the position code algorithm for contact searching a new global search method for general contact systems is developed and implemented in the dyna3d program along with a recent contact interface algorithm the concept of position codes for efficient global contact searching is presented with the position code algorithm the problem of sorting and searching in three dimensions is transformed to a process of sorting and searching within a one dimensional array the cost of contact searching is of the order of n log 2 n where n is the number of nodes in the system the proposed algorithms are uncomplicated and the implementation into any finite element code is straightforward

characterizing robust local error bounds for linear inequality systems under data uncertainty abstract we present necessary and sufficient conditions for the existence of robust local error bounds for linear inequality system in the face of data uncertainty where the uncertain data belong to a prescribed compact uncertainty set the robust local error bound for an uncertain system is defined in terms of the existence of local error bound for its robust counterpart where the uncertain linear inequality is enforced for every possible value of the data in the uncertainty set some of these conditions are expressed using the projection of the origin and others are given by way of normal cones at the boundary points of the solution set in the case of commonly used interval data uncertainty we show that a qualification condition completely characterizes the existence of robust local error bounds

bounds for a nonparametric t table summary a simple inequality for bounding the tail probabilities of normalized sums of independent symmetric random variables is used to produce bounds on the tail probabilities of the usual student t statistic under the same hypothesis the relative difference between the resulting t scores and the usual ones is shown to be asymptotically negligible as the sample size increases and the tail probability decreases to zero as an example a table of upper 0 025 cutoff bounds is given and compared to the usual bounds some key word8 nonparametric test permutation test student t test the following theorem is based on an approach first introduced by fisher 1935 and may be used to facilitate the application of the sign permutation test he introduced since the theorem provides bounds on tail probabilities of normalized sums of independent symmetric random variables it may prove useful in a theoretical context as well

distribution free bounds for serial correlation coefficients in heteroskedastic symmetric time series abstract we consider the problem of testing whether the observations x 1 x n of a time series are independent with unspecified possibly nonidentical distributions symmetric about a common known median various bounds on the distributions of serial correlation coefficients are proposed exponential bounds eaton type bounds chebyshev bounds and berry esseen zolotarev bounds the bounds are exact in finite samples distribution free and easy to compute the performance of the bounds is evaluated and compared with traditional serial dependence tests in a simulation experiment the procedures proposed are applied to u s data on interest rates commercial paper rate

a contact domain method for large deformation frictional contact problems part 2 numerical aspects this second part of the work describes the numerical aspects of the developed contact domain method for large deformation frictional contact problems the theoretical basis of this contact method is detailed in the first part of this work starting from this the present contribution focuses on describing important algorithmic details that go along with the finite element implementation for two dimensional problems important aspects are the construction of the contact domain mesh via a constraint delaunay triangulation the linearization of the discretized contact contributions and some important technical aspects about the extrapolation procedure used for the predictive active set strategy finally a set of numerical examples is presented to demonstrate the performance of the developed contact strategy demanding static and dynamic contact problems in the context of large deformations including frictional effects as well as self contact show the wide applicability and the robustness of the proposed method

berry esseen theorems for quadratic forms of gaussian stationary processes letx1 x2 be a gaussian stationary process with spectral densityf and let z j frac 1 sqrt t left sum limits l 1 t j 1 left x l x l j 1 ex l x l j 1 right right j 1 p the present paper gives a berry esseen type theorem for the joint distribution of z1 zp

a mortar segment to segment contact method for large deformation solid mechanics abstract contact modeling is still one of the most difficult aspects of non linear implicit structural analysis most 3d contact algorithms employed today use node on segment approaches for contacting dissimilar meshes two pass node on segment contact approaches have the well known deficiency of locking due to over constraint in this work we develop and demonstrate a segment to segment contact approach based on the mortar method by eliminating the over constraint this method appears to be much more robust than the node on segment approach furthermore node on segment approaches suffer when individual nodes slide out of contact at contact surface boundaries or when contacting nodes slide from facet to facet this causes jumps in the contact forces due to the discrete nature of the constraint enforcement and difficulties in convergence for implicit solution techniques these jumps in forces are avoided in the segment to segment approach since penetration is measured by the occluded weighted volume which varies smoothly with perturbations until now all mortar schemes have been developed for small deformation sliding and have mainly been applied on flat surfaces here we will present the integration scheme and the linearization approach used for handling the contact surface integrals in the event of large sliding the schemes are designed to conserve linear momentum and can be applied to arbitrarily curved 3d surfaces although expensive our numerical examples demonstrate that the approach is far more robust than even smoothed node on segment contact techniques that is problems previously not solvable with node on segment can now be solved with our segment to segment contact

