a generalized computational approach to stability of static equilibria of nonlinearly elastic rods in the presence of constraints abstract we present a generalized approach to stability of static equilibria of nonlinearly elastic rods subjected to general loading boundary conditions and constraints of both point wise and integral type based upon the linearized dynamics stability criterion discretization of the governing equations leads to a non standard singular generalized eigenvalue problem a new efficient sparse matrix friendly algorithm is presented to determine its few left most eigenvalues which in turn yield stability instability information for conservative problems the eigenvalue problem arising from the linearized dynamics stability criterion is also shown to be equivalent to that arising in the determination of constrained local minima of the potential energy we illustrate the method with several examples a novel variational formulation for extensible and unshearable rods is also proposed within the context of one of the example problems

longest fault free paths in star graphs with vertex faults the star graph sn has been recognized as an attractive alternative to the hypercube since s1 s2 and s3 have trivial structures we focus our attention on sn with n 4 in this paper let fv denote the set of faulty vertices in sn we show that when fv n 5 sn with n 6 contains a fault free path of length n 2 fv 2 n 2 fv 1 between arbitrary two vertices of even odd distance since sn is bipartite with two partite sets of equal size the path is longest for the worst case scenario the situation of n 4 and fv n 5 is also discussed

panpositionable hamiltonicity and panconnectivity of the arrangement graphs abstract the arrangement graph an k is a generalization of the star graph it is more flexible in its size than the star graph there are some results concerning hamiltonicity and pancyclicity of the arrangement graphs in this paper we propose a new concept called panpositionable hamiltonicity a hamiltonian graph g is panpositionable if for any two different vertices x and y of g and for any integer l satisfying d x y l v g d x y there exists a hamiltonian cycle c of g such that the relative distance between x and y on c is l a graph g is panconnected if there exists a path of length l joining any two different vertices x and y with d x y l v g 1 we show that an k is panpositionable hamiltonian and panconnected if k 1 and n k 2

static and dynamic stability results for a class of three dimensional configurations of kirchhoff elastic rods we analyze the dynamical stability of a naturally straight inextensible and unshearable elastic rod under tension and controlled end rotation within the kirchhoff model in three dimensions the cases of clamped boundary conditions and isoperimetric constraints are treated separately we obtain explicit criteria for the static stability of arbitrary extrema of a general quadratic strain energy we exploit the equivalence between the total energy and a suitably defined norm to prove that local minimizers of the strain energy under explicit hypotheses are stable in the dynamic sense due to liapounov we also extend our analysis to damped systems to show that static equilibria are dynamically stable in the liapounov sense in the presence of a suitably defined local drag force

hyper hamiltonian laceability on edge fault star graph the star graph possess many nice topological properties edge fault tolerance is an important issue for a network since the edges in the network may fail sometimes in this paper we show that the n dimensional star graph is n 3 edge fault tolerant hamiltonian laceable n 3 edge fault tolerant strongly hamiltonian laceable and n 4 edge fault tolerant hyper hamiltonian laceable all these results are optimal in a sense described in this paper

optimal isoparametric finite elements and error estimates for domains involving curved boundaries we describe a practical procedure for the triangulation of arbitrary n dimensional regular bounded domains by isoparametric simplicial elements preserving the optimal order of accuracy along similar lines we prove general error estimates for the finite element solution of second order elliptic problems various kinds of nonhomogeneous boundary conditions can be dealt with such as dirichlet neumann and robin boundary conditions

construction of shape functions for the h and p versions of the fem using tensorial product this paper presents an uniform and unified approach to construct h and p shape functions for quadrilaterals triangles hexahedral and tetrahedral based on the tensorial product of one dimensional lagrange and jacobi polynomials the approach uses indices to denote the one dimensional polynomials in each tensorization direction the appropriate manipulation of the indices allows to obtain hierarchical or non hierarchical and inter element c continuous or non continuous bases for the one dimensional elements quadrilaterals triangles and hexahedral the optimal weights of the jacobi polynomials are determined the sparsity profiles of the local mass and stiffness matrices plotted and the condition numbers calculated a brief discussion of the use of sum factorization and computational implementation is considered

new basis functions and computational procedures for p version finite element analysis new basis functions and solution procedures for p version finite element analysis are described they are used in a highly efficient p version finite element solver for linear elastostatics and dynamics which has been used in an industrial environment for over two years using two sample applications it is shown that using the techniques proposed here p version finite element analysis can have a substantially lower computational cost for given accuracy than standard finite element methods this makes the industrial applicability of p version finite element analysis much wider than is commonly believed

