2004-01-1230Synchronizer Design A Mathematical and Dimensional Treatise

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[ToG13]Poisson Surface Reconstruction

Screened Poisson Surface ReconstructionMICHAEL KAZHDANJohns Hopkins UniversityandHUGUES HOPPEMicrosoft ResearchPoisson surface reconstruction creates watertight surfaces from oriented point sets.In this work we extend the technique to explicitly incorporate the points as interpolation constraints.The extension can be interpreted as a generalization of the underlying mathematical framework to a screened Poisson equation.In contrast to other image and geometry processing techniques,the screening term is deﬁned over a sparse set of points rather than over the full domain.We show that these sparse constraints can nonetheless be integrated efﬁciently.Because the modiﬁed linear system retains the sameﬁnite-element discretization,the sparsity structure is unchanged,and the system can still be solved using a multigrid approach. Moreover we present several algorithmic improvements that together reduce the time complexity of the solver to linear in the number of points, thereby enabling faster,higher-quality surface reconstructions.Categories and Subject Descriptors:I.3.5[Computer Graphics]:Compu-tational Geometry and Object ModelingAdditional Key Words and Phrases:screened Poisson equation,adaptive octree,ﬁnite elements,surfaceﬁttingACM Reference Format:Kazhdan,M.,and Hoppe,H.Screened Poisson surface reconstruction. ACM Trans.Graph.NN,N,Article NN(Month YYYY),PP pages.DOI=10.1145/XXXXXXX.YYYYYYY/10.1145/XXXXXXX.YYYYYYY1.INTRODUCTIONPoisson surface reconstruction[Kazhdan et al.2006]is a well known technique for creating watertight surfaces from oriented point samples acquired with3D range scanners.The technique is resilient to noisy data and misregistration artifacts.However, as noted by several researchers,it suffers from a tendency to over-smooth the data[Alliez et al.2007;Manson et al.2008; Calakli and Taubin2011;Berger et al.2011;Digne et al.2011].In this work,we explore modifying the Poisson reconstruc-tion algorithm to incorporate positional constraints.This mod-iﬁcation is inspired by the recent reconstruction technique of Calakli and Taubin[2011].It also relates to recent work in im-age and geometry processing[Nehab et al.2005;Bhat et al.2008; Chuang and Kazhdan2011],in which a dataﬁdelity term is used to“screen”the associated Poisson equation.In our surface recon-struction context,this screening term corresponds to a soft con-straint that encourages the reconstructed isosurface to pass through the input points.The approach we propose differs from the traditional screened Poisson formulation in that the position and gradient constraints are deﬁned over different domain types.Whereas gradients are constrained over the full3D space,positional constraints are introduced only over the input points,which lie near a2D manifold. We show how these two types of constraints can be efﬁciently integrated,so that we can leverage the original multigrid structure to solve the linear system without incurring a signiﬁcant overhead in space or time.To demonstrate the beneﬁts of screening,Figure1compares results of the traditional Poisson surface reconstruction and the screened Poisson formulation on a subset of11.4M points from the scan of Michelangelo’s David[Levoy et al.2000].Both reconstructions are computed over a spatial octree of depth10,corresponding to an effective voxel resolution of10243.Screening generates a model that better captures the input data(as visualized by the surface cross-sections overlaid with the projection of nearby samples), even though both reconstructions have similar complexity(6.8M and6.9M triangles respectively)and required similar processing time(230and272seconds respectively,without parallelization).1 Another contribution of our work is to modify both the octree structure and the multigrid implementation to reduce the time complexity of solving the Poisson system from log-linear to linear in the number of input points.Moreover we show that hierarchical point clustering enables screened Poisson reconstruction to attain this same linear complexity.2.RELA TED WORKReconstructing surfaces from scanned points is an important and extensively studied problem in computer graphics.The numerous approaches can be broadly categorized as follows. Combinatorial Algorithms.Many schemes form a triangula-tion using a subset of the input points[Cazals and Giesen2006]. Space is often discretized using a tetrahedralization or a voxel grid,and the resulting elements are partitioned into inside and outside regions using an analysis of cells[Amenta et al.2001; Boissonnat and Oudot2005;Podolak and Rusinkiewicz2005], eigenvector computation[Kolluri et al.2004],or graph cut [Labatut et al.2009;Hornung and Kobbelt2006].Implicit Functions.In the presence of sampling noise,a common approach is toﬁt the points using the zero set of an implicit func-tion,such as a sum of radial bases[Carr et al.2001]or piecewise polynomial functions[Ohtake et al.2005;Nagai et al.2009].Many techniques estimate a signed-distance function[Hoppe et al.1992; 1The performance of the unscreened solver is measured using our imple-mentation with screening weight set to zero.The implementation of the original Poisson reconstruction runs in412seconds.ACM Transactions on Graphics,V ol.VV,No.N,Article XXX,Publication date:Month YYYY.2•M.Kazhdan and H.HoppeFig.1:Reconstruction of the David head ‡,comparing traditional Poisson surface reconstruction (left)and screened Poisson surface reconstruction which incorporates point constraints (center).The rightmost diagram plots pixel depth (z )values along the colored segments together with the positions of nearby samples.The introduction of point constraints signiﬁcantly improves ﬁt accuracy,sharpening the reconstruction without amplifying noise.Bajaj et al.1995;Curless and Levoy 1996].If the input points are unoriented,an important step is to correctly infer the sign of the resulting distance ﬁeld [Mullen et al.2010].Our work extends Poisson surface reconstruction [Kazhdan et al.2006],in which the implicit function corresponds to the model’s indicator function χ.The function χis often deﬁned to have value 1inside and value 0outside the model.To simplify the derivations,inthis paper we deﬁne χto be 12inside and −12outside,so that its zero isosurface passes near the points.The function χis solved using a Laplacian system discretized over a multiresolution B-spline basis,as reviewed in Section 3.Alliez et al.[2007]form a Laplacian system over a tetrahedral-ization,and constrain the solution’s biharmonic energy;the de-sired function is obtained as the solution to an eigenvector prob-lem.Manson et al.[2008]represent the indicator function χusing a wavelet basis,and efﬁciently compute the basis coefﬁcients using simple local sums over an adapted octree.Calakli and Taubin [2011]optimize a signed-distance function to have value zero at the points,have derivatives that agree with the point normals,and minimize a Hessian smoothness norm.The resulting optimization involves a bilaplacian operator,which requires estimating derivatives of higher order than in the Laplacian.The reconstructed surfaces are shown to have good accuracy,strongly suggesting the importance of explicitly ﬁtting the points within the optimization.This motivated us to explore whether a Laplacian system could be extended in this respect,and also be compatible with a multigrid solver.Screened Poisson Surface Fitting.The method of Nehab et al.[2005],which simultaneously ﬁts position and normal constraints,may also be viewed as the solution of a screened Poisson equation.The ﬁtting algorithm assumes that a 2D parametric domain (i.e.,a plane or triangle mesh)is already established.The position and derivative constraints are both deﬁned over this 2D domain.In contrast,in Poisson surface reconstruction the 2D domain manifold is initially unknown,and therefore the goal is to infer an indicator function χrather than a parametric function.This leads to a hybrid problem with derivative (Laplacian)constraints deﬁned densely over 3D and position constraints deﬁned sparsely on the set of points sampled near the unknown 2D manifold.3.REVIEW OF POISSON SURFACE RECONSTRUCTIONThe approach of Poisson surface reconstruction is based on the observation that the (inward pointing)normal ﬁeld of the boundary of a solid can be interpreted as the gradient of the solid’s indicator function.Thus,given a set of oriented points sampling the boundary,a watertight mesh can be obtained by (1)transforming the oriented point samples into a continuous vector ﬁeld in 3D,(2)ﬁnding a scalar function whose gradients best match the vector ﬁeld,and (3)extracting the appropriate isosurface.Because our work focuses primarily on the second step,we review it here in more detail.Scalar Function Fitting.Given a vector ﬁeld V :R 3→R 3,thegoal is to solve for the scalar function χ:R 3→R minimizing:E (χ)=∇χ(p )− V (p ) 2d p .(1)Using the Euler-Lagrange formulation,the minimum is obtainedby solving the Poisson equation:∆χ=∇· V .System Discretization.The Galerkin formulation is used totransform this into a ﬁnite-dimensional system [Fletcher 1984].First,a basis {B 1,...,B N }:R 3→R is chosen,namely a collection of trivariate (usually triquadratic)B-spline functions.With respect to this basis,the discretization becomes:∆χ,B i [0,1]3= ∇· V ,B i [0,1]31≤i ≤Nwhere ·,· [0,1]3is the standard inner-product on the space of(scalar-and vector-valued)functions deﬁned on the unit cube:F ,G [0,1]3=[0,1]3F (p )·G (p )d p , U , V [0,1]3=[0,1]3U (p ), V (p ) d p .Since the solution is itself expressed in terms of the basis functions:χ(p )=N∑i =1x i B i (p ),ACM Transactions on Graphics,V ol.VV ,No.N,Article XXX,Publication date:Month YYYY .Screened Poisson Surface Reconstruction•3ﬁnding the coefﬁcients{x i}of the solution reduces to solving the linear system Ax=b where:A i j= ∇B i,∇B j [0,1]3and b i= V,∇B i [0,1]3.(2) The basis functions{B1,...,B N}are chosen to be compactly supported,so most pairs of functions do not have overlapping support,and thus the matrix A is sparse.Because the solution is expected to be smooth away from the input samples,the linear system is discretized byﬁrst adapting an octree to the input samples and then associating an(appropriately scaled and translated)trivariate B-spline function to each octree node. This provides high-resolution detail in the vicinity of the surface while reducing the overall dimensionality of the system.System Solution.Given the hierarchy deﬁned by an octree of depth D,a multigrid approach is used to solve the linear system. The basis functions are partitioned according to the depths of their associated nodes and,for each depth d,a linear system A d x d=b d is deﬁned using the corresponding B-splines{B d1,...,B d Nd},such thatχ(p)=∑D d=0∑i x d i B d i(p).Because the octree-selected B-spline functions do not form a complete grid at each depth,it is generally not possible to prolong the solution x d at depth d into the solution x d+1at depth d+1. (The B-spline associated with a given node is a sum of B-spline functions associated not only with its own child nodes,but also with child nodes of its neighbors.)Instead,the constraints at depth d+1are adjusted to account for the part of the solution already realized at coarser depths.Pseudocode for a cascadic solver,where the solution is only relaxed on the up-stroke of the V-cycle,is given in Algorithm1.Algorithm1:Cascadic Poisson Solver1For d∈{0,...,D}Iterate from coarse toﬁne2For d ∈{0,...,d−1}Remove the constraints3b d=b d−A dd x d met at coarser depths4Relax A d x d=b d Adjust the system at depth dHere,A dd is the N d×N d matrix used to transform solution coefﬁcients at depth d into constraints at depth d:A dd i j= ∇B d i,∇B d j [0,1]3.Note that,by deﬁnition,A d=A dd.Isosurface Extraction.Solving the Poisson equation,one obtains a functionχthat approximates the indicator function.Ideally,the function’s zero level-set should therefore correspond to the desired surface.In practice however,the functionχcan differ from the true indicator function due to several sources of error:—The point sampling may be noisy,possibly containing outliers.—The Galerkin discretization is only an approximation of the continuous problem.—The point sampling density is approximated during octree construction.To mitigate these errors,in[Kazhdan et al.2006]the implicit function is adjusted by globally subtracting the average value of the function at the input samples.4.INCORPORA TING POINT CONSTRAINTSThe original Poisson surface reconstruction algorithm adjusts the implicit function using a single global offset such that its average value at all points is zero.However,the presence of errors can cause the implicit function to drift so that no global offset is satisfactory. Instead,we seek to explicitly interpolate the points.Given the set of input points P with weights w:P→R≥0,we add to the energy of Equation1a term that penalizes the function’s deviation from zero at the samples:E(χ)=V(p)−∇χ(p) 2d p+α·Area(P)∑p∈P∑p∈Pw(p)χ2(p)(3)whereαis a weight that trades off the importance ofﬁtting the gradients andﬁtting the values,and Area(P)is the area of the reconstructed surface,estimated by computing the local sampling density as in[Kazhdan et al.2006].In our implementation,we set the per-sample weights w(p)=1,although one can also use conﬁdence values if these are available.The energy can be expressed concisely asE(χ)= V−∇χ, V−∇χ [0,1]3+α χ,χ (w,P)(4)where ·,· (w,P)is the bilinear,symmetric,positive,semi-deﬁnite form on the space of functions in the unit-cube,obtained by taking the weighted sum of function values:F,G (w,P)=Area(P)∑p∈P w(p)∑p∈Pw(p)·F(p)·G(p).4.1Interpretation as a Screened Poisson EquationThe energy in Equation4combines a gradient constraint integrated over the spatial domain with a value constraint summed at discrete points.As shown in the appendix,its minimization can be interpreted as a screened Poisson equation(∆−α˜I)χ=∇· V with an appropriately deﬁned operator˜I.4.2DiscretizationWe apply a discretization similar to that in Section3to the minimization of the energy in Equation4.The coefﬁcients of the solutionχwith respect to the basis{B1,...,B N}are again obtained by solving a linear system of the form Ax=b.The right-hand-side b is unchanged because the constrained value at the sample points is zero.Matrix A now includes the point constraints:A i j= ∇B i,∇B j [0,1]3+α B i,B j (w,P).(5) Note that incorporating the point constraints does not change the sparsity of matrix A because B i(p)·B j(p)is nonzero only if the supports of the two functions overlap,in which case the Poisson equation has already introduced a nonzero entry in the matrix.As in Section3,we solve this linear system using a cascadic multigrid algorithm–iterating over the octree depths from coarsest toﬁnest,adjusting the constraints,and relaxing the system.Similar to Equation5,the matrix used to transform a solution at depth d to a constraint at depth d is expressed as:A dd i j= ∇B d i,∇B d j [0,1]3+α B d i,B d j (w,P).ACM Transactions on Graphics,V ol.VV,No.N,Article XXX,Publication date:Month YYYY.4•M.Kazhdan and H.HoppeFig.2:Visualizations of the reconstructed implicit function along a planar slice through the cow ‡(shown in blue on the left),for the original Poisson solver,and for the screened Poisson solver without and with scale-independent screening.This operator adjusts the constraint b d (line 3of Algorithm 1)not only by removing the Poisson constraints met at coarser resolutions,but also by modifying the constrained values at points where the coarser solution does not evaluate to zero.4.3Scale-Independent ScreeningTo balance the two energy terms in Equation 3,it is desirable to adjust the screening parameter αsuch that (1)the reconstructed surface shape is invariant under scaling of the input points with respect to the solver domain,and (2)the prolongation of a solution at a coarse depth is an accurate estimate of the solution at a ﬁner depth in the cascadic multigrid approach.We achieve both these goals by adjusting the relative weighting of position and gradient constraints across the different octree depths.Noting that the magnitude of the gradient constraint scales with resolution,we double the weight of the interpolation constraint with each depth:A ddi j = ∇B d i ,∇B dj [0,1]3+2d α B d i ,B dj (w ,P ).The adaptive weight of 2d is chosen to keep the Laplacian and screening constraints around the surface in balance.To see this,assume that the points are locally planar,and consider the row of the system matrix corresponding to an octree node overlapping the points.The coefﬁcients of the system in that row are the sum of Laplacian and screening terms.If we consider the rows corresponding to the child nodes that overlap the surface,we ﬁnd that the contribution from the Laplacian constraints scales by a factor of 1/2while the contribution from the screening term scales by a factor of 1/4.2Thus,scaling the screening weights by a factor of two with each resolution keeps the two terms in balance.Figure 2shows the beneﬁt of scale-independent screening in reconstructing a cow model.The leftmost image shows a plane passing through the bounding cube of the cow,and the images to the right show the values of the computed indicator function along that plane,for different implementations of the solver.As the ﬁgure shows,the unscreened Poisson solver provides a good approximation of the indicator functions,with values inside (resp.outside)the surface approximately 1/2(resp.-1/2).However,applying the same solver to the screened Poisson equation (second from right)provides a solution that is only correct near the input samples and returns to zero near the faces of the bounding cube,2Forthe Laplacian term,the Laplacian scales by a factor of 4with reﬁnement,and volumetric integrals scale by a factor of 1/8.For the screening term,area integrals scale by a factor of 1/4.potentially resulting in spurious surface sheets away from the surface.It is only with scale-independent screening (right)that we obtain a high-quality solution to the screened Poisson ing this resolution adaptive weighting,our system has the property that the reconstruction obtained by solving at depth D is identical to the reconstruction that would be obtained by scaling the point set by 1/2and solving at depth D +1.To see this,we consider the two energies that guide the reconstruc-tion,E V (χ)measuring the extent to which the gradients of the so-lution match the prescribed vector ﬁeld,and E (w ,P )(χ)measuring the extent to which the solution meets the screening constraint:E V (χ)=V (p )−∇χ(p )2d p E (w ,P )(χ)=Area (P )∑p ∈P w (p )∑p ∈Pw (p )χ2(p ).Scaling by 1/2,we obtain a new point set (˜w ,˜P)with positions scaled by 1/2,unchanged weights,˜w (p )=w (2p ),and scaled area,Area (˜P )=Area (P )/4;a new scalar ﬁeld,˜χ(p )=χ(2p );and a new vector ﬁeld,˜ V (p )=2 V (2p ).Computing the correspondingenergies,we get:E ˜ V (˜χ)=1E V(χ)and E (˜w ,˜P )(˜χ)=1E (w ,P )(χ).Thus,scaling the screening weight by a factor of two with eachsuccessive depth ensures that the sum of energies is unchanged (up to multiplication by a constant)so the minimizer remains the same.4.4Boundary ConditionsIn order to deﬁne the linear system,it is necessary to deﬁne the behavior of the function space along the boundary of the integration domain.In the original Poisson reconstruction the authors imposed Dirichlet boundary conditions,forcing the implicit function to havea value of −12along the boundary.In the present work we extend the implementation to support Neumann boundary conditions as well,forcing the normal derivative to be zero along the boundary.In principle these two boundary conditions are equivalent for watertight surfaces,since the indicator function has a constant negative value outside the model.However,in the presence of missing data we ﬁnd Neumann constraints to be less restrictive because they only require that the implicit function have zero derivative across the boundary of the integration domain,a property that is compatible with the gradient constraint since the guiding vector ﬁeld V is set to zero away from the samples.(Note that when the surface does cross the boundary of the domain,the Neumann boundary constraints create a bias to crossing the domain boundary orthogonally.)Figure 3shows the practical implications of this choice when reconstructing the Angel model,which was only scanned from the front.The left image shows the original point set and the reconstructions using Dirichlet and Neumann boundary conditions are shown to the right.As the ﬁgure shows,imposing Dirichlet constraints creates a water-tight surface that closes off before reaching the boundary while using Neumann constraints allows the surface to extend out to the boundary of the domain.ACM Transactions on Graphics,V ol.VV ,No.N,Article XXX,Publication date:Month YYYY .Screened Poisson Surface Reconstruction•5Fig.3:Reconstructions of the Angel point set‡(left)using Dirichlet(center) and Neumann(right)boundary conditions.Similar results can be seen at the bases of the models in Figures1 and4a,with the original Poisson reconstructions obtained using Dirichlet constraints and the screened reconstructions obtained using Neumann constraints.5.IMPROVED ALGORITHMIC COMPLEXITYIn this section we discuss the efﬁciency of our reconstruction al-gorithm.We begin by analyzing the complexity of the algorithm described above.Then,we present two algorithmic improvements. Theﬁrst describes how hierarchical clustering can be used to re-duce the screening overhead at coarser resolutions.The second ap-plies to both the unscreened and screened solver implementations, showing that the asymptotic time complexity in both cases can be reduced to be linear in the number of input points.5.1Efﬁciency of basic solverLet us begin by analyzing the computational complexity of the unscreened and screened solvers.We assume that the points P are evenly distributed over a surface,so that the depth of the adapted octree is D=O(log|P|)and the number of octree nodes at depth d is O(4d).We also note that the number of nonzero entries in matrix A dd is O(4d),since the matrix has O(4d)rows and each row has at most53nonzero entries.(Since we use second-order B-splines, basis functions are supported within their one-ring neighborhoods and the support of two functions will overlap only if one is within the two-ring neighborhood of the other.)Assuming that the matrices A dd have already been computed,the computational complexity for the different steps in Algorithm1is: Step3:O(4d)–since A dd has O(4d)nonzero entries.Step4:O(4d)–since A d has O(4d)nonzero entries and the number of relaxation steps performed is constant.Steps2-3:∑d−1d =0O(4d)=O(4d·d).Steps2-4:O(4d·d+4d)=O(4d·d).Steps1-4:∑D d=0O(4d·d)=O(4D·D)=O(|P|·log|P|). There still remains the computation of matrices A dd .For the unscreened solver,the complexity of computing A dd is O(4d),since each entry can be computed in constant time.Thus, the overall time complexity remains O(|P|·log|P|).For the screened solver,the complexity of computing A dd is O(|P|)since deﬁning the coefﬁcients requires accumulating the screening contribution from each of the points,and each point contributes to a constant number of rows.Thus,the overall time complexity is dominated by the cost of evaluating the coefﬁcients of A dd which is:D∑d=0d−1∑d =0O(|P|)=O(|P|·D2)=O(|P|·log2|P|).5.2Hierarchical Clustering of Point ConstraintsOurﬁrst modiﬁcation is based on the observation that since the basis functions at coarser resolutions are smooth,it is unnecessary to constrain them at the precise sample locations.Instead,we cluster the weighted points as in[Rusinkiewicz and Levoy2000]. Speciﬁcally,for each depth d,we deﬁne(w d,P d)where p i∈P d is the weighted average position of the points falling into octree node i at depth d,and w d(p i)is the sum of the associated weights.3 If all input points have weight w(p)=1,then w d(p i)is simply the number of points falling into node i.This alters the computation of the system matrix coefﬁcients:A dd i j= ∇B d i,∇B d j [0,1]3+2dα B d i,B d j (w d,P d).Note that since d>d ,the value B d i,B d j (w d,P d)is obtained by summing over points stored with theﬁner resolution.In particular,the complexity of computing A dd for the screened solver becomes O(|P d|)=O(4d),which is the same as that of the unscreened solver,and both implementations now have an overall time complexity of O(|P|·log|P|).On typical examples,hierarchical clustering reduces execution time by a factor of almost two,and the reconstructed surface is visually indistinguishable.5.3Conforming OctreesTo account for the adaptivity of the octree,Algorithm1subtracts off the constraints met at all coarser resolutions before relaxing at a given depth(steps2-3),resulting in an algorithm with log-linear time complexity.We obtain an implementation with linear complexity by forcing the octree to be conforming.Speciﬁcally, we deﬁne two octree cells to be mutually visible if the supports of their associated B-splines overlap,and we require that if a cell at depth d is in the octree,then all visible cells at depth d−1must also be in the tree.Making the tree conforming requires the addition of new nodes at coarser depths,but this still results in O(4d)nodes at depth d.While the conforming octree does not satisfy the condition that a coarser solution can be prolonged into aﬁner one,it has the property that the solution obtained at depths{0,...,d−1}that is visible to a node at depth d can be expressed entirely in terms of the coefﬁcients at depth d−ing an accumulation vector to store the visible part of the solution,we obtain the linear-time implementation in Algorithm2.3Note that the weight w d(p)is unrelated to the screening weight2d introduced in Section4.3for scale-independent screening.ACM Transactions on Graphics,V ol.VV,No.N,Article XXX,Publication date:Month YYYY.6•M.Kazhdan and H.HoppeHere,P d d−1is the B-spline prolongation operator,expressing a solution at depth d−1in terms of coefﬁcients at depth d.The number of nonzero entries in P d d−1is O(4d),since each column has at most43nonzero entries,so steps2-5of Algorithm2all have complexity O(4d).Thus,the overall complexity of both the unscreened and screened solvers becomes O(|P|).Algorithm2:Conforming Cascadic Poisson Solver1For d∈{0,...,D}Iterate from coarse toﬁne.2ˆx d−1=P d−1d−2ˆx d−2Upsample coarseraccumulation vector.3ˆx d−1=ˆx d−1+x d−1Add in coarser solution.4b d=b d−A d d−1ˆx d−1Remove constraintsmet at coarser depths.5Relax A d x d=b d Adjust the system at depth d.5.4Implementation DetailsThe algorithm is implemented in C++,using OpenMP for multi-threaded parallelization.We use a conjugate-gradient solver to re-lax the system at each multigrid level.With the exception of the octree construction,most of the operations involved in the Poisson reconstruction can be categorized as operations that either“accu-mulate”or“distribute”information[Bolitho et al.2007,2009].The former do not introduce write-on-write conﬂicts and are trivial to parallelize.The latter only involve linear operations,and are par-allelized using a standard map-reduce approach:in the map phase we create a duplicate copy of the data for each thread to distribute values into,and in the reduce phase we merge the copies by taking their sum.6.RESULTSWe evaluate the algorithm(Screened)by comparing its accuracy and computational efﬁciency with several prior methods:the original Poisson reconstruction of Kazhdan et al.[2006](Poisson), the Wavelet reconstruction of Manson et al.[2008](Wavelet),and the Smooth Signed Distance reconstruction of Calakli and Taubin [2011](SSD).For the new algorithm,we set the screening weight toα=4and use Neumann boundary conditions in all experiments.(Numerical results obtained using Dirichlet boundaries were indistinguishable.) For the prior methods,we set algorithmic parameters to values recommended by the authors,using Haar Wavelets in the Wavelet reconstruction and setting the value/normal/Hessian weights to 1/1/0.25in the SSD reconstruction.For Poisson,SSD,and Screened we set the“samples-per-node”parameter to1and the “bounding-box-scale”parameter to1.1.(For Wavelet the bounding box scale is hard-coded at1and there is no parameter to adjust the sampling density.)6.1AccuracyWe run three different types of experiments.Real Scanner Data.To evaluate the accuracy of the different reconstruction algorithms on real-world data,we gathered several scanned datasets:the Awakening(10M points),the Stanford Bunny (0.2M points),the David(11M points),the Lucy(1.0M points), and the Neptune(2.4M points).For each dataset,we randomly partitioned the points into two equal-sized subsets:input points for the reconstruction algorithms,and validation points to measure point-to-reconstruction distances.Figure4a shows reconstructions results for the Neptune and David models at depth10.It also shows surface cross-sections overlaid with the validation points in their vicinity.These images reveal that the Poisson reconstruction(far left),and to a lesser extent the SSD reconstruction(center left),over-smooth the data,while the Wavelet reconstruction(center left)has apparent derivative discontinuities.In contrast,our screened Poisson approach(far right)provides a reconstruction that faithfullyﬁts the samples without introducing noise.Figure4b shows quantitative results across all datasets,in the form of RMS errors,measured using the distances from the validation points to the reconstructed surface.(We also computed the maximum error,but found that its sensitivity to individual outlier points made it an unreliable and unindicative statistic.)As theﬁgure indicates,the Screened Poisson reconstruction(blue)is always more accurate than both the original Poisson reconstruction algorithm(red)and the Wavelet reconstruction(purple),and generates reconstruction whose RMS errors are comparable to or smaller than those of the SSD reconstruction(green).Clean Uniformly Sampled Data.To evaluate reconstruction accuracy on clean data,we used the approach of Osada et al.[2001] to generate oriented point sets by uniformly sampling the surfaces of the Fandisk,Armadillo Man,Dragon,and Raptor models.For each model,we generated datasets of100K and1M points and reconstructed surfaces from each point set using the four different reconstruction algorithms.As an example,Figure5a shows the reconstructions of the fandisk and raptor models using1M point samples at depth10.Despite the lack of noise in the input data,the Wavelet reconstruction has spurious high-frequency detail.Focusing on the sharp edges in the model,we also observe that the screened Poisson reconstruction introduces less smoothing,providing a reconstruction that is truer to the original data than either the original Poisson or the SSD reconstructions.Figure5b plots RMS errors across all models,measured bidirec-tionally between the original surface and the reconstructed surface using the Metro tool[Cignoni and Scopigno1998].As in the case of real scanner data,screened Poisson reconstruction always out-performs the original Poisson and Wavelet reconstructions,and is comparable to or better than the SSD reconstruction. Reconstruction Benchmark.We use the benchmark of Berger et al.[2011]to evaluate the accuracy of the algorithms under different simulations of scanner error,including nonuniform sampling,noise,and misalignment.The dataset consists of mul-tiple virtual scans of implicit surfaces representing the Anchor, Dancing Children,Daratech,Gargoyle,and Quasimodo models. As an example,Figure6a visualizes the error in the reconstructions of the anchor model from a virtual scan consisting of210K points (demarked with a dashed rectangle in Figure6b)at depth9.The error is visualized using a red-green-blue scale,with red signifyingACM Transactions on Graphics,V ol.VV,No.N,Article XXX,Publication date:Month YYYY.。