berry esseen type bounds for signed linear rank statistics with a broad range of scores the berry esseen type bounds of order n 1 2 for the rate of convergence to normality are derived for the signed linear rank statistics under the hypothesis of symmetry the results are obtained with a broad range of regression constants and scores restricted by only mild conditions while almost all previous results are obtained with continuously differentiable score generating functions the proof is very short and elementary based on the conditioning argument

a level set enhanced natural kernel contact algorithm for impact and penetration modeling summary a natural kernel contact nkc algorithm under the framework of the semi lagrangian reproducing kernel particle method semi lagrangian rkpm is proposed to model multi body contact with specific consideration for impact and penetration modeling the nkc algorithm utilizes the interaction of the semi lagrangian kernel functions associated with contacting bodies to serve as the non penetration condition the effects of friction are represented by introducing a layer of the friction like elasto plasticity material between contacting bodies this approach allows the frictional contact conditions and the associated kinematics to be naturally embedded in the semi lagrangian rkpm inter particle force calculation the equivalence in the karush kuhn tucker conditions between the proposed nkc algorithm and the conventional contact kinematic constraints as well as the associated state variable relationships are identified a level set method is further introduced in the nkc algorithm to represent the contact surfaces without pre defined potential contact surfaces the stability analysis performed in this work shows that temporal stability in the semi lagrangian rkpm with nkc algorithms is related to the velocity gradient between contacting bodies the proposed methods have been verified by several benchmark problems and applied to the simulation of impact and penetration processes copyright 2014 john wiley sons ltd

convergent hierarchy of sdp relaxations for a class of semi infinite convex polynomial programs and applications abstract in this paper we examine semidefinite linear programming approximations to a class of semi infinite convex polynomial optimization problems where the index sets are described in terms of convex quadratic inequalities we present a convergent hierarchy of semidefinite linear programming relaxations under a mild well posedness assumption we also provide additional conditions under which the hierarchy exhibits finite convergence these results are derived by first establishing characterizations of optimality which can equivalently be reformulated as linear matrix inequalities a separation theorem of convex analysis and a sum of squares polynomial representation of positivity of real algebraic geometry together with a special variable transformation play key roles in achieving the results finally as applications we present convergent relaxations for a broad class of robust convex polynomial optimization problems

global error bounds for piecewise convex polynomials in this paper by examining the recession properties of convex polynomials we provide a necessary and sufficient condition for a piecewise convex polynomial to have a holder type global error bound with an explicit holder exponent our result extends the corresponding results of li siam j control optim 33 5 1510 1529 1995 from piecewise convex quadratic functions to piecewise convex polynomials

robust global error bounds for uncertain linear inequality systems with applications abstract in this paper we examine global error bounds for a linear inequality system in the face of data uncertainty by building upon recent developments in robust optimization where the uncertain parameters are assumed to be in prescribed uncertainty sets we present necessary and sufficient dual conditions for the existence of robust global error bounds as a consequence we obtain a robust hoffman error bound in the case of commonly used interval data uncertainty extending the well known hoffman s error bound we then introduce the notion of radius of robust global error bound under interval data uncertainty and present a formula for finding the radius by examining the stability of robust global error bounds it provides the radius of the largest interval uncertainty set in which the uncertain system admits a robust global error bound as an immediate application to robust linear programming we provide conditions for robust feasibility and give a formula for radius of robust feasibility of an uncertain linear program