stability of an elastic rod buckling into a soft wall the conjugate point theory of the calculus of variations is extended to apply to the buckling of an elastic rod in an external field we show that the operator approach presented by manning mannin

edge bipancyclicity of star graphs under edge fault tolerant abstract the star graph s n is one of the most famous interconnection networks it has been shown by li t k li cycle embedding in star graphs with edge faults appl math comput 167 2005 891 900 that s n contains a cycle of length from 6 to n when the number of fault edges in the graph does not exceed n 3 in this paper we improve this result by showing that for any edge subset f of s n with f n 3 every edge of s n f lies on a cycle of every even length from 6 to n provided n 3

embedding hamiltonian paths in augmented cubes with a required vertex in a fixed position it is proved that there exists a path p l x y of length l if d a q n x y l 2 n 1 between any two distinct vertices x and y of aq n obviously we expect that such a path p l x y can be further extended by including the vertices not in p l x y into a hamiltonian path from x to a fixed vertex z or a hamiltonian cycle in this paper we prove that there exists a hamiltonian path r x y z l from x to z such that d r x y z l x y l for any three distinct vertices x y and z of aq n with n 2 and for any d a q n x y l 2 n 1 d a q n y z furthermore there exists a hamiltonian cycle s x y l such that d s x y l x y l for any two distinct vertices x and y and for any d a q n x y l 2 n 1

upwind residual discretization of enhanced boussinesq equations for wave propagation over complex bathymetries in this paper we consider the solution of the enhanced boussinesq equations of madsen and sorensen 1992 55 by means of residual based discretizations in particular we investigate the applicability of upwind and stabilized variants of continuous galerkin finite element and residual distribution schemes for the simulation of wave propagation and transformation over complex bathymetries these techniques have been successfully applied to the solution of the nonlinear shallow water equations see e g hauke 1998 39 and ricchiuto and bollermann 2009 61 in a first step toward the construction of a hybrid model coupling the enhanced boussinesq equations with the shallow water equations in breaking regions this paper shows that equal order and even low order second upwind stabilized techniques can be used to model non hydrostatic wave propagation over complex bathymetries this result is supported by theoretical truncation and dispersion error analyses and by thorough numerical validation

vertex pancyclicity of augmented cubes with maximal faulty edges abstract the n dimensional augmented cube denoted as aqn a variation of the hypercube possesses some properties superior to those of the hypercube in this paper we show that every vertex in aqn lies on a fault free cycle of every length from 4 to 2n even if there are up to 2n 3 link faults we also show that this result is optimal

fault tolerant cycle embedding in alternating group graphs abstract cycle embedding is an important issue in evaluating the efficiency of interconnection networks and is also an extension of the theoretical research on hamiltonicity in this paper we study the fault tolerant hamiltonicity of alternating group graphs which were recently proposed as interconnection topologies for parallel and distributed systems a cycle of length l is said to be an l cycle let f be a set of faulty vertices in an n dimensional alternating group graph ag n and let m be the number of vertices in ag n f a previous result in j m chang j s yang y l wang y cheng panconnectivity fault tolerant hamiltonicity and hamiltonian connectivity in alternating group graphs networks 44 2004 302 310 showed that for n 4 ag n f is hamiltonian i e ag n f possesses a hamiltonian cycle if f n 2 and ag n f is hamiltonian connected i e every two vertices of ag n f are connected by a hamiltonian path if f n 3 in this paper we show the following results i ag n f is pancyclic i e ag n f contains an l cycle for each l with 3 l m if f n 2 ii ag n f is vertex pancyclic i e every vertex of ag n f is contained in an l cycle for each l with 3 l m if f n 3 and iii ag n f is edge 4 pancyclic i e every edge of ag n f is contained in an l cycle for each l with 4 l m if f n 4 the first result is an improvement over the previous one and the last two results are new characterization of fault tolerant pancyclicity on ag n all the results we achieved are the best possible in the sense that the number of faulty vertices cannot be increased

stability results for constrained calculus of variations problems an analysis of the twisted elastic loop problems with a variational structure are ubiquitous throughout the physical sciences and have a distinguished scientific history constrained variational problems have been much less studied particularly the theory of stability which determines which solutions are physically realizable in this paper we develop stability exchange results appropriate for parameter dependent calculus of variations problems with two particular features either the parameter appears in the boundary conditions or there are isoperimetric constraints in particular we identify an associated distinguished bifurcation diagram which encodes the direction of stability exchange at folds we apply the theory to a twisted elastic loop which can naturally be formulated as a calculus of variations problem with both isoperimetric constraints and parameter dependent boundary conditions in combination with a perturbation expansion that classifies certain pitchfork bifurcations as sub or super critical the distinguished diagram for the twisted loop provides a classification of the stability properties of all equilibria in particular an unanticipated sensitive dependence of stability properties on the ratio of twisting to bending stiffness is revealed

