empirical likelihood based confidence interval for the mean with a heavy tailed distribution empirical likelihood based confidence intervals for a mean were introduced by owen biometrika 75 1988 237 249 where at least a finite second moment is required this excludes some important distributions for example those in the domain of attraction of a stable law with index between 1 and 2 in this article we use a method similar to qin and wong scand j statist 23 1996 209 219 to derive an empirical likelihood based confidence interval for the mean when the underlying distribution has heavy tails our method can easily be extended to obtain a confidence interval for any order of moment of a heavy tailed distribution

positive soliton solutions for generalized quasilinear schrodinger equations with critical growth this paper is concerned with the positive solutions for generalized quasilinear schrodinger equations in rn with critical growth which have appeared from plasma physics as well as high power ultrashort laser in matter by using a change of variables and variational argument we obtain the existence of positive solutions for the given problem

soliton solutions for generalized quasilinear schrodinger equations abstract by introducing a new variable replacement we study the existence of nontrivial solutions for generalized quasilinear schrodinger equations which appear from plasma physics as well as high power ultrashort laser in matter

quasilinear asymptotically periodic schrodinger equations with subcritical growth abstract in this article the existence of one solution for a class of asymptotically periodic equations in the euclidean space is established the basic tools employed here are the mountain pass theorem and the concentration compactness principle by using a change of variable the quasilinear equation is reduced to a semilinear equation whose respective associated functional is well defined in h 1 r n and satisfies the geometric hypotheses of the mountain pass theorem

convergence rates for the bootstrapped product limit process on etablit des taux d approximation forte pour le processus limite produit du bootstrap et le processus quantile correspondant

normal and stable convergence of integral functions of the empirical distribution function we prove general invariance principles for integral functions of the empirical process as corollaries we derive probabilistic proofs of the sufficiency criteria for a distribution to belong to the domain of attraction of the normal and stable laws with index 0 a 2 in the process we obtain equivalent statements of these criteria in terms of the tail behaviour of the underlying quantile function we also give a representation of any stable random variable with index 0 a 2 in terms of a linear combination of two independent and identically distributed poisson integrals the role of a fixed number of extreme terms is exactly determined

what portion of the sample makes a partial sum asymptotically stable or normal let a sequence of independent and identically distributed random variables with the common distribution function in the domain of attraction of a stable law of index 0 2 be given we show that if at each stage n a number k n depending on n of the lower and upper order statistics are removed from the n th partial sum of the given random variables then under appropriate conditions on k n the remaining sum can be normalized to converge in distribution to a standard normal random variable a further analysis is given to show which ranges of the order statistics contribute to asymptotic stable law behaviour and which to normal behaviour our main tool is a new brownian bridge approximation to the uniform empirical process in weighted supremum norms

improved enhanced strain four node element with taylor expansion of the shape functions a class of enhanced strain four node elements with taylor expansion of the shape function derivatives is presented a new concept of enhancement using besides the standard enhanced strain fields also two other enhanced fields is developed on the basis of the hu washizu principle for first order taylor expansion enhanced modes become uncoupled thus only a negligible amount of computing effort for the static condensation of enhanced modes is needed furthermore the formulation permits a symbolic integration which leads to a closed form solution for the element tangent matrix several numerical examples show that the element is stable invariant passes the patch test and yields good results especially in the highly distorted regime 1997 by john wiley sons ltd

finite strain formulation and fe implementation of a constitutive model for powder compaction abstract a finite strain formulation is developed implemented and tested for a constitutive model capable of describing the transition from granular to fully dense state during cold forming of ceramic powder this constitutive model as well as many others employed for geomaterials embodies a number of features such as pressure sensitive yielding complex hardening rules and elastoplastic coupling posing considerable problems in a finite strain formulation and numerical implementation a number of strategies are proposed to overcome the related problems in particular a neo hookean type of modification to the elastic potential and the adoption of the second piola kirchhoff stress referred to the intermediate configuration to describe yielding an incremental scheme compatible with the formulation for elastoplastic coupling at finite strain is also developed and the corresponding constitutive update problem is solved by applying a return mapping algorithm

