on weak type inequalities for dyadic maximal functions we obtain sharp estimates for the localized distribution function of the dyadic maximal function m d given the local l1 norms of and of g where g is a convex increasing function such that g x x as x using this we obtain sharp refined weak type estimates for the dyadic maximal operator

dyadic like maximal operators on integrable functions and bellman functions related to kolmogorov s inequality for each q 1 we precisely evaluate the main bellman functions associated with the behavior of dyadic maximal operators on n on integrable functions actually we do that in the more general setting of tree like maximal operators these are related to and refine the corresponding kolmogorov inequality which we show is actually sharp for this we use the effective linearization introduced by the first author in 2005 for such maximal operators on an adequate set of functions

discontinuous galerkin time discretization in elastoplasticity motivation numerical algorithms and applications discontinuous galerkin discretizations promise to become a very flexible tool in hp adaptive space time discretizations this is very attractive for moving interphase problems such as the free boundary between the elastic and plastic phase in elastoplastic time evolution the mathematical model of which involves variational inequalities and so the distributional time derivative is not obviously generalized to discontinuous test functions this paper motivates and introduces a discontinuous galerkin dg time discretization solution algorithms and examples are established which support feasibility and accuracy of the proposed schemes dg 0 and dg 1 the methods are compared with a backward euler and crank nicholson scheme 2002 published by elsevier science b v

split group codes we construct a class of codes of length n such that the minimum distance d outside of a certain subcode is up to a constant factor bounded below by the square root of n a well known property of quadratic residue codes the construction using the group algebra of an abelian group and a special partition or splitting of the group yields quadratic residue codes duadic codes and their generalizations as special cases we show that most of the special properties of these codes have analogues for split group codes and present examples of new classes of codes obtained by this construction

adaptive numerical analysis in primal elastoplasticity with hardening the quasi static viscoplastic resp elastoplastic evolution problem with isotropic or kinematic hardening is considered with emphasis on optimal convergence and adapted mesh refining in the spatial discretization within one time step of an implicit time discretization the finite element method leads to a minimisation problem for non smooth convex functions on discrete subspaces for piecewise constant resp affine ansatz functions the stress resp displacement approximations are experimentally and theoretically shown to converge linearly an a posteriori error estimate then justifies an automatic adaptive mesh refining algorithm numerical examples support the superiority of the adapted mesh

the distribution function inequality and products of toeplitz operators and hankel operators abstract in this paper we study hankel operators and toeplitz operators through a distribution function inequality on the lusin area integral function and the littlewood paley theory a sufficient condition and a necessary condition are obtained for the boundedness of the product of two hankel operators they lead to a way to approach sarason s conjecture on products of toeplitz operators and shed light on the compactness of the product of hankel operators an elementary necessary and sufficient condition for the product of two toeplitz operators to be a compact perturbation of a toeplitz operator is obtained moreover a necessary condition is given for the product of hankel operators to be in the commutator ideal of the algebra generated by the toeplitz operators with symbols in a sarason algebra

duadic codes a new family of binary cyclic n n 1 2 and n n 1 2 codes are introduced which include quadratic residue qr codes when n is prime these codes are defined in terms of their idempotent generators and they exist for all odd n p 1 a 1 p 2 a 2 cdots p r a r where each p i is a prime equiv pm 1 pmod 8 dual codes are identified the minimum odd weight of a duadic n n 1 2 code satisfies a square root bound when equality holds in the sharper form of this bound vectors of minimum weight hold a projective plane the unique projective plane of order 8 is held by the minimum weight vectors in two inequivalent 73 37 9 duadic codes all duadic codes of length less than 127 are identified and the minimum weights of their extensions are given one of the duadic codes of length 113 has greater minimum weight than the qr code of that length

reliable and efficient equilibrated a posteriori finite element error control in elastoplasticity and elastoviscoplasticity with hardening this paper establishes the reliability and efficiency of equilibrated a posteriori estimates for l 2 stress error control of conforming displacement finite element approximations of incremental plasticity and viscoplasticity with hardening explicit expressions for upper bounds of the reliability constant that enters the guaranteed upper error bound illustrate its crucial dependence on the hardening material constants numerical experiments show that adaptive finite element solutions with marking strategy based on the max refinement rule and local equilibrated error estimators lead to optimal empirical convergence rates 2005 elsevier b v all rights reserved