fully tensorial nodal and modal shape functions for triangles and tetrahedra this paper presents nodal and modal shape functions for triangle and tetrahedron finite elements the functions are constructed based on the fully tensorial expansions of one dimensional polynomials expressed in barycentric co ordinates the nodal functions obtained from the application of the tensorial procedure are the standard h lagrange shape functions presented in the literature the modal shape functions use jacobi polynomials and have a natural global c0 inter element continuity an efficient gauss jacobi numerical integration procedure is also presented to decrease the number of points for the consistent integration of the element matrices an example illustrates the approximation properties of the modal functions copyright 2005 john wiley sons ltd

stability and folds it is known that when one branch of a simple fold in a bifurcation diagram represents linearly stable solutions the other branch represents unstable solutions the theory developed here can predict instability of some branches close to folds without knowledge of stability of the adjacent branch provided that the underlying problem has a variational structure first one particular bifurcation diagram is identified as playing a special role the relevant diagram being specified by the choice of functional plotted as ordinate the results are then stated in terms of the shape of the solution branch in this distinguished bifurcation diagram in many problems arising in elasticity the preferred bifurcation diagram is the loaddisplacement graph the theory is particularly useful in applications where a solution branch has a succession of folds

conditional edge fault tolerant edge bipancyclicity of hypercubes the hypercube has been one of the most popular interconnection networks for parallel computer communication systems in this paper we assume that each node is incident with at least two fault free links under this assumption we show that every fault free edge lies on a fault free cycle of every even length from 6 to 2 n inclusive even if it has up to 2n 5 link faults the result is optimal with respect to the number of link faults tolerated

conditional diagnosability of arrangement graphs under the pmc model abstract processor fault diagnosis has played an important role in measuring the reliability of a multiprocessor system and the diagnosabilities of many well known multiprocessor systems have been investigated the conditional diagnosability has been widely accepted as a measure of diagnosability by assuming an additional condition that any fault set can t contain all the neighbors of any node in a multiprocessor system this paper considers the conditional diagnosability of an n k arrangement graph a n k a flexible interconnection network model for multiprocessor systems under the classical pmc diagnostic model and determines that the conditional diagnosability of a n k k 2 n k 2 is 4 k 4 n k 3 which is about four times its traditional diagnosability

singular hierarchical scalar basis functions for triangular cells a new family of hierarchical basis functions is proposed for triangular cells these functions incorporate singular behavior to model fields with corner singularities the functions are of the additive kind and combine a traditional polynomial complete representation on triangles with additional singular terms that incorporate general exponents that may be adjusted for the specific wedge angle of interest the condition numbers arising from the use of these functions is investigated

fault diagnosability of arrangement graphs the growing size of the multiprocessor system increases its vulnerability to component failures it is crucial to locate and to replace the faulty processors to maintain a system s high reliability the fault diagnosis is the process of identifying faulty processors in a system through testing in this paper we show that the largest connected component of the survival graph contains almost all of the remaining vertices in the n k arrangement graph a n k when the number of moved faulty vertices is up to twice or three times the traditional connectivity using this fault resiliency we establish the conditional diagnosability of a n k under the comparison model and prove that the conditional diagnosability of a n k is 3k 2 n k 3 for k 4 n k 2 and the conditional diagnosability of a n n 1 is 3n 7 for n 5

fault hamiltonicity and fault hamiltonian connectivity of the arrangement graphs the arrangement graph a sub n k is a generalization of the star graph there are some results concerning fault hamiltonicity and fault hamiltonian connectivity of the arrangement graph however these results are restricted in some particular cases and thus are less completed we improve these results and obtain a stronger and simpler statement let n k spl ges 2 and f spl sube v a sub n k spl cup e a sub n k we prove that a sub n k f is hamiltonian if f spl les k n k 2 and a sub n k f is hamiltonian connected if f spl les k n k 3 these results are optimal

hamiltonian cycle embedding for fault tolerance in balanced hypercubes abstract the balanced hypercube bh n defined by wu and huang is a variant of the hypercube network yang proposed that fault tolerance of balanced hypercube bh n is an important issue in parallel computing which needs further study yang 2010 24 in this paper we prove that there exists a fault free hamiltonian path between any two adjacent vertices in bh n with 2 n 2 faulty edges as a corollary we derive that for any fault free edge e there exists a fault free hamiltonian cycle containing e in bh n with 2 n 2 faulty edges which is optimal in the sense of the number of faulty edges