consistent treatment of boundaries with mortar contact formulations using dual lagrange multipliers abstract computational modelling of contact problems raises two basic questions which method should be used to enforce the contact conditions and how should this method be discretised the most popular enforcement methods are the lagrange multiplier method the penalty method and combinations of these two a frequently used discretisation method is the so called node to segment approach however this approach might lead to problems like jumps in contact forces loss of convergence or failure to pass the patch test thus in the last few years several segment to segment contact algorithms based on the mortar method were proposed combination of a mortar discretisation with a penalty based enforcement of the contact conditions leads to unphysical penetrations on the other hand a lagrange multiplier mortar method requires additional unknowns hence condensation of the lagrange multipliers is desirable to preserve the initial size of the system of equations this can be achieved by interpolating the lagrange multipliers with so called dual shape functions discretising two contacting bodies leads to opposed contact surface representations of finite element edges called slave and master elements respectively in current versions of dual lagrange multiplier mortar formulations an inconsistency at the boundary appears when only a part of a slave element instead of the entire element belongs to the contact area we present a modified definition of the dual shape functions in such slave elements the basic idea is to construct dual shape functions that fulfill the so called biorthogonality condition within the contact area this leads to consistent mortar matrices also in the boundary region to avoid ill conditioning of the stiffness matrix the modified mortar matrices are weighted with appropriate weighting factors in doing so the corresponding modified lagrange multiplier nodal values are of the same order as the unmodified ones various examples demonstrate the performance of the modified mortar contact algorithm

two dimensional mortar contact methods for large deformation frictional sliding this paper presents a mortar based formulation for the solution of two dimensional frictional contact problems involving finite deformation and large sliding as is widely recognized traditional node to surface contact formulations have several drawbacks in solution of deformable to deformable contact problems including lack of general patch test passage degradation of spatial convergence rates and robustness issues associated with the faceted representation of contacting surfaces the mortar finite element method initially proposed as a technique to join dissimilarly meshed domains has been shown to preserve optimal convergence rates in tied contact problems see discretization methods and iterative solvers based on domain decomposition springer verlag heidelberg 2001 for a recent review and is examined here as an alternative spatial discretization method for large sliding contact in particular a novel description for frictional sliding conditions in large deformation mortar formulations is proposed in this work in recent years the mortar element method has already been successfully implemented to solve frictional contact problems with linearized kinematics see int j numer meth engng 1993 36 3451 however in the presence of large deformations and finite sliding one must face difficulties associated with the definition and linearization of contact virtual work in the case where the mortar projection has a direct dependence on the tangential relative motion along the interface in this paper such a formulation is presented with particular emphasis on key aspects of the linearization procedure and on the robust description of the friction kinematics some novel techniques are proposed to treat the non smoothness in the contact geometry and the searching required to define mortar segments a number of numerical examples illustrate the performance and accuracy of the proposed formulation copyright 2004 john wiley sons ltd

exact inequalities for sums of asymmetric random variables with applications let rm bs 1 dots rm bs n be independent identically distributed random variables each having the standardized bernoulli distribution with parameter p in 0 1 let m p 1 p 2 p 2 2 sqrt p p 2 4 p 2 if 0 p le frac12 and m p 1 if frac12 le p 1 let m ge m p let f be such a function that f and f are nondecreasing and convex then it is proved that for all nonnegative numbers c 1 dots c n one has the inequality mathsf e f c 1 mathrm b s 1 dots c n mathrm b s n le mathsf e f big s m mathrm b s 1 dots mathrm bs n big where s m big frac1n sum i 1 n c i 2m big frac1 2m the lower bound m p on m is exact for each p in 0 1 moreover operatorname mathsf e f c 1 mathrm b s 1 dots c n mathrm b s n is schur concave in c 1 2m ldots c n 2m

resolution of fourth order problems by the mortar element method we present a resolution of fourth order problems by the mortar element method in the case of spectral discretizations we prove that this approach leads to a well posed discrete problem and the numerical analysis gives an optimal error estimate