the uncertainty principle on considere l existence et la regularite des solutions d equations aux derivees partielles la construction de solutions fondamentales explicites et les valeurs propres d operateurs de schrodinger

an optimal adaptive finite element method for elastoplasticity an adaptive finite element algorithm for problems in elastoplasticity with hardening is proven to be of optimal convergence with respect to the notion of approximation classes the results rely on the equivalence of the errors of the stresses and energies resulting from jensen s inequality numerical experiments study the influence of the hardening and bulk parameters to the convergence behavior of the afem algorithm this is the first optimal adaptive fem for a variational inequality

sharp general local estimates for dyadic like maximal operators and related bellman functions for each 1q p we precisely evaluate the main bellman functions associated with the local lp lq estimates of the dyadic maximal operator on actually we do that in the more general setting of tree like maximal operators and with respect to general convex and increasing growth functions we prove that these bellman functions equal to analogous extremal problems for the hardy operator which can be viewed as a symmetrization principle for such operators under certain mild conditions on the growth functions we show that for the latter extremals exist although for the original bellman functions do not and analyzing them we give a determination of the corresponding bellman function

two weight l p estimates for paraproducts in non homogeneous settings we give a necessary and sufficient condition for the two weight l p l p estimates for paraproducts in non homogeneous settings 1 1 p we are mainly interested in the case p 2 p 2 since the case p 2 p 2 is a well known and easy corollary of the carleson embedding theorem the necessary and sufficient condition is given in terms of testing conditions of sawyer type for p 2 p 2 only one direct testing condition is required but for p 2 p 2 both direct and adjoint testing conditions are needed an interesting feature is that the adjoint testing condition is that it is a testing condition not for the adjoint of the paraproduct but for some auxiliary operator

duadic codes over z sub 2k duadic codes constitute a well known family of binary cyclic codes they are generalized in this correspondence to the setting of abelian codes over the ring z sub 2k self duality isoduality and type ii properties are studied

polyadic constacyclic codes for any given positive integer m a necessary and sufficient condition for the existence of type i m adic constacyclic codes is given furthermore for any given integer s a necessary and sufficient condition for s to be a multiplier of a type i polyadic constacyclic code is given as an application some optimal codes from type i polyadic constacyclic codes including generalized reed solomon codes and alternant maximum distance separable codes are constructed

nonlinear equations and weighted norm inequalities we study connections between the problem of the existence of positive solutions for certain nonlinear equations and weighted norm inequalities in particular we obtain explicit criteria for the solvability of the dirichlet problem u v u w u 0 on u 0 on on a regular domain in rn in the superlinear case q 1 the coefficients v w are arbitrary positive measurable functions or measures on we also consider more general nonlinear differential and integral equations and study the spaces of coefficients and solutions naturally associated with these problems as well as the corresponding capacities our characterizations of the existence of positive solutions take into account the interplay between v w and the corresponding green s kernel they are not only sufficient but also necessary and are established without any a priori regularity assumptions on v and w we also obtain sharp two sided estimates of solutions up to the boundary some of our results are new even if v 1 and is a ball or half space the corresponding weighted norm inequalities are proved for integral operators with kernels satisfying a refined version of the so called 3g inequality by an elementary integration by parts argument this also gives a new unified proof for some classical inequalities including the carleson measure theorem for poisson integrals and trace inequalities for riesz potentials and green potentials

invertible toeplitz products we will discuss invertibility of toeplitz products tftg for analytic f and g on the bergman space and the hardy space we will furthermore describe when these toeplitz products are fredholm

