat Capacities of Gases（气体的热容）infinitesimal无穷小的§17.8 The Quasi-Static Adiabatic Process for an Ideal Gas（理想气体准静态绝热过程）compression 压缩Poisson formula 泊松公式process equations 过程方程。

数据科学基础课件-第2章高维空间(High-Dimensional Space)

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符号说明
一般按下列约定使用符号
小写字母表示标量变量和函数粗体小写字母表示向量，如
x表示向量；xi 表示x中的第i维
大写字母表示矩阵
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主要内容
The Law of Large Numbers The Geometry of High Dimensions Properties of the Unit Ball Generating Points Uniformly at Random from a Ball Gaussians in High Dimension Separating Gaussians Fitting a Single Spherical Gaussian to Data Random Projection and Johnson-Lindenstrauss Lemma
数据科学基础高维空间(High-Dimensional Space)
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事物的次要因素与统计规律
客观世界中作用于事物的因素分为基本因素和次要因素，分别决定事物的必然规律和统计规律
人们所能认识而且能够控制的因素是基本因素，而大量的次要因素未能为人们所认识或未能被人们所控制
统计规律是随机事件的整体性规律，是事件系统所具有的必然性
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Generating Points Uniformly at Random from a Ball
从单位球的表面均匀随机产生点
均匀随机：随机选取，并且每个点被选取的概率都是等同的
d = 2,从单位圆的周长上均匀随机பைடு நூலகம்生点
两个维度分别独立地从区间[-1,1]上均匀随机产生，则可能得到的点在以原点为中心，边长为2的正方形中
also concentrated at its equator

台球运动物理计算方法

台球运动物理计算方法英文回答：Physics plays a crucial role in the game of billiards. Understanding the principles of physics can help players improve their skills and make accurate shots. In this article, I will explain some of the key physics concepts involved in playing billiards.One important concept in billiards is the concept of momentum. Momentum is the product of an object's mass andits velocity. When a cue ball collides with another ball, momentum is transferred from the cue ball to the other ball. According to the law of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision. This means that if the cueball is moving at a high velocity, the other ball will also gain a significant velocity after the collision. Understanding this concept can help players predict the paths of the balls and plan their shots accordingly.Another important concept is the concept of angular momentum. When a ball is spinning, it has angular momentum. The conservation of angular momentum states that the total angular momentum of a system remains constant unless acted upon by an external torque. In billiards, players often apply spin to the cue ball to control its path after collision with other balls. By applying spin, players can change the direction and speed of the cue ball, allowingfor more precise shots. For example, by applying topspin, the cue ball will have a forward roll after collision, while applying backspin will cause the cue ball to reverse its direction.Friction also plays a role in billiards. When the cue ball strikes another ball, friction between the two surfaces affects the outcome of the collision. Friction can cause the cue ball to spin or slide after impact, altering its trajectory. By understanding the effects of friction, players can adjust their shots to achieve the desired outcome.In addition to these concepts, the angle of incidence and the angle of reflection are important in billiards. When the cue ball strikes a ball at a certain angle, itwill bounce off at an equal angle in the opposite direction. This principle is known as the law of reflection. By understanding this principle, players can plan their shotsto achieve desired positionings and angles.中文回答：台球运动中的物理学起着至关重要的作用。