Digital Object Identifiers for scientific data

Digital Object Identifiers for scientific dataDr Norman PaskinInternational DOI FoundationOxford OX2 8HY UKn.paskin@Paper presented at 19th International CODATA Conference, Berlin, Nov 10 2004 AbstractThe Digital Object Identifier (DOI) is a system for identifying content “objects” in the digital environment. DOIs are names assigned to any entity for use on Internet digital networks. Scientific data sets may be identified by DOIs, and several efforts are now underway in this area. This paper outlines the underlying architecture of the DOI system and two such efforts which are applying DOIs to content objects as scientific data.DOIs provide persistent identification together with current information about the object. The system is managed by the International DOI Foundation (IDF), an open membership consortium including both commercial and non-commercial partners, and has recently been accepted for standardisation within ISO. Several million DOIs have been assigned by DOI Registration Agencies in the US, Australasia, and Europe. DOI is a development combining several existing standards, notably the Handle resolution system and the indecs Data Dictionary. DOIs can be used for any form of management of data, whether commercial or non-commercial.The DOI system has several components: a specified numbering syntax, a resolution service, a data model, and procedures for the implementation of DOIs. Any existing numbering schemes, and any existing metadata schemes, that provide an accepted numbering or descriptive syntax for a particular community or area of interest (such as formal ISO standards or accepted community practice) can be used within the DOI System.IntroductionA Digital Object Identifier (DOI) is a name (not a location) for an entity on digital networks. It provides a system for persistent and actionable identification and interoperable exchange of managed information on digital networks1.It has long been recognised that unique identifiers are essential for the management of information in any digital environment. Identifiers assigned in one context may be encountered, and may be re-used, in another place (or time) without consulting the assigner, who cannot assume that his assumptions will be known to someone else. Interoperability requires the design of these identifiers so as to enable their use in services outside the direct control of the issuing assigner. The necessity of allowinginteroperability adds the requirement of persistence to an identifier: it implies interoperability with the future. Further, since the services outside the direct control of the issuing assigner are by definition arbitrarily, interoperability implies the requirement of extensibility. Hence DOI is designed as a generic framework applicable to any digital object, providing a structured, extensible means of identification, description and resolution. The entity assigned a DOI can be a representation of any logical entity.The DOI system is built using several existing standards-based components which have been brought together and further developed to provide a consistent system2: the entire system has recently been accepted for standardisation3 within ISO (ISOTC46/SC9)4. The DOI was developed as a cross-industry, cross-sector, not-for-profit effort managed by an open membership collaborative development body, the International DOI Foundation (IDF)5 founded in 1998. The DOI is in widespread use, with over 15 million DOIs assigned, from over 1000 naming authorities (allocators). DOI forms a key feature of scientific primary publishing as part of the CrossRef system6 (providing a pre-publication processing tool enabling cross-references to be persistent and not rely simply on URLs and bibliographic citation matching). DOIs are being adopted for use in government documents (such as EC, OECD, UK government, etc). In use, a DOI is a mechanism “behind the scenes”, and need not be explicitly declared (though this may be useful): in e.g. a web context a DOI may be used in a http form as a URL, whilst retaining the advantages of managed persistence. Its functionality may readily be used to offer an interoperable common system for identification of science data. Two projects considered as examples here are the TIB project (on citation of primary data sets) and the Names for Life project (on biological taxonomy).DOI system componentsThe DOI system provides a ready-to-use packaged system of several components: • a specified standard numbering syntax,• a resolution service (based on the existing Handle System),• a data model incorporating a data dictionary(based on the indecs Data Dictionary); and•an implementation mechanism through policies and procedures for the governance and application of DOIs.DOI syntaxThe DOI syntax is a standard (NISO Z39.84, DOI Syntax). It provides an identifier “container” which can accommodate any existing identifier7: e.g.10.1234/NP567810.5678/ISBN-0-7645-4889-4 and10.2224/2004-10-ISO-DOIare all valid DOI syntax: the portion following the “/” character (the DOI Suffix) may be an existing identifier. The word “identifier” can mean several different things: (1) Labels, the output of numbering schemes e.g. “ISBN 3-540-40465-1”; (2) specifications for using labels: e.g. on internet URL, URN, URI (URI = UniformResource Identifier); or (3) implemented systems: labels, following a specification, in a system - e.g. the DOI system, which is a packaged system offering label, tools and implementation mechanisms. The DOI system is an example of identifier sense (3); it may include identifiers in sense (1) as a suffix and may also conform to identifier specifications8 in sense (2).DOI resolutionResolution is the process in which an identifier is the input (a request) to a network service to receive in return a specific output of one or more pieces of current information (state data) related to the identified entity: e.g. a location (such as URL) where the object can be found. Resolution provides a level of managed indirection between an identifier and the output. The resolution component allows reditection on a TCP/IP network from a DOI to associated data. Initial applications have been resolution to a single location (URL), providing a tool for persistence (since even if a URL is changed, the DOI still functions and redirects to the new location). However more useful resolution may be to multiple associated data such as multiple locations, metadata, common services, or to extensible assigner-defined data. The resolution tool used in the DOI system is the Handle system9 (IETF RFCs 3650, 3651, 3652). This conforms to the functional requirements of the URI and URN concepts, and has many advantages over other mechanisms including global scalability, security, and opacity10.The Handle system implementation in DOI has been supplemented by expanded technical infrastructure and features specific to DOI applications11. Handle multiple resolution allows one entity to be resolved to multiple other entities; it can therefore be used to embody e.g. a parent-children relationship, or any other relationship, and is therefore suitable for describing relationships of data sets. Handle per se (deliberately) has no pre-existing constraints to define a framework to express relationships (analogy: spreadsheet software ): DOI is an application of Handle which adds this constraint for a specific purpose of content management (analogy: a spreadsheet application). In DOI the constraints are metadata defining the entities, using a semantically interoperable data dictionary.DOI data modelThe DOI data model embraces both a data dictionary and a framework for applyingit12. Together these provide tools for defining what a DOI specifies (through use of a data dictionary), and how DOIs relate to each other, (through a grouping mechanism of Application Profiles which associate DOIs with defined common properties). This provides semantic interoperability, enabling information that originates in one context to be used in another in ways that are as highly automated as possible.The DOI system uses an interoperable structured data dictionary. The data dictionary component is designed to ensure maximum interoperability with existing metadataelement sets; the framework allows the terms to be grouped in meaningful ways (DOI Application Profiles) so that certain types of DOIs all behave predictably in an application through association with specified Services. This provides a means of integrating the features of Handle resolution with a structured data approach. DOIs need not make use of this data model, but it is envisaged that many will: any DOI intended to allow interoperability (i.e. which has the possibility of use in services outside of the direct control of the issuing Registration Agency) is subject to DOI Metadata policy, which is based on the registration of terms in the iDD.A data dictionary is a set of terms, with their definitions, used in a computerized system. Some data dictionaries are structured, with terms related through hierarchies and other relationships: structured data dictionaries are derived from ontologies. An ontology combines a data dictionary with a logical data model, providing a consistent and logical world view. It differs from the traditional taxonomic approach to knowledge representation in that it does not follow a rigid/parent child hierarchical structure (terms may inherit meaning from more than one parent) and a more complex relationship is maintained.An interoperable data dictionary contains terms from different computerized systems or metadata schemes, and shows the relationships they have with one another in a formal way. The purpose of an interoperable data dictionary is to support the use together of terms from different systems. The IDF is the Registration Authority for one such Dictionary, the ISO/IEC MPEG-21 Rights Data Dictionary, and the developer of a wider indecs Data Dictionary which includes this.DOI implementationDOI is implemented through a federation of Registration Agencies which use policies and tools developed through a parent body, the International DOI Foundation (IDF). The IDF, as governance body of the DOI system, safeguards (owns or licences on behalf of registrants) all Intellectual Property Rights relating to the DOI System. It works with RAs and with the underlying technical standards of the DOI components to ensure that any improvements made to the DOI system (including creation, maintenance, registration, resolution and policymaking of DOIs) are available to any DOI registrant. DOI resolution is freely available to any user encountering a DOI13. The DOI System has the flexibility to deliver identification and resolution services that fulfil the requirements of any application domain. However, these don't come "in a box". Someone needs to build the specific social and technical structures to support the particular requirements of a community. The rules about what is identified, and whether two things being identified are (or are not) "the same thing", are made at a lower level: in a specific application of the DOI. This is a role of DOI Registration Agencies. This provides an identification system of enormous flexibility and power -- while hugely increasing the importance of an explicit structured metadata layer, since without this the identifier essentially can have no meaning at all outside a specific application14.The IDF provides implementation through agreed standards ofgovernance and scope, policy, “rules of the road”. It also provides a technical infrastructure (resolution mechanism, proxy servers, mirrors, back-up, centraldictionary) and a social infrastructure (persistence commitments, fall-back procedures, cost-recovery (on a self-sustaining model), and shared use of the system. The IDF is not a standards body, but a central authority and maintenance agency. The IDF is already the appointed registration authority for the ISO/IEC MPEG 21 Rights Data Dictionary, and is proposed as the registration authority for the DOI System within ISO TC46/SC9. IDF delegates and licenses authority through Registration Agencies, each of which can develop its own applications and use DOI in “own brand” ways appropriate for their community.DOIs and scientific dataAn earlier presentation15 outlined the rationale for assigning DOIs to data, and some early suggestions for applications together with a more detailed presentation of the DOI system as it stood at that time.The identification of scientific data is logically a separate issue from the identification of the primary publication of such data to the scientific community in the form of articles, tables, etc. DOI is already the core technology for maintaining cross-reference via persistent links between a citation and internet access to article, in the CrossRef system used by over 350 publishers representing the majority of STM articles. DOI is used in a pre-publication link builder and is now being extended to specialist uses such as constrained Google searching. Currently 9,000 DOIs per day are added to CrossRef; over 12 million DOIs now registered with CrossRef, of which over 850,000 are assigned to books and conference proceedings.The DOI as a long-term linking option from data to source publication is of fundamental importance. For example, in the Landolt-Börnstein series of tables of Numerical Data and Functional Relationships in Science and Technology, the automatic generation of 30,000 LB documents is to be done with DOIs (already assigned to book publications): in the online version of the LB collection, a new feature of all 2004 volumes will be improved metadata and cross reference linking enabled in this way16.Some projects or communities have developed their own identifier schemes, which may be useful for their own area. A recent example is the Life Science Identifier17 developed by I3C/IBM: this provides a community agreement around a simple URN mechanism, which is non-generically extensible and non-globally resolvable but meaningful within that community for certain purposes. Such identifiers can be incorporated into a DOI if needed to make them globally interoperable and extensible and take advantage of other features provided in the DOI system.Recently two projects in particular have proposed DOI applications: these are briefly described here as illustrative of two different areas of DOI use.DOIs for scientific data sets: TIB projectDOIs could logically be assigned to every single data point in a set; however in practice, the allocation of a DOI is more likely to be to a meaningful set of datafollowing the indecs Principle of Functional Granularity18: identifiers should be assigned at the level of granularity appropriate for a functional use which is envisaged.The German National Library of Science and Technology (TIB), the world's largest library of science and technology participated in a project made possible by a grant from the Deutsche Forschungsgemeinschaft (German Research Foundation), to implement the use of DOIs to persistently identify scientific data sets. This follows from earlier work by a National Committee of CODATA, the Committee on Data for Science and Technology of the International Council for Science (), resulting in a report "Concept of Citing Scientific Primary Data" in May 2002 recommending the use of DOIs. A continuation as a project for pilot implementation funded by DFG Oct 2003 to Oct 2005 at TIB (German National Library of Science & Technology) is co-ordinated by the World Data Center for Climate (WDCC) at the Max-Planck-Institut für Meteorologie in Hamburg.A team from several data centres, led by Dr Michael Lautenschlager at the World Data Centre for Climate, will focus on providing a means of publicly registering data sets with a persistent identifier and structured basic description. The pilot deployment will use geo-reference data (e.g. from observational stations, satellites, and climate models), but will in principle be extensible to any scientific data. This use of DOI will provide for the effective publication of primary data using a persistent identifier for long-term data referencing, allowing scientists to cite and re-use valuable primary data. The DOI’s persistent and globally resolvable identifier, associated to both a stable link to the data and also a standardised description of the identified data, offers the necessary functionality and also ready interoperability with other material such as scientific articles.The key problem this project addresses is the reliable re-use of existing data sets, in terms both of attribution of data source (the proposed solution being to make data publications citable in a standard way as are articles through the Science Citation Index), and the archiving of data in context so as to be discoverable and interoperable (usable by others). The extensibility of the mechanism is provided by allocating DOIs for data sets, with associated metadata using a core management metadata (applicable to all datasets) and structured metadata extensions (mapped to a common ontology) applicable to specific science disciplines.Application scenario19:During her research for the World Data Center Climate (WDCC) Dr. Weather gains primary data about the weather in Hannover in the year 2003. Primary data is tested, evaluated, stored and administrated at the WDCC. Primary data is registered and allocated DOI at the TIB, with quality control of metadata, etc (e.g. the assigned data cannot be changed once allocated).Dr Weather can now cite this with a resolvable DOI e.g/WDCC/W_Han_2003_MMB_2DOI:10.159410.1594 (Prefix) = TIB as the registration agency.WDCC =institute.researchW_Han_2003_MMB_2 = internal name of the DataThe DOI is resolvable directly, or via http as/10.1594/WDCC/W_Han_2003_MMB_2Usage scenario 1:Dr. Storm is reading publications from Dr. Weather in a journal and would like to analyse her data under different aspects. The DOI may be resolved to obtain the data set for use. In his publication ”Comparison of the weather from Hannover and Miami” Dr. Storm cites Dr. Weather’s data using its DOI, referring to the uniqueness and own identity of the original data.Citation example:Weather, 2003: “Weather in Hannover for 2003”(doi: 10.1594/WDCC/W_Han_2003_MMB_2)Usage scenario 2:Mr. Nice is writing a paper about the sales figures of ice cream in Hannover in 2003, but he has no information about the weather. He searches via TIB central registration agency metadata search; the result isdoi:10.1594/WDCC/W_Han_2003_MMB_2He resolves the DOI to find the data. The metadata refers him to the WDCC as publisher and data archive. In his paper he cites the data using the DOI.DOIs for taxonomic data: Names for Life projectThe aim of this project is “future-proofing biological nomenclature”20; it proposes DOIs as persistent identifiers of taxonomic definitions. A name ascribed to a given group in a biological taxonomy is fixed in both time and scope and may or may not be revised when new information is available. Change occurs (e.g. new species are recognised, species reassigned as the founding species of new genera; synonyms; species split into subspecies which later became separate species) resulting in changes of names, genera, families, classes, and relationships over time. When taxonomic revisions do occur, resulting in the division or joining of previously described taxa, authors frequently fail to address synonymies or formally emend the descriptions of higher taxa that are affected. DOI is proposed as a tool to manage a data model of nomenclature and taxonomy (enabling disambiguation of synonyms and competing taxonomies) using a metadata resolution service (enabling dissemination of archived and updated information objects through persistent links to articles, strain records, gene annotations and any other data.21Whereas the different Codes of Nomenclature guarantee persistence of a formal name, the serial, cumulative nature of effective and valid publication allows the name to obsolesce in relation to the taxon it originally denoted. In contrast, it is the taxon itself that persists, and the granularity with which it is defined increases over time. The formal name provides an archival record of taxonomic definition only for a single point in time: the date of publication. A robust and persistent taxonomy requires taxonomic definition to be a maintained, networked resource, rather than a retrospective sequence of names and emendations. A commonly referenced terminology based on persistent, increasingly refined taxa is needed to replace or augment a static nomenclature that diverges over time from the taxonomy it initially denotes. This disjunction of nomenclature and taxonomy results in an accumulation of names of dubious value in the literature and databases.The Names for Life project is developing a model for assigning DOIs to prokaryotic taxa as a test case. Though the definition of a taxon may be refined and its nomenclature redefined, the DOI will persist, leaving a forward-pointing trail that can be used to reliably locate digital and physical resources, even when a name may be deemed obsolete. Forward linking from a synonym to a record of the publication that asserts synonymy is especially important, as there is currently no mandatory mechanism for asserting and resolving names that become ambiguous. The model seeks to strengthen the association of names with taxa by using DOIs to track the taxonomic definition of a name over time. It is extensible to the level of individual genes within a given species. However, the real power of this method lies in the ability of DOIs to become embedded in the information environment, providing a direct and persistent link to the full record of taxonomic and nomenclatural revision and ensuring consistency and accuracy throughout online scientific resources. A DOI-based infrastructure for formally associating nomenclature with taxonomy enables a name to be used unambiguously and persistently, only one mouse-click away from a record of its current definition and historical development. References1 Paskin, Norman. "Components of DRM Systems: Identification and Metadata" in E. Becker et al (eds) "Digital Rights Management: Technological, Economic, Legal, and Political Aspects in the European Union" in the series Lecture Notes in Computer Science (Springer-Verlag, 2003) pp. 26-61./topics/drm_paskin_20030113_b1.pdf2 The DOI Handbook/hb.html3 Resolutions of the ISO TC46/SC9 meeting in Washington, document SC9N3954 ISO TC 46/SC 9, Information and Documentation - Identification and Description http://www.collectionscanada.ca/iso/tc46sc9/index.htm5 International DOI Foundation, 6 CrossRef, 7 DOI Factsheet: DOI and Numbering Schemes:/factsheets/DOIIdentifiers.html8 DOI Factsheet: DOI and Internet Identifier Specifications/factsheets/DOIIdentifierSpecs.html9 Handle System: 10 Dyson, Esther: "Online Registries: The DNS and Beyond”. Release 1.0, September 2003/doi:10.1340/309registries11 DOI Factsheet: DOI and Handle /factsheets/DOIHandle.html12 DOI Factsheet: DOI and Data Dictionaries/factsheets/DOIDataDictionaries.html13 IDF re-affirms DOI as an open specification. DOI news October 2004/news/DOINewsOct04.html14 DOI Factsheet: DOI Applications/factsheets/DOIApplications.html15 Paskin, Norman. "Digital Object Identifiers and Digital Preservation of the Record of Science". Proceedings of ICSTI Seminar: Symposium on Digital Preservation of the Record of Science, ICSTI, 14 - 15 February 2002, IOS Press, 2002./topics/020210_CSTI.pdf16 Dr. Rainer Poerschke, Editorial Director Landolt-Börnstein, personal communication17 Salamone, S: “LSID: An Informatics Lifesaver”/archive/011204/lsid.html18 Rust, Godfrey; Bide, Mark (2000). "The <indecs> Metadata Framework: Principles, model and data dictionary."/pdf/framework.pdf19 "Pilot Implementation: Publication and Citation of Scientific Primary Data": Jan Brase and Michael Lautenschlager. Presentation to International DOI Foundation meeting June 2004/idf-members/members_meeting2004/presentations/CorkLondon-PrimData-DOI-0604-v3.ppt20 Garrity, G. M.; Lyons, C. "Future-proofing biological nomenclature". Omics, 2003, Volume 7, Number 1, pgs. 31-33. This material was presented at: Workshop on Data Management for Molecular and Cell Biology Feb. 2-3, 2003 Lister Hill Center, NLM, NIH Campus, Bethesda, MD. A version of the paper as presented is at the workshop website: /~jag/wdmbio/garrity.htm21 "Names for Life": Catherine Lyons. Presentation to International DOI Foundation meeting June 2004/idf-members/members_meeting2004/presentations/n4_220604.ppt。