convergence of dg 1 in elastoplastic evolution the discontinuous galerkin dg methodology provides a hierarchy of time discretization schemes for evolutionary problems such as elastoplasticity with the prandtl reus flow rule a dg time discretization has been proposed for a variational inequality in the context of rate independent inelastic material behaviour in alberty and carstensen in cmme 191 4949 4968 2002 with the help of duality in convex analysis to justify certain jump terms this paper establishes the first a priori error analysis for the dg 1 scheme with discontinuous piecewise linear polynomials in the temporal and lowest order finite elements for the spatial discretization compared to a generalized mid point rule the dg 1 formulation distributes the action of the material law in the form of the variational inequality in time and so it introduces an error in the material law this may result in a suboptimal convergence rate for the dg 1 scheme and this paper shows that the stress error in the l infty l 2 norm is merely o h k 3 2 based on a seemingly sharp error analysis the numerical investigation for a benchmark problem with known analytic solution provides empirical evidence of a higher convergence rate of the dg 1 scheme compared to dg 0

riesz transforms and spectral multipliers of the hodge laguerre operator abstract on r d endowed with the laguerre probability measure we define a hodge laguerre operator l acting on differential forms here is the laguerre exterior differentiation operator defined as the classical exterior differential except that the partial derivatives x i are replaced by the laguerre derivatives x i x i and is the adjoint of with respect to inner product on forms defined by the euclidean structure and the laguerre measure we prove dimension free bounds on l p 1 p for the riesz transforms l 1 2 and l 1 2 as applications we prove the strong hodge de rahm kodaira decomposition for forms in l p and deduce existence and regularity results for the solutions of the hodge and de rham equations in l p we also prove that for suitable functions m the operator m l is bounded on l p 1 p

a variational formulation of rate independent phase transformations using an extremum principle we propose a rate independent mesoscopic model for the hysteretic evolution of phase transformations in shape memory alloys the model uses the deformation and phase indicator function as basic unknowns and the potentials for the elastic energy and for the dissipation as constitutive laws using the associated functionals admissible processes are defined to be the ones which are stable at all times and which satisfy the energy inequality

error estimates for space time discretizations of a rate independent variational inequality this paper deals with error estimates for space time discretizations in the context of evolutionary variational inequalities of rate independent type after introducing a general abstract evolution problem we address a fully discrete approximation and provide a priori error estimates the application of the abstract theory to a semilinear case is detailed in particular we provide explicit space time convergence rates for classical strain gradient plasticity and the isothermal souza auricchio model for shape memory alloys

quasi static small strain plasticity in the limit of vanishing hardening and its numerical approximation the quasi static rate independent evolution of the prager ziegler type model of plasticity with hardening is shown to converge to the rate independent evolution of the prandtl reuss elastic perfectly plastic model based on the concept of energetic solutions we study the convergence of the solutions in the limit for hardening coefficients converging to 0 by using the abstract method of gamma convergence for rate independent systems an unconditionally convergent numerical scheme is devised and two and three dimensional numerical experiments are presented a two sided energy inequality is a posteriori verified to document experimental convergence rates

averaging techniques for reliable a posteriori fe error control in elastoplasticity with hardening averaging techniques are popular tools in adaptive finite element methods for numerical simulation in continuum mechanics since they provide efficient a posteriori error control in this paper the reliability of any averaging estimator is shown for low order finite element methods in one time step of elastoplasticity with hardening the constants and higher order terms are effected by the hardening and the smoothness of given right hand sides but are independent of the structure of a shape regular mesh since it involves a different functional analytical framework the case of perfect plasticity is excluded from this paper

hermitian self dual abelian codes hermitian self dual abelian codes in a group ring fq2 g where fq2 is a finite field of order q2 and g is a finite abelian group are studied using the well known discrete fourier transform decomposition for a semisimple group ring a characterization of hermitian self dual abelian codes in fq2 g is given together with an alternative proof of necessary and sufficient conditions for the existence of such a code in fq2 g i e there exists a hermitian self dual abelian code in fq2 g if and only if the order of g is even and q 2l for some positive integer l later on the study is further restricted to the case where f22l g is a principal ideal group ring or equivalently g a z2k with 2 a based on the characterization obtained the number of hermitian self dual abelian codes in f22l a z2k can be determined easily when a is cyclic this result answers an open problem of jia et al concerning hermitian self dual cyclic codes in many cases f22l a z2k contains a unique hermitian self dual abelian code the criteria for such cases are determined in terms of l and the order of a finally the distribution of finite abelian groups a such that a unique hermitian self dual abelian code exists in f22l a z2 is established together with the distribution of odd integers m such that a unique hermitian self dual cyclic code of length 2 m over f22l exists