design of simple low order finite elements for large strain analysis of nearly incompressible solids a simple four node quadrilateral and an eight node hexahedron for large strain analysis of nearly incompressible solids are proposed based on the concept of deviatoric volumetric split and the replacement of the compatible deformation gradient with an assumed modified counterpart the formulation developed is applicable to arbitrary material models the closed form of the corresponding exact tangent stiffnesses which have a particularly simple structure is derived it ensures asymptotically quadratic rates of convergence of the newton raphson scheme employed in the solution of the implicit finite element equilibrium equations from a practical point of view the incorporation of the proposed elements into existing codes is straightforward it requires only small changes in the routines of the standard displacement based 4 node quadrilateral and 8 node brick a comprehensive set of numerical examples involving hyperelasticity as well as multiplicative elasto plasticity is provided it illustrates the performance of the proposed elements over a wide range of applications including strain localisation problems metal forming simulation and adaptive analysis

quasilinear elliptic equations with critical growth via perturbation method abstract we consider a class of quasilinear schrodinger equations which include the modified nonlinear schrodinger equations a new perturbation approach is used to treat the critical exponent case giving new existence results

the asymptotic distribution of sums of extreme values from a regularly varying distribution on donne une description complete de la distribution asymptotique de la somme des k n valeurs extremes superieures x n 1 kd n n x n 2 kd n n x n n

on limiting distributions of intermediate order statistics from stationary sequences abstract the problem of finding the asymptotic distribution of the maximum term from a stationary dependent sequence of random variables r v s has been extensively investigated in the literature of particular interest are the cases in which the concept of approximate independence is formulated mathematically in terms of conditions such as strong mixing or for normal sequences conditions on the rate of decay of the covariances our objective in this paper is to obtain analogous results for so called intermediate order statistics a sequence is given of intermediate order statistics and intermediate rank sequence these conditions parallel those used to obtain the corresponding result in the extreme order statistic problem a primary difference being that certain more rapid mixing rates have to be assumed using our procedure it is convenient to deal directly with an appropriate level exceedance problem and to regard that of asymptotic distributions as a specialization

the asymptotic distribution of trimmed sums on donne une condition necessaire et suffisante pour l existence de constantes de normalisation et de centrage

closed form matrix exponential and its application in finite strain plasticity summary a new method to compute numerically efficient closed form representation of matrix exponential and its derivative is developed for 3 3 matrices with real eigenvalues the matrix exponential is obtained by automatic differentiation of an appropriate scalar generating function in a general case and highly accurate asymptotic expansions are derived for special cases in which the general formulation exhibits ill conditioning for instance for almost equal eigenvalues accuracy and numerical efficiency of the closed form matrix exponential as compared with the truncated series approximation are studied the application of the closed form matrix exponential in the finite strain elastoplasticity is also presented to this end several time discrete evolution laws employing the exponential map are discussed for j2 plasticity with isotropic hardening and nonlinear kinematic hardening of armstrong frederick type the discussion is restricted to the case of elastic isotropy and implicit time integration schemes in this part the focus is on a general automatic differentiation based formulation of finite strain plasticity models numerical efficiency of the corresponding incremental schemes is studied in the context of the fem copyright 2014 john wiley sons ltd

