some remarks on quasiconvexity and rank one convexity we explore some necessary conditions for quasiconvexity in an attempt to show that rank one convexity does not imply quasiconvexity when the target space for deformations is two dimensional an interesting construction is presented showing how rank one directions may fit with each other making the task harder than in higher dimensions

displacement rank of the drazin inverse in this paper we study the displacement rank of the drazin inverse both sylvester displacement and the generalized displacement are discussed we present upper bounds for the ranks of the displacements of the drazin inverse the general results are applied to the group inverse of a structured matrix such as close to toeplitz generalized cauchy toeplitz plus hankel and bezoutians

recurrent neural network for computing the drazin inverse this paper presents a recurrent neural network rnn for computing the drazin inverse of a real matrix in real time this recurrent neural network rnn is composed of n independent parts subnetworks where n is the order of the input matrix these subnetworks can operate concurrently so parallel and distributed processing can be achieved in this way the computational advantages over the existing sequential algorithms can be attained in real time applications the rnn defined in this paper is convenient for an implementation in an electronic circuit the number of neurons in the neural network is the same as the number of elements in the output matrix which represents the drazin inverse the difference between the proposed rnn and the existing ones for the drazin inverse computation lies in their network architecture and dynamics the conditions that ensure the stability of the defined rnn as well as its convergence toward the drazin inverse are considered in addition illustrative examples and examples of application to the practical engineering problems are discussed to show the efficacy of the proposed neural network

on the theory of relaxation in nonlinear elasticity with constraints on the determinant we consider vectorial variational problems in nonlinear elasticity of the form i u int w du rm d x where w is continuous on matrices with a positive determinant and diverges to infinity along sequences of matrices whose determinant is positive and tends to zero we show that under suitable growth assumptions the functional int w rm qc du rm d x is an upper bound on the relaxation of i and coincides with the relaxation if the quasiconvex envelope wqc of w is polyconvex and has p growth from below with p geqq n this includes several physically relevant examples we also show how a constraint of incompressibility can be incorporated in our results

a condition for the holder regularity of local minimizers of a nonlinear elastic energy in two dimensions we prove the local holder continuity of strong local minimizers of the stored energy functional e u int omega lambda nabla u 2 h rm det nabla u rm d x subject to a condition of positive twist the latter turns out to be equivalent to requiring that u maps circles to suitably star shaped sets the convex function h s grows logarithmically as s to 0 linearly as s to infty and satisfies h s infty if s leqq 0 these properties encode a constitutive condition which ensures that material does not interpenetrate during a deformation and is one of the principal obstacles to proving the regularity of local or global minimizers the main innovation is to prove that if a local minimizer has positive twist a e on a ball then an euler lagrange type inequality holds and a caccioppoli inequality can be derived from it the claimed holder continuity then follows by adapting some well known elliptic regularity theory we also demonstrate the regularizing effect that the term int omega h rm det nabla u rm d x can have by analysing the regularity of local minimizers in the class of shear maps in this setting a more easily verifiable condition than that of positive twist is imposed with the result that local minimizers are holder continuous

strong matching preclusion for n dimensional torus networks the strong matching preclusion number of a graph is the minimum number of edges and or vertices whose deletion results in the remaining graph that has neither perfect matchings nor almost perfect matchings in 14 wang et al proved that c k c k is super strongly matched where k 3 is odd in this paper we show that c k 1 c k 2 c k n is super strongly matched where n 3 is an integer and k i 3 is an odd integer for each i 1 n our studies generalize the results of wang et al 14

dirac harmonic equations for differential forms abstract in this paper we introduce the dirac harmonic equation for differential forms and prove some basic norm inequalities including the caccioppoli type inequality poincare type inequality and the weak reverse holder inequality for the solutions of this kind of differential equations

strong matching preclusion of n k star graphs the strong matching preclusion number of a graph is the minimum number of vertices and edges whose deletion results in a graph that has neither perfect matchings nor almost perfect matchings this is an extension of the matching preclusion problem that was introduced by park and ihm the generalized n k star graph was introduced to address scaling issues of the star graph and it has many desirable properties in this paper the goal is to find the strong matching preclusion number of n k star graphs and to categorize all optimal strong matching preclusion sets of these graphs since bipartite graphs generally have low strong matching preclusion numbers we assume that k n 2