SAE J 1231-2004

2.1.1 SAE PUBLICATIONS
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Except for nominal sizes and thread specifications, dimensions and tolerances are given in SI units. Tolerance on all dimensions not otherwise limited shall be ±0.25 mm. Angular tolerance on axis of ends on elbows shall be ±2.50 degrees for sizes up to and including 9.52 mm and ±1.50 degrees for sizes larger than 9.52 mm.
3.3 The Oring boss thread dash sizes correspond to the number of sixteenth inch increments in the outside diameter of the tubing with which they are designed to be used.

作者姓名钟柳强

作者姓名：钟柳强论文题目：求解两类Maxwell 方程组棱元离散系统的快速算法和自适应方法作者简介：：钟柳强，男，1980年10月出生，2006年9月起师从湘潭大学许进超教授，2009年6月获博士学位。

中文摘要目前，电磁场的研究及应用已经影响到科学技术的各个领域，但是面对电磁场实际应用中大量复杂的问题，如复杂电磁波的传播环境，复杂电磁器件的分析和设计等，不仅数学上的经典解析方法无能为力，而且实验手段也未能给予全面的解决。

随着计算机技术及数值方法的发展，计算电磁场为解决实际电磁场工程中越来越复杂的建模与仿真、优化设计等问题提供了新的重要研究手段，为电磁场的理论研究和工程应用开辟了一条新的研究途径。

棱有限元方法是对 Maxwell 方程组进行数值求解的一种基本离散化方法，它能够有效地克服经典的连续节点有限元在求解某些电磁场边值问题或特征值问题时会产生非物理解这一缺陷，从而在工程应用领域得到了越来越广泛的应用。

由于该离散系统通常是大规模, 且高度病态,因此构造其快速求解算法十分必要. 另外由于许多 Maxwell 方程组存在强奇性, 这时若采用一致加密网格进行计算,则会引起自由度的过度增长, 自适应方法是克服该缺陷的有效途径,因此研究求解 Maxwell 方程组的自适应有限元方法具有重要意义.上述两方面的研究是当前计算电磁场中的热点, 其中面临许多难点问题.本文比较系统地研究了求解两类典型 Maxwell 方程组棱有限元离散系统的快速算法和自适应棱有限元方法。

主要内容和结果如下:首先，针对H(curl) 椭圆方程组的高阶棱元离散系统，设计和分析了相应的快速迭代法和高效预条件子。

关于H(curl) 椭圆方程组棱元离散系统的快速算法，已有的大部分研究工作都是针对第一类 Nédélec 线性棱元离散系统。

而在某些时候，高阶Nédélec 棱有限元比线性棱元更具有优势，如可以减少误差的数值耗散，具有更好的逼近性等。

AP physics C 2004 真题多项选择试题题目

AP physics C 2004 真题多项选择试题题目Questions 40-4136. Three 1/2 μF capacitors are connected in series as shown in the diagram above. Thecapacitance of the combination is (A) 0.1 μF (B) 1 μF (C) 2/3 μF(D) ? μF (E) 1/6 μF37. A hair dryer is rated as 1200 W, 120 V. Its effective internal resistance is(A) 0.1 Ω (B) A particle of charge +e and mass m moves with 10 Ω (C) 12Ω speed v perpendicular to a uniform magnetic field (D) 120 Ω (E) B directed into the page. The path of the particle is 1440 Ω a circl eof radius r, as shown above. 40. Which of the following correctly gives thedirection of motion and the equationrelating v and r ?Direction Equation(A) Clockwise eBr = mv 2 (B) Clockwise eBr = mv 38. A point charge+Q is inside an uncharged (C) Counterclockwise eBr = mv conducting spherical shell that in turn is near 2(D) Counterclockwise eBr = mv several isolated point charges, as shown above. 22(E) Counterclockwise eBr = mv The electric field at point P inside the shell depends on the magnitude of 41. The period of revolution of the particle (A) Q only is (B) the charge distribution on the sphere only (A) mr/eB (B) meB/(C) Q and the charge distribution on the sphere (D) all of the point charges (C) 2πm/eB (D) 2/,meB(E) all of the point charges a nd the charge (E)2/,mreBdistribution on the sphere 42. A 20 μF parallel-plate capacitor is fully charged to 30 39. In a certain region, the electric field along V. The energy stored in the capacitor is most nearly the x-axis is given by 3-3-4(A) 9 x 10 J (B) 9 x 10 J (C) 6 x 10 J 2E = ax + b, where a = 40 V/m -4-7(D) 2 x 10 J (E) 2 x 10 J and b = 4 V/m. The potentialdifference between the origin 43. A potential difference V is maintained between and x = 0.5 m is two large, parallel conducting plates. An (A) -36 V (B) -7 V (C) -3 V (D) 10 V electron starts from rest on the surface of one (E) 16 V plate and accelerates toward the other. Its speed as it reaches the second plate isproportional to(A) 1/V(B)1VV(C)(D) V 2(E) V44. A wire of radius R has a current I uniformly 48. Two conducting cylindrical wires are made outdistributed across its cross-sectional area. of the same material. Wire X has twice theAmpere's law is used with a concentric length and twice the diameter of wire Y. Whatcircular path of radius r, with r < R, to /R of their resistances?is the ratio Rxycalculate the magnitude of the magnetic (A) 1/4 (B) ? (C) 1 (D) 2 (E) 4field B at a distance r from the center of the wire. Which of the following equationsresults from a correct application ofAmpere's law to this situation? 22(A) B(2πr) = μI (B) B(2πr) =μI(r/R) 00(C) B(2πr) = 0 (D) B(2πR) = μI (E) B(2πR) 022= μI(r/R) 0Questions 45-4649. A solid metallic sphere of radius R has chargeQ uniformly distributed on its outer surface. Agraph of electric potential V as a function ofposition r is shown above. Which of thefollowing graphs best represents the magnitudeof the electric field E as a function of position r Particles of charge Q and -4Q are located on the for this sphere? x-axis as shown in the figure above. Assumethe particles are isolated from all other charges.45. Which of the following describes the directionof the electric field at point P ?(A) +x (B) +y (C)-y(D) Components in both the -x- and+y-directions(E) Components in both the+x- and -y-directions46. At which of the labeled points on the x-axis is the electric field zero?(A) A (B) B (C) C (D) D (E) E47. When the switch S is open in the circuitshown above, the reading on the ammeter Ais 2.0 A. When the switch is closed, thereading on the ammeter is(A) doubled(B) increased slightly but not doubled(C) the same(D) decreased slightly but not halved (E) halved50. Two parallel wires, each carrying a current I, repel each other with a force F. If bothcurrents are doubled, the force of repulsion is (A) 2F (B) F (C) 4F22(D) F (E) 8F 4251. A circular current-carrying loop lies so that the plane of the loop is perpendicular to a constant 54. A conducting loop of wire that is initially magnetic field of strength B. Suppose that the around a magnet is pulled away from the radius R of the loop could be made to increase magnet to the right, as indicated in the figure with time t so that R = at, where a is a constant. above, inducing a current in the loop. What is What is the magnitude of the emf that would be the direction of the force on the magnet and generated around the loop as a function of t ? 2the direction of the magnetic field at the (A) 2πBat(B) 2πBat (C) 2πBt 223center of the loop due to the (D) πBat (E) (π/3)Bat induced current? Direction ofMagnetic Field atDirection of Center of Loop dueForce on the Magnet to Induced Current(A) To the right To the right(B) To the right To the left(C) To the left To the right 52. The figures above show parts of two circuits, (D) To the left To the left(E) No direction; To the left each containing a battery of emf ε and internal the force is zero. resistance r. The current in each battery is 1 A, but the direction of the current in one battery is opposite to that in the other. If the potential differences across the batteries' terminals are 10 V and 20 V as shown, what are the valuesof ε and r ? 55. A square loop of wire carrying a current I is (A) ε = 5 V, r = 15 Ω initially in the plane of the page and is located in a uniform magnetic field B that points (B) ε =IOV, r=100 Ω toward the bottom of the page, as shown above. (C) ε = 15 V, r = 5 Ω Which of the following shows the correct initialrotati on of the loop due to the force exerted on (D) ε = 20 V, r = 10 Ωit by the magnetic field? (E) The values cannot be computed unless the complete circuits are shown.53. A charged particle can move withconstant velocity through a regioncontaining both an electric field and amagnetic field only if the(A) electric field is parallel to the magnetic field(B) electric field is perpendicular to the magnetic field(C) electric field is parallel to the velocity vector(D) magnetic field is parallel to the velocity vector(E) magnetic field is perpendicular to the velocity vectorQuestions 59-6156. In the circuit shown above, the equivalent The diagram above shows equipotential lines resistance of the three resistors is produced by an unknown charge distribution. A, (A) 10.5 Ω (B) 15Ω (C) 20 ΩB, C, D, and E are points in the plane. (D) 50 Ω (E) 115 Ω59. Which vector below best describes the direction Questions 57-58of the electric field at point A ?(A) (B) (C) (D)(E) None of these; the field is zero.60. At which point does the electric field havethe greatest magnitude? (A) A As shown in the figure above, six particles, each (B) B with charge +Q, are held fixed and ate equally(C) C spaced around the circumference of a circle of(D) D radius R.(E) E57. What is the magnitude of the resultantelectric field at the center of the circle? 61. How much net work must be done by anexternal force to move a -1 μC point charge 6Q(A) 0 (B) (C) from rest at point C to rest at point E ? 24,,R0(A) -20 μJ(B) -10 μJ 23Q32Q (D) 22(C) 10 μJ ,,,,4R4R00(D) 20 μJ 3Q(E) 30μJ (E) 2,,2R 058. With the six particles held fixed, how muchwork would be required to bring a seventhparticle of charge + Q from very far awayand place it at the center of the circle?23Q6Q(A) 0 (B) (C) 2,,,,24RR00229Q3Q(D) (E) ,,,,2R00R62. One of Maxwell's equations can be written 65. A physics problem starts: "A solid sphere hascharge distributed uniformly throughout. . . " d,as. This equation expresses ,,,Eds,It may be correctly concluded that the dt(A) electric field is zero everywhere inside the the fact that sphere (A) a changingmagnetic field produces (B) electric field inside the sphere is the same an electric field as the electric field outside (B) a changing electric field produces a (C) electric potential on the surface of the magnetic field sphere is not constant (C) the net magnetic flux through a (D) electric potential in the center of the sphere closed surface depends on the is zero current inside (E) sphere is not made of metal (D) the net electric flux through a closed surface depends on the charge inside Questions 66-67 relate to the circuit represented (E) electric charge is conserved below. The switch S, after being open for a long time, is then closed., ,12 V4 HS63. The plates of a parallel-plate capacitor of cross 66. What isthe current in the circuit after the sectional area A are separated by a distance d, switch has been closed a long time? as shown above. Between the plates is a (A) 0 A dielectric material of constant K. The plates are (B) 1.2 A connected in series with a variable resistance R (C) 2 A and a power supply of potential difference V. (D) 3 A The capacitance C of this capacitor will (E) 12 A increase if which of the following isdecreased? (A) A (B) R (C) K 67. What is the potential difference across the (D) d (E) V resistor immediately after the switch is closed? (A) 0 V(B) 2 V(C) 7.2 V(D) 8 V(E) 12 V68. A uniform spherical charge distribution hasradius R.. Which of the following is true of the electric field strength due to this charge 64. The currents in three parallel wires, X, Y, and Z, distribution at a distance r from the center of each have magnitude l and are in the directions the charge? shown above. Wire Y is closer to wire X than to (A) It is greatest when r = 0. wire Z. The magnetic force on wire Y is (B) It is greatest when r = R/2. (A) zero (B) into the page (C) out of the page (C) It is directly proportional to r when r > (D) toward the bottom of the page R. (E) toward the left (D) It is directly proportional to r when r < R. 2(E) It is directlyproportional to r.69. When a negatively charged rod is brought near, but does not touch, the initially uncharged electroscope shown above, the leaves spring apart (I). When the electroscope is then touched with a finger, the leaves collapse (II). When next the finger and finally the rod are removed, the leaves spring apart a second time (III). The charge on the leaves is(A) positive in both I and III(B) negative in both I and III(C) positive in I, negative in III(D) negative in I, positive in III(E) impossible to determine in either I or III70. A sheet of copper in the plane of the page is connected to a battery as shown above, causing electrons to drift through the copper toward the bottom of the page. The copper sheet is in a magnetic field B directed intothe page. P and P are points at the edges of 12the strip. Which of the following statements is true?(A) P is at a higher potential than P. 12(B) P is at a higher potential than P. 21(C) P and P are at equal positive potential. 12(D) P and P are at equal negative potential. 12(E) Current will cease to flow in the copper sheet.。

Engineered O-Rings Catalog ORD 5710 美国Parker O-Rin

Engineered O-Rings Catalog ORD 5710 USASimple solutionsfor complex sealing problemsIn the O-Ring Division’s monitoring each step of the process Finite element analysisElement Analysistion process and ensures theselection of the right materialand geometry for a customer’sapplication. As an addedbenefit, FEAused to predict service life.a simple interfacespecific glands and seals. Itversions of these books, availableas ORD 5703 (US) and 5705(Europe), provide engineersfor static and dynamic seals,with world productionamounting tobillions per year.In 1937,Niels A. Christensen, aDanish emigrant to the USA,was awarded a patent for thisring with the perfectgeometricalshape.In 1949,Parker O-ring materialsled to the aeronautical specifica-tion MIL-P-5515 B and to the dimensionalstandards MS 29512 and 513, which werebased on Parker O-rings. Since then, theO-ring has become a vital sealingelement in all kinds of fluidpower equipment.advice from Parker sealing experts isnever far away.Parker O-Ring division’s manufacturing facilities span 4 continents and 9countries. Some of these The division’s North American headquarters, located in Lexington KY , isApplicationsTransportation•Brakes/ABS•Cooling/air conditioning •Fuel and diesel injection, spark plugs•Quick connects, couplings, gear units•Shock absorbers •Steering systems•Transmissions and radiator sealsAerospace•Aircraft engines, wheels and brakes•Control and actuation systems•Fuel systems•Space shuttle launch vehiclesMedical•Dyalizers•Syringes, infusions•USP Class VI and FDA “White Listed” formulations are availableSemiconductor Processing•For wet, dry and thermal processes•Parker UHP Processing:Parker uses totally enclosed and dedicated manufacturing areas for compounding,preparation, molding, cleaning and final packaging of o-rings in critical compounds for semiconductor processing applicationsFluid Power•Accumulators •Cylinders, valves •Filters •Fittings •Pumps•Rotary actuatorsConsumer Products•Appliances•Compounds meeting the requirements/recommen-dations: FDA, NSF, WRC,DVGW, BGA, KTW •Heating/plumbing •Sanitary equipmentChemical Processing Industry (CPI)•Equipment and components requiring extremely high chemical inertness attemperatures up to +320°CEnergy/Oil Field•Drilling•Exploration •Production •TransportationParker O-rings are used in many applications and industries, including:1-800-C-Parker Parker O-Ring Division Worldwide LocationsNorth AmericaUSAParker Hannifin CorporationO-Ring Division2360 Palumbo Drive Lexington, KY 40509 Phone: (859) 269-2351Fax: (859) 335-5128 Parker Hannifin CorporationO-Ring Division104 Hartmann Drive Lebanon, TN 37087Phone: (615) 444-0191Fax: (615) 449-7312 Parker Hannifin CorporationO-Ring Division109 Industrial Park Drive Livingston, TN 38570 CanadaParker Hannifin CorporationO-Ring Division255 Hughes RoadOrillia, Ontario L3V 2M3 Phone: (705) 325-2391Fax: (705) 325-5721 MexicoParker Hannifin CorporationO-Ring DivisionPSDM Business Unit Diagonal Lorenzo de la Garza #13 Ciudad IndustrialH. Matamoros, Tam. 87490 Parker Hannifin CorporationO-Ring DivisionBRCO Business UnitCalle Sexta Y Vizcaya #95 Col. EuzkadiH. Matamoros, Tam. 87370 EuropeAustriaSee GermanyBelgiumParker Hannifin SA NVParc Industriel Sud, Zone II 15, Rue du Bosquet1400 NivellesPhone:+(32) 67-28 09 00 Fax:+(32) 67-28 09 99 Czech RepublicParker Hannifin s.r.o. Podebradská 100528912 SadskáPhone: +(420) 325-55 5111 Fax: +(420) 325-55 5112 DenmarkPolar Seals A/S Bjergvangen 23060 EspergærdePhone: +(45) 49 12 17 00 Fax: +(45) 49 12 17 01FinlandParker Hannifin OyYlastontie 16FIN-01510 VantaaPhone: +(358) 9-47 67 31Fax: +(358) 9-47 67 32 00FranceParker Hannifin RakZ.l. du Mont-BlancB.P. 482, Ville-la-Grand74108 Annemasse-CédexPhone: +(33) 4-50 87 80 80Fax: +(33) 4-50 87 80 76GermanyParker Hannifin GmbHO-Ring DivisionStuifenstr. 55D-74385 PleidelsheimPhone:+(49) 71 44-206-0Fax: +(49) 71 44-2 37 49HungaryParker Hannifin CorporationBudapest Representation OfficeVezer u. 156-1581148 BudapestPhone: +(36) 1-2 52 81 37Fax: +(36) 1-2 52 81 29IrelandSee United KingdomItalyParker Seals S.p.A.Via Marzaghette 2I-25030, Adro (BS)Phone: +(39) 030 754 811Fax: +(39) 030 745 8210Parker Hannifin S.p.A.Via Priv. Archimede, 120094 Corsico (Mi)Phone: +(39) 02-4 51 92-1Fax: +(39) 02-4 47 93 40NetherlandsParker Hannifin B.V.Edisonstraat 1P.O. Box 3407570 AH OldenzaalPhone: +(31) 541-58 50 00Fax: +(31) 541-58 54 59NorwayParker Hannifin A/SBerghagenP.O. Box 3008N-1402 SkiPhone: +(47) 64 91 10 00Fax: +(47) 64 91 10 90PolandParker Hannifin Sp. z.o.o.ul. Parowcowa 8B02-445 WarsawPhone: +(48) 22-8 63 49 42/43Fax: +(48) 22-8 63 49 44RussiaParker Hannifin CorporationKomsomolsky Prospect 42Office 407119827 GSP Moscow G-48Phone: +(7) 095-234 0054Fax: +(7) 095-242 0907Slovakiasee Czech RepublicSwedenParker Hannifin Sweden ABBox 831416308 SpangaPhone: +(46) 8-7 60 29 60Fax: +(46) 8-7 61 81 70SwitzerlandSee GermanySpainParker Hannifin Espana S.A.Paseo Cordellas, 5708290 Cerdanyola-del-Valles(Barcelona)Phone: +(34) 93-6 91 50 62Fax: +(34) 93-6 91 46 19United KingdomParker Hannifin plcSeal GroupParkway, Globe ParkMarlow, Bucks SL7 1YBPhone: +(44) 16 28-40 40 88Fax: +(44) 16 28-40 40 89Asia PacificAustraliaParker Hannifin Australia Pty. Ltd.9 Carrington Road2154 (NSW) Castle HillPhone: +(61) 2-96 34 77 77Fax: +(61) 2-98 42 51 11ChinaParker HannifinFluid Power Systems(Shanghai) Co., Ltd.280 Yun Qiao RoadJian Qiao Export Processing ZoneShanghai 201206Phone: +(86) 21-5031 2525Fax: +(86) 21-5834 3714Parker Asun Sealing CompanyNo. 26 Tian Bao RoadTian Bao Industrial ZoneDong Guan CityGuang Dong, P.R.O.C.Hong KongParker Hannifin Hong Kong Ltd.8/F Kin Yip Plaza9 Cheung Y ee StreetCheung Sha Wan, KowloonPhone: +(852) 24 28 80 08Fax: +(852) 24 80 42 56JapanParker Hannifin Japan Ltd.Osaka Sales OfficeNo. 2 Tani Bldg.1-4-25, Nishi-Miyahara,Yodogawa-KuPhone: +(81) 6-48 07-32 88Fax: +(81) 6-48 07-32 99KoreaParker Hannifin Korea Ltd.902 Dae Heung Bldg.648-23 Yeaksam-dongKangnam-Ku, Seoul 135-080Phone: +(82) 2-5 61 04 14Fax: +(82) 2-5 56 81 87SingaporeParker Hannifin Singapore Pte., Ltd.No. 11 Fourth Chin Bee RoadJurong Town 61 9702Phone: +(65) 261 5233Fax: +(65) 265 5125TaiwanParker Hannifin Taiwan, Ltd.8F-1, No 102 Sung Lung RoadTaipeiPhone: +(886) 2 8787 3780Fax: +(886) 2 8787 3782AfricaParker Hannifin Africa Pty. Ltd.Parker Place10 Berne AvenueAeroportKempton Park, South AfricaPhone: +(27) 11-3 92 72 80Fax: +(27) 11-3 92 72 13Latin AmericaArgentinaParker Hannifin Argentina SAICStephenson 27111667 Tortuguitas - Malvinas Arg.Buenos AiresPhone: +(54) 1-1 47 52-41 29Fax: +(54) 1-1 47 52-37 04BrazilParker Hannifin do BrasilIndustria e Comercia Ltda.Via Anhanguera, Km 25,305275 Sao Paulo / SPPhone: +(55) 11-39 17-10 99Fax: +(55) 11-39 17-08 17Continental HeadquartersManufacturing plants1/2-2.5M-CE。