on the formulation of closest point projection algorithms in elastoplasticity part ii globally convergent schemes this paper presents the formulation of numerical algorithms for the solution of the closest point projection equations that appear in typical implementations of return mapping algorithms in elastoplasticity the main motivation behind this work is to avoid the poor global convergence properties of a straight application of a newton scheme in the solution of these equations the so called newton cppm the mathematical structure behind the closest point projection equations identified in part i of this work delineates clearly different strategies for the successful solution of these equations in particular primal and dual closest point projection algorithms are proposed in non augmented and augmented lagrangian versions for the imposition of the consistency condition the primal algorithms involve a direct solution of the original closest point projection equations whereas the dual schemes involve a two level structure by which the original system of equations is staggered with the imposition of the consistency condition driving alone the iterative process newton schemes in combination with appropriate line search strategies are considered resulting in the desired asymptotically quadratic local rate of convergence and the sought global convergence character of the iterative schemes these properties together with the computational performance of the different schemes are evaluated through representative numerical examples involving different models of finite strain plasticity in particular the avoidance of the large regions of no convergence in the trial state observed in the standard newton cppm is clearly illustrated

limit theorems and inequalities for the uniform empirical process indexed by intervals the uniform empirical process u is considered as a process indexed by intervals powerful new exponential bounds are established for the process indexed by both points and intervals these bounds trivialize the proof of the chibisov o reilly theorem concerning the convergence of the process with respect to 11 q 11 metrics and are used to prove an interval analogue of the chibisov o reilly theorem a strong limit theorem related to the well known holder condition for brownian bridge u is also proved connections with related work of csdki eicker jaeschke and stute are mentioned as an application we introduce a new statistic for testing uniformity which is the natural interval analogue of the classical anderson darling statistic

the asymptotic distribution of extreme sums converges in distribution along subsequences of the integers n to nondegenerate limits and completely describe the possible subsequential limiting distributions we also give a necessary and sufficient condition for the existence of an and cn such that en be asymptotically normal along a given subsequence and with suitable an and cn determine the limiting distributions of en along the whole sequence n when f is in the domain of attraction of an extreme value distribution

on the numerical treatment and analysis of finite deformation ductile single crystal plasticity abstract this contribution is concerned with the numerical analysis and simulation of instability phenomena such as shearband localization in plastic flow processes within the framework of ductile single fcc crystal viscoplasticity to this end a family of implicit constitutive algorithms and their implementation are considered in detail issues of accuracy and conservation of plastic incompressibility are examined moreover the implementation within an overall newton raphson finite element solution strategy relies on the correct evaluation of the algorithmic tangent moduli which result from linearizing the stress update integrator likewise these algorithmic tangent moduli are employed within the numerical analysis of the spatial localization tensor examples demonstrating the performance of the proposed strategy at the local constitutive level as well as at the global structural level are given

generalized quasilinear asymptotically periodic schrodinger equations with critical growth this paper is concerned with the following quasilinear schrodinger equations div g 2 u u g u g u u 2 v x u f x u g u g u 2 2 g u x r n u x 0 x r n where n 3 2 2 n n 2 g u 0 u g t d t and 0 is a parameter by using a change of variable the quasilinear equation is reduced to a semilinear one whose associated functional is well defined in h 1 r n we establish the existence of positive solutions for this problem by using the mountain pass theorem in combination with the concentration compactness principle under appropriate assumptions on v x and f x u recent results from the literature are improved and extended

weak convergence for weighted empirical processes of dependent sequences in this paper we establish weak convergence theorems for weighted empirical processes of strong mixing p mixing and associated sequences we apply these results to obtain weak convergence of integral functionals of empirical processes and of mean residual life processes in reliability theory to carry out the proofs we develop two rosenthal type inequalities for strong mixing and associated sequences

strong invariance principles for sequential bahadur kiefer and vervaat error processes of long range dependent sequences in this paper we study strong approximations invariance principles of the sequential uniform and general bahadur kiefer processes of long range dependent sequences we also investigate the strong and weak asymptotic behavior of the sequential vervaat process that is the integrated sequential bahadur kiefer process properly normalized as well as that of its deviation from its limiting process the so called vervaat error process it is well known that the bahadur kiefer and the vervaat error processes cannot converge weakly in the i i d case in contrast to this we conclude that the bahadur kiefer and vervaat error processes as well as their sequential versions do converge weakly to a dehling taqqu type limit process for certain long range dependent sequences