an inequality of optimal order for the tail probabilities of the t statistic under symmetry abstract an inequality for the tail probabilites of the t statistic under the hypotheses of independence and symmetry is presented and is shown to yield bounds for the upper quantiles that approach those of the normal and hence the smallest of such bounds possible as the corresponding upper tail area tends to 0

improved eaton bounds for linear combinations of bounded random variables with statistical applications abstract the problem of evaluating tail probabilities for linear combinations of independent possibly nonidentically distributed bounded random variables arises in various statistical contexts mainly connected with nonparametric inference a remarkable inequality on such tail probabilities has been established by eaton the significance of eaton s inequality is substantiated by a recent result of pinelis showing that the minimum b ep of eaton s bound b e and a traditional chebyshev bound yields an inequality that is optimal within a fairly general class of bounds eaton s bound however is not directly operational because it is not explicit apparently it never has been studied numerically and its many potential statistical applications have not yet been considered a simpler inequality recently proposed by edelman for linear combinations of iid bernoulli variables is also considered but it appears considerably less tight than eaton s original bound this article has three main objectives first

a berry esseen bound for functions of independent random variables the rate of convergence in the central limit theorem for functions of independent random variables is studied in a unifying approach the basic result sharpens and extends a theorem of van zwet applications to u l and r statistics are also given improving or extending the results of helmers and van zwet helmers and huskova does and van es and helmers

a large deformation mortar formulation of self contact with finite sliding this paper presents a new numerical method in which self contact phenomena associated with a body undergoing large deformations and sliding can be described in particular the approach relies on a particular extension of the mortar approach appropriate for this class of problems a bounding volume hierarchy organized as a binary tree is built for the self contact surface based on the geometry and the mesh connectivity of the surface a curvature criterion using a new algorithm to detect subsurface adjacency is used to accelerate the self contact searching procedure to ensure that the mortar traction fields are properly defined on contiguous surface patches a novel facet sorting algorithm is also proposed based on the mesh connectivity of the contact element pairs found by the self contact searching algorithm several two and three dimensional numerical examples show the new self contact mortar formulation to be very efficient and also demonstrate that it can be combined with multi body contact algorithms to simulate a very general class of contact problems

a mortar based approach for the enforcement of periodic boundary conditions on arbitrarily generated meshes a new approach for the enforcement of periodic boundary conditions on representative volume element rve problems is presented the strategy is based on a mortar formulation and considers two and three dimensional problems in the finite deformation frame the mortar discretization is combined with the lagrange multiplier method for the enforcement of periodicity constraints at each pair of corresponding boundaries of the rve in a weak integral sense the interpolation of the lagrange multipliers is undertaken with dual shape functions which can be locally eliminated from the rve system of equations by static condensation avoiding an increase on the system size the numerical treatment within a newton based finite element solution procedure for the rve equilibrium problem is discussed in detail the resulting method is able to efficiently enforce periodic configurations over complex rves at finite strains with arbitrarily generated finite element meshes several numerical examples are presented to demonstrate the robustness of the method and the quality of results

permutational extreme values of autocorrelation coefficients and a pitman test against serial dependence somewhat more difficult this problem which is shown to reduce to a particular case of the well known travelling salesman problem is explicitly solved here for the autocorrelation coefficient of order one allowing for a simple computation of permutational critical values for pitman tests against serial dependence the case of higher order autocorrelations is however of a different nature and requires another approach

a spectral element methodology tuned to parallel implementations abstract we present in this paper a modification of the conforming spectral element method for the approximation of the poisson equation this new procedure allows the implementation on a parallel machine in an easier and faster way the resulting method is nonconforming but the numerical analysis shows that the error between the exact solution and the discrete solution is of the same asymptotic order as the error of the original conforming method

perturbation analysis of error bounds for systems of conic linear inequalities in banach spaces for a general constrained or unconstrained system of conic inequalities we provide sufficient conditions to ensure the existence of a common error bound for each of the systems obtained from the original one when the given data undergoes a small perturbation moreover we also give some dual characterizations on the existence of error bounds for systems of conic inequalities