JCR期刊影响因子及分区情况(全部学科)

中文分类工程技术工程技术工程技术工程技术工程技术工程技术工程技术工程技术工程技术工程技术工程技术工程技术工程技术工程技术工程技术工程技术工程技术工程技术工程技术
分区 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
2001-2003年主办国平均因子 0.27 0.02 0.14 0.23 0.28 0.21 0.15 0.19 0.16 0.06 0.02 0.01 0.01 0.25 0.03 0.24 0.23 0.06 0.20 美国英国法国荷兰法国法国英国波兰美国英国俄罗斯德国俄罗斯俄罗斯美国西班牙巴西德国加拿大
785 AI EDAM 786 AIRCR ENG AEROSP TEC 787 ALCATEL TELECOMMUN R 789 ANALOG INTEGR CIRC S 790 ANN CHIM-SCI MAT 791 ANN TELECOMMUN 795 ANTI-CORROS METHOD M 802 805 807 808 809 810 AUTOM CONTROL COMP S 811 AUTOMAT REM CONTR+ 813 AVIAT WEEK SPACE TEC 817 BOL SOC ESP CERAM V 818 BRAZ J CHEM ENG 825 BWK-ENERGIE-FACHMAG 827 CAN J CIVIL ENG ARCH METALL ASHRAE J ASSEMBLY AUTOM ATOM ENERGY+
工程技术工程技术工程技术工程技术工程技术工程技术工程技术工程技术工程技术工程技术工程技术工程技术工程技术

AMM第644-650卷目录PART 4

Table of ContentsPreface liii PART 4An Improved Scheme of One-Time Password Identity Authentication Based on theS/KEY SystemJ.Y. Li, H. Shi, Y.Q. Deng, J. Gong and Y. Guan (2763)The New Key-Stream Generator Based on the OFB Mode of AESH. Shi, J.W. Lu, Y.F. Ji, C. Wu, J. Gong and Y.Q. Deng (2768)Collaboration Research on Web 2.0B. Wu and C.Y. Zhang (2772)An Online E-Payment System Applying to Auto Insurance Based on Proxy Blind Signature L.M. Sha and S.Z. Yang (2776)Network Security Situation Awareness Based on Phishing DetectionJ.Y. Zhang, C.G. Song and X. Jin (2784)Supermarket Trolley Positioning System Based on ZigBeeZ. Zhang, X.P. Tao, L. Zeng and C. Wang (2788)Study of Web Service Discovery Algorithm Based on SemanticL. Zhao and W. Zhang (2793)Research on Usage Intention of Community Information SystemW.P. Li, J. Yang, K.S. Kim and W. Sun (2797)Discussion on the Application of Networking Technology in Intelligent Campus ConstructionA. Wang and X.Q. Zhang (2804)Design of Pesticide Safety Evaluation of SoftwareX.H. Zhang and Y. Lin (2808)The Key Technology and Application of the Internet of ThingsC.M. Li, R. Wang and L. Huang (2812)A Combined Method for Chinese Micro-Blogging Topic TrackingX. Zhang, B. Shang, L.L. Dong and Y.J. Zhu (2816)A Software Design Model Based on Big DataZ.L. He, X.H. Xiao and Y.H. He (2821)Research on Security of P2P TechnologyL.H. Wang (2826)Research of Network Information Platform Construction of ERP System in Manufacturing J.H. Zhang (2830)Optimization of Clustering Algorithm in Ad Hoc NetworkQ. Yu and P. Zong (2834)Research and Improvement of Dynamic Source Routing Protocol Based on Ad HocP. Zong and J. Qin (2838)Safety Strategy of Campus Network Realize Based on Core SwitchY.Y. Lu, Y. Yang and B. Zang (2842)Complex Opinion Network Correlation ClusteringF.Y. Wang, S. Qiu and Q. Li (2846)The Application of Database Technology in Network Management SystemG.L. Cheng and M.Z. Li (2850)Research on the SDN-Based Architecture of Space-Sky Information NetworkD.M. Yuan and R.W. Ren (2854)Study on the Campus Website ConstructionC. Liu (2857)Research on QoS Guarantee Technology for Intercom System Based on SIPZ. Li, Q.Y. Yang, Y.C. Zhou and H. Ren (2863)Applied Research for Campus Student Credit Management System under the Cloud Storage Y.J. Kang and L. Ma (2868)Assess on E-Commerce Transaction Based on Web TechnologyK. Xiao (2872)NTP DRDoS Attack Vulnerability and MitigationA. Alfraih Abdulaziz Nasser and W.B. Chen (2875)Binary Tree Model-Based Mobile Ad Hoc Network Dynamic Address AllocationMechanism ResearchJ.L. Liu and L. Zhu (2881)A High-Throughout Design of CAVLC Decoder for H.264/AVCY. Wang and X.Q. Su (2886)A Distributed Comprehensive-QoS Multicast Routing Algorithm on WSNsW.J. Xiao and S. Zhong (2890)Mobile Game Development with Flash as the EditorH.T. Zhang, Q.J. Sun and Y.C. Liu (2898)Design and Implementation of Service Traffic Awareness System in LTE NetworkJ. Wang, Z.Z. Zhang and Y.L. Luo (2902)A Hadoop-Based Performance Optimization of Network Stream Input FormatX.P. Wang, J.T. Luo, W. Gao and Y. Liu (2906)Dynamic Non-Cooperative Structured Deep Web SelectionS. Deng (2911)Multimedia Technology of Digital Tourism Based on Android SystemJ. Zhang (2915)Vulnerability Assessment of Information System Based on Weighted Directional Graph andComplex Network TechnologyY.Z. Li (2920)Key Technologies Analysis on Management System Data WarehouseX.F. Yang (2925)Research on Action Design System Based on TechnologyL. Xu, W. Lei and W.M. Xu (2929)Numerical Analysis and Performance Test Based on Multi-Media Internet Architecture J.P. Fan (2934)The Architecture and Implementation for International Trade Settlement Software DesignG.J. Zhang (2939)A Web Services Security Policy Description ModelH. Zeng, Y.W. Zhao and D.F. Ma (2943)The Simulation Platform in City Traffic Environment Based on TinyOS for WirelessSensor NetworksT.J. Ren, H.X. Lv, Z.Q. Wang, Y.R. Chen and Y.L. Liu (2947)Automatic Threat Assessment of Malware Based on Behavior AnalysisJ.G. Jiang, X.J. Ma, X.L. Qiu, M. Yu and C. Liu (2952)Design of Wireless Sensor Networks Border Router Based on IPv6D.W. Xu, L.L. Deng and S. Ren (2957)Research of Network Virtualization in Data CenterX.L. Tan, W.B. Wang and Y.Q. Yao (2961)The Software Support Analysis of Information SystemH. Wang, X.Y. Li, X.N. Wang and W.N. Liu (2965)Study on a Novel GIS-Based Routing StrategyY.W. Wang and D.Y. Ji (2969)Development of a New Routing Protocol Based on GPSR for Wireless Sensor NetworksC.F. Xing, L. Yang and Q.L. Han (2973)The Study of Network Information Security Based on Information Filtering Technology L.L. Wei and W. Yang (2978)The Implementation of Cloud Storage System Based on OpenStack SwiftZ.Y. Duan and Y.Z. Cao (2981)Research and Design on Multilevel Secure Database Inference ControlH.Y. Zhao, R.G. Liu and X.G. Liu (2985)Research on Secure Model in WiFi/WiMAX Mixed Networks Based on Pre-Authentication Z.T. Ni, Y. Zhong and L. Huang (2988)Research on Database Front-End Applications Exploration Based on PowerbuilderL. Huang, Y. Wang and Z.T. Ni (2992)Research on Dynamic Self-Adaptive Network Security Model Based on Mobile Agent K.Q. Fan (2996)Research on the Implementation Methods of Security Management of Distributed DatabaseApplication SystemN. Zheng and Y. Gao (3000)Research on Shared Information Platform for Expressway Management Information SystemC. Wang and Y.L. Li (3004)Research on Ad Hoc Network Security Protection Model Based on Mobile AgentQ. An, Y.J. Luo, H.Y. Zhao and J. Zhao (3008)Research on Information Resources Sharing Patterns Based on Cloud ComputingW.J. Yang, Y.J. Luo, H.Y. Zhao and X.T. Li (3012)Research on the Model of Personalized Recommendation System Based on Multi Agent Q. Wang, J.Z. Ping, L.L. Yu and Z.J. Wang (3016)Research of Music Retrieval System Based on Emotional Music TemplateX. Wang (3020)A New Trust Model in P2P NetworkX.L. Li, L.C. Wu, J.J. Xiang, H.L. Ma and F. Liao (3024)Research on Relay Node Placement Based on Hybrid Greedy Optimization Algorithm inWireless Sensor NetworksH. Xu and H. Zhang (3028)Security Research of the Mobile E-Government TerminalS.Y. Guan, Y. Fan and H.L. Lv (3032)Analysis of College Students' Online Business in ChinaA. Abuduaini and N. Aishanjiang (3036)Thought about the Construction of Digital Employment Information Service System of RuralMigrant Workers in the West Area of JilinX.L. Wang (3040)Design and Implementation on Sina Micro-Blog Client Based on the Android SystemC.Y. Shi (3045)On SOA Community Informationization Foundation Database Generic Interface Design Y.B. Zhou (3049)Research on Storage Strategy of Unstructured Small Files in HDFSL.T. Wu, T.N. Wang and H.R. Hu (3053)The Building of the Database of Art Resources Research for Academy of Fine ArtsM. Zhao (3057)Research and Implementation of Auxiliary Teaching System Based on C/S ModelY.J. Cong (3061)The Improvement of the Public Service System Based on Web TechnologyR. Qian (3065)Design of Extended Event Service Model Based on CORBAC.X. Zhao (3069)Modeling and Analysis of NOTAM Distribution Services Based on Petri NetJ. Hu, X.Y. Song and J.Z. Sun (3073)Research of the Database Access Technology FrameworkX.D. Zhang, Z.M. Teng and D.W. Zhao (3077)Dynamic Visual Elements in the Digital Media DesignT. Sun (3081)Design Research on the Resident Electronic Health Recorder SystermN. Liu (3085)The Web Development Technology Research of Cross Platform Mobile Application S. Sun and S.X. Cao (3090)The Universal Middleware Architecture Based on the Web of ThingsR. Zhang and P. Zhang (3094)Development of Travel Reservation System for Mobile PlatformL.J. Sun (3099)Research on Statistics Based Multi-Priority MAC Protocol for Ad Hoc NetworksP. Wang, H. Li, B.L. Ye, C. Chen and Y.B. Wang (3103)LEACH-EO: A More Energy-Efficient LEACH Protocol for WSNJ. Zhang, H. Yan, Y. Cui, H. Rong and J.P. Wang (3108)Authorization Management System of Micro Video Based on FFmpegQ. Guo, Y.G. Xu and S.X. Cao (3112)Research on Network Video Data Acquisition and Analysis Based on Big DataH. Ji and S.X. Cao (3116)The Design and Implementation of Community Property Management SystemQ.H. Wu and H. Zhao (3120)The Integration of Sports Information in Personalized NetworkH. Zhao, Q.H. Wu and J.B. Zhao (3124)Situation and Development Strategies of Sports Entertainment Groups inNetwork EnvironmentJ.B. Zhao, H.J. Ji and H. Zhao (3129)Reverse Engineering OWL 2 Ontologies to UML ModelsW.J. Li (3133)The Study on Educational iOS and Android Application Program of Sports Skillsand KnowledgeN. Liu and D.Y. Yang (3137)Research on Development of Books Interview PlatformH.M. Zhang and N. Li (3141)The Development of Information Integration System for Oil Production Equipment M.T. Wang (3145)The Design and Implementation of Oil Production Equipment Data Management System M.T. Wang (3149)The Development on Information Collection System Based Internet of ThingsC.W. Luo, X.W. Yin and C.D. Ni (3153)Design and Implementation of Computer Equipment Management System Based onOracle DatabaseX.M. Jiang (3157)Agricultural Products Traceability System Design Based on IOTX. Qian, D. Wang and W.M. Luo (3160)Design and Implementation of the Hospital Information Management System Based onthe M. Li and S.Y. Yang (3166)Professional Software Analysis and Comparison for Graphic DesignR.H. Wang (3170)A Network Security Risk Computation Approach Based on Attack GraphsC. Wang (3174)Application of Computer Network of Virtual Reality in Design of ArtJ. You (3178)Cryptographic Protocol Verification Based on the Extension RuleH. Lin (3181)The Frame Study of Translation System Design Based on Database ManagementL.H. Liu, F.J. Meng, Y. Lei, Y. Sun, J.Q. Mu, Z.L. Zhu, Y. Yan, Y.H. Zhang, L. Sun and Z. Lv (3185)Efficiency Analysis of Command Networks with Cross-Level of Different GroupsL.F. Yu, J.B. Wu, J. Liu, B.X. Xiu and W.M. Zhang (3189)Study and Practice Based on Network TechnologyW.H. Zhao, D.P. Xu, H.Y. Gong and Y. Li (3195)Application Research on Virtual Reality TechnologyY. Li, H.Y. Gong, D.P. Xu and W.H. Zhao (3199)Network Topology Discovery Algorithm Based on OSPF Link State AdvertisementZ.J. Shen and Y.S. Ge (3203)A Cloud-Based Mobile Telemedicine Consultation System Based on iPadH. Wang, T.H. Li and F. Wu (3208)Design of Network System Security System of Digital LibraryS. Liu (3212)Information Management System of Metrological Evaluation Based on SSH Framework S. Zhang, J.M. Zhu, Y.H. Qin and L.L. Qu (3216)Design and Implementation for the Upper Computer Software of the Two-DimensionalTurntable System Based on MFCY.N. Xiang Li and X.J. Yang (3220)Available Storage Space Sensitive Replica Placement Strategy of HDFSW.T. Zhao, Y. Ding and X.H. Zhang (3224)LBSN-Based Personalized Routes RecommendationL.C. Zhu, Z.J. Li and S.X. Jiang (3230)An Intelligent Human-Computer Collaborative Method for Creative DesignJ.W. Wang (3235)Research of Cloud Manufacturing Technology in the Development of Digital IntelligentProduction Control PlatformG.L. Feng (3241)A Remote and Unified Software Automated Deployment PlatformJ.P. Zhao, X.Y. Liu, H.H. Wu, X.L. Chen, L. Yang and D.H. Zhang (3245)Design and Implementation of Multi Granularity Access Framework Based on AOP Q. Wang and Y.B. Wang (3251)A Smart Grid Data Global Placement Strategy Based on Cloud ComputingY.K. Li, D. Xin and H.G. Liu (3256)Design and Implementation of Binary Utilities GeneratorJ.Q. Shen, J. Wu, Z.F. Zhang and H.Q. Ren (3260)SERP: A Simple Energy-Hops-Based Routing Protocol in WSNsM.X. Li, X.C. Zhou, X.H. Fan and S. Wang (3266)Human Error Simulation of Manufacturing Cell Based on Human-Machine Integrated ModelD.F. Zhao, X.D. Zhang, C.J. Gong and C.C. Wang (3270)A Methodology for the Exploration of 802.11BH. Yang (3275)Research on Data Aggregation Application Based on MashupM.Y. Cai and B. Pan (3279)Research on ASIC Firewall Based on State Detection TechnologyS.Q. Wang and H.Y. Chen (3283)Detection Technology for Hostile Attacks to Campus Wireless NetworkL. Ma and H.X. Yang (3287)Research on the Detection Method of the Malicious Attacks on Campus NetworkJ.L. Wang (3291)Detecting Overlapping Communities with MDS and Local Expansion FCML. Li, Z.M. Xia, S.H. Li, L. Pan and Z.H. Huang (3295)Comparison Analysis of RESTful and SOAP-WSDL Applied in the Image Management System R.Y. He (3300)Study on Digital Content Representation from Direct Label Graph to RDF/OWL Language into Semantic WebK.A.L. Khamis, L. Zhong and H.Z. Song (3304)Research on Multilevel Secure Database Inference ChannelH.Y. Zhao, J. Meng and X. Zhang (3310)Design and Realization of IOT-Based Video Monitoring SystemJ. Yin and C.H. Li (3314)Storage Model Based on Oracle InterMedia for Surveillance VideoB. Sun, W.S. Luo, L.B. Du and Q. Lu (3318)A Noise-Optimal Integrator for High-Precision SC Sigma Delta ModulatorsX.L. Wang and Y.W. Zhang (3322)Research on Vehicle Networking Transfer Channel Based on MAC Safety Information System Y. Zhou, T.J. Ren, Z.Q. Wang and Y.L. Liu (3329)Application of Neural Network in Network Intrusion DetectionZ. Yang and H. Du (3334)The Study of the Ontology and Context Verification Based Intrusion Detection ModelG.F. Guo (3338)Environmental Monitoring System Designing: A Internet of Things ApproachG.H. Wu, F. Liu, J.X. Li and W. Wang (3342)Remote Inspection System Algorithm Research of Wireless Base StationM.D. Bai and Y. Dong (3346)Application Research of Visual Simulation Technology in the Field of Marine EngineRoom SimulatorH.S. Shen, J.D. Zhang, Y.B. Li and F. Han (3350)Application of Function Point EstimatingC.H. Zhou (3357)Design and Research of Computer System High Confidence Fault TolerantJ.Q. Qi (3361)FMPC: A Fast Multi-Dimensional Packet Classification AlgorithmZ.H. Guo, L. Li, Q. Wang, M. Lin and R. Pan (3365)Code Protection Technology on iOSJ.T. Weng, Q. Mu, X.Y. Liao, Y.Z. Li, Q.X. Zhang and Y. Tan (3371)Distribution of Database in Cloud Based on Associated MatrixL.Y. Yao and W. Yang (3375)Finite Element Numerical Simulation Research on Fractured Horizontal Well’s Productivity M.X. Liu, J.H. Li and L. Zhang (3379)Research of Augmented Reality for Children’s Books on the Basis of ArtoolkitsW.G. Yang (3383)Research and Practice of Cloud Computing Based on HadoopA.S. Lu, J.J. Cai, W. Jin and L. Wang (3387)Review on Application of Virtual Reality in the Physical SimulationZ.J. Cai (3390)Overhead Analysis of Loop Parallelization with OpenMP DirectivesL.Y. Xiang, Z.Y. Fang, Y. Wang, G.N. Qu and Z. Chen (3394)Design and Implementation of Cloud Management SystemH.Y. Yu, T.X. Yang and X. Fu (3398)Study on Replacing-Element Imagery Design of Dongba Characters Combined withChinese CharactersW.J. Song, Y.F. Yang and R.P. Xu (3402)Research on Multilayer Security Audit Research Based on Attack Graph in Cloud Computing L.B. Wen (3408)An Efficient Secure Multichannel Traffic Management Scheme in 2.4 GHz Home AutomationNetwork with IoT FunctionsM. Wei and P. Wang (3412)Chapter 5: Electronics and Microelectronics, Embedded and IntegratedSystems, Power and Energy, Electric and Magnetic SystemsA Study on Reconfiguring On-Chip Cache with Non-Volatile MemoryM.Q. Wang, J.T. Diao, N. Li, X. Wang and K. Bu (3421)A Circuit Model of the MemcapacitorW. Wang, H. Xu, Y.W. Hou and H.J. Liu (3426)Titanium Oxide Memristor Based Digital Encoder CircuitY.W. Hou, X. Xu, W. Wang, X.B. Tian and H.J. Liu (3430)Application of Digital Coordinate Transformation to a New Posthole Broadband SeismometerC.Y. Peng, B. Xue and J.S. Yang (3434)Research and Design of Asynchronous FIFO Based on FPGAB.Q. Liu, M.Z. Liu, G. Yang, X.B. Mao and H.L. Li (3440)Wind Power Allocation Based on Predictive Power CorrectionZ.H. Feng, T.J. Jia, X.M. Xiao and F.J. Zhang (3445)The Application of LED Lighting in Museum Exhibition HallY. Zheng, L.W. Huang, M.M. Wang, H.Q. Chen and L.Z. Zhang (3449)A High Reliable Communication Method for the Terminal of a Networked and DistributedPower Supply SystemE. Lu, B. Huang, S.S. Li and Y. Yang (3453)A New Method of Cross-Correlation by Magnetic Dipole for Estimating MagnetizationDirection under the Influence of Remanent MagnetizationL. Shi, L.H. Guo and F.Y. Guo (3459)The Condition Assessment of Distribution Transformer Based on Improved AnalyticHierarchy ProcessX.P. Meng, L. Li, H. Wang and X. Ji (3463)Effects of Different Sample Resistances on the Insulator Leakage Current Acquisition Results P.C. Miao and Z.N. Xu (3468)Research and Design of Video Acquisition System Based on FPGAB.L. Liu, B.Q. Liu, L. Pan and L. Wang (3472)High Rate Data Transmission System Based on OFDM for Well LoggingQ.S. Gu, W. Chen and R.Q. Wu (3476)Application of On-Line Ultrasonic and UHF Partial Discharge Detection in 1000kV GISF. Chen, H.Z. Tang and H.G. Li (3480)Synchronization of Hyperchaotic Memristor-Based Chua’s CircuitsH.L. Huang, Y. Peng and J.J. Huang (3485)Prediction of Nuclear Power Project Cost Based on Improved Non-Equidistant GM (1,1) Modeland Exponential Regression ModelB.Y. Liu, D.X. Niu, J.P. Qiu, H. Xu and Y. Wang (3489)Design Principle and Applicative Value of Photovoltaic SystemM. Chen, L. Chen, X. Tang and Y.H. Hu (3493)Research of Signal Integrality in PCB Design for ARM9 Core BoardL.Y. Su (3497)Formal Analysis of Memory Leak DefectsW. Zhang, Z.Y. Ma, Q.L. Lu, L. Wan and D.W. 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2004.4_Modeling_and_Simulation_of_Combined_Extrusion_for_Spark_Plug_Body_parts