positive solutions of asymptotically linear schrodinger poisson systems with a radial potential vanishing at infinity in this paper we study the schrodinger poisson system sp u v x u x u k x f u inr3 u2 u 0 inr3 and prove the existence of positive solutions for system sp when the nonlinearity f has growth at most linear for small allowing the potential v x to vanish at infinity in addition also we obtain the nonexistence of a nontrivial positive solution for 14

a re formulation of the exponential algorithm for finite strain plasticity in terms of cauchy stresses abstract the role of the stress measure to be chosen as the argument in the definition of yield functions is discussed in the context of finite strain plasticity theory motivated by physical arguments the exponential algorithm for multiplicative finite strain plasticity is revisited such that cauchy stresses are adopted as arguments in the yield function using logarithmic strain measures the return map algorithm is formulated in principal axes the algorithmic tangent moduli are obtained in a slightly modified unsymmetric format compared to the standard formulation in terms of kirchhoff stresses however the global structure of the exponential algorithm is unchanged the algorithm is applied to the re formulation of the cam clay model in terms of cauchy stresses the typical calibration procedure of the cam clay model based on cauchy stresses is demonstrated as an alternative a modification of the cam clay model which allows re calibration of cauchy stress based test data to be used within the framework of a kirchhoff based finite strain model is also discussed the relevance of the adequate choice of the stress measure is illustrated by means of selected numerical analyses

reduction principles for quantile and bahadur kiefer processes of long range dependent linear sequences in this paper we consider quantile and bahadur kiefer processes for long range dependent linear sequences these processes unlike in previous studies are considered on the whole interval 0 1 as it is well known quantile processes can have very erratic behavior on the tails we overcome this problem by considering these processes with appropriate weight functions in this way we conclude strong approximations that yield some remarkable phenomena that are not shared with i i d sequences including weak convergence of the bahadur kiefer processes a different pointwise behavior of the general and uniform bahadur kiefer processes and a somewhat strange behavior of the general quantile process

soliton solutions for quasilinear schrodinger equations ii abstract for a class of quasilinear schrodinger equations we establish the existence of ground states of soliton type solutions by a variational method

existence and multiplicity of solutions for a class of generalized quasilinear schrodinger equations abstract this paper focuses on the following generalized quasilinear schrodinger equations div g 2 u u g u g u u 2 v x u f x u x r n where n 3 g s r r is a nondecreasing function with respect to s by using a change of variables and variational methods we obtain the existence and multiplicity of nontrivial solutions for the above problem when the nonlinearity is superlinear but does not satisfy the ambrosetti rabinowitz type condition

on a class of asymptotically linear elliptic problems in rn under these conditions p is an asymptotically linear problem when this equation is considered in a bounded domain 0 r with say the dirichlet boundary condition there is a large literature on existence and multiplicity results of particular interest is then the case of resonance where s and s is the asymptotic linearization of the problem in other words s d s l 0 l 0 is the operator given by

existence of solutions for a class of nonlinear schrodinger equations with potential vanishing at infinity abstract in this paper we investigate the existence of positive ground state solution for the following class of elliptic equations u v x u k x f u in r n where n 3 v k are nonnegative continuous functions and f is a continuous function with a quasicritical growth here we prove a hardy type inequality and use it together with variational method to get a ground state solution

the convergence rate for the normal approximation of extreme sums abstract this paper derives the normal convergence rate for sums of extreme values the exact rates are obtained under some regularity and smoothing conditions on the tail of the distribution of the sample

a ground state solution for an asymptotically periodic quasilinear schrodinger equation abstract this article is concerned with the existence of positive ground state solutions for an asymptotically periodic quasilinear schrodinger equation by using a change of variables the quasilinear problem is transformed into a semilinear one then we use a nehari type constraint to get the existence result