数学专业英语词汇（U）_数学物理英语词汇

u statistic u统计量ulm factor 乌姆因子ultra filter base 超滤子基ultra ideal 超理想ultra power 超幂ultrabarrelled space 超桶型空间ultrabornological space 超有界型空间ultrafilter 超滤子ultrafilter space 超滤子空间ultrahyperbolic equation 超双曲型方程ultrametric space 超度量空间ultraproduct 超积ultraspherical polynomials 特种球多项式umbilical point 脐点unary operation 一元运算unary relation 一元关系unbiased confidence estimation 无偏置信估计unbiased estimate 无偏估计unbiased estimating equation 无偏估计方程unbiased estimator 无偏估计量unbiased sample 无偏样本unbiased test 无偏检验unbiasedness 无偏性unbounded function 无界函数unbounded interval 无界区间unbounded operator 无界算子unbounded quantifier 无界量词unbounded sequence 无界序列unbounded set 无界集unboundedness 无界性uncertainty 不定uncertainty principle 测不准原理unconditional convergence 无条件收敛unconditional inequality 无条件不等式unconditional jump 无条件跳跃unconditionally convergent 无条件收敛的unconditionally convergent series 无条件收敛级数unconnected graph 不连通图unconnected space 不连通空间unconnectedness 不连通性uncorrelated 不相关的uncorrelated random variables 不相关随机变量uncountability 不可数性uncountable 不可数的uncountable ordinal 不可数序数undecidability 不可判定性undecidability theorem 不可判定性定理undecidable theory 不可判定理论underdeterminate system 欠定组underdeterminate system of partial differential equations 欠定偏微分方程组underlying graph 底图underlying group 基础群underlying topological space 基础拓扑空间underlying topology 基础拓扑undetermined 未定的undetermined coefficient 末定系数undetermined number 未定数undirected edge 无向棱undirected graph 无向图undisturbed differential equation 无扰动微分方程unduloid 波状体unequal 不等的ungula of the cone 锥的蹄状体ungula of the cylinder 柱的蹄状体ungula of the prism 棱柱的蹄状体uniaxial 单轴的unicity 唯一性uniconvergence space 单收敛空间unicursal 单行的unicursal curve 有理曲线unicursal graph 单行图unicursal involution 单行对合unicursal surface 单行曲面unidirectional 单方面的unified field theory 统一场论uniform 匀的uniform approximation 一致逼近uniform boundedness principle 一致有界原理uniform continuity 一致连续性uniform convergence 一致收敛uniform cover 一致覆盖uniform distribution 均匀分布uniform equicontinuity 一致同等连续性uniform invariant 一致不变量uniform isomorphism 一致同胚uniform limit 一致极限uniform scale 等分标尺uniform space 一致空间uniform stability 一致稳定性uniform structure 一致结构uniform topology 一致拓扑uniformity 一致结构uniformity generated by a pseudometric 伪度量一致性uniformizable 可一致化的uniformizable point 单值化点uniformizable space 单值化空间uniformization 单值化uniformization principle 一般单值化定理uniformization theorem 单值化定理uniformization theory 单值化理论uniformizing covering surface 单值化覆盖面uniformizing function 单值化函数uniformly bounded 一致有界的uniformly bounded sequence of functions 一致有界函数序列uniformly bounded series 一致有界级数uniformly bounded set 一致有界集uniformly continuous 一致连续的uniformly continuous map 一致连续映射uniformly convergent 一致收敛的uniformly convergent sequence of functions 一致收敛函数序列uniformly convex 一致凸的uniformly convex space 一致凸空间uniformly distributed random variable 均匀分布随机变量uniformly elliptic operator 一致椭圆算子uniformly equicontinuous 一致同等连续的uniformly equivalent metric 一致等价度量uniformly equivalent space 一致等价空间uniformly integrable 一致可积的uniformly locally compact space 一致局部紧空间uniformly most powerful test 一致最大功效检定uniformly open map 一致开映射uniformly strongly elliptic operator 一致强椭圆算子uniformly summable family of functions 一致可积函数族unilateral 单侧的unilateral surface 单侧曲面unimodal 单峰的unimodal distribution 单峰分布unimodular