an adaptive least squares mixed finite element method for elasto plasticity a least squares mixed finite element method for the incremental formulation of elasto plasticity using a plastic flow rule of von mises type with isotropic hardening is presented this approach is based on the use of the stress tensor in addition to the displacement field as independent process variables the nonlinear least squares functional is shown to constitute an a posteriori error estimator on which an adaptive refinement strategy may be based for the finite element implementation under plane strain conditions quadratic i e next to lowest order raviart thomas elements are used for the stress approximation while the displacement is represented by standard quadratic conforming elements computational results for a benchmark problem of elasto plasticity under plane strain conditions are presented in order to illustrate the effectiveness of the least squares approach

numerical analysis of time depending primal elastoplasticity with hardening the quasi static elastoplastic evolution problem with combined isotropic and kinematic hardening is considered with emphasis on optimal convergence of the lowest order scheme in each time step of a generalized midpoint scheme such as the implicit euler or the crank nicolson scheme the spatial discretization consists of minimizing a convex but nonsmooth function on a subspace of continuous piecewise linear resp piecewise constant trial functions an a priori error estimate is established for the fully discrete method which for smooth data and a smooth exact solution proves linear convergence as the mesh size tends to zero strong convergence of the time derivatives is established under mild conditions on the mesh and time step sizes numerical experiments confirm our theoretical predictions on the improved spatial convergence and indicate that the crank nicolson scheme is not always superior over the implicit euler scheme in practice

efficient numerical methods for the large scale parallel solution of elastoplastic contact problems parts of the work of the first author were supported by the deutsche forschungsgemeinschaft dfg within priority program 1480 modelling simulation and compensation of thermal effects for complex machining processes through grant number bl 256 11 3 the third author is supported by the national science foundation through award no oci 1148116 the second and third authors are supported in part by the computational infrastructure in geodynamics initiative cig through the national science foundation under award no ear 0949446 and the university of california davis this publication is based in part on the work supported by award no kus c1 016 04 made by king abdullah university of science and technology kaust some computations for this paper were performed on the brazos and hurr clusters at the institute for applied mathematics and computational science iamcs at texas a m university part of brazos was supported by nsf award dms 0922866 hurr is supported by award no kus c1 016 04 made by king abdullah university of science and technology kaust

edge residuals dominate a posteriori error estimates for low order finite element methods we prove that up to higher order perturbation terms edge residuals yield global upper and local lower bounds on the error of linear finite element methods both in h1 and l2 norms we present two proofs one uses the standard l2 projection and the other relies on a new weighted clement type interpolation operator

wavelets and the angle between past and future the main result the riesz projectionp or equivalently hilbert transformt is bounded in the weighted spacel2 w wherewis a matrix valued weight if and only ifsupi 1 i iw 1 2 1 i iw 1 1 2 wheresupremumis taken over all intervalsi motivation for this problem comes from stationary processes riesz projection is bounded means the angle between past and future of a stationary process with spectral measurewis nonzero in the scalar case the result is the well known hunt muckenhoupt wheeden theorem the main step in our proof is to show that a vector haar system forms an unconditional basis inl2 w as a byproduct of our approach we get some new results about bases of wavelets in weighted spaces in both scalar and vector valued cases

on the superlinear convergence in computational elasto plasticity we consider the convergence properties of return algorithms for a large class of rate independent plasticity models based on recent results for semismooth functions we can analyze these algorithms in the context of semismooth newton methods guaranteeing local superlinear convergence this recovers results for classical models but also extends to general hardening laws multi yield plasticity and to several non associated models the superlinear convergence is also numerically shown for a large scale parallel simulation of drucker prager elasto plasticity and an example for the modified cam clay model