Modeling And Simulation Of Combined Extrusion ForSpark Plug Body PartsT.Canta, D. Noveanu, D. FrunzaDepartment of Materials Processing, Technical University of Cluj, 103 Muncii Avenue,400641 Cluj, RomaniaAbstract. The paper presents the modeling and simulation for the extrusion technology of a new type of spark plug body for Dacia Supernova car. This technology was simulated using the finite elements modeling and analysis SuperForm software, designed for the simulation of plastic deformation processes. There is also presented a comparison between the results of the simulation and the industrial results.INTRODUCTIONThe producers of spark plugs for car engines obtain the body part by extrusion technology using 5-6 stages for deformation and sometime the part, is rotated between two stages to ensure a big strain at both ends. A Romanian company produced by cold extrusion, a wide range of spark plug bodies, all having the maximum transversal dimension at one of the ends of the part. The modern engines use a type of spark plugs, which have the maximum transversal dimension in themedium zone of part height.FIGURE 1. The spark plug bodyThe equipment used for that, allow four stages of deformation (the first stage is dedicated for cutting the bar and the last stage is needed for piercing the part). The challenge was to design the extrusion technology which fit their needs by modeling and simulation using a commercial software MSC SuperForm[1].FEM SIMULATIONIn order to simulate the cold extrusion of the spark plug body there were performed the following steps:1.Establish the material behavior during cold deformation – obtaining the real σ-ε curves;2.Determining the contact conditions;3.Introduction of the geometry for the extrusion tools and for the initial billet;4.Introduction of material data, friction condition and equipment data;5.Analysis;© 2004 American Institute of Physics 0-7354-0188-8/04/$22.00edited by S. Ghosh, J. C. Castro, and J. K. LeeCP712,Materials Processing and Design: Modeling, Simulation and Applications,NUMIFORM 2004,6.Results interpretation.EXPERIMENTSMaterial BehaviorThe material used for this kind of parts is S 18 A, a low carbon steel, designed to be used in cold plastic deformation technologies. The chemical composition is: Cmax0.18; Mn 0.25 ... 0.50; Si max =0.10; P max =0.025; S max =0.030; Al=0.02 ... 0.07; Ni max =0.20; Cr max =0.20; Cu max =0.20. There was obtained the real σ-ε curve. The material data needed for simulation, were obtained from cold torsion test, and by using a data acquisition system there was obtained the τ-γ curve. Considering as valid one of the three yielding criteria: Tresca, Von Mises and their average there was plotted the real σ-ε curve as in the next figure:FIGURE 2. The real σ-ε curve[2]For comparison it was also plotted the real σ-ε curve from a cold upsetting test.Contact conditionsThe friction coefficient can be determined in different ways: the most used method is the ring-upsetting test [3]. For comparison it can be used an alternative method i.e. based on the Ekelund equation[4]:.h d K pµ+=3112 (1)Starting from relation (1) it can be determined the friction coefficient as:()()112221123h /d p h /d p p p −−=µ (2) where:p 1 - average pressure of sample 1 p 2 - average pressure of sample 2 d 1 - diameter of sample 1 d 2 - diameter of sample 2 h 1 - height of sample 1 h 2 - height of sample 2There were pressed cylindrical samples Φ15 x 10 and Φ18 x 10. The axial pressure was continuously recorded via a data acquisition system, and by using equation (2) resulted the continuous variation of the friction coefficient versus strain, presented in Figure 2.FIGURE 3. Determination of friction coefficientFinite elements analysisPre-processingThe shape of the dies and the punches and of the initial billet was realized using the SuperForm pre-processor. They are presented in Figure 4.FIGURE 4. Shape of the dies and punchesThe equipment data were provided by theRomanian company, which have a multi stage 2.8 MNcrank shaft press type Peltzer.AnalysisThe diameter of the billet is near hexagonal size(15.6 mm); this fact leads to smaller strains. In thistechnology, only the first stage occurs in a closed die(Stage 1); the other stages occur in open dies. So, thestresses in tools are smaller and there is not necessaryto cut very accurate the material.The hexagonal zone is formed inside the die instage 2; this fact ensures very good conditions fordeformation. The flange forms in stage 3 by upsettingthe zone under the hexagon. It must be mentioned thatin this stage the hexagonal zone is not deformed in thepunch. It is only driven in the tool. In the third stagethe punch is not driven in die; it stops 1 mm before thedie, and the flow was directed to avoid any penetrationof the material in the slot. The last stage ofdeformation achieves the final dimensions of the part,by backward extrusion.Considering axi-symmetricity, just one half of thepart is analyzed [5]. The element used is quadrilateralwith 4 nodes. Totally there are 276 elements. Young’smodulus was assumed to be 2.1x105 MPa andPoisson’s ratio to be 0.3.The initial yield stress is 298 MPa. Analysis withwork hardening was performed. The hardening curvewhich was introduced shown in Figure 5.FIGURE 5. Strain-hardening curveThe friction coefficient used for the contactsurfaces of the punches and dies is 0.1, the Coulombprinciple being adopted.The whole analysis process is divided into 318steps, in 4 stages.The next figures shows the shape of the billet aswell as the punch and die geometry at the end of eachstage. The plotted parameter is total equivalent stress.FIGURE 6. Results of the simulation at the endof stage 1Initial billet Workpiece after first stageWorkpiece aftersecond stageWorkpiece afterthird stageWorkpiece after fourth stageFIGURE 7. Results of the simulation at the end of stage 2FIGURE 8. Results of the simulation at the end of stage 3FIGURE 9. Results of the simulation at the end of stage 4It is important to use a punch with an optimal shape. So, there were studied 8 types of punches. The stresses distribution on their active zone was simulated. It was chosen the punch that achieves the most uniform distribution of stresses.The final shape of the spark-plug body with the finite elements obtained at the end of the simulation is shown in figure 10.FIGURE 10. Final shape of the spark plug bodyFIGURE 11. The workpiece after each stageFIGURE 12. Half of the final partCONCLUSIONSThe results of the simulation agree well with those of industrial process.1. The loads on the punches at the end of the four stages obtained by simulation are close to those recorded in industrial trials using a data acquisitionsystem.FIGURE 13. Plot of the loads on the punches where Body_6 represents punch 1, Body_7 represents punch 2, Body_8 represents punch 3, Body_9 represents punch 4,Table 1. Comparison Between Loads Obtained by FEMSimulation and by Industrial TrialsStage 4Stage 3Stage 2Stage 1Load (FEM)[kN] Load (Ind.)[kN]177 537.7 260.8 239.6These small differences occur due to the material properties and to the friction coefficient in industry trials.2. Concerning the shape and dimensions, there are also very small differences between FEM simulation andindustrial trials.Table 2. Comparison Between Dimensions Obtained by FEM Simulation and by Industrial Trials Length of the part (FEM) Length of the part (Ind.) Diameter of the part (FEM) Diameter of the part (Ind.)The differences are due to the elastic deformation of the press and dies, and also as a result of different height of the initial billet resulted after shearing of the initial billet.REFERENCES1. Sabadus, D., Frunza, D., Noveanu, D., Canta, T.,“Simulation and Modeling for Complex Extrusion of New Spark Plugs Body Parts”, Acta Technica Napocensis, vol. 45, Part 1, Cluj Napoca, 2002, pp. 375-380. 2. Tintelecan, C., Canta, T. “Finite Element Analysis of theComplex Shape Workpieces”, Proc. of Int. Conference MATEHN’98, Cluj Napoca, 1998, pp. 363-368 3. Male, A.T., and Crockcroft, M. G. “A Method for theDetermination of the Coefficient of Friction of Metals under Conditions of Bulk Plastic Deformation” Journal of the Insitute of Metals, vol. 93, pp. 38-46, 1964-65. 4. Ekelund, S., Steel, 93 (Aug.21), 1933, pp. 27-29. 5. MARC/Superform User’s Guide.。

IEEE STD's

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1364-2001 IEEE Standard Verilogr Hardware Description Language.pdf
1364.1-2002 IEEE Standard for Verilogr Register Transfer Level Synthesis.pdf
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1361-2003 Ieee Guide For Selection, Charging, Test, And Evaluation Of Lead-Acid Batteries Used In Stand-Along Photovoltaic (Pv) Systems.pdf
12207.2-1997 - Software Lifecycle Processes.pdf
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数学期刊名称缩写