group 幺模群unimodular map 幺模映射unimodular matrix 幺模阵unimodular number 单模数unimodularly bounded function 幺模有界函数union 并集union of sets 集的并unipotent element 幂幺元unipotent group 幂单群unipotent matrix 幂单矩阵unique existence 唯一存在性unique factorization domain 唯一析因整环unique factorization theorem 唯一析因定理unique solution 唯一解uniquely defined 唯一定义的uniqueness 唯一性uniqueness condition 唯一性条件uniqueness theorem 唯一性定理unirational variety 单有理簇uniserial algebra 单列代数unit ball 单位球unit character 单位特贞unit circle 单位圆unit disk 单位园板unit divisor 单位因子unit dyad 单位并向量unit filter 单位滤子unit function 单位函数unit group 单位群unit ideal 单位理想unit idele 单位伊代尔unit interval 单位区间unit line 单位线unit lower triangular matrix 单位下三角阵unit matrix 单位矩阵unit of angle 角的单位unit of area 面积单位unit of volume 体积单位unit operator 恒等算子unit point 单位点unit representation 恒等表示unit simplex 单位单形unit sphere 单位球unit square 单位平方形unit tangent 单位切向量unit tensor 单位张量unit theorem 单元定理unit transformation 恒等变换unit vector 单位向量unitarily equivalent operator 酉等价算子unitarily equivalent representation 酉等价表示unitarity 酉性unitary 单式的unitary algebra 单式代数unitary bundle 酉丛unitary connection 酉朕络unitary geometry 酉几何unitary group 酉群unitary homomorphism 单式同态unitary invariant 酉不变量unitary matrix 酉矩阵unitary modular group 特殊酉群unitary operator 酉算子unitary r module 单式r模unitary representation 酉表示unitary similar matrix 酉相似矩阵unitary space 酉空间unitary transfer 酉朕络unitary transformation 酉变换unity 单位元素unity element 单位元素unity group 单位群univalent 单叶的univalent function 单叶函数univariable series 单变量级数universal affirmative proposition 全称肯定命题universal bundle 通用丛universal class 全类universal coefficient formula 万有系数公式universal coefficient theorem 万有系数定理universal covering 通用覆盖universal covering group 通用覆盖群universal covering manifold 通用覆盖廖universal covering space 万有覆盖空间universal covering surface 万有覆盖面universal curve 万有曲线universal domain 万有域universal enveloping algebra 通用包络代数universal function 通用函数universal map 通用映射universal negative proposition 全称否定命题universal proposition 一般命题universal quantifier 全称量词universal relation 通用关系universal set 通用集合universal subgroup 通用子群universal validity 一般有效性universal variety 普遍簇universally japanese ring 伪几何环universally maximal left ideal 普遍极大左理想universally maximal twosided ideal 普遍极大双侧理想universally minimal right ideal 普遍极小右理想universally valid formula 普遍有效公式unknown 末知的unknown number 未知数unlimited 无限的unlimited covering manifold 无限覆盖廖unlimitedness 无穷unmixed ideal 纯理想unordered pair 无序对unparted hyperboloid 单叶双曲面unramified covering 非分歧覆盖unramified covering surface 非分歧覆盖面unramified extension 非分歧扩张unramified manifold 非分歧廖unramified prime ideal 非分歧素理想unramified ring 非分歧环unsolvability 不可解性unsolvable 不可解的unsolvable equation 不可解方程unstability 不稳定性unstable 不稳定的unstable solution 不稳定解unweighted mean 未加权平均数upper bound 上界upper central series 上中心列upper class 上类upper control limit 上控制限upper derivative 上导数upper envelope 上包络upper half plane 上半平面upper limit 上极限upper limit of integration 积分的上限upper pure value 上纯值upper quartile 上四分位数upper semi continuous decomposition 上半连续分解upper semicontinuity 上半连续性upper semicontinuous 上半连续的upper semilattice 上半格upper triangular matrix 上三角形矩阵upper value of game 对策上方值upper variation 正变差useful direction 有效方向utility 效用utility function 效用函数utility theory 效用理论。