embedding of meshes in mobius cubes the hypercube is one of the most popular interconnection networks since it has simple structure and is easy to implement mobius cubes form a class of hypercube variants that give better performance with the same number of edges and vertices in this paper we consider embedding of meshes in mobius cubes the main results obtained in this paper are 1 for n 1 there exists a 2x2 n 1 mesh that can be embedded in the n dimensional mobius cube with dilation 1 and expansion 1 2 for n 4 there exists a 4x2 n 2 mesh that can be embedded in the n dimensional mobius cube with dilation 2 and expansion 1 3 for n 4 there are two disjoint 4x2 n 3 meshes that can be embedded in the 0 type n dimensional mobius cube with dilation 1 4 for n 4 there are two disjoint 4x2 n 3 meshes that can be embedded in the 1 type n dimensional mobius cube with dilation 2 results of 1 and 3 are optimal in the sense that the dilations of the embeddings are 1

an eigen based high order expansion basis for structured spectral elements we present an eigen based high order expansion basis for the spectral element approach with structured elements the new basis exhibits a numerical efficiency significantly superior in terms of the conditioning of coefficient matrices and the number of iterations to convergence for the conjugate gradient solver to the commonly used jacobi polynomial based expansion basis this basis results in extremely sparse mass matrices and it is very amenable to the diagonal preconditioning ample numerical experiments demonstrate that with the new basis and a simple diagonal preconditioner the number of conjugate gradient iterations to convergence has essentially no dependence or only a very weak dependence on the element order the expansion bases are constructed by a tensor product of a set of special one dimensional 1d basis functions the 1d interior modes are constructed such that the interior mass and stiffness matrices are simultaneously diagonal and have identical condition numbers the 1d vertex modes are constructed to be orthogonal to all the interior modes the performance of the new basis has been investigated and compared with other expansion bases

hierarchical finite element bases for triangular and tetrahedral elements we describe a hierarchical basis for the p version of the finite element method in two and three dimensions the corresponding stiffness matrices are shown to have good sparsity properties and better conditioning than those generated from existing hierarchical bases

looping probabilities of elastic chains a path integral approach we consider an elastic chain at thermodynamic equilibrium with a heat bath and derive an approximation to the probability density function or pdf governing the relative location and orientation of the two ends of the chain our motivation is to exploit continuum mechanics models for the computation of dna looping probabilities but here we focus on explaining the novel analytical aspects in the derivation of our approximation formula accordingly and for simplicity the current presentation is limited to the illustrative case of planar configurations a path integral formalism is adopted and in the standard way the first approximation to the looping pdf is obtained from a minimal energy configuration satisfying prescribed end conditions then we compute an additional factor in the pdf which encompasses the contributions of quadratic fluctuations about the minimum energy configuration along with a simultaneous evaluation of the partition function the original aspects of our analysis are twofold first the quadratic lagrangian describing the fluctuations has cross terms that are linear in first derivatives this seemingly small deviation from the structure of standard path integral examples complicates the necessary analysis significantly nevertheless after a nonlinear change of variable of riccati type we show that the correction factor to the pdf can still be evaluated in terms of the solution to an initial value problem for the linear system of jacobi ordinary differential equations associated with the second variation the second novel aspect of our analysis is that we show that the hamiltonian form of these linear jacobi equations still provides the appropriate correction term in the inextensible unshearable limit that is commonly adopted in polymer physics models of e g dna prior analyses of the inextensible case have had to introduce nonlinear and nonlocal integral constraints to express conditions on the relative displacement of the end points our approximation formula for the looping pdf is of quite general applicability as in contrast to most prior approaches no assumption is made of either uniformity of the elastic chain nor of a straight intrinsic shape if the chain is uniform the jacobi system evaluated at certain minimum energy configurations has constant coefficients in such cases our approximate pdf can be evaluated in an entirely explicit closed form we illustrate our analysis with a planar example of this type and compute an approximate probability of cyclization i e of forming a closed loop from a uniform elastic chain whose intrinsic shape is an open circular arc

conditional matching preclusion for the arrangement graphs the matching preclusion number of a graph is the minimum number of edges whose deletion results in a graph that has neither perfect matchings nor almost perfect matchings for many interconnection networks the optimal sets are precisely those induced by a single vertex recently the conditional matching preclusion number of a graph was introduced to look for obstruction sets beyond those induced by a single vertex it is defined to be the minimum number of edges whose deletion results in a graph with no isolated vertices that has neither perfect matchings nor almost perfect matchings in this paper we find this number and classify all optimal sets for the arrangement graphs one of the most popular interconnection networks