applying nagata patches to smooth discretized surfaces used in 3d frictional contact problems the accurate solution of large deformation frictional contact problems using the finite element method is still a challenging task due to the strong nonlinearities involved this paper presents a smoothing method applicable to 3d contact surfaces discretized with an arbitrary mesh topology the quadratic nagata patch interpolation is adopted to define the smooth surface the resulting contact surface passes through all nodes of the mesh while providing a smooth description with at least g 1 continuity at the nodes and quasi g 1 continuity between the patches thus the proposed method avoids the non physical oscillations in the contact force which are induced by the traditionally used faceted contact surfaces description when slave nodes slide over several master segments moreover it allows the accurate evaluation of kinematic variables leading to important improvements in terms of convergence rate within the newton raphson iteration loop the developed global and local contact search algorithms designed for contact surfaces described by nagata patches are described in detail three numerical examples were selected to illustrate the advantages of the proposed smoothing method including a complex industrial example of sheet metal forming process the results show the significant improvements attained with the proposed approach in terms of efficiency robustness and accuracy when compared with the traditional faceted contact surfaces description 2014 published by elsevier b v

combined rank tests for the two sample problem with randomly censored data abstract in the two sample problem under random censorship we consider the uncensored observations and the censored ones as two separate groups for each group a suitable rank statistic is obtained and these two are then combined to a final one this idea which was first employed in akritas 1983 is shown here to produce tests that a closely resemble the ordinary rank tests for the uncensored case and do not require the calculation of the kaplan meier estimator b are comparatively easy to apply and to understand and c allow results on asymptotic normality to follow simply from standard results for the uncensored case it is shown that the loss due to using two separate rankings rather than one complete ranking is asymptotically negligible the optimal score function for each of the two separate rank statistics is seen to depend on the censoring distribution whereas in akritas 1983 no assumption on the form of the censoring distribution was made unrestricted adaptation here we pursue rest

a generalized farkas lemma with a numerical certificate and linear semi infinite programs with sdp duals abstract in this paper we establish a new non homogeneous farkas lemma for a linear semi infinite inequality system where the dual statement is given in terms of linear matrix inequalities and thus it can be numerically verified by solving a semidefinite linear program it is achieved by way of employing a special variable transformation together with a strong separation theorem consequently we establish a duality theorem for a class of parametric linear semi infinite programs which admit semi definite linear programming sdp dual problems a numerical example is given to show how a parametric linear semi infinite optimization problem can be solved by way of solving its sdp dual problem using the matlab toolbox cvx

node to node scheme for three dimensional contact mechanics using polyhedral type variable node elements abstract a node to node contact scheme which is applicable for three dimensional contact analyses involving large deformations is developed with the aid of polyhedral elements the key issue is to transform nonmatching meshes into matching meshes in a seamless manner because polyhedral elements are allowed to have arbitrary numbers of polygonal faces and nodes they can be used as transition elements for coupling nonmatching meshes in this paper the polyhedral elements make it possible to always maintain node to node contact during the contact deformation the present approach guarantees that the patch test is passed and the nonpenetration condition is satisfied and hence it yields smoother contact pressure with faster convergence than the conventional node to surface or surface to surface contact scheme

a constrained optimization methodology for the detection phase in contact mechanics simulations the detection phase in computational contact mechanics can be subdivided into a global search and a local detection when potential contact is detected by the former a rigorous local detection determines which surface elements come or may come in contact in the current increment we first introduce a rigorous definition of the closest point for non differentiable lower dimensional manifolds we then simplify the detection by formulating an optimization problem subject to inequality constraints the formulation is then solved using different techniques from the field of mathematical optimization for both linear and quadratic finite element meshes the resulting general and robust detection scheme is tested on a set of problems and compared with other techniques commonly used in computational geometry

finite sample exact tests for linear regressions with bounded dependent variables we introduce tests for finite sample linear regressions with heteroskedastic errors the tests are exact i e they have guaranteed type i error probabilities when bounds are known on the range of the dependent variable without any assumptions about the noise structure we provide upper bounds on probability of type ii errors and apply the tests to empirical data