Abbreviations of Names of SerialsThis list gives the form of references used in Mathematical Reviews(MR).The abbreviation is followed by the complete title,the place of publication and other pertinent information.∗not previously listed E available electronically §journal reviewed cover-to-cover V videocassette series †monographic series¶bibliographic journal∗Abh.Braunschw.Wiss.Ges.Abhandlungen derBraunschweigischen Wissenschaftlichen Gesellschaft.J.Cramer Verlag,Braunschweig.(Formerly Abh.Braunschweig.Wiss.Ges.)Abh.Braunschweig.Wiss.Ges.Abhandlungen derBraunschweigischen Wissenschaftlichen Gesellschaft.Goltze,G¨o ttingen.(Continued as Abh.Braunschw.Wiss.Ges.)§Abh.Math.Sem.Univ.Hamburg Abhandlungen aus dem Mathematischen Seminar der Universit¨a t Hamburg.Vandenhoeck&Ruprecht,G¨o ttingen.ISSN0025-5858.†Abh.Math.-Naturwiss.Kl.Akad.Wiss.Lit.Mainz Abhandlungen der Mathematisch-NaturwissenschaftlichenKlasse.Akademie der Wissenschaften und der Literaturin Mainz.[Transactions of the Mathematical-ScientiﬁcSection.Academy of Sciences and Literature in Mainz]Steiner,Stuttgart.ISSN0002-2993.§Abstr.Appl.Anal.Abstract and Applied Analysis.Mancorp,Tampa,FL.ISSN1085-3375.¶Abstracts Amer.Math.Soc.Abstracts of Papers Presented to the American Mathematical Society.Amer.Math.Soc.,Providence,RI.ISSN0192-5857.Acad.Roy.Belg.Bull.Cl.Sci.(6)Acad´e mie Royale deBelgique.Bulletin de la Classe des Sciences.6e S´e rie.Acad.Roy.Belgique,Brussels.ISSN0001-4141.Acad.Roy.Belg.Cl.Sci.M´e m.Collect.8o(3)Acad´e mieRoyale de Belgique.Classe des Sciences.M´e moires.Collection in-8o.3e S´e rie.Acad.Roy.Belgique,Brussels.ISSN0365-0936.Acad.Serbe Sci.Arts Glas Acad´e mie Serbe des Scienceset des Arts.Glas.Classe des Sciences Naturelles etMath´e matiques.Srpska Akad.Nauk.i Umetnost.,Belgrade.ISSN0374-7956.†Acc`e s Sci.Acc`e s Sciences.[Access to Sciences]De Boeck Univ.,Brussels.§E ACM J.Exp.Algorithmics The ACM Journal ofExperimental Algorithmics.ACM,New York.ISSN1084-6654.E ACM Trans.Math.Software Association for ComputingMachinery.Transactions on Mathematical Software.ACM,New York.ISSN0098-3500.∗§Acta Acad.Paedagog.Agriensis Sect.Mat.(N.S.)Acta Academiae Paedagogicae Agriensis.Nova Series.SectioMatematicae.Eszterh´a zy K´a roly Coll.,Eger.∗§Acta Anal.Funct.Appl.Acta Analysis Functionalis Applicata.AAFA.Yingyong Fanhanfenxi Xuebao.SciencePress,Beijing.ISSN1009-1327.§E Acta Appl.Math.Acta Applicandae Mathematicae.An International Survey Journal on Applying Mathematics andMathematical Applications.Kluwer Acad.Publ.,Dordrecht.ISSN0167-8019.§Acta Arith.Acta Arithmetica.Polish Acad.Sci.,Warsaw.ISSN0065-1036.Acta Astronom.Sinica Acta Astronomica Sinica.TianwenXuebao.Kexue Chubanshe(Science Press),Beijing.(Translated in Chinese Astronom.Astrophys.)ISSN0001-5245.Acta Astrophys.Sinica Acta Astrophysica Sinica.TiantiWuli Xuebao.Kexue Chubanshe(Science Press),Beijing.(Translated in Chinese Astronom.Astrophys.)ISSN0253-2379.Acta Automat.Sinica Acta Automatica Sinica.ZidonghuaXuebao.Kexue Chubanshe(Science Press),Beijing.ISSN0254-4156.Acta Cienc.Indica Math.Acta Ciencia Indica.Mathematics.Pragati Prakashan,Meerut.ISSN0970-0455.Acta Cient.Venezolana Acta Cient´ıﬁca Venezolana.Asociaci´o n Venezolana para el Avance de la Ciencia.Asoc.Venezolana Avance Cien.,Caracas.ISSN0001-5504.Acta Comment.Univ.Tartu.Math.Acta etCommentationes Universitatis Tartuensis de Mathematica.Univ.Tartu,Fac.Math.,Tartu.ISSN1406-2283.E Acta Cryst.Sect.A Acta Crystallographica.Section A:Foundations of Crystallography.Munksgaard,Copenhagen.ISSN0108-7673.§Acta Cybernet.Acta Cybernetica.J´o zsef Attila Univ.Szeged,Szeged.ISSN0324-721X.Acta Hist.Leopold.Acta Historica Leopoldina.DeutscheAkad.Naturforscher Leopoldina,Halle an der Saale.ISSN0001-5857.§E Acta Inform.Acta Informatica.Springer,Heidelberg.ISSN0001-5903.§Acta Math.Acta Mathematica.Inst.Mittag-Lefﬂer, Djursholm.ISSN0001-5962.§E Acta Math.Acad.Paedagog.Nyh´a zi.(N.S.)Acta Mathematica.Academiae Paedagogicae Ny´ıregyh´a ziensis.New Series.Bessenyei Gy¨o rgy Coll.,Ny´ıregyh´a za.ISSN0866-0182.§Acta Math.Appl.Sinica Acta Mathematicae Applicatae Sinica.Yingyong Shuxue Xuebao.Kexue Chubanshe(Science Press),Beijing.ISSN0254-3079.§Acta Math.Appl.Sinica(English Ser.)Acta Mathematicae Applicatae Sinica.English Series.Yingyong ShuxueXuebao.Science Press,Beijing.ISSN0168-9673.§E Acta Math.Hungar.Acta Mathematica Hungarica.Akad.Kiad´o,Budapest.ISSN0236-5294.§Acta rm.Univ.Ostraviensis Acta Mathematica et Informatica Universitatis Ostraviensis.Univ.Ostrava,Ostrava.ISSN1211-4774.§Acta Math.Sci.(Chinese)Acta Mathematica Scientia.Series A.Shuxue Wuli Xuebao.Chinese Edition.KexueChubanshe(Science Press),Beijing.(See also Acta Math.Sci.(English Ed.))ISSN1003-3998.§Acta Math.Sci.(English Ed.)Acta Mathematica Scientia.Series B.English Edition.Shuxue Wuli Xuebao.SciencePress,Beijing.(See also Acta Math.Sci.(Chinese))ISSN0252-9602.§E Acta Math.Sin.(Engl.Ser.)Acta Mathematica Sinica.English Series.Springer,Heidelberg.ISSN1000-9574.§Acta Math.Sinica Acta Mathematica Sinica.Chinese Math.Soc.,Acta Math.Sinica m.,Beijing.ISSN0583-1431.§E Acta enian.(N.S.)Acta Mathematica Universitatis Comenianae.New enius Univ.Press,Bratislava.ISSN0862-9544.§Acta Math.Vietnam.Acta Mathematica Vietnamica.Nat.Center Natur.Sci.Tech.,Hanoi.ISSN0251-4184.∗Acta Mech.Sin.Engl.Ser.Acta Mechanica Sinica.English Series.The Chinese Society of Theoretical and AppliedMechanics.Chinese J.Mech.Press,Beijing.(FormerlyActa Mech.Sinica(English Ed.))ISSN0567-7718.Acta Mech.Sinica(Beijing)Acta Mechanica Sinica.LixueXuebao.Chinese J.Mech.Press,Beijing.(See also ActaMech.Sinica(English Ed.))ISSN0459-1879.Acta Mech.Sinica(English Ed.)Acta Mechanica Sinica.English Edition.Lixue Xuebao.Kexue Chubanshe(SciencePress),Beijing.(Continued as Acta Mech.Sin.Engl.Ser.)(See also Acta Mech.Sinica(Beijing))ISSN0567-7718.∗Acta Mech.Solida Sin.Acta Mechanica Solida Sinica.Chinese Journal of Solid Mechanics.Huazhong Univ.Sci.Tech.,Wuhan.ISSN0894-9166.†Acta Numer.Acta Numerica.Cambridge Univ.Press, Cambridge.ISSN0962-4929.Acta Phys.Polon.B Jagellonian University.Institute ofPhysics and Polish Physical Society.Acta Physica PolonicaB.Jagellonian Univ.,Krak´o w.ISSN0587-4254.Acta Phys.Sinica Acta Physica Sinica.Wuli Xuebao.Chinese Phys.Soc.,Beijing.ISSN1000-3290.Acta put.Manage.Eng.Ser.Acta Polytechnica Scandinavica.Mathematics,Computingand Management in Engineering Series.Finn.Acad.Tech.,Espoo.ISSN1238-9803.§Acta Sci.Math.(Szeged)Acta Universitatis Szegediensis.Acta Scientiarum Mathematicarum.Univ.Szeged,Szeged.ISSN0001-6969.Acta Sci.Natur.Univ.Jilin.Acta Scientiarum NaturaliumUniversitatis Jilinensis.Jilin Daxue.Ziran Kexue Xuebao.Jilin University.Natural Sciences Journal.Jilin Univ.Nat.Sci.J.,Editor.Dept.,Changchun.ISSN0529-0279.Acta Sci.Natur.Univ.Norm.Hunan.Acta ScientiarumNaturalium Universitatis Normalis Hunanensis.HunanShifan Daxue Ziran Kexue Xuebao.J.Hunan Norm.Univ.,Editor.Dept.,Changsha.ISSN1000-2537.Acta Sci.Natur.Univ.Pekinensis See Beijing DaxueXuebao Ziran Kexue BanActa Sci.Natur.Univ.Sunyatseni Acta ScientiarumNaturalium Universitatis Sunyatseni.Zhongshan DaxueXuebao.Ziran Kexue Ban.Journal of Sun Yatsen University.Natural Sciences.J.Zhongshan Univ.,Editor.Dept.,Guangzhou.ISSN0529-6579.Acta Tech.CSA V Acta Technica CSA V.Acad.Sci.CzechRepub.,Prague.ISSN0001-7043.§Acta Univ.Carolin.Math.Phys.Acta Universitatis Carolinae.Mathematica et Physica.Karolinum,Prague.ISSN0001-7140.§Acta Univ.Lodz.Folia Math.Acta UniversitatisLodziensis.Folia Mathematica.Wydawn.Uniw.Ł´o dzkiego,Ł´o d´z.ISSN0208-6204.Acta Univ.Lodz.Folia Philos.Acta UniversitatisLodziensis.Folia Philosophica.Wydawn.Uniw.Ł´o dzkiego,Ł´o d´z.ISSN0208-6107.∗§Acta Univ.M.Belii Ser.Math.Acta Universitatis Matthiae Belii.Natural Science Series.Series Mathematics.MatejBel Univ.,Bansk´a Bystrica.(Formerly Acta Univ.MathaeiBelii Nat.Sci.Ser.Ser.Math.)§Acta Univ.Mathaei Belii Nat.Sci.Ser.Ser.Math.Matej Bel University.Acta.Natural Science Series.Series Mathematics.Matej Bel Univ.,Bansk´a Bystrica.(Continued as Acta Univ.M.Belii Ser.Math.)Acta Univ.Oulu.Ser.A Sci.Rerum Natur.ActaUniversitatis Ouluensis.Series A.Scientiae RerumNaturalium.Univ.Oulu,Oulu.ISSN0355-3191.§Acta Univ.Palack.Olomuc.Fac.Rerum Natur.Math.Acta Universitatis Palackianae Olomucensis.Facultas Rerum Naturalium.Mathematica.ISSN0231-9721.†Acta Univ.Ups.Stud.Philos.Ups.Acta Universitatis Upsaliensis.Studia Philosophica Upsaliensia.Uppsala Univ., Uppsala.ISSN0585-5497.†Acta Univ.Upsaliensis Skr.Uppsala Univ.C Organ.Hist.Acta Universitatis Upsaliensis.Skrifter r¨o randeUppsala anisation och Historia.[ActaUniversitatis Upsaliensis.Publications concerning Uppsalaanization and History]Uppsala Univ.,Uppsala.ISSN0502-7454.†Actualit´e s Math.Actualit´e s Math´e matiques.[Current Mathematical Topics]Hermann,Paris.†Actualit´e s Sci.Indust.Actualit´e s Scientiﬁques etIndustrielles.[Current Scientiﬁc and Industrial Topics]Hermann,Paris.†Adapt.Learn.Syst.Signal mun.Control Adaptive and Learning Systems for Signal Processing,Communications,and Control.Wiley,New York.Adv.Appl.Clifford Algebras Advances in Applied Clifford Algebras.Univ.Nac.Aut´o noma M´e xico,M´e xico.ISSN0188-7009.†Adv.Appl.Mech.Advances in Applied Mechanics.Academic Press,Boston,MA.ISSN0065-2165.∗†Adv.Astron.Astrophys.Advances in Astronomy andAstrophysics.Gordon and Breach,Amsterdam.ISSN1025-8206.†Adv.Book Class.Advanced Book Classics.Perseus, Reading,MA.†Adv.Bound.Elem.Ser.Advances in Boundary Elements put.Mech.,Southampton.(Continued as Int.Ser.Adv.Bound.Elem.)ISSN1368-258X.†Adv.Chem.Phys.Advances in Chemical Physics.Wiley, New York.†put.Econom.Advances in Computational Economics.Kluwer Acad.Publ.,Dordrecht.§E put.Math.Advances in ComputationalMathematics.Baltzer,Bussum.ISSN1019-7168.†put.Sci.Advances in Computing Science.Springer,Vienna.ISSN1433-0113.∗†Adv.Des.Control Advances in Design and Control.SIAM, Philadelphia,PA.§Adv.Differential Equations Advances in Differential Equations.Khayyam,Athens,OH.ISSN1079-9389.†Adv.Discrete Math.Appl.Advances in DiscreteMathematics and Applications.Gordon and Breach,Amsterdam.ISSN1028-3129.†Adv.Fluid Mech.Advances in Fluid put.Mech.,Southampton.ISSN1353-808X.†Adv.Fuzzy Systems Appl.Theory Advances in Fuzzy Systems—Applications and Theory.World Sci.Publishing,River Edge,NJ.§E Adv.in Appl.Math.Advances in Applied Mathematics.Academic Press,Orlando,FL.ISSN0196-8858.§Adv.in Appl.Probab.Advances in Applied Probability.Appl.Probab.Trust,Shefﬁeld.ISSN0001-8678.∗†Adv.Ind.Control Advances in Industrial Control.Springer, London.†Adv.Lectures Math.Advanced Lectures in Mathematics.Vieweg,Braunschweig.ISSN0932-7134.§E Adv.Math.Advances in Mathematics.Academic Press, Orlando,FL.ISSN0001-8708.§Adv.Math.(China)Advances in Mathematics(China).Shuxue Jinzhan.Peking Univ.Press,Beijing.ISSN1000-0917.†Adv.Math.Econ.Advances in Mathematical Economics.Springer,Tokyo.†Adv.Math.Sci.Advances in the Mathematical Sciences.Amer.Math.Soc.,Providence,RI.§Adv.Math.Sci.Appl.Advances in Mathematical Sciences and Applications.An International Journal.Gakk¯o tosho,Tokyo.ISSN1343-4373.§Adv.Nonlinear Var.Inequal.Advances in Nonlinear Variational Inequalities.An International Journal.Internat.Publ.,Orlando,FL.ISSN1092-910X.†Adv.Numer.Math.Advances in Numerical Mathematics.Teubner,Stuttgart.†Adv.Partial Differ.Equ.Advances in Partial Differential Equations.Wiley-VCH,Berlin.†Adv.Partial Differential Equations Advances in Partial Differential Equations.Akademie Verlag,Berlin.†Adv.Ser.Dynam.Systems Advanced Series in Dynamical Systems.World Sci.Publishing,River Edge,NJ.†Adv.Ser.Math.Phys.Advanced Series in Mathematical Physics.World Sci.Publishing,River Edge,NJ.†Adv.Ser.Math.Sci.Eng.Advanced Series in Mathematical Science and Engineering.World Fed.Publ.,Atlanta,GA.†Adv.Ser.Neurosci.Advanced Series in Neuroscience.World Sci.Publishing,River Edge,NJ.†Adv.Ser.Nonlinear Dynam.Advanced Series in Nonlinear Dynamics.World Sci.Publishing,River Edge,NJ.†Adv.Ser.Stat.Sci.Appl.Probab.Advanced Series on Statistical Science&Applied Probability.World Sci.Publishing,River Edge,NJ.†Adv.Ser.Theoret.Phys.Sci.Advanced Series onTheoretical Physical Science.World Sci.Publishing,RiverEdge,NJ.∗†Adv.Soft Comput.Advances in Soft Computing.Physica, Heidelberg.†Adv.Spat.Sci.Advances in Spatial Science.Springer, Berlin.†Adv.Stud.Contemp.Math.Advanced Studies inContemporary Mathematics.Gordon and Breach,New York.∗§Adv.Stud.Contemp.Math.(Pusan)Advanced Studies in Contemporary Mathematics(Pusan).Adv.Stud.Contemp.Math.,m.,Saga.ISSN1229-3067.†Adv.Stud.Pure Math.Advanced Studies in PureMathematics.Kinokuniya,Tokyo.†Adv.Textb.Control Signal Process.Advanced Textbooks in Control and Signal Processing.Springer,London.∗†Adv.Texts Phys.Advanced Texts in Physics.Springer,Berlin.ISSN1439-2674.§E Adv.Theor.Math.Phys.Advances in Theoretical and Mathematical Physics.Internat.Press,Cambridge,MA.ISSN1095-0761.†Adv.Theory put.Math.Advances in the Theory of Computation and Computational Mathematics.Nova Sci.Publ.,Commack,NY.†Adv.Top.Math.Advanced Topics in Mathematics.PWN, Warsaw.§E Aequationes Math.Aequationes Mathematicae.Birkh¨a user,Basel.ISSN0001-9054.§Afrika Mat.(3)Afrika Matematika.Journal of the African Mathematical Union.Journal de l’Union Math´e matiqueAfricaine.S´e rie3.Union Math.Africaine,Caluire.†Agr´e g.Math.Agr´e gation de Math´e matiques.Masson,Paris.AI Commun.AI Communications.The European Journal onArtiﬁcial Intelligence.IOS,Amsterdam.ISSN0921-7126.†AIAA Ed.Ser.AIAA Education Series.AIAA,Washington, DC.†AIP Conf.Proc.AIP Conference Proceedings.Amer.Inst.Phys.,New York.ISSN0094-243X.†AIP Ser.Modern Acoust.Signal Process.AIP Series in Modern Acoustics and Signal Processing.Amer.Inst.Phys.,New York.†AKP Class.AKP Classics.A K Peters,Wellesley,MA.∗†Al-Furq¯a n Islam.Herit.Found.Publ.Al-Furq¯a n Islamic Heritage Foundation Publication.Al-Furq¯a n Islam.Herit.Found.,London.†Albion Math.Appl.Ser.Albion Mathematics&Applications Series.Albion,Chichester.§E Algebr.Represent.Theory Algebras and Representation Theory.Kluwer Acad.Publ.,Dordrecht.ISSN1386-923X.Algebra and Logic Algebra and Logic.Consultants Bureau,New York.(Translation of Algebra Log.and Algebra iLogika)ISSN0002-5232.†Algebra Ber.Algebra Berichte.[Algebra Reports]Fischer, Munich.ISSN0942-1270.§E Algebra Colloq.Algebra Colloquium.Springer,Singapore.ISSN1005-3867.§Algebra i Analiz Rossi˘ıskaya Akademiya Nauk.Algebrai Analiz.“Nauka”S.-Peterburg.Otdel.,St.Petersburg.(Translated in St.Petersburg Math.J.)ISSN0234-0852.§Algebra i Logika Sibirski˘ıFond Algebry i Logiki.Algebrai Logika.Izdat.NII Mat.-Inform.Osnov Obuch.NGU,Novosibirsk.(Continued as Algebra Log.)(Translatedin Algebra and Logic)ISSN0373-9252.∗§Algebra Log.Algebra i Logika.Institut Diskretno˘ıMatematiki i Informatiki.Sib.Fond Algebry Log.,Novosibirsk.(Formerly Algebra i Logika)(Translatedin Algebra and Logic)ISSN0373-9252.†Algebra Logic Appl.Algebra,Logic and Applications.Gordon and Breach,Amsterdam.ISSN1041-5394.§E Algebra Universalis Algebra Universalis.Univ.Manitoba, Winnipeg,MB.ISSN0002-5240.§Algebras Groups Geom.Algebras,Groups and Geometries.Hadronic Press,Palm Harbor,FL.ISSN0741-9937.§E Algorithmica Algorithmica.An International Journal in Computer Science.Springer,New York.ISSN0178-4617.†Algorithms Combin.Algorithms and Combinatorics.Springer,Berlin.ISSN0937-5511.†Algorithms Comput.Math.Algorithms and Computation in Mathematics.Springer,Berlin.ISSN1431-1550.§Aligarh Bull.Math.The Aligarh Bulletin of Mathematics.Aligarh Muslim Univ.,Aligarh.Aligarh J.Statist.The Aligarh Journal of Statistics.AligarhMuslim Univ.,Aligarh.ISSN0971-0388.§pok Alkalmazott Matematikai Lapok.Magyar Tudom´a nyos Akad.,Budapest.ISSN0133-3399.∗Allg.Stat.Arch.Allgemeines Statistisches Archiv.AStA.Journal of the German Statistical Society.Physica,Heidelberg.ISSN0002-6018.†´Alxebra´Alxebra.[Algebra]Univ.Santiago deCompostela,Santiago de Compostela.†Am.Univ.Stud.Ser.IX Hist.American University Studies.Series IX:ng,New York.ISSN0740-0462.∗§E AMA Algebra Montp.Announc.AMA.AlgebraMontpellier Announcements.AMA Algebra Montp.Announc.,Montpellier.§E Amer.J.Math.American Journal of Mathematics.Johns Hopkins Univ.Press,Baltimore,MD.ISSN0002-9327.Amer.J.Math.Management Sci.American Journal ofMathematical and Management Sciences.Amer.Sci.Press,Syracuse,NY.ISSN0196-6324.E Amer.J.Phys.American Journal of Physics.Amer.Assoc.Phys.Teach.,College Park,MD.ISSN0002-9505.Amer.Math.Monthly The American MathematicalMonthly.Math.Assoc.America,Washington,DC.ISSN0002-9890.†Amer.Math.Soc.Colloq.Publ.American Mathematical Society Colloquium Publications.Amer.Math.Soc.,Providence,RI.ISSN0065-9258.†Amer.Math.Soc.Transl.Ser.2American Mathematical Society Translations,Series2.Amer.Math.Soc.,Providence,RI.(Selected translations of Russian language publications Tr.St.-Peterbg.Mat.Obshch.)ISSN0065-9290.E Amer.Statist.The American Statistician.Amer.Statist.Assoc.,Alexandria,V A.ISSN0003-1305.†Amer.Univ.Stud.Ser.V Philos.American University Studies.Series V:ng,New York.ISSN0739-6392.†AMS Progr.Math.Lecture Ser.AMS Progress in Mathematics Lecture Series.Amer.Math.Soc.,Providence,RI.†AMS Short Course Lecture Notes AMS Short Course Lecture Notes.Amer.Math.Soc.,Providence,RI.†AMS-MAA Joint Lecture Ser.AMS-MAA Joint Lecture Series.Amer.Math.Soc.,Providence,RI.†AMS/IP Stud.Adv.Math.AMS/IP Studies in Advanced Mathematics.Amer.Math.Soc.,Providence,RI.ISSN1089-3288.E An.Acad.Brasil.Ciˆe nc.Anais da Academia Brasileira deCiˆe ncias.Acad.Brasil.Ciˆe nc.,Rio de Janeiro.ISSN0001-3765.†An.F´ıs.Monogr.Anales de F´ısica.Monograf´ıas.[Annals of Physics.Monographs]CIEMAT,Madrid.§An.S¸tiint¸.Univ.Al.I.Cuza Ias¸i Inform.(N.S.)Analele S¸tiint¸iﬁce ale Universit˘a t¸ii“Al.I.Cuza”din Ias¸i.Informatic˘a.Serie Nou˘a.Ed.Univ.“Al.I.Cuza”,Ias¸i.ISSN1224-2268.§An.S¸tiint¸.Univ.Al.I.Cuza Ias¸i.Mat.(N.S.)Analele S¸tiint¸iﬁce ale Universit˘a tii“Al.I.Cuza”din Ias¸i.SerieNou˘a.Matematic˘a.Univ.Al.I.Cuza,Ias¸i.ISSN1221-8421.§An.S¸tiint¸.Univ.Ovidius Constant¸a Ser.Mat.Universit˘a t¸ii “Ovidius”Constant¸a.Analele S¸tiint¸iﬁce.Seria Matematic˘a.“Ovidius”Univ.Press,Constant¸a.ISSN1223-723X.§An.Univ.Bucures¸ti Mat.Analele Universit˘a t¸ii Bucures¸ti.Matematic˘a.Univ.Bucharest,Bucharest.ISSN1013-4123.An.Univ.Craiova rm.Analele Universitˇa t¸iidin Craiova.Seria Matematic˘a-Informatic˘a.Univ.Craiova,Craiova.ISSN1223-6934.∗§An.Univ.Oradea Fasc.Mat.Analele Universit˘a t¸ii din Oradea.Fascicola Matematica.Univ.Oradea,Oradea.ISSN1221-1265.§An.Univ.Timis¸oara Ser.Mat.-Inform.Universit˘a t¸ii din Timis¸oara.Analele.Seria Matematic˘a-Informatic˘a.Univ.Timis¸oara,Timis¸oara.ISSN1224-970X.An.Univ.Timis¸oara Ser.S¸tiint¸.Fiz.Analele Universit˘a t¸iidin Timis¸oara.Seria S¸tiint¸e Fizice.Univ.Vest Timis¸oara,Timis¸oara.†Anal.Appl.Analysis and its Applications.IOS,Amsterdam.ISSN1345-4240.§E Anal.Math.Analysis Mathematica.Akad.Kiad´o,Budapest.ISSN0133-3852.†Anal.Methods Spec.Funct.Analytical Methods and Special Functions.Gordon and Breach,Amsterdam.ISSN1027-0264.†Anal.Modern.Apl.Analiz˘a Modern˘a s¸i Aplicat¸ii.[Modern Analysis and Applications]Ed.Acad.Romˆa ne,Bucharest.§Analysis(Munich)Analysis.International Mathematical Journal of Analysis and its Applications.Oldenbourg,Munich.ISSN0174-4747.E Analysis(Oxford)Analysis.Blackwell,Oxford.ISSN0003-2638.†Angew.Statist.¨Okonom.Angewandte Statistik und¨Okonometrie.[Applied Statistics and Econometrics]Vandenhoeck&Ruprecht,G¨o ttingen.§E Ann.Acad.Sci.Fenn.Math.Annales AcademiæScientiarium Fennicæ.Mathematica.Acad.Sci.Fennica,Helsinki.ISSN1239-629X.§Ann.Acad.Sci.Fenn.Math.Diss.AcademiæScientiarum Fennicæ.Annales.Mathematica.Dissertationes.Acad.Sci.Fennica,Helsinki.ISSN1239-6303.§E Ann.Appl.Probab.The Annals of Applied Probability.Inst.Math.Statist.,Hayward,CA.ISSN1050-5164.§E b.Annals of Combinatorics.Springer,Singapore.(Continued as b.)ISSN0218-0006.∗§E b.Annals of Combinatorics.Birkh¨a user,Basel.(Formerly b.)ISSN0218-0006.§Ann.Differential Equations Annals of DifferentialEquations.Weifen Fangcheng Niankan.Fuzhou Univ.,Fuzhou.ISSN1002-0942.†Ann.Discrete Math.Annals of Discrete Mathematics.North-Holland,Amsterdam.Ann.´Econom.Statist.Annales d’´Economie et deStatistique.Inst.Nat.Statist.´Etud.´Econom.,Amiens.ISSN0769-489X.§Ann.Fac.Sci.Toulouse Math.(6)Annales de la Facult´e des Sciences de Toulouse.Math´e matiques.S´e rie6.Univ.Paul Sabatier,Toulouse.ISSN0240-2963.†Ann.Fac.Sci.Univ.Kinshasa Annales de la Facult´e des Sciences.Universit´e de Kinshasa.[Annals of the Facultyof Science.University of Kinshasa]Presses Univ.Kinshasa,Kinshasa.Ann.Fond.Louis de Broglie Fondation Louis de Broglie.Annales.Fond.Louis de Broglie,Paris.ISSN0182-4295.§E Ann.Global Anal.Geom.Annals of Global Analysis and Geometry.Kluwer Acad.Publ.,Dordrecht.ISSN0232-704X.∗E Ann.Henri Poincar´e Annales Henri Poincar´e.A Journal of Theoretical and Mathematical Physics.Birkh¨a user,Basel.(Merged from Ann.Inst.H.Poincar´e Phys.Th´e or.and Helv.Phys.Acta)ISSN1424-0637.∗Ann.I.S.U.P.Annales de l’I.S.U.P..Univ.Paris,Inst.Stat., Paris.§E Ann.Inst.Fourier(Grenoble)Universit´e de Grenoble.Annales de l’Institut Fourier.Univ.Grenoble I,Saint-Martin-d’H`e res.ISSN0373-0956.§E Ann.Inst.H.Poincar´e Anal.Non Lin´e aire Annales de l’Institut Henri Poincar´e.Analyse Non Lin´e aire.Gauthier-Villars,´Ed.Sci.M´e d.Elsevier,Paris.ISSN0294-1449.Ann.Inst.H.Poincar´e Phys.Th´e or.Annales de l’InstitutHenri Poincar´e.Physique Th´e orique.Gauthier-Villars,´Ed.Sci.M´e d.Elsevier,Paris.(Merged into Ann.HenriPoincar´e)ISSN0246-0211.§E Ann.Inst.H.Poincar´e Probab.Statist.Annales de l’Institut Henri Poincar´e.Probabilit´e s et Statistiques.Gauthier-Villars,´Ed.Sci.M´e d.Elsevier,Paris.ISSN0246-0203.E Ann.Inst.Statist.Math.Annals of the Institute ofStatistical Mathematics.Kluwer Acad.Publ.,Norwell,MA.ISSN0020-3157.†Ann.Internat.Soc.Dynam.Games Annals of the International Society of Dynamic Games.Birkh¨a userBoston,Boston,MA.†Ann.Israel Phys.Soc.Annals of the Israel Physical Society.IOP,Bristol.ISSN0309-8710.Ann.Japan Assoc.Philos.Sci.Annals of the JapanAssociation for Philosophy of Science.Japan Assoc.Philos.Sci.,Tokyo.ISSN0453-0691.§Ann.Mat.Pura Appl.(4)Annali di Matematica Pura ed Applicata.Serie Quarta.Zanichelli,Bologna.ISSN0003-4622.E Ann.Math.Artiﬁcial Intelligence Annals of Mathematicsand Artiﬁcial Intelligence.Baltzer,Bussum.ISSN1012-2443.§Ann.Math.Blaise Pascal Annales Math´e matiques Blaise Pascal.Univ.Blaise Pascal,Lab.Math.Pures Appl.,Aubi`e re.ISSN1259-1734.§Ann.Math.Sil.Annales Mathematicae Silesianae.Wydawn.Uniw.´Sl‘askiego,Katowice.(See also Pr.Nauk.Uniw.´Sl.Katow.)ISSN0860-2107.†Ann.New York Acad.Sci.Annals of the New York Academy of Sciences.New York Acad.Sci.,New York.ISSN0077-8923.§E Ann.of Math.(2)Annals of Mathematics.Second Series.Princeton Univ.Press,Princeton,NJ.ISSN0003-486X.†Ann.of Math.Stud.Annals of Mathematics Studies.Princeton Univ.Press,Princeton,NJ.E Ann.of Sci.Annals of Science.Taylor&Francis,London.ISSN0003-3790.E Ann.Oper.Res.Annals of Operations Research.Baltzer,Bussum.ISSN0254-5330.E Ann.Phys.(8)Annalen der Physik(8).Wiley-VCH,Berlin.ISSN0003-3804.E Ann.Physics Annals of Physics.Academic Press,Orlando,FL.ISSN0003-4916.§Ann.Polon.Math.Annales Polonici Mathematici.Polish Acad.Sci.,Warsaw.ISSN0066-2216.§Ann.Probab.The Annals of Probability.Inst.Math.Statist., Bethesda,MD.ISSN0091-1798.§E Ann.Pure Appl.Logic Annals of Pure and Applied Logic.North-Holland,Amsterdam.ISSN0168-0072.§E Ann.Sci.´Ecole Norm.Sup.(4)Annales Scientiﬁques de l’´Ecole Normale Sup´e rieure.Quatri`e me S´e rie.Gauthier-Villars,´Ed.Sci.M´e d.Elsevier,Paris.ISSN0012-9593.§Ann.Sci.Math.Qu´e bec Annales des SciencesMath´e matiques du Qu´e bec.Groupe Cherch.Sci.Math.,Montreal,QC.ISSN0707-9109.§Ann.Scuola Norm.Sup.Pisa Cl.Sci.(4)Annali della Scuola Normale Superiore di Pisa.Classe di Scienze.SerieIV.Scuola Norm.Sup.,Pisa.§Ann.Statist.The Annals of Statistics.Inst.Math.Statist., Hayward,CA.ISSN0090-5364.§Ann.Univ.Ferrara Sez.VII(N.S.)Annali dell’Universit`a di Ferrara.Nuova Serie.Sezione VII.Scienze Matematiche.Univ.Ferrara,Ferrara.§Ann.Univ.Mariae Curie-Skłodowska Sect.A Annales Universitatis Mariae Curie-Skłodowska.Sectio A.Mathematica.Uniw.Marii Curie-Skłodowskiej,Lublin.ISSN0365-1029.Ann.Univ.Sarav.Ser.Math.Annales UniversitatisSaraviensis.Series Mathematicae.Univ.Saarlandes,Saarbr¨u cken.ISSN0933-8268.§Ann.Univ.Sci.Budapest.E¨o tv¨o s Sect.Math.Annales Universitatis Scientiarum Budapestinensis de RolandoE¨o tv¨o s Nominatae.Sectio Mathematica.E¨o tv¨o s Lor´a ndUniv.,Budapest.ISSN0524-9007.§put.AnnalesUniversitatis Scientiarum Budapestinensis de RolandoE¨o tv¨o s Nominatae.Sectio Computatorica.E¨o tv¨o s Lor´a ndUniv.,Budapest.ISSN0138-9491.†Annu.Rev.Fluid Mech.Annual Review of FluidMechanics.Annual Reviews,Palo Alto,CA.ISSN0066-4189.Annuaire Univ.Soﬁa rm.Godishnik naSoﬁ˘ıskiya Universitet“Sv.Kliment Okhridski”.Fakultetpo Matematika i Informatika.Annuaire de l’Universit´e deSoﬁa“St.Kliment Ohridski”.Facult´e de Math´e matiques etInformatique.Presses Univ.“St.Kliment Ohridski”,Soﬁa.ISSN0205-0808.Annuaire Univ.Soﬁa Fac.Phys.Godishnik na Soﬁ˘ıskiyaUniversitet“Sv.Kliment Okhridski”.Fizicheski Fakultet.Annuaire de l’Universit´e de Soﬁa“St.Kliment Ohridski”.Facult´e de Physique.Presses Univ.“St.Kliment Ohridski”,Soﬁa.ISSN0584-0279.†Anu.Filol.Univ.Barc.Anuari de Filologia(Universitat de Barcelona).[Philology Yearbook(University ofBarcelona)]Univ.Barcelona,Barcelona.†Anwend.orientier.Stat.Anwendungsorientierte Statistik.[Applications-Oriented Statistics]Lang,Frankfurt am Main.ISSN1431-7982.Anz.¨Osterreich.Akad.Wiss.Math.-Natur.Kl.¨Osterreichische Akademie der Wissenschaften.Mathematisch-Naturwissenschaftliche Klasse.Anzeiger.¨Osterreich.Akad.Wissensch.,Vienna.∗§E ANZIAM J.The ANZIAM Journal.The Australian& New Zealand Industrial and Applied Mathematics Journal.Austral.Math.Soc.,Canberra.(Formerly J.Austral.Math.Soc.Ser.B)ISSN0334-2700.†Aportaciones Mat.Aportaciones Matem´a ticas.[Mathematical Contributions]Soc.Mat.Mexicana,M´e xico.†Aportaciones un.Aportaciones Matem´a ticas: Comunicaciones.[Mathematical Contributions:Communications]Soc.Mat.Mexicana,M´e xico.∗†Aportaciones Mat.Invest.Aportaciones Matem´a ticas: Investigaci´o n.[Mathematical Contributions:Research]Soc.Mat.Mexicana,M´e xico.(Formerly Aportaciones Mat.Notas Investigaci´o n)†Aportaciones Mat.Notas Investigaci´o n Aportaciones Matem´a ticas:Notas de Investigaci´o n.[MathematicalContributions:Research Notes]Soc.Mat.Mexicana,M´e xico.(Continued as Aportaciones Mat.Invest.)†Aportaciones Mat.Textos Aportaciones Matem´a ticas: Textos.[Mathematical Contributions:Texts]Soc.Mat.Mexicana,M´e xico.§E Appl.Algebra put.Applicable Algebra in Engineering,Communication and Computing.Springer,Heidelberg.ISSN0938-1279.§E Appl.Anal.Applicable Analysis.An International Journal.Gordon and Breach,Yverdon.ISSN0003-6811.§E Appl.Categ.Structures Applied Categorical Structures.A Journal Devoted to Applications of Categorical Methods inAlgebra,Analysis,Order,Topology and Computer Science.Kluwer Acad.Publ.,Dordrecht.ISSN0927-2852.†put.Control Signals Circuits Applied and Computational Control,Signals,and Circuits.Birkh¨a userBoston,Boston,MA.ISSN1522-8363.§E put.Harmon.Anal.Applied and Computational Harmonic Analysis.Time-Frequency and Time-Scale Analysis,Wavelets,Numerical Algorithms,andApplications.Academic Press,Orlando,FL.ISSN1063-5203.†Appl.Log.Ser.Applied Logic Series.Kluwer Acad.Publ., Dordrecht.†Appl.Math.Applications of Mathematics.Springer,New York.ISSN0172-4568.§Appl.Math.Applications of Mathematics.Acad.Sci.Czech Repub.,Prague.ISSN0862-7940.∗†Appl.Math.Applied Mathematics.Chapman&Hall/CRC, Boca Raton,FL.(Formerly put.)§E put.Applied Mathematics andComputation.North-Holland,New York.ISSN0096-3003.†Appl.Math.Engrg.Sci.Texts Applied Mathematics and Engineering Science Texts.CRC,Boca Raton,FL.∗rm.Applied Mathematics and Informatics.Tbilisi Univ.Press,Tbilisi.ISSN1512-0074.∗§Appl.Math.J.Chinese Univ.Ser.A Applied Mathematics.A Journal of Chinese Universities.Series A.Appl.Math.J.Chinese Univ.,m.,Hangzhou.(FormerlyGaoxiao Yingyong Shuxue Xuebao Ser.A)(See also Appl.Math.J.Chinese Univ.Ser.B)ISSN1000-4424.§Appl.Math.J.Chinese Univ.Ser.B Applied Mathematics.A Journal of Chinese Universities.Ser.B.Appl.Math.J.Chinese Univ.,m.,Hangzhou.(See also Appl.Math.J.Chinese Univ.Ser.A and Gaoxiao Yingyong Shuxue。