solution of one time step problems in elastoplasticity by a slant newton method we discuss a solution algorithm for quasi static elastoplastic problems with hardening such problems can be described by a time dependent variational inequality where the displacement and the plastic strain fields serve as primal variables after discretization in time one variational inequality of the second kind is obtained per time step and can be reformulated as a minimization problem with a convex energy functional which depends smoothly on the displacement and nonsmoothly on the plastic strain there exists an explicit formula for minimizing the energy functional with respect to the plastic strain for a given displacement by substitution the energy functional can be written as a functional depending only on the displacement the theorem of moreau from convex analysis states that the energy functional is differentiable with an explicitly computable first derivative the second derivative of the energy functional does not exist due to the lack of smoothness of the plastic strain across the elastoplastic interface which separates the continuum in elastically and plastically deformed parts a newton like method exploiting slanting functions of the energy functional s first derivative instead of the nonexistent second derivative is applied such a method is called a slant newton method for short the local superlinear convergence of the algorithm in the discrete case is shown and sufficient regularity assumptions are formulated which would guarantee the local superlinear convergence also in the continuous case

bellman functions and dimension free lp estimates for the riesz transforms in bessel settings abstract in this article we prove dimension free l p boundedness of riesz transforms associated with a bessel differential operator we obtain explicit estimates of the l p norms for the bessel riesz transforms in terms of p establishing a linear behavior with respect to p we use the bellman function technique to prove a bilinear dimension free inequality involving poisson semigroups defined through this bessel operator

abelian codes in principal ideal group algebras we study abelian codes in principal ideal group algebras pigas we first give an algebraic characterization of abelian codes in any group algebra and provide some general results for abelian codes in a piga which can be viewed as cyclic codes over a semisimple group algebra it is shown that every abelian code in a piga admits generator and check elements these are analogous to the generator and parity check polynomials of cyclic codes a characterization and an enumeration of euclidean self dual and euclidean self orthogonal abelian codes in a piga are given which generalize recent analogous results for self dual cyclic codes in addition the structures of reversible and complementary dual abelian codes in a piga are established again extending results on reversible and complementary dual cyclic codes finally asymptotic properties of abelian codes in a piga are studied an upper bound for the minimum distance of abelian codes in a non semisimple piga is given in terms of the minimum distance of abelian codes in semisimple group algebras abelian codes in a non semisimple piga are then shown to be asymptotically bad similar to the case of repeated root cyclic codes

the bellman functions of dyadic like maximal operators and related inequalities abstract for each p 1 we precisely evaluate the main bellman functions associated with the dyadic maximal operator on r n and the dyadic carleson imbedding theorem actually we do that in the more general setting of tree like maximal operators these provide refinements of the sharp lp inequalities for those operators for this we introduce an effective linearization for such maximal operators on an adequate set of functions

the theory of weights and the dirichlet problem for elliptic equations in this work we consider questions from the area of partial differential equations and the related questions from harmonic analysis specifically we will study the dirichlet problem for second order divergence form elliptic operators with bounded measurable coefficients roughly speaking we consider the following question suppose that we are given two operators lo and li and that we have good estimates for the dirichlet problem for lo good in this context could mean several different things for instance it might mean that there exists p 1 p oo so that the dirichlet problem is solvable in a suitable sense with lp data what are the optimal conditions on the difference between the coefficients of lo and l1 which guarantee that the dirichlet problem for li also has good estimates this question has been extensively studied recently cf f j k r f and d4 our work uses in a crucial way the results in r f the main results in d4 and r f are proved using an ingenious differential inequality for a family of harmonic measures introduced in d4 another of our goals in this article is to give new direct proofs of the results in d4 and r f without the use of this differential inequality theorems 2 4 2 5 and 2 18 these direct approaches have already had important applications k p2 an interesting class of examples for the theorems quoted above arises when one pulls back the laplacian via a quasiconformal mapping of the plane into itself specializing our theorem to this case suggests a new characterization of the class of am weights introduced in connection with several problems in harmonic analysis by muckenhoupt mul and coifman c fefferman co f we shall present in theorem 2 3 a criterion in terms of carleson measures which is very close to log w e bmo and is necessary and sufficient for w e ad