invertibility and weak continuity of the determinant for the modelling of cavitation and fracture in nonlinear elasticity in this paper we present and analyze a variational model in nonlinear elasticity that allows for cavitation and fracture the main idea in unifying the theories of cavitation and fracture is to regard both cavities and cracks as phenomena of the creation of a new surface accordingly we define a functional that measures the area of the created surface this functional has relationships with the theory of cartesian currents we show that the boundedness of that functional implies sequential weak continuity of the determinant of the deformation gradient and that the weak limit of one to one almost everywhere deformations is also one to one almost everywhere we then use these results to obtain the existence of minimizers of variational models that incorporate elastic energy and this created surface energy taking into account orientation preserving and non interpenetration conditions

local and global norm comparison theorems for solutions to the nonhomogeneous a harmonic equation abstract we establish local and global norm inequalities for solutions of the nonhomogeneous a harmonic equation a x g d u h d v for differential forms as applications of these inequalities we prove the sobolev poincare type imbedding theorems and obtain l p estimates for the gradient operator and the homotopy operator t from the banach space l s d l to the sobolev space w 1 s d l 1 l 1 2 n these results can be used to study both qualitative and quantitative properties of solutions of the a harmonic equations and the related differential systems

quasiconvex elastodynamics weak strong uniqueness for measure valued solutions a weak strong uniqueness result is proved for measure valued solutions to the system of conservation laws arising in elastodynamics the main novelty brought forward by the present work is that the underlying stored energy function of the material is assumed strongly quasiconvex the proof employs tools from the calculus of variations to establish general convexity type bounds on quasiconvex functions and recasts them in order to adapt the relative entropy method to quasiconvex elastodynamics

successive matrix squaring algorithm for computing the drazin inverse1this project is supported by the national nature science foundation of china doctoral point foundation of china and youth science foundation of universities in shanghai of china 1 this paper derives a successive matrix squaring sms algorithm to approximate the drazin inverse which can be expressed in the form of successive squaring of a composite matrix t given an n by n matrix a the study shows that the drazin inverse of a can be computed in parallel time ranging from o logn to o log 2n provided that there are enough processors to support matrix multiplication in time o logn the sms algorithm is generalized to higher order schemes where the composite matrix is repeatedly raised to an integer power l 2 this form of expression leads to a simplified notation compared to that of earlier methods we argue that there is no obvious advantage in choosing l other than 2 our derived error bound for the approximation of a d is new

integral estimates for null lagrangians sobolev spaces of differential forms are studied lp projections onto exact forms are introduced as a tool to obtain integral estimates for null lagrangians new results on compensated compactness are given and mean coercive variational integrals are found existence of minima of certain mean coercive functionals is established

semicontinuity problems in the calculus of variations soit f r 3 r une fonction deux fois continument differentiable et pour u w 1 1 a b f u a b a b f x u x u x dx si f r n r m r nm r satisfait 1 f est mesurable en x continue en cs et 2 0 f x s a x c s p p ou p 1 a est une fonction localement sommable non negative et c une constante non negative alors la fonctionnelle f u a b est sequentiellement faiblement semi continue inferieurement sur w 1 p r m si et seulement si f x s est quasi convexe pour chaque s et presque chaque x

quasiconvexity and relaxation of nonconvex problems in the calculus of variations keywords quasiconvexity relaxation reference caa article 1982 002doi 10 1016 0022 1236 82 90046 5view record in web of science record created on 2008 11 25 modified on 2017 05 12

symbolic computation of drazin inverses by specializations in this paper we show how to reduce the computation of drazin inverses over certain computable fields to the computation of drazin inverses of matrices with rational functions as entries as a consequence we derive a symbolic algorithm to compute the drazin inverse of matrices whose entries are elements of a finite transcendental field extension of a computable field the algorithm is applied to matrices over the field of meromorphic functions in several complex variables on a connected domain and to matrices over the field of laurent formal power series