geodesic pancyclicity of twisted cubes the hypercube is one of the most popular interconnection networks since it has simple structure and is easy to implement an n dimensional twisted cube tq n is an important variation of the hypercube q n and preserves many of its desirable properties the problem of embedding linear arrays and cycles into a host graph has attracted substantial attention in recent years the geodesic cycle embedding problem is for any two distinct vertices to find all the possible lengths of cycles that include a shortest path joining them in this paper we prove that tq n is geodesic 2 pancyclic for each odd integer n 3 this result implies that tq n is edge pancyclic for each odd integer n 3 moreover tq nxk 2 is also demonstrated to be geodesic 4 pancyclic

two level domain decomposition preconditioning for the p version finite element method in three dimensions this paper presents a flexible approach to domain decomposition preconditioning for problems expressed in terms of local stiffness matrices of subdomains evaluation of the preconditioner requires fully parallelizable local computations and the solution of a global auxiliary problem with few variables per subdomain convergence factors can be bounded using properties of the local stiffness matrices only the method is applied to the p version finite element method for three dimensional elasticity we treat each element as a subdomain and compute explicit convergence bounds

bipanconnectivity of faulty hypercubes with minimum degree abstract in this paper we consider the conditionally faulty hypercube q n with n 2 where each vertex of q n is incident with at least m fault free edges 2 m n 1 we shall generalize the limitation m 2 in all previous results of edge bipancyclicity we also propose a new edge fault tolerant bipanconnectivity called k edge fault tolerant bipanconnectivity a bipartite graph is k edge fault tolerant bipanconnected if g f remains bipanconnected for any f e g with f k for every integer m under the same hypothesis we show that q n is n 2 edge fault tolerant edge bipancyclic and bipanconnected and the results are optimal with respect to the number of edge faults tolerated this not only improves some known results on edge bipancyclicity and bipanconnectivity of hypercubes but also simplifies the proof

longest fault free paths in star graphs with edge faults in this paper we aim to embed longest fault free paths in an n dimensional star graph with edge faults when n spl ges 6 and there are n 3 edge faults a longest fault free path can be embedded between two arbitrary distinct vertices exclusive of two exceptions in which at most two vertices are excluded since the star graph is regular of degree n 1 n 3 edge faults is maximal in the worst case when n spl ges 6 and there are n 4 edge faults a longest fault free path can be embedded between two arbitrary distinct vertices the situation of n 6 is also discussed

edge fault tolerant bipanconnectivity of hypercubes this paper shows that for any two distinct vertices u and v with distance d in the hypercube q n n 3 with at most 2n 5 faulty edges and each vertex incident with least two fault free edges there exist fault free uv paths of length in q n for every with d 4 2 n 1 and d 0 mod2 this result improves some known results on edge fault bipanconnectivity of hypercubes the proof is based on the recursive structure of q n

fault tolerant strong menger edge connectivity and 3 extra edge connectivity of balanced hypercubes abstract a connected graph g is called strongly menger edge connected if for any two distinct vertices x y of g there are min deg g x deg g y edge disjoint paths between x and y the g g 0 extra edge connectivity of the connected graph g denoted by g g is the minimal cardinality of a set of edges of g if exists whose deletion disconnects g and each remaining component contains more than g vertices in this paper we show that the n dimensional balanced hypercube b h n which is a variant of hypercube q n is still strongly menger edge connected even when there are 2 n 4 faulty vertices resp 2 n 2 faulty edges for n 2 moreover under the restricted condition that each vertex has at least two fault free edges we show that b h n is still strongly menger edge connected even when there are 6 n 8 faulty edges for n 2 these results are all optimal with respect to the maximum number of tolerated edge faults furthermore we showed that the 3 extra edge connectivity of b h n is 8 n 8 for n 2

edge fault tolerant pancyclicity of arrangement graphs the arrangement graph a n k is a well known interconnection network day and tripathi proved that a n k is pancyclic for n k 2 in this paper we improve this result and we demonstrate that a n k is also pancyclic even if it has no more than k n k 2 faulty edges for n k 2 our result is optimal concerning the edge fault tolerance