a posteriori error analysis for finite element solutions of a frictional contact problem in this paper we derive and analyze a residual type a posteriori error estimator for finite element approximations of a frictional contact problem for linearized elastic materials the reliability of the estimator is rigorously shown the efficiency of the estimator is also studied results from several numerical examples are reported illustrating the good performance of the estimator in adaptive solution of the frictional contact problem

polyadic codes revisited we generalize the notions of duadic codes triadic codes polyadic codes and split group codes to include noncyclic abelian codes necessary and sufficient conditions for the existence of such codes and properties such as a duality property and a lower bound on the minimum weight of the subcode of odd like codewords are studied this construction and its modification lead to many good codes eight of which have minimum distance better than the lower bound given in brouwer s table

finite element analysis of a holonomic elastic plastic problem a thorough analysis of the finite element method is given for a holonomic elastic plastic problem an inequality of the cea s lemma type is proved which is the basis of error estimates for various finite element solutions difficulty caused by a non differentiable term in the problem can be overcome by using two convergent procedures an iterative procedure and a regularization procedure an a posteriori quantitative error estimate is derived for the regularized solution

a duality based path following semismooth newton method for elasto plastic contact problems a fenchel dualization scheme for the one step time discretized contact problem of quasi static elasto plasticity with combined kinematic isotropic hardening is considered the associated path is induced by a coupled moreau yosida tikhonov regularization of the dual problem the sequence of solutions to the regularized problems is shown to converge strongly to the optimal displacement stress strain triple of the original elasto plastic contact problem in the space continuous setting this property relies on the density of the intersection of certain convex sets which is shown as well it is also argued that the mappings associated with the resulting problems are newton or slantly differentiable consequently each regularized subsystem can be solved mesh independently at a local superlinear rate of convergence for efficiency purposes an inexact path following approach is proposed and a numerical validation of the theoretical results is given

sharp logarithmic estimates for positive dyadic shifts the paper contains the study of sharp logarithmic estimates for positive dyadic shifts a a given on probability spaces x x equipped with a tree like structure for any k 0 k 0 we determine the smallest constant l l k l l k such that e a f d k r f d l k e where t t 1 log t 1 t t t 1 log t 1 t e is an arbitrary measurable subset of x and f is an integrable function on x the proof exploits bellman function method we extract the above estimate from the existence of an appropriate special function enjoying certain size and concavity type conditions as a corollary a dual exponential bound is obtained

non convex potentials and microstructures in finite strain plasticity a mathematical model for a finite strain elastoplastic evolution problem is proposed in which one time step of an implicit time discretization leads to generally non convex minimization problems the elimination of all internal variables enables a mathematical and numerical analysis of a reduced problem within the general framework of calculus of variations and nonlinear partial differential equations the results for a single slip system and von mises plasticity illustrate that finite strain elastoplasticity generates reduced problems with non quasiconvex energy densities and so allows for non attainment of energy minimizers and microstructures

a characterization of two weight norm inequalities for fractional and poisson integrals caracterisation de deux inegalites de normes ponderees pour les integrales fractionnaires et de poisson applications aux operateurs differentiels elliptiques degeneres

consta abelian polyadic codes in this correspondence the class of polyadic codes is generalized to the class of consta abelian polyadic codes which in particular includes the class of constacyclic polyadic codes properties such as the equivalence of polyadic codes and the mth root lower bound for the minimum weight of a subcode of certain types of polyadic codes are preserved in the consta abelian case sufficient conditions for the existence of this class of codes are established for the special case of constacyclic codes the characterization of negacyclic self dual codes of length coprime to the characteristic of the field in terms of negacyclic duadic codes is also given