美国数学竞赛amc8的常用数学英语单词

美国数学竞赛amc8的常用数学英语单词等于equals, is equal to, is equivalent to 大于is greater than 小于is lesser than 大于等于is equal or greater than 小于等于is equal or lesser than运算符operator 数字digit 数number 自然数natural number公理axiom 定理theorem 计算calculation 运算operation 算术arithmetic 证明prove 假设hypothesis, hypotheses（pl.）命题proposition加plus（prep.）, add（v.）, addition（n.）被加数augend, summand 加数addend 和sum减minus（prep.）, subtract（v.）, subtraction（n.）被减数minuend 减数subtrahend 差remainder乘times（prep.）, multiply（v.）, multiplication（n.被乘数multiplicand, faciend 乘数multiplicator 积product除divided by（prep.）, divide（v.）, division（n.）被除数dividend 除数divisor 商quotient整数integer 小数decimal 小数点decimal point分数fraction 分子numerator 分母denominator 比ratio正positive 负negative 零null, zero, nought, nil十进制decimal system 二进制binary system 十六进制hexadecimal system权weight, significance 进位carry 截尾truncation四舍五入round 下舍入round down 上舍入round up有效数字significant digit 无效数字insignificant digit代数algebra 公式formula, formulae（pl.）单项式monomial 多项式polynomial, multinomial 系数coefficient未知数unknown, x-factor, y-factor, z-factor等式，方程式equation 一次方程simple equation 二次方程quadratic equation 不等式inequation 三次方程cubic equation 四次方程quartic equation阶乘factorial 对数logarithm 指数，幂exponent乘方power 二次方，平方square 三次方，立方cube四次方the power of four, the fourth powern次方the power of n, the nth power开方evolution, extraction 二次方根，平方根square root三次方根，立方根cube root 四次方根the root of four, the fourth rootn次方根the root of n, the nth root集合aggregate 元素element 空集void 子集subset 交集intersection 并集union 补集complement映射mapping 图象image 函数function 定义域domain, field of definition 值域range 周期性periodicity常量constant 变量variable 单调性monotonicity 奇偶性parity数列，级数series 微积分calculus 微分differential 导数derivative积分integral 定积分definite integral 不定积分indefinite integral有理数rational number 无理数irrational number 实数real number虚数imaginary number 复数complex number极限limit 无穷大infinite（a.）infinity（n.）无穷小infinitesimal矩阵matrix 行列式determinant几何geometry 点point 线line 面plane 体solid 线段segment射线radial 平行parallel 相交intersect角angle 角度degree 弧度radian 周角perigon锐角acute angle 直角right angle 钝角obtuse angle 平角straight angle底base 边side 高height直角边leg 斜边hypotenuse 勾股定理Pythagorean theorem三角形triangle 锐角三角形acute triangle 直角三角形right triangle钝角三角形obtuse triangle 不等边三角形scalene triangle等腰三角形isosceles triangle 等边三角形equilateral triangle长length 宽width四边形quadrilateral 平行四边形parallelogram 矩形rectangle菱形rhomb, rhombus, rhombi（pl.）, diamond 正方形square梯形trapezoid 直角梯形right trapezoid 等腰梯形isosceles trapezoid多边形polygon 正多边形equilateral polygon 五边形pentagon六边形hexagon 七边形heptagon 八边形octagon 九边形enneagon十边形decagon 十一边形hendecagon 十二边形dodecagon圆circle 圆心centre（BrE）, center（AmE）半径radius 直径diameter 圆周率pi 弧arc 半圆semicircle扇形sector 环ring 椭圆ellipse圆周circumference 周长perimeter 面积area 轨迹locus, loca（pl.）相似similar 全等congruent立方体cube 多面体polyhedron 四面体tetrahedron 五面体pentahedron 六面体hexahedron 平行六面体parallelepiped 七面体heptahedron八面体octahedron 九面体enneahedron 十面体decahedron十一面体hendecahedron 十二面体dodecahedron 二十面体icosahedron棱锥pyramid 棱柱prism 棱台frustum of a prism旋转rotation 轴axis 圆锥cone 圆柱cylinder 圆台frustum of a cone球sphere 半球hemisphere底面undersurface 表面积surface area 体积volume空间space 坐标系coordinates 坐标轴x-axis, y-axis, z-axis 原点origin横坐标x-coordinate 纵坐标y-coordinate 双曲线hyperbola 抛物线parabola三角trigonometry 正弦sine 余弦cosine 反正弦arc sine 反余弦arc cosine 正切tangent 余切cotangent 反正切arc tangent 反余切arc cotangent正割secant 余割cosecant 反正割arc secant 反余割arc cosecant相位phase 周期period 振幅amplitude内切圆inscribed circle 外切圆circumcircle内心incentre（BrE）, incenter（AmE）外心excentre（BrE）, excenter（AmE）旁心escentre（BrE）, escenter（AmE）垂心orthocentre（BrE）, orthocenter（AmE）重心barycentre（BrE）, barycenter（AmE）统计statistics 平均数average 加权平均数weighted average概率，或然率probability标准差root-mean-square deviation, standard deviation 分布distribution 正态分布normal distribution 非正态分布abnormal distribution图表graph 条形统计图bar graph 柱形统计图histogram折线统计图broken line graph 曲线统计图curve diagram扇形统计图pie diagram比例propotion 百分比percent 百分点percentage 百分位数percentile排列permutation 组合combination。