fault free longest paths in star networks with conditional link faults the star network which belongs to the class of cayley graphs is one of the most versatile interconnection networks for parallel and distributed computing in this paper adopting the conditional fault model in which each node is assumed to be incident with two or more fault free links we show that an n dimensional star network can tolerate up to 2n 7 link faults and be strongly fault free hamiltonian laceable where n 4 in other words we can embed a fault free linear array of length n 1 n 2 in an n dimensional star network with up to 2n 7 link faults if the two end nodes belong to different partite sets the same partite set the result is optimal with respect to the number of link faults tolerated it is already known that under the random fault model an n dimensional star network can tolerate up to n 3 faulty links and be strongly hamiltonian laceable for n 3

embedding meshes into twisted cubes the n dimensional twisted cube tn n is a variation of the hypercube in this paper we study embedding of meshes into tn n we prove three major results in this paper 1 for any integer n 1 a 2x2 n 1 mesh can be embedded into tn n with dilation 1 and expansion 1 2 for any integer n 4 an mxk m 3 k 3 mesh cannot be embedded into tn n with dilation 1 3 for any integer n 4 two node disjoint 4x2 n 3 meshes can be embedded into tn n with dilation 2 and expansion 1

an a posteriori estimator of eigenvalue eigenvector error for penalty type discontinuous galerkin methods we provide an abstract framework for analyzing discretization error for eigenvalue problems discretized by discontinuous galerkin methods such as the local discontinuous galerkin method and symmetric interior penalty discontinuous galerkin method the analysis applies to clusters of eigenvalues that may include degenerate eigenvalues we use asymptotic perturbation theory for linear operators to analyze the dependence of eigenvalues and eigenspaces on the penalty parameter we first formulate the dg method in the framework of quadratic forms and construct a companion infinite dimensional eigenvalue problem with the use of the companion problem the eigenvalue vector error is estimated as a sum of two components the first component can be viewed as a non conformity error that we argue can be neglected in practical estimates by properly choosing the penalty parameter the second component is estimated a posteriori using auxiliary subspace techniques and this constitutes the practical estimate

the problem of selecting the shape functions for a p type finite element abstract the paper addresses the question of the optimal selection of the shape functions for p type finite elements and discusses the effectivity of the conjugate gradient and multilevel iteration method for solving the corresponding linear system the selection of the shape functions is of major importance for the performance of the solver based on iterative methods neither the theory nor practice of the optimal selection of the shape functions is available yet we have seen that the condensation approach which has obvious advantages from the point of parallel computations is a very effective tool for keeping the condition number under the control and is especially advantageous for the conjugate gradient method

on the surface area of the n k star graph we present an explicit formula for the surface area of the n k star graph i e the number of nodes at a certain distance from the identity node in the graph by identifying the unique cycle structures associated with the nodes in the graph deriving a distance expression in terms of such structures between the identity node of the graph and any other node and enumerating those cycle structures satisfying the distance restriction the above surface area derivation process can also be applied to some of the other node symmetric interconnection structures defined on the symmetric group when the aforementioned distance expression is available

isoperimetric conjugate points with application to the stability of dna minicircles a conjugate point test determining an index of the constrained second variation in one dimensional isoperimetric calculus of variations problems is described the test is then implemented numerically to determine stability properties of equilibria within a continuum mechanics model of dna minicircles

conditional matching preclusion for hypercube like interconnection networks the conditional matching preclusion number of a graph with n vertices is the minimum number of edges whose deletion results in a graph without an isolated vertex that does not have a perfect matching if n is even or an almost perfect matching if n is odd we develop some general properties on conditional matching preclusion and then analyze the conditional matching preclusion numbers for some hl graphs hypercube like interconnection networks

weak vertex pancyclicity of n k star graphs the n k star graph s n k for short is an attractive alternative to the hypercube and also a generalized version of the n star it is isomorphic to the n star n complete graph if k n 1 k 1 jwo et al have already demonstrated in 1991 that an n star contains a cycle of every even length from 6 to n this work shows that every vertex in an s n k lies on a cycle of length l for every email protected email protected n n k when email protected email protected n 4 and n 6 additionally for email protected email protected n 2 each vertex in an s n k is contained in a cycle of length ranged from 6 to n n k moreover each constructed cycle of an available length in an s n k can contain a desired 1 edge