ts5a23157[1]

FEATURESV +NC1COM1NC2COM2APPLICATIONSNC1V+NC2COM2IN1NO1GND NO2RSE PACKAGE (TOP VIEW)COM1IN212345678910DESCRIPTION/ORDERING INFORMATIONTS5A23157 SCDS165D–MAY 2004–REVISED MAY 2008DUAL 10-ΩSPDT ANALOG SWITCH•Specified Break-Before-Make Switching DGS PACKAGE •Low ON-State Resistance (10Ω)(TOP VIEW)•Control Inputs Are 5-V Tolerant •Low Charge Injection•Excellent ON-Resistance Matching •Low Total Harmonic Distortion• 1.8-V to 5.5-V Single-Supply Operation•Latch-Up Performance Exceeds 100mA Per JESD 78,Class II•ESD Performance Tested Per JESD 22–2000-V Human-Body Model (A114-B,Class II)–1000-V Charged-Device Model (C101)•Sample-and-Hold Circuits •Battery-Powered Equipment •Audio and Video Signal Routing •Communication CircuitsThe TS5A23157is a dual single-pole double-throw (SPDT)analog switch designed to operate from 1.65V to 5.5V.This device can handle both digital and analog signals.Signals up to 5.5V (peak)can be transmitted in either direction.ORDERING INFORMATIONT APACKAGE (1)(2)ORDERABLE PART NUMBER TOP-SIDE MARKING (3)VSSOP (MSOP-10)–DGSTape and reel TS5A23157DGSR JBR –40°C to 85°C QFN –RSETape and reelTS5A23157RSERJB_(1)Package drawings,thermal data,and symbolization are available at /packaging .(2)For the most current package and ordering information,see the at the end of this document,or see the TI website at .(3)RSE:The marking has one additional character that designates the assembly/test site.FUNCTION TABLEINPUT NC TO COM,NO TO COM,IN COM TO NC COM TO NO L ON OFF HOFFONPlease be aware that an important notice concerning availability,standard warranty,and use in critical applications ofTexas Instruments semiconductor products and disclaimers thereto appears at the end of this data sheet.PRODUCTION DATA information is current as of publication date.Copyright ©2004–2008,Texas Instruments IncorporatedProducts conform to specifications per the terms of the Texas Instruments standard warranty.Production processing does not necessarily include testing of all parameters.ABSOLUTE MAXIMUM RATINGS (1)TS5A23157SCDS165D–MAY 2004–REVISED MAY SUMMARY OF CHARACTERISTICS2:1Multiplexer/Demultiplexer Configuration (2×SPDT)Number of channels 2ON-state resistance (r on )10ΩON-state resistance match 0.15Ωbetween channels (Δr on )ON-state resistance flatness 4Ω(r on(flat))Turn-on/turn-off time (t ON /t OFF ) 5.7ns/3.8ns Break-before-make time (t BBM )0.5ns Charge injection (Q C )7pC Bandwidth (BW)220MHzOFF isolation (OSIO)–65dB at 10MHz Crosstalk 9XTALK)–66dB at 10MHz Total harmo nic distortion (THD)0.01%Leakage current ±1µA(I COM(OFF)/I NC(OFF))Package options10-pin DGS and RSEover operating free-air temperature range (unless otherwise noted)MINMAX UNIT V +Supply voltage range(2)–0.5 6.5V V NC V NO Analog voltage range (2)(3)(4)–0.5V ++0.5V V COM V NC ,V NO ,V COM <0or V NC ,V NO ,I I/OK Analog port diode current ±50mA V COM >V +I NC I NO On-state switch current V NC ,V NO ,V COM =0to V +±50mA I COM V IN Digital input voltage range (2)(3)–0.56.5V I IKDigital input clamp currentV IN <0–50mA Continuous current through V +or GND±100mA DGS package 56.5θJA Package thermal impedance (5)°C/W RSE package243T stg Storage temperature range–65150°C(1)Stresses beyond those listed under "absolute maximum ratings"may cause permanent damage to the device.These are stress ratings only,and functional operation of the device at these or any other conditions beyond those indicated under "recommended operating conditions"is not implied.Exposure to absolute-maximum-rated conditions for extended periods may affect device reliability.(2)All voltages are with respect to ground,unless otherwise specified.(3)The input and output voltage ratings may be exceeded if the input and output clamp-current ratings are observed.(4)This value is limited to 5.5V maximum.(5)The package thermal impedance is calculated in accordance with JESD 51-7.2Submit Documentation FeedbackCopyright ©2004–2008,Texas Instruments IncorporatedProduct Folder Link(s):TS5A23157ELECTRICAL CHARACTERISTICS FOR 5-V SUPPLYTS5A23157 SCDS165D–MAY 2004–REVISEDMAY 2008V +=4.5V to 5.5V,T A =–40°C to 85°C (unless otherwise noted)(1)T A =25°C(2)All unused digital inputs of the device must be held at V+or GND to ensure proper device operation.Refer to the TI application report,Implications of Slow or Floating CMOS Inputs ,literature number SCBA004.Copyright ©2004–2008,Texas Instruments Incorporated Submit Documentation Feedback3Product Folder Link(s):TS5A23157TS5A23157SCDS165D–MAY2004–REVISED ELECTRICAL CHARACTERISTICS FOR5-V SUPPLY(continued)V+=4.5V to5.5V,T A=–40°C to85°C(unless otherwise noted)4Submit Documentation Feedback Copyright©2004–2008,Texas Instruments IncorporatedProduct Folder Link(s):TS5A23157ELECTRICAL CHARACTERISTICS FOR3.3-V SUPPLY TS5A23157 SCDS165D–MAY2004–REVISED MAY2008 V+=3V to3.6V,T A=–40°C to85°C(unless otherwise noted)(1)T A=25°C(2)All unused digital inputs of the device must be held at V+or GND to ensure proper device operation.Refer to the TI application report,Implications of Slow or Floating CMOS Inputs,literature number SCBA004.Copyright©2004–2008,Texas Instruments Incorporated Submit Documentation Feedback5Product Folder Link(s):TS5A23157ELECTRICAL CHARACTERISTICS FOR 2.5-V SUPPLYTS5A23157SCDS165D–MAY 2004–REVISED MAY V +=2.3Vto 2.7V,T A =–40°C to 85°C (unless otherwise noted)(1)T A =25°C(2)All unused digital inputs of the device must be held at V+or GND to ensure proper device operation.Refer to the TI application report,Implications of Slow or Floating CMOS Inputs ,literature number SCBA004.6Submit Documentation FeedbackCopyright ©2004–2008,Texas Instruments IncorporatedProduct Folder Link(s):TS5A23157ELECTRICAL CHARACTERISTICS FOR1.8-V SUPPLY TS5A23157 SCDS165D–MAY2004–REVISED MAY2008 V+=1.65V to1.95V,T A=–40°C to85°C(unless otherwise noted)(1)T A=25°C(2)All unused digital inputs of the device must be held at V+or GND to ensure proper device operation.Refer to the TI application report,Implications of Slow or Floating CMOS Inputs,literature number SCBA004.Copyright©2004–2008,Texas Instruments Incorporated Submit Documentation Feedback7Product Folder Link(s):TS5A23157TYPICAL CHARACTERISTICSV COM − Vr o n −ΩV COM − Vr o n − ΩTemperature − 5CL e a k a g e − nAV COM − Vr o n − WV + − Supply Voltage − Vt O N /t O FF − n sT A − Temperature − 5Ct O N /t O F F − n sTS5A23157SCDS165D–MAY 2004–REVISED MAY Figure 1.r on vs V COMFigure 2.r on vs V COM (V +=3V)Figure 3.r on vs V COM (V +=5V)Figure 4.Leakage Current vs Temperature(V +=5.5V)Figure 5.t ON and t OFF vs V +Figure 6.t ON and t OFF vs Temperature(V +=5V)8Submit Documentation FeedbackCopyright ©2004–2008,Texas Instruments IncorporatedProduct Folder Link(s):TS5A23157Frequency −HzT H D + N o i s e − %0.00000.00020.00040.00060.00080.00100.00120.00140.00160.00180.0020Frequency − MHzL o s s − d B102030405060708090100−60−40−200204060801000T A − Temperature − 5CI C C + − n ATS5A23157 SCDS165D–MAY 2004–REVISED MAY 2008TYPICAL CHARACTERISTICS (continued)Figure 7.Frequency Response (V +=3V)Figure 8.Total Harmonic Distortion (THD)vs Frequency (V +=3V)Figure 9.Power-Supply Current vs Temperature(V +=5V)Copyright ©2004–2008,Texas Instruments Incorporated Submit Documentation Feedback9Product Folder Link(s):TS5A23157TS5A23157SCDS165D–MAY2004–REVISED PIN DESCRIPTIONPIN DESCRIPTION1IN1Digital control to connect COM to NO or NC2NO1Normally open3GND Digital ground4NO2Normally open5IN2Digital control to connect COM to NO or NC6COM2Common7NC2Normally closed8V+Power supply9NC1Normally closed10COM1CommonPARAMETER DESCRIPTIONSYMBOL DESCRIPTIONV COM Voltage at COMV NC Voltage at NCV NO Voltage at NOr on Resistance between COM and NC or COM and NO ports when the channel is ONΔr on Difference of r on between channelsr on(flat)Difference between the maximum and minimum value of r on in a channel over the specified range of conditions Leakage current measured at the NC port,with the corresponding channel(NC to COM)in the OFF state underI NC(OFF)worst-case input and output conditionsLeakage current measured at the NO port,with the corresponding channel(NO to COM)in the OFF state underI NO(OFF)worst-case input and output conditionsLeakage current measured at the NC port,with the corresponding channel(NC to COM)in the ON state and the outputI NC(ON)(COM)being openLeakage current measured at the NO port,with the corresponding channel(NO to COM)in the ON state and the outputI NO(ON)(COM)being openLeakage current measured at the COM port,with the corresponding channel(NO to COM or NC to COM)in the ON state I COM(ON)and the output(NC or NO)being openV IH Minimum input voltage for logic high for the control input(IN)V IL Minimum input voltage for logic low for the control input(IN)V IN Voltage at INI IH,I IL Leakage current measured at INTurn-on time for the switch.This parameter is measured under the specified range of conditions and by the propagationt ONdelay between the digital control(IN)signal and analog outputs(COM/NC/NO)signal when the switch is turning ON.Turn-off time for the switch.This parameter is measured under the specified range of conditions and by the propagationt OFFdelay between the digital control(IN)signal and analog outputs(COM/NC/NO)signal when the switch is turning OFF.Break-before-make time.This parameter is measured under the specified range of conditions and by the propagationt BBMdelay between the output of two adjacent analog channels(NC and NO)when the control signal changes state.Charge injection is a measurement of unwanted signal coupling from the control(IN)input to the analog(NC,NO,orQ C COM)output.This is measured in coulombs)and measured by the total charge induced due to switching of the control input.Charge injection,Q C=C L×ΔV O,C L is the load capacitance andΔV O is the change in analog output voltage.C NC(OFF)Capacitance at the NC port when the corresponding channel(NC to COM)is OFFC NO(OFF)Capacitance at the NO port when the corresponding channel(NC to COM)is OFFC NC(ON)Capacitance at the NC port when the corresponding channel(NC to COM)is ONC NO(ON)Capacitance at the NO port when the corresponding channel(NC to COM)is ONC COM(ON)Capacitance at the COM port when the corresponding channel(COM to NC or COM to NO)is ONC IN Capacitance of INOFF isolation of the switch is a measurement of OFF-state switch impedance.This is measured in dB in a specificO ISO frequency,with the corresponding channel(NC to COM or NO to COM)in the OFF state.OFF isolation,O ISO=20LOG (V NC/V COM)dB,V COM is the input and V NC is the output.10Submit Documentation Feedback Copyright©2004–2008,Texas Instruments IncorporatedProduct Folder Link(s):TS5A23157TS5A23157 SCDS165D–MAY2004–REVISED MAY2008PARAMETER DESCRIPTION(continued)SYMBOL DESCRIPTIONCrosstalk is a measurement of unwanted signal coupling from an ON channel to an OFF channel(NC to NO or NO toX TALK NC).This is measured at a specific frequency and in dB.Crosstalk,X TALK=20log(V NC1/V NO1),V NO1is the input and V NC1is the output.Bandwidth of the switch.This is the frequency where the gain of an ON channel is–3dB below the dc gain.Gain isBWmeasured from the equation,20log(V NC/V COM)dB,where V NC is the output and V COM is the input.I+Static power-supply current with the control(IN)pin at V+or GNDΔI+This is the increase in I+for each control(IN)input that is at the specified voltage,rather than at V+or GND.PARAMETER MEASUREMENT INFORMATIONVI COM r on +V COM *V NO ńNCI COM WChannel ONV INV IN = V IH or V ILV NO V NCV Channel OFFV NC V INV COM = 0 to V +OFF-State Leakage Currentor V IN = V IH or V ILV NC or V NO = 0 to V +Channel ONV NC or V NO = Open, V COM = 0 to V +ON-State Leakage Currentor V IN = V IH or V ILV NC or V NO = 0 to V +, V COM = OpenV NO VV IN = V IH or V IL V BIAS = V + or GND Capacitance is measured at NC,NO, COM, and IN inputs duringON and OFF conditions.TS5A23157SCDS165D–MAY 2004–REVISED MAY Figure 10.ON-State Resistance on )Figure 11.ON-and OFF-State Leakage Current (I COM(ON),I NC(OFF),I NO(OFF),I NC(ON),I NO(ON))Figure 12.Capacitance IN ,C COM(ON),C NC(OFF),C NO(OFF),C NC(ON),C NO(ON))VV V C LGND V +V NC 500 ΩR L C L 50 pF V +GND V NO t ON TEST GND V +500 Ω50 pF V +GNDt OFF V IN V COM LogicInput Logic Input SwitchOutput VC L V 050%V IN t r < 5 ns t f < 5 ns V I = V +/2R L = 50 ΩC L = 35 pFLogic Input Switch Output V Gain +20log V COM V NC dB Channel ON: NC to COM TS5A23157 SCDS165D–MAY 2004–REVISED MAY 2008PARAMETER MEASUREMENT INFORMATION (continued)Figure 13.Turn-On (t ON )and Turn-Off (t OFF )TimeFigure 14.Break-Before-Make (t BBM )TimeFigure 15.Frequency Response (BW)OFF Isolation +20log V COM V NCdB Channel OFF: NC to COM VCrosstalk +20log V NO V NCdB Channel ON: NC to COM V Channel OFF: NO to COM VC L OFF V IN V OUT ON OFF V GEN V INH V INL Logic InputTS5A23157SCDS165D–MAY 2004–REVISED MAY PARAMETER MEASUREMENT INFORMATION (continued)Figure 16.OFF Isolation (O ISO )Figure 17.Crosstalk (X TALK)Figure 18.Charge Injection (Q C )TS5A23157 SCDS165D–MAY2004–REVISED MAY2008 PARAMETER MEASUREMENT INFORMATION(continued)Figure19.Total Harmonic Distortion(THD)PACKAGING INFORMATIONOrderable Device Status(1)PackageType PackageDrawingPins PackageQtyEco Plan(2)Lead/Ball Finish MSL Peak Temp(3)TS5A23157DGSR ACTIVE MSOP DGS102500Green(RoHS&no Sb/Br)CU NIPDAU Level-1-260C-UNLIMTS5A23157DGSRE4ACTIVE MSOP DGS102500Green(RoHS&no Sb/Br)CU NIPDAU Level-1-260C-UNLIMTS5A23157DGSRG4ACTIVE MSOP DGS102500Green(RoHS&no Sb/Br)CU NIPDAU Level-1-260C-UNLIMTS5A23157DGST ACTIVE MSOP DGS10250Green(RoHS&no Sb/Br)CU NIPDAU Level-1-260C-UNLIMTS5A23157DGSTE4ACTIVE MSOP DGS10250Green(RoHS&no Sb/Br)CU NIPDAU Level-1-260C-UNLIMTS5A23157DGSTG4ACTIVE MSOP DGS10250Green(RoHS&no Sb/Br)CU NIPDAU Level-1-260C-UNLIMTS5A23157RSER ACTIVE UQFN RSE103000Green(RoHS&no Sb/Br)CU NIPDAU Level-1-260C-UNLIMTS5A23157RSERG4ACTIVE UQFN RSE103000Green(RoHS&no Sb/Br)CU NIPDAU Level-1-260C-UNLIM(1)The marketing status values are defined as follows:ACTIVE:Product device recommended for new designs.LIFEBUY:TI has announced that the device will be discontinued,and a lifetime-buy period is in effect.NRND:Not recommended for new designs.Device is in production to support existing customers,but TI does not recommend using this part in a new design.PREVIEW:Device has been announced but is not in production.Samples may or may not be available.OBSOLETE:TI has discontinued the production of the device.(2)Eco Plan-The planned eco-friendly classification:Pb-Free(RoHS),Pb-Free(RoHS Exempt),or Green(RoHS&no Sb/Br)-please check /productcontent for the latest availability information and additional product content details.TBD:The Pb-Free/Green conversion plan has not been defined.Pb-Free(RoHS):TI's terms"Lead-Free"or"Pb-Free"mean semiconductor products that are compatible with the current RoHS requirements for all6substances,including the requirement that lead not exceed0.1%by weight in homogeneous materials.Where designed to be soldered at high temperatures,TI Pb-Free products are suitable for use in specified lead-free processes.Pb-Free(RoHS Exempt):This component has a RoHS exemption for either1)lead-based flip-chip solder bumps used between the die and package,or2)lead-based die adhesive used between the die and leadframe.The component is otherwise considered Pb-Free(RoHS compatible)as defined above.Green(RoHS&no Sb/Br):TI defines"Green"to mean Pb-Free(RoHS compatible),and free of Bromine(Br)and Antimony(Sb)based flame retardants(Br or Sb do not exceed0.1%by weight in homogeneous material)(3)MSL,Peak Temp.--The Moisture Sensitivity Level rating according to the JEDEC industry standard classifications,and peak solder temperature.Important Information and Disclaimer:The information provided on this page represents TI's knowledge and belief as of the date that it is provided.TI bases its knowledge and belief on information provided by third parties,and makes no representation or warranty as to the accuracy of such information.Efforts are underway to better integrate information from third parties.TI has taken and continues to take reasonable steps to provide representative and accurate information but may not have conducted destructive testing or chemical analysis on incoming materials and chemicals.TI and TI suppliers consider certain information to be proprietary,and thus CAS numbers and other limited information may not be available for release.In no event shall TI's liability arising out of such information exceed the total purchase price of the TI part(s)at issue in this document sold by TI to Customer on an annual basis.OTHER QUALIFIED VERSIONS OF TS5A23157:•Automotive:TS5A23157-Q1NOTE:Qualified Version Definitions:•Automotive-Q100devices qualified for high-reliability automotive applications targeting zero defectsTAPE AND REEL INFORMATION*All dimensions are nominal Device Package Type Package DrawingPinsSPQ Reel Diameter (mm)Reel Width W1(mm)A0(mm)B0(mm)K0(mm)P1(mm)W (mm)Pin1Quadrant 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Synchronizer