quasiregular mappings in even dimensions o introduction 1 notation 2 some exterior algebra 3 differential forms in lnm i2 a n 4 differential systems for quasiregular mappings 5 liouville theorem in even dimensions 6 hodge theory in lp r n 7 the beltrami equation in even dimensions 8 the beurling ahlfors operator 9 regularity theorems for quasiregular mappings 10 the caccioppoli type estimate 11 removability theorems for quasiregular mappings 12 some examples appendix the 4 dimensional case

recurrent neural network approach based on the integral representation of the drazin inverse in this letter we present the dynamical equation and corresponding artificial recurrent neural network for computing the drazin inverse for arbitrary square real matrix without any restriction on its eigenvalues conditions that ensure the stability of the defined recurrent neural network as well as its convergence toward the drazin inverse are considered several illustrative examples present the results of computer simulations

w1 p quasiconvexity and variational problems for multiple integrals abstract variational problems for the multiple integral i u g u x dx where r m and u r n are studied a new condition on g called w1 p quasiconvexity is introduced which generalizes in a natural way the quasiconvexity condition of c b morrey it being shown in particular to be necessary for sequential weak lower semicontinuity of i in w 1 p r n and for the existence of minimizers for certain related integrals counterexamples are given concerning the weak continuity properties of jacobians in w 1 p r n p n m an existence theorem for nonlinear elastostatics is proved under optimal growth hypotheses

a quasiregular analogue of a theorem of hardy and littlewood suppose that f is analytic in the unit disk a theorem of hardy and littlewood relates the holder continuity of f over the unit disk to the growth of the derivative we prove here a quasiregular analogue of this result in certain domains in n dimensional space we replace values of the derivatives with a local integral average in the process we generalize a result on the continuity of quasiconformal mappings due to nakki and palka

the representation and approximation for drazin inverse we present a unified representation theorem for drazin inverse specific expression and computational procedures for drazin inverse can be uniformly derived numerical examples are tested and the application to the singular linear equations is also considered

strong matching preclusion for augmented cubes the strong matching preclusion number of a graph is the minimum number of vertices and edges whose deletion results in a graph that has neither perfect matchings nor almost perfect matchings the concept was introduced by park and son in this paper we study the strong matching preclusion problem for the augmented cube graphs as a result we find smp aqn and classify all optimal solutions

strong matching preclusion for non bipartite torus networks the strong matching preclusion number of a graph is the minimum number of vertices and edges whose deletion results in the remaining graph that has neither perfect matchings nor almost perfect matchings the torus network is one of the most popular interconnection network topologies for massively parallel computing systems because of its desirable properties it is known that bipartite torus networks have low strong matching preclusion numbers hu et al 13 proved that non bipartite torus networks with an odd number of vertices have good strong matching preclusion properties to complete the study of strong matching preclusion problem for non bipartite torus networks in this paper we establish the strong matching preclusion number and classify all optimal strong matching preclusion sets for the n dimensional non bipartite torus network with an even number of vertices where n 3

the algorithm for computing the drazin inverses of two variable polynomial matrices we propose a finite algorithm for computing drazin inverse of two variable polynomial matrices based on greville s finite algorithm for computing drazin inverse of a constant matrix also a three dimensional recursive algorithm to do that is deduced examples show that these methods are feasible and the implementation is developed in the symbolic package matlab

quasiconvexity at the boundary positivity of the second variation and elastic stability for one dimensional problems of the calculus of variations there is a well developed theory relating the positivity of the second variation at a critical point i e linearized stability to strong relative minima these results largely due to weierstrass are usually proved by the method of fields of extremals as is described in bolza 1904 and morrey 1966 or by an argument involving a careful use of taylor series as in hestenes 1966 chapter 3 14

a finite algorithm for the drazin inverse of a polynomial matrix based on greville s finite algorithm for drazin inverse of a constant matrix we propose a finite numerical algorithm for the drazin inverse of polynomial matrices we also present a new proof for decell s finite algorithm through greville s finite algorithm