geodesic pancyclicity and fault tolerant panconnectivity of augmented cubes abstract choudum and sunitha s a choudum v sunitha augmented cubes networks 40 2002 71 84 proposed the class of augmented cubes as a variation of hypercubes and showed that augmented cubes possess several embedding properties that the hypercubes and other variations do not possess recently hsu et al h c hsu p l lai c h tsai geodesic pancyclicity and balanced pancyclicity of augmented cubes information processing letters 101 2007 227 232 showed that the n dimensional augmented cube aq n n 2 is weakly geodesic pancyclic i e for each pair of vertices u v aq n and for each integer l satisfying max 2 d u v 3 l 2 n where d u v denotes the distance between u and v in aq n there is a cycle of length l that contains a u v geodesic in this paper we obtain a stronger result by proving that aq n n 2 is indeed geodesic pancyclic i e for each pair of vertices u v aq n and for each integer l satisfying max 2 d u v 3 l 2 n every u v geodesic lies on a cycle of length l to achieve the result we first show that aq n f n 3 remains panconnected and thus is also edge pancyclic if f aq n is any faulty vertex the result of fault tolerant panconnectivity is the best possible in the sense that the number of faulty vertices in aq n n 3 cannot be increased

assessment of finite and spectral element shape functions for efficient iterative simulations of interior acoustics several shape function families currently used in the spectral element and the finite element method fem are reviewed widely known shape functions such as the conventional lagrange functions various p fem shapes and recent developments in the area of spectral methods are compared especially shape functions derived from bernstein polynomials are discussed due to their ease of formulation for almost any geometric entity their applicability and efficiency for acoustic simulations are assessed in particular the efficiency is measured in terms of performance of current krylov solvers

higher degree immersed finite element spaces constructed according to the actual interface abstract we discuss the construction of higher degree immersed finite element ife spaces that can be used to solve two dimensional second order elliptic interface problems having general interfaces without requiring the mesh to be aligned with the material interfaces the optimal approximation capability of the proposed piecewise p th degree ife spaces are demonstrated by numerical experiments with interpolations numerical solutions to interface problems generated from a partially penalized method based on the proposed higher order ife spaces also suggest optimal convergence in both the l 2 and h 1 norms under mesh refinement

numerical solution of a bending torsion model for elastic rods aiming at simulating elastic rods we discretize a rod model based on a general theory of hyperelasticity for inextensible and unshearable rods after reviewing this model and discussing topological effects of periodic rods we prove convergence of the discretized functionals and stability of a corresponding discrete flow our experiments numerically confirm thresholds e g for michell s instability and indicate a complex energy landscape in particular in the presence of impermeability

strong matching preclusion the matching preclusion problem introduced by brigham et al r c brigham f harary e c violin and j yellen perfect matching preclusion congressus numerantium 174 2005 185 192 studies how to effectively make a graph have neither perfect matchings nor almost perfect matchings by deleting as small a number of edges as possible extending this concept we consider a more general matching preclusion problem called the strong matching preclusion in which deletion of vertices is additionally permitted we establish the strong matching preclusion number and all possible minimum strong matching preclusion sets for various classes of graphs

higher order triangular basis functions and solution performance of the cg method new sets of hierarchical higher order basis functions in fem for triangle elements are constructed using a systematic orthogonalization approach that yield better conditioning and investigated with different preconditioners jacobi icc ilu and sainv presented theoretical and numerical results indicate that certain preconditioners are insensitive to the condition number of the basis functions advantageous properties of basis functions in relation to preconditioners are viewed from the perspective of similarity and congruence transforms of the basis functions this provides an alternative view for a systematic construction of the basis functions that couples with a specific preconditioner to optimize the solution performance

a self stabilizing 23 approximation algorithm for the maximum matching problem the matching problem asks for a large set of disjoint edges in a graph it is a problem that has received considerable attention in both the sequential and the self stabilizing literature previous work has resulted in self stabilizing algorithms for computing a maximal 12 approximation matching in a general graph as well as computing a 23 approximation on more specific graph types in this paper we present the first self stabilizing algorithm for finding a 23 approximation to the maximum matching problem in a general graph we show that our new algorithm when run under a distributed adversarial daemon stabilizes after at most o n2 rounds however it might still use an exponential number of time steps

a posteriori error estimates for fourth order elliptic problems we extend the dichotomy principle of babuska and yu math numerica sinica 13 1991 89 math numerica sinica 13 1991 307 and adjerid et al math mod meth appl s 9 1999 261 siam j sci comput 21 1999 728 for estimating the finite element discretization error to fourth order elliptic problems we show how to construct a posteriori error estimates from jumps of the third partial derivatives of the finite element solution when the finite element space consists of piecewise polynomials of odd degree and from the interior residuals for even degree approximations on meshes of square elements these estimates are shown to converge to the true error under mesh refinement we also show that these a posteriori error estimates are asymptotically correct for more general finite element spaces computational results from several examples show that the error estimates are accurate and efficient on rectangular meshes