构造圆物理

Reading books is not just a form of entertainment; it is a useful activity that offers a wide range of benefits for individuals. Whether it is fiction or non-fiction, books provide a wealth of knowledge, improve literacy skills, stimulate the imagination, enhance empathy, and contribute to personal growth and development. Let’s explore some of the reasons why reading books is valuable.1.Knowledge acquisition: Books are treasure troves of information.They cover a wide range of topics, from science and history to philosophy and art. Reading allows us to dive deep into these subjects, learning about newideas, facts, and perspectives. It broadens our horizons, making us moreinformed and well-rounded individuals.2.Enhancement of literacy skills: Reading is essential for developingstrong literacy skills. It improves vocabulary, expands language proficiency, and strengthens reading comprehension abilities. As we read more, we become more proficient in expressing ourselves verbally and in writing. This has aprofound impact on academic and professional success.3.Imagination and creativity: Books have the power to transport us todifferent worlds and stimulate our imagination. They allow us to visualizesettings, characters, and events, creating vivid mental images. This imaginative exercise can spark creativity in our own lives and inspire innovative thinking.4.Empathy development: Reading fiction exposes us to diversecharacters and their experiences. It helps us understand and empathize with people from different backgrounds, cultures, and perspectives. By delving into the lives of others, we cultivate empathy, compassion, and tolerance, which are crucial for building a more inclusive and harmonious society.5.Stress reduction and relaxation: Engaging in a good book is anexcellent way to unwind and de-stress. Reading can transport us to a fictional realm or help us delve into a subject that fascinates us. This escape from reality promotes relaxation and rejuvenation, offering a break from the pressures of daily life.6.Cognitive development: Reading exercises our brains, improvingcognitive functions such as memory, concentration, and critical thinking. Itchallenges us to analyze and interpret information, stimulating mental agility and problem-solving skills. Research has shown that reading can even helpdelay age-related cognitive decline.7.Personal growth and self-reflection: Books often contain valuable lifelessons and insights. They offer different perspectives on personal and societal issues, allowing us to reflect on ourselves and the world around us. Reading can inspire personal growth, encouraging introspection and fostering a betterunderstanding of ourselves and others.nguage improvement: Reading books, especially well-written ones,exposes us to proper grammar, sentence structures, and language nuances. This exposure to high-quality writing enhances our language skills, making us more effective communicators. It helps us develop a rich vocabulary and improves our writing style.9.Open-mindedness and critical thinking: Reading exposes us to avariety of ideas and perspectives. It challenges our preconceived notions and biases, promoting open-mindedness and critical thinking. It encourages us to question assumptions, consider different viewpoints, and develop our owninformed opinions.10.Entertainment and escapism: Lastly, reading books is simplyenjoyable. It allows us to experience thrilling adventures, emotional journeys, and fascinating worlds. It provides entertainment, escapism, and relaxation,offering a much-needed break from the digital distractions and fast-pacedsociety we live in.In conclusion, reading books is a valuable and useful activity that offers a multitude of benefits. It expands our knowledge, enhances literacy skills, stimulates the imagination, nurtures empathy, promotes personal growth, and provides relaxation and entertainment. So, let’s pick up a book and embark on a journey of learning and discovery.。

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