gradient methods for computing the drazin inverse solution the problem of computing the vector a db in the cases when it provides a solution of a singular linear system is reduced to the problem of finding a least squares solution of an appropriate linear system later the presented ideas are extended to arbitrary linear systems as a consequence we present iterative methods for computing the vector a db in general the functionality of the exposed algorithms is based on a specific representation of the drazin inverse solution as well as the properties that we introduce convergence results of the proposed methods are also considered illustrative numerical examples are presented

grobner basis computation of drazin inverses with multivariate rational function entries in this paper we show how to apply grobner bases to compute the drazin inverse of a matrix with multivariate rational functions as entries when the coefficients of the rational functions depend on parameters we give sufficient conditions for the drazin inverse to specialize properly in addition we extend the method to weighted drazin inverses we present an empirical analysis that shows a good timing performance of the method

computation of the lower semicontinuous envelope of integral functionals and non homogeneous microstructures abstract a numerical method is established for computing the weakly lower semicontinuous envelope of integral functionals with non quasiconvex integrands the convergence of the method is proved and it is shown that the method is capable of capturing curved and non homogeneous microstructures numerical examples are given to show the effectiveness of the method for capturing curved and non homogeneous laminated microstructures

strong matching preclusion for torus networks the torus network is one of the most popular interconnection network topologies for massively parallel computing systems strong matching preclusion that additionally permits more destructive vertex faults in a graph is a more extensive form of the original matching preclusion that assumes only edge faults in this paper we establish the strong matching preclusion number and all minimum strong matching preclusion sets for bipartite torus networks and 2 dimensional nonbipartite torus networks

on rank one convex and polyconvex conformal energy functions with slow growth we make some remarks about rank one convex and polyconvex functions on the set of all real n n matrices that vanish on the subset k n consisting of all conformal matrices and grow like a power function at infinity we prove that every non negative rank one convex function that vanishes on k n and grows below a power of degree n 2 must vanish identically in odd dimensions n 3 we prove that every non negative polyconvex function that vanishes on k n must vanish identically if it grows below a power of degree n while in even dimensions such polyconvex functions can exist that also grow like a power of half dimension degree

successive matrix squaring algorithm for computing outer inverses abstract in this paper we derive a successive matrix squaring sms algorithm to approximate an outer generalized inverse with prescribed range and null space of a given matrix a c r m n we generalize the results from the papers l chen e v krishnamurthy i macleod generalized matrix inversion and rank computation by successive matrix powering parallel computing 20 1994 297 311 y wei successive matrix squaring algorithm for computing drazin inverse appl math comput 108 2000 67 75 y wei h wu j wei successive matrix squaring algorithm for parallel computing the weighted generalized inverse a mn appl math comput 116 2000 289 296 and obtain an algorithm for computing various classes of outer generalized inverses of a instead of particular matrices used in these articles we use an appropriate matrix r c s n m s r numerical examples are presented

extensions of faddeev s algorithms to polynomial matrices starting from algorithms introduced in ky m vu an extension of the faddeev s algorithms in proceedings of the ieee multi conference on systems and control on september 3 5th 2008 san antonio tx which are applicable to one variable regular polynomial matrices we introduce two dual extensions of the faddeev s algorithm to one variable rectangular or singular matrices corresponding algorithms for symbolic computing the drazin and the moore penrose inverse are introduced these algorithms are alternative with respect to previous representations of the moore penrose and the drazin inverse of one variable polynomial matrices based on the leverrier faddeev s algorithm complexity analysis is performed algorithms are implemented in the symbolic computational package mathematica and illustrative test examples are presented

null lagrangians weak continuity and variational problems of arbitrary order abstract we consider the problem of minimizing integral functionals of the form i u f x k u x dx where r p u r and k u denotes the set of all partial derivatives of u with orders k the method is based on a characterization of null lagrangians l ku depending only on derivatives of order k applications to elasticity and other theories of mechanics are given