conjugate points revisited and neumann neumann problems the theory of conjugate points in the calculus of variations is reconsidered with a perspective emphasizing the connection to finite dimensional optimization the object of central importance is the spectrum of the second variation operator analogous to the eigenvalues of the hessian matrix in finite dimensions with a few basic properties of this spectrum one can gain a new perspective on the classic result that stability requires the lack of conjugate points furthermore we show how the spectral perspective allows the extension of the conjugate point approach to variants of the classic problems in the literature such as problems with neumann neumann boundary conditions

embedding binary trees into crossed cubes the recently introduced interconnection network crossed cube has attracted much attention in the parallel processing area due to its many attractive features like the ordinary hypercube the n dimensional crossed cube is a regular graph with 2 sup n vertices and n2 sup n 1 edges the diameter of the crossed cube is approximately half that of the ordinary hypercube these advantages of the crossed cube motivated the study of how well it can simulate other networks such as the complete binary tree we show that the 2 sup n 1 node complete binary tree can be embedded into the n dimensional crossed cube with dilation 1

on embedding rings into a star related network abstract it is shown that in the star graph it is always possible to form a hamiltonian path between two nodes as long as the distance between them is odd this result leads to the proof of hamiltonicity for the clustered star graph the results can readily be used in optimal embedding of a linear array of processors or a ring in the star graph the embedding problem is also solved when one or more processors are faulty in the network the length of the linear array and the ring in this case is shown to be n m where m is the dimension of the smallest star graph which contains all the faulty processors

embedding of cycles in arrangement graphs arrangement graphs have been proposed as an attractive interconnection topology for large multiprocessor systems the authors study these graphs by proving the existence of hamiltonian cycles in any arrangement graph they also prove that an arrangement graph contains cycles of all lengths ranging between 3 and the size of the graph they show that an arrangement graph can be decomposed into node disjoint cycles in many different ways

cycle embedding in star graphs with edge faults the star graph is one of the famous interconnection networks edge fault tolerance is an important issue for networks and the cycle embedding problem is widely discussed in many researches in this paper we show that the cycles of even lengths from 6 to n can be embedded into the n dimensional star graph when the number of edge fault in the graph does not exceed n 3 since the graph is bipartite and n 1 regular our result is optimal

brief paper quantized consensus in hamiltonian graphs the main contribution of this paper is an algorithm to solve an extended version of the quantized consensus problem over networks represented by hamiltonian graphs i e graphs containing a hamiltonian cycle which we assume to be known in advance given a network of agents we assume that a certain number of tokens should be assigned to the agents so that the total number of tokens weighted by their sizes is the same for all the agents the algorithm is proved to converge almost surely to a finite set containing the optimal solution a worst case study of the expected convergence time is carried out thus proving the efficiency of the algorithm with respect to other solutions recently presented in the literature moreover the algorithm has a decentralized stop criterion once the convergence set is reached

embedding longest fault free paths onto star graphs with more vertex faults the n dimensional star graph sn belongs to a class of bipartite graphs and it is recognized as an attractive alternative to the hypercube since s1 s2 and s3 have trivial structures we focus our attention on sn with n 4 in this paper let f sn be the set of vertex faults previously it was shown that when f sn n 5 sn with n 6 can embed a longest fault free path of length at least n 2 f sn 1 respectively n 2 f sn 2 between two arbitrary vertices in different partite sets respectively the same partite set longest fault free paths in star graphs with vertex faults theoretical computer science 262 2001 215 227 in this paper we improve the above result by tolerating more faults f sn n 3 to embed a longest fault free path between two arbitrary vertices in sn n 4

conditional matching preclusion sets abstract the matching preclusion number of a graph is the minimum number of edges whose deletion results in a graph that has neither perfect matchings nor almost perfect matchings for many interconnection networks the optimal sets are precisely those induced by a single vertex in this paper we look for obstruction sets beyond these sets we introduce the conditional matching preclusion number of a graph it is the minimum number of edges whose deletion results in a graph with no isolated vertices that has neither perfect matchings nor almost perfect matchings we find this number and classify all optimal sets for several basic classes of graphs

the super connectivity of the pancake graphs and the super laceability of the star graphs a k container c u v of a graph g is a set of k disjoint paths joining u to v a k container c u v of g is a k container if it contains all the vertices of g a graph g is k connected if there exists a k container between any two distinct vertices let g be the connectivity of g a graph g is super connected if g is i connected for all 1 i g a bipartite graph g is k laceable if there exists a k container between any two vertices from different parts of g a bipartite graph g is super laceable if g is i laceable for all 1 i g in this paper we prove that the n dimensional pancake graph pn is super connected if and only if n 3 and the n dimensional star graph sn is super laceable if and only if n 3