a variational formulation for finite deformation wrinkling analysis of inelastic membranes this paper is concerned with a novel fully variational formulation for finite deformation analysis of inelastic membranes with wrinkling in contrast to conventional approaches every aspect of the physical problem derives from minimization of suitable energy functionals a variational formulation of finite strain plasticity theory which leads to a minimization problem for the constitutive updates serves as the starting point for the derivations in order to take into account the kinematics induced by wrinkles and slacks a relaxed version of the finite strain functional is postulated in effect the local incremental stress strain relations are established via differentiation of the relaxed energy functional with respect to the strains hence the presented formulation is fully analogous to that of hyperelasticity with the sole exception that the aforementioned functional depends on history variables and accordingly it is path dependent the advantages associated with the developed variational method are manifold from a practical point of view the possibility of applying standard optimization algorithms to solve the minimization problem describing inelastic membranes is remunerative from a mathematical point of view on the other hand the energy of the system induces some sort of natural metric representing an essential requirement for error estimation and thus for adaptive finite element methods the presented derivation of the model allows to consider possible material symmetries in the elastic as well as plastic response of the material as a prototype a von mises type model is implemented the efficiency and performance of the resulting algorithm are demonstrated by means of numerical examples

a primal dual finite element approximation for a nonlocal model in plasticity we study the numerical approximation of a static infinitesimal plasticity model of kinematic hardening with a nonlocal extension here the free energy to be minimized is a combination of the elastic energy and an additional term depending on the curl of the plastic variable first we introduce the stress as dual variable and provide an equivalent primal dual formulation resulting in a local flow rule the discretization is based on curl conforming nedelec elements to obtain optimal a priori estimates the finite element spaces have to satisfy a uniform inf sup condition this can be guaranteed by adding locally defined face and element bubbles second the discrete variational inequality system is reformulated as a nonlinear equality we show that the classical radial return algorithm applied to the mixed inequality formulation is equivalent to a semismooth newton method for the nonlinear system of equations numerical results illustrate the convergence of the applied discretization and the solver

adaptive finite element methods in computational mechanics we present a general approach to adaptivity for finite element methods and give applications to linear elasticity non linear elasto plasticity and nonlinear conservation laws including numerical results

a tfeti domain decomposition solver for elastoplastic problems we propose an algorithm for the efficient parallel implementation of elastoplastic problems with hardening based on the so called tfeti total finite element tearing and interconnecting domain decomposition method we consider an associated elastoplastic model with the von mises plastic criterion and the linear isotropic hardening law such a model is discretized by the implicit euler method in time and the consequent one time step elastoplastic problem by the finite element method in space the latter results in a system of nonlinear equations with a strongly semismooth and strongly monotone operator the semismooth newton method is applied to solve this nonlinear system corresponding linearized problems arising in the newton iterations are solved in parallel by the above mentioned tfeti domain decomposition method the proposed tfeti based algorithm was implemented in matlab parallel environment and its performance was illustrated on a 3d elastoplastic benchmark numerical results for different time discretizations and mesh levels are presented and discussed and a local quadratic convergence of the semismooth newton method is observed

extremal problems related to maximal dyadic like operators abstract we obtain sharp estimates for the localized distribution function of the dyadic maximal function m d when belongs to l p using this we obtain sharp estimates for the quasi norm of m d in l p given the localized l 1 norm and certain weak l p conditions

perfect dyadic operators weighted t 1 theorem and two weight estimates abstract perfect dyadic operators were first introduced in 1 where a local t b theorem was proved for such operators in 3 it was shown that for every singular integral operator t with locally bounded kernel on r n r n there exists a perfect dyadic operator t such that t t is bounded on l p d x for all 1 p in this paper we show a decomposition of perfect dyadic operators on real line into four well known operators two selfadjoint operators paraproduct and its adjoint based on this decomposition we prove a sharp weighted version of the t 1 theorem for such operators which implies a 2 conjecture for such operators with constant which only depends on t 1 bmo d t 1 bmo d and the constant in testing conditions for t moreover the constant depends on these parameters at most linearly in this paper we also obtain sufficient conditions for the two weight boundedness for a perfect dyadic operator and simplify these conditions under additional assumptions that weights are in the muckenhoupt class a d

on the bellman function of nazarov treil and volberg we give an explicit formula for the bellman function associated with the dual bound related to the unconditional constant of the haar system