专利名称：Synchronizer发明人：Braun, Eugene Ralph 申请号：EP98114454.6申请日：19980801公开号：EP0897068B1公开日：20031203专利内容由知识产权出版社提供摘要：A synchronizer (22) (e.g. pin-type, double acting) with friction clutches (26,50 and 28,52), jaw clutches (30,34 and 32,36), a shift flange (42), self-energizing ramps(13b,13c,13d,13e) affixed to a shaft (12), a spring (58) loaded pre-energizer assembly (56), and self-energizing ramps (45a,45b,45c,45d) affixed to a self-energizer member (44). Engagement of the ramps in response to an operator shift (Fo) applied to the shift flange provides an additive axial force (Fa) for increasing the engagement force of the friction clutches. The member (44) is secured for rotation with and sliding movement relative to the flange (42). Spring washers (46,48) react in opposite directions between member (44) and the jaw members (34,36) for limiting the amount of additive axial force (Fa). Blocker shoulders (42d,54c and 42e,54d) prevent asynchronous engagement of the jaw clutches. Spring washers (68,70) are interposed between the friction clutches and the blocker shoulders for returning the shift flange to a neutral position and disengage the self-energizing ramps in response the removal of the shift force (Fo) prior to completion of the a shift.申请人：EATON CORP地址：US国籍：US代理机构：Patentanwälte Rüger, Barthelt & Abel 更多信息请下载全文后查看。

Computer tomography method for a periodically movi

专利名称：Computer tomography method for aperiodically moving object发明人：Thomas Köhler,Michael Grass,Roland Proksa申请号：US10552399申请日：20040402公开号：US07426257B2公开日：20080916专利内容由知识产权出版社提供专利附图：摘要：The invention relates to a computer tomography method in which a periodically moving object, in particular an organ of the body, is irradiated by a cone-shaped beam cluster () along a trajectory which runs on a cylindrical surface. The radiation transmittedthrough the object is measured by means of a detector unit (), and at the same time the periodic movement of the object is recorded. In order to reconstruct the absorption distribution of the object, the measured values or the corresponding beams are rebinned to form a number of parallel projections, where for each of these projections a measured value is determined whose beam irradiates the object. The point in time at which this measured value was acquired is allocated to the respective projection. For the reconstruction, which may for example be carried out using a filtered back-projection, only projections whose allocated points in time lie within a predefined, specific time range (H) within a period of the object movement are used.申请人：Thomas Köhler,Michael Grass,Roland Proksa地址：Norderstedt DE,Buchholz in der Nordheide DE,Hamburg DE国籍：DE,DE,DE更多信息请下载全文后查看。

CARR保护系统数字化测试分析平台的研制

TECHNOLOGY AND INFORMATION70 科学与信息化2022年5月上CARR保护系统数字化测试分析平台的研制罗忠王一石贾月光中国原子能科学研究院反应堆工程技术研究所北京 102413摘要为了提高中国先进研究堆（CARR）保护系统的测试效率，研制了CARR保护系统数字化测试分析平台。

该平台软件采用扁平化设计和模块化设计思想，实现一键闭环自动测试，自动执行每一个测试用例、同步记录，对测试结果自动分析判断，生成测试报告。

通过在保护系统测试中的应用，提高了测试效率，进一步保证了保护系统的可靠性和安全性。

关键词中国先进研究堆；保护系统；测试分析Development of Digital Testing and Analysis Platform for CARR Protection System Luo Zhong, Wang Yi-shi, Jia Yue-guangDivision of Reactor Engineering Technology Research, China Institute of Atomic Energy, Beijing 102413, ChinaAbstract In order to improve the testing efficiency of China Advanced Research Reactor (CARR) protection system, a digital testing and analysis platform for CARR protection system is developed. The platform software adopts the idea of flat design and modular design, realizes one-key closed-loop automatic test, automatically executes each test case, synchronizes records, automatically analyzes and judges test results, and generates test reports. Through the application in the protection system test, the test efficiency is improved, and the reliability and safety of the protection system are further ensured.Key words China Advanced Research Reactor; protection system; testing and analysis引言中国先进研究堆保护系统采用数字化技术有三个通道站，每个通道站包含安全计算机（AP ）和通道监测计算机（TP ）[1]。

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图论讲义第6章-染色应用

§6.5 染色应用举例—求图的边色数及色数的算法一、排课表问题—求二部图的正常)(G χ′边染色1. 问题：有m 位教师m x x x ,,,21 ，n 个班级n y y y ,,,21 。

教师x i 每周需要给班级y j 上p ij 次（节）课。

要求制订一张周课时尽可能少的课程表。

2. 图论模型：构造二部图),(Y X G =，其中X ＝{m x x x ,,,21 }，Y ＝{n y y y ,,,21 }，顶点i x 与j y 之间连ij p 条边。

一个课时的安排方案对应于二部图G 的一个匹配。

排课表问题等价于：将E (G )划分成一些匹配，使得匹配的数目尽可能地少。

按)(G χ′的定义，这个最小的数目便是)(G χ′。

由定理6.2.1，()()G G χ′=Δ。

因此，排课表问题等价于：求二部图G 的边正常)(G Δ染色。

如§6.1中所述，虽然求简单图的正常（1+Δ）边染色存在多项式时间算法，但求简单图G 的边色数)(G χ′及其相应的正常边染色是一个NPC 问题[28]。

尽管如此，求二部图的边正常Δ染色却有多项式时间算法。

求图的边色数的近似算法可参考文献[29]~[51]。

[28] I. Holyer, The NP-completeness of edge-coloring, SIAM J. Computing , 10: 4(1981), 718-720.[29] E. Petrank, The hardness of approximation: gap location, Computational Complexity , 4 (1994), 133-157.[30] D. Leven and Z. Galil, NP completeness of finding the chromatic index of regular graphs, J. Algorithms , 4(1983) 35-44.[31] P. Crescenzi, V . Kann, R. Silvestri, and L. Trevisan, Structure in approximation classes, SIAM J. Comp., 28 (1999), 1759-1782.[32] J. Misra and D. Gries, A constructive proof of Vizing's theorem. Inform. Process. Lett. 41 (1992), 131-133.[33] O. Terada, and T. Nishizeki, Approximate algorithms for the edge-coloring of graphs, Trans. Inst. Eletron. Commun. Engr. Japan J65-D , 11(1982), 1382-1389.[34] M. Chrobak, and T. Nishizeki, Improved edge-coloring algorithms for planar graphs, J. Algorithms , 11(1990), 102-116.[35] I. Caragiannis, A. Ferreira, C. Kaklamanis, S. Perennes, P. Persiano and H. Rivano, Approximate constrained bipartite edge coloring, Discrete Applied Mathematics , 143(2004), 54-61[36] M. R. Salavatipour, A polynomial time algorithm for strong edge coloring of partial k -trees, Discrete Applied Mathematics , 143(2004), 285-291.[37] D.A. Grable, A. Panconesi, Nearly optimal distributed edge coloring in O (log log n ) rounds, Proceedings of the Eighth Annual ACM-SIAM Symposium on Discrete Algorithms, January, (1997), 278–285.[38] Yijie Han, Weifa Liang and Xiaojun Shen, Very fast parallel algorithms for approximate edge coloring, Discrete Applied Mathematics, 108(2001), 227-238.[39] M. Fürer and B. Raghavachari, Parallel edge coloring approximation, Parallel Process. Lett. , 6 (1996), 321–329.[40] H.J. Karloff and D.B. Shmoys, Efficient parallel algorithms for edge coloring problems. J. Algorithms 8 (1987), 39–52.[41] W. Liang, Fast parallel algorithms for the approximate edge-coloring problem. Inform. Process. Lett. 56 (1995), 333–338.[42] W. Liang, X. Shen and Q. Hu, Parallel algorithms for the edge-coloring and edge-coloring update problems. J. Parallel Distrib. Comput. 32 (1996), 66-73.[43] R. Motwani, J. Naor and M. Naor, The probabilistic method yields deterministic parallel algorithms. J. Comput. System Sci. 49 (1994), 478-516.[44] D. Bertsimas, C-P. Teo, and R. V ohra, On dependent randomized rounding algorithms, Proc. 5th Int. Conf. on Integer Prog. and Combinatorial Optimization , Lecture Notes in Comput. Sci. 1084, Springer-Verlag, (1996), 330-344.[45] M.K. Goldberg, Edge-colorings of multigraphs: recoloring technique, J. Graph Theory , 8(1984), 123-127.[46] D.S. Hochbaum, T. Nishizeki and D.B. Shmoys, Better than “Best Possible” algorithm to edge color multi graphs, Journal of Algorithms , 7(1986), 79-104[47] T. Nishizeki and K. Kashiwagi, On the 1.1 edge-coloring of multigraphs, SIAM J. Disc. Math. , 3(1990), 391-410.[48] J. Kahn, Asymptotics of the chromatic index for multigraphs, Journal of Combinatorial Theory (Ser. B ), 68(1996), 233-254.[49] X. Zhou H. Susuki, and T. Nishizeki, A linear algorithm for edge-coloring series-parallel multigraphs, J. Algorithms , 20(1996), 174-201.[50] X. Zhou H. Susuki, and T. Nishizeki, An NC parallel algorithm for edge-coloring series-parallel multigraphs, J. Algorithms , 23(1997), 359-374.[51] B. Berger and J. Rompel, Simulating (log c n )-wise independence in NC. J. ACM 38 (1991), 1026–1046.3. 求二部图),(Y X G =的边正常)(G Δ染色的算法z 算法思想：给G 添加必要的顶点使得||||Y X =，再添加必要的边使得G 成为)(G Δ正则二部图，所得图记为*G ，然后反复运用匈牙利算法求*G 的完美匹配。

基于调制核回归和正则化Richardson-Lucy 算法的中子图像复原方法

基于调制核回归和正则化Richardson-Lucy 算法的中子图像复原方法乔双;王巧;孙佳宁【摘要】由于中子成像系统中的诸多物理因素影响，使其得到的中子图像通常会发生严重的图像降质。

本文将调制核回归（SK）引入到TV‐RL算法中，提出了一种中子图像去模糊去噪方法SK‐TV‐RL ，即基于SK的TV‐RL算法。

该方法能解决以往算法噪声放大的问题，并能复原降质图像中的细节信息。

对比实验结果表明，无论基于客观评价还是主观评价，该方法都能有效地提高图像复原质量。

%The neutron image obtained from neutron imaging system usually gets serious degradation because of the influence of physical constraints and other factors of the sys‐tem .To solve this problem ,by combining the steering‐kernel regression (SK) with TV‐RL algorithm ,a neutron image restoration method SK‐TV‐RL was proposed .The method is capable of suppressing noise w hile restoring details of the blurred imaging re‐sultsefficiently .Experimental results show that comparing with the other methods ,the method can improve the restoration quality both visually and quantitatively .【期刊名称】《原子能科学技术》【年(卷),期】2015(000)004【总页数】4页(P765-768)【关键词】中子成像;Richardson-Lucy算法;调制核回归【作者】乔双;王巧;孙佳宁【作者单位】东北师范大学物理学院，吉林长春130024;东北师范大学物理学院，吉林长春 130024;东北师范大学数学与统计学院，吉林长春 130024【正文语种】中文【中图分类】TP391由于中子成像系统物理条件因素的限制，其成像结果不可避免的会受到γ射线污染、中子散射、CCD电子噪声等因素的影响，这使得中子数字成像系统所得到的图像往往会发生严重降质，如对比度低、图像模糊、含有多种噪声等［1］。

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For multiple print copies contact: SAE Customer Service Tel: 877-606-7323 (inside USA and Canada) Tel: 724-776-4970 (outside USA) Fax: 724-776-1615 Email: CustomerService@ ISBN 0-7680-1319-4 Copyright © 2004 SAE International Positions and opinions advanced in this paper are those of the author(s) and not necessarily those of SAE. The author is solely responsible for the content of the paper. A process is available by which discussions will be printed with the paper if it is published in SAE Transactions. Persons wishing to submit papers to be considered for presentation or publication by SAE should send the manuscript or a 300 word abstract of a proposed manuscript to: Secretary, Engineering Meetings Board, SAE. Printed in USA
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SAE TECHNICAL PAPER SERIES
vent so functional harmony is achieved in concert with the selected physical parameters. Event charts are presented with illustrations and necessary stack for dimensioning and tolerancing the synchronizer components. The components that play significant role in each event are identified and related to specific physical parameter. 2.0 Introduction In a synchromesh transmission a synchronizer is a friction clutch which synchronizes the rotational speed of the transmission output shaft and the gear to be engaged allowing smooth gear change. The location of synchronizers is much heeded to minimize the effect of system inertia and relative speeds of the rotating components. Increasing trend towards higher engine power and higher engine speeds due to multi valves per cylinder have resulted in higher shift efforts. Concurrently, the driver still demands smooth shiftability. These conflicting expectations require greater efficiency from the synchronizer design. Generally, in order to meet these conflicting expectations larger size synchronizers as well as multicone synchronizers are packaged on the shafts to do more work in a given time. However the basic design of the synchronizer and its components has remained an excruciating challenge. Synchronizer technology is a myth and the essence of smooth shifting transmission is shrouded therein. It must be recognized that synchronizer endures incessant punishment, more so than any other transmission components, and is expected to continue to work flawlessly for the life of the vehicle. Additionally, the driver abuse adversely affects the synchronizer performance eventually resulting in malfunction. 3.0 Significant Parameters: Algorithms and Nomograms Listed below are significant physical parameters that are crucial to the synchronizer design for satisfactory compliance with the functional objectives:
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2004-01-1230
Synchronizer Design: A Mathematical and Dimensional Treatise
Synchronizer Design: A Mathematical and Dimensional Treatise
Syed T. Razzacki
DaimlerChrysler, Inc.
Reprinted From: Transmission & Driveline Symposium 2004 (SP-1817)
2004 SAE World Congress Detroit, Michigan March 8-11, 2004
400 Commonwealth Drive, Warrendale, PA 15096-0001 U.S.A. Tel: (724) 776-4841 Fax: (724) 776-5760 Web:
Syed T. Razzacki
DaimlerChrysler, Inc.
Copyright © 2004 SAE International
1.0 Abstract The manual transmission synchronizer design has been a real challenge and is usually referred to as a myth and black magic. A mathematical algorithm and dimensioning and tolerancing scheme has been developed to dispel this myth. A unique and logical user-friendly method for designing synchronizer is devised. The knowledge that existed in the public domain is advanced to higher level to show that the design and calculations of physical parameters must go hand in hand. The paper attempts to demonstrate the fact that the calculations of synchronizer physical parameters should be supported by scrupulously dimensioning and tolerancing the components design to achieve the intended functional objective. A mathematical algorithm is developed which facilitates establishing the sleeve and blocker ring pointing angle relationship with the synchronizer size, coefficient of friction, cone torque, and index torque. The relationship is presented graphically in a unique manner identifying the clash and hard shift zones. As such, it allows sizing the synchronizer and selection of the parameters for a given application for comfortable shiftability between the two extremes of clash and hard shift. Synchronization episode is separated in to the following six distinct events: Event I. Strut contacts blocker ring Event II. End of strut loading, strut out of detent Event III. Sleeve point hits ring point, ring clocked Event IV. Sleeve chamfer passes through ring chamfer Event V. Sleeve tooth point contacts clutching tooth point Event VI. Sleeve tooth chamfer passes through gear clutching tooth chamfer Arithmetic stack and calculations are utilized to iteratively dimension and tolerance the components for