a new computational framework for electro activation in cardiac mechanics abstract this paper presents a novel computational framework for the numerical simulation of the electromechanical response of the myocardium during the cardiac cycle the paper presents the following main novelties 1 two new mixed formulations tailor made for active stress and active strain coupling approaches have been developed and used in conjunction with two different ionic models namely bueno orovio et al 2008 and ten tusscher et al 2004 taking as a reference the mixed formulations introduced by bonet et al 2015 in the context of nonlinear elasticity the proposed formulations include as unknown fields the geometry and the transmembrane potential and possibly a lagrange multiplier enforcing weakly the incompressibility constraint as well as the deformation gradient tensor its cofactor its determinant the gradient of the transmembrane potential and their respective work conjugates the finite element implementation of these formulations is shown in this paper where a static condensation procedure is presented in order to yield an extremely competitive computational approach 2 a comprehensive and rigorous study of different ionic models i e bueno orovio and ten tusscher and electromechanical activation couplings i e active strain and active stress has been carried out 3 an analytical and numerical analysis of the possible loss of ellipticity and polyconvexity of one of the most widely used constitutive models in the context of cardiac mechanics is carried out in this paper putting forward possible polyconvexifications of the existing model 4 in addition an invariant representation of guccione s constitutive model is proposed finally a series of numerical examples are included in order to demonstrate the applicability and robustness of the proposed formulations

additive results for the drazin inverse of block matrices and applications in this paper we consider the drazin inverse of a sum of two matrices and derive additive formulas under conditions weaker than those used in some recent papers on the subject as a corollary we get the main results from the paper of yang and liu h yang x liu the drazin inverse of the sum of two matrices and its applications j comput appl math 235 2011 1412 1417 as an application we give some new representations for the drazin inverse of a block matrix

some properties of the degree for a class of sobolev maps we prove that a map u w loc1 1 m n whose differential and adjoint are integrable with exponents n 1 p n and n n 1 q respectively possesses an integer valued degree with the usual properties here m c 0 1 and n c 1 1 are n dimensional oriented riemannian manifolds with m possibly non empty

one dimensional variational problems whose minimizers do not satisfy the euler lagrange equation in this paper we consider the problem of minimizing i u text int a b text f x u x u x dx 1 1 in the set a of absolutely continuous function u a b satisfying the end conditions u left a right text alpha text quad u left b right text beta text 1 2 where and are given constant in 1 1 a b is a finite interval denotes frac d dx and the integrand f f x u p is assumed to be smooth nonnegative and to satisfy the regularity condition f pp text 0 text 1 3

computation of moore penrose generalized inverses of matrices with meromorphic function entries abstract in this paper given a field with an involutory automorphism we introduce the notion of moore penrose field by requiring that all matrices over the field have moore penrose inverse we prove that only characteristic zero fields can be moore penrose and that the field of rational functions over a moore penrose field is also moore penrose in addition for a matrix with rational functions entries with coefficients in a field k we find sufficient conditions for the elements in k to ensure that the specialization of the moore penrose inverse is the moore penrose inverse of the specialization of the matrix as a consequence we provide a symbolic algorithm that given a matrix whose entries are rational expression over c of finitely many meromorphic functions being invariant by the involutory automorphism computes its moore penrose inverve by replacing the functions by new variables and hence reducing the problem to the case of matrices with complex rational function entries

the computation of drazin inverse and its application in markov chains in this paper we established a representation for projector aa d based on which we developed two methods to compute drazin inverse and discussed the technique for accelerating the convergence at last we applied them to the computation of markov chains which provided unconditioned and practical ways to the analysis of markov chains

generalized poincare inequalities for solutions to the a harmonic equation in certain domains abstract we first prove local versions of the poincare inequality for solutions to the a harmonic equation then as applications of the local results we obtain the global versions of the poincare inequality for solutions to the a harmonic equation in l s 0 averaging domains and l s averaging domains respectively these results can be considered as generalizations of the classical poincare theorem

numerical analysis of oscillations in nonconvex problems we study numerically the pattern of the minimizing sequences of nonconvex problems which do not admit a minimizer

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