extremizers and sharp weak type estimates for positive dyadic shifts we find the exact bellman function for the weak l1 norm of local positive dyadic shifts we also describe a sequence of functions self similar in nature which in the limit extremize the local weak type 1 1 inequality

numerical approximation of incremental infinitesimal gradient plasticity we investigate a representative model of continuum infinitesimal gradient plasticity the formulation is an extension of classical rate independent infinitesimal plasticity based on the additive decomposition of the symmetric strain tensor into elastic and plastic parts it is assumed that dislocation processes contribute to the storage of energy in the material whereby the curl of the plastic distortion appears in the thermodynamic potential and leads to an additional nonlocal backstress tensor the formulation is cast into a numerical framework by a saddle point approximation of the corresponding minimization problem in each incremental loading step this allows one to reformulate the nonlocal dissipation inequality to a point wise flow rule and yields a solution scheme which is a direct extension of the standard approach in classical plasticity our numerical results show the regularizing effects of the additional physically motivated terms copyright 2008 john wiley sons ltd

optimal control of static elastoplasticity in primal formulation an optimal control problem of static plasticity with linear kinematic hardening and von mises yield condition is studied the problem is treated in its primal formulation where the state system is a variational inequality of the second kind first order necessary optimality conditions are obtained by means of an approximation by a family of control problems with state system regularized by huber type smoothing and a subsequent limit analysis the equivalence of the optimality conditions with the c stationarity system for the equivalent dual formulation of the problem is proved numerical experiments are presented which demonstrate the viability of the huber type smoothing approach

numerical analysis of the primal problem of elastoplasticity with hardening the finite element method is a reasonable and frequently utilised tool for the spatial discretization within one time step in an elastoplastic evolution problem in this paper we analyse the finite element discretization and prove a priori and a posteriori error estimates for variational inequalities corresponding to the primal formulation of hencky plasticity the finite element method of lowest order consists in minimising a convex function on a subspace of continuous piecewise linear resp piecewise constant trial functions an a priori error estimate is established for the fully discrete method which shows linear convergence as the mesh size tends to zero provided the exact displacement field u is smooth near the boundary of the plastic domain which is unknown a priori it is most likely that u is non smooth in this situation automatic mesh refinement strategies are believed to improve the quality of the finite element approximation we suggest such an adaptive algorithm on the basis of a computable a posteriori error estimate this estimate is reliable and efficient in the sense that the quotient of the error by the estimate and its inverse are bounded from above the constants depend on the hardening involved and become larger for decreasing hardening

sharp results in the integral form john nirenberg inequality we consider the strong form of the john nirenberg inequality for the l 2 based bmo we construct explicit bellman functions for the inequality in the continuous and dyadic settings and obtain the sharp constant as well as the precise bound on the inequality s range of validity both previously unknown the results for the two cases are substantially different the paper not only gives another instance in the short list of such explicit calculations but also presents the bellman function method as a sequence of clear steps adaptable to a wide variety of applications

nonlinear complementarity functions for plasticity problems with frictional contact in this paper a unifying framework for the numerical treatment of frictional contact in combination with elastoplasticity with hardening is presented both kinds of problems lead to the mathematical structure of variational inequalities which are discretized by introducing additional variables for the contact stresses or the deviatoric stresses leading to a mixed formulation by defining a family of nonlinear complementarity functions which can be applied to both frictional and plastic yield conditions these inequality constraints are reformulated as equalities combined with the equilibrium equations a system of nonlinear equations is obtained that is solved in terms of a semismooth newton method to obtain a larger domain of convergence and better stability properties the introduction of additional scaling parameters is motivated and their benefit to the convergence of the scheme is demonstrated due to the locality of the contact and plastic constraints the resulting method can be interpreted as a primal dual active set strategy furthermore for linear hardening laws our method is a generalization of the well known radial return algorithm which is obtained for a special suboptimal choice of the plastic scaling parameters the efficiency and the generality of the proposed quasi newton scheme is demonstrated by several numerical examples including the simulation of a three dimensional contact problem with several elastoplastic bodies exponential isotropic hardening and coulomb friction