existence of solutions for a quasilinear schrodinger equation with subcritical nonlinearities abstract in this paper we consider the existence of solutions for the quasilinear schrodinger equation u v x u u 2 u g x u in r n where n 3 and g x u is a superlinear but subcritical function under periodic or asymptotically periodic assumptions on the nonlinearities we prove the existence of bounded states for this equation by the mountain pass theorem

the central limit theorem and the law of iterated logarithm for empirical processes under local conditions a clt and a lil are proved under weak l2 gaussian bracketing conditions weaker than the usual ones these results have wide applicability and in particular provide an improvement of the jain marcus central limit theorem for c s valued random variables

multiple solutions for quasilinear schrodinger equations with a parameter abstract in this paper we study the following quasilinear schrodinger equations of the form u v x u u 2 u 2 2 u g x u x r n where 1 1 2 v c r n r g c r n r r using some special techniques the existence of positive solutions negative solutions and sequence of high energy solutions are studied

tangent operators and design sensitivity formulations for transient non linear coupled problems with applications to elastoplasticity tangent operators and design sensitivities are derived for transient non linear coupled problems the solution process and the formation of tangent operators are presented in a systematic manner and sensitivities for a generalized response functional are formulated via both the direct differentiation and adjoint methods the derived formulations are suitable for finite element implementations analyses of systems with materials that exhibit history dependent response may be obtained directly by applying the analyses of transient non linear coupled systems rate independent elastoplasticity is investigated as a case study and a problem with an analytical solution is analysed for demonstration purposes

new conditions on nonlinearity for a periodic schrodinger equation having zero as spectrum abstract we consider the semilinear schrodinger equation u v x u f x u for x r n u x 0 as x where f is a superlinear and subcritical nonlinearity we mainly study the case when both v and f are periodic in x and 0 is a boundary point of a spectral gap of v we extend a linking theorem of kryszewski and szulkin 15 and establish a new variational setting which is more suitable to the above case we obtain two theorems on the existence of ground state solutions with mild assumptions on f

solutions for a quasilinear schrodinger equation a dual approach abstract we consider quasilinear stationary schrodinger equations of the form 1 u u 2 u g x u x r n introducing a change of unknown we transform the search of solutions u x of 1 into the search of solutions v x of the semilinear equation 2 v 1 1 2f 2 v g x f v x r n where f is suitably chosen if v is a classical solution of 2 then u f v is a classical solution of 1 variational methods are then used to obtain various existence results

laws of the iterated logarithm for order statistics of uniform spacings let x 1 x 2 cdots be a sequence of independent uniformly distributed random variables on lbrack 0 1 rbrack and let k n be the k th largest spacing induced by the order statistics of x 1 cdots x n 1 we show that lim sup nk n log n 2 log 2n 1 k quad text almost surely and lim inf nk n log n log 3n c quad text almost surely where log 2 leq c leq 0 and log j is the j times iterated logarithm

infinitely many solutions of quasilinear schrodinger equation with sign changing potential abstract in this paper we study the following quasilinear schrodinger equation of the form u v x u u 2 u g x u x r n where the potential v x is allowed to be sign changing and the primitive of the nonlinearity g x u is of superlinear growth at infinity in u and is also allowed to be sign changing we obtain the existence of infinitely many nontrivial solutions by using dual approach and mountain pass theorem

cam clay plasticity part iii extension of the infinitesimal model to include finite strains the infinitesimal version of the modified cam clay model of critical state soil mechanics is reformulated to include finite deformation effects central to the formulation are the choice of a hardening law that is appropriate for cases involving large plastic volumetric strains and the use of a class of two invariant stored energy functions appropriate for cam clay type models that includes as special cases the constant elastic shear modulus approximation as well as the pressure dependent shear modulus elastic model the analytical model is cast within the framework of finite deformation theory based on a multiplicative decomposition of the deformation gradient for the fully elasto plastic case return mapping is done implicitly in the space defined by the invariants of the elastic logarithmic principal stretches which requires the solution at each stress point of no more than three simultaneous non linear equations a finite element analysis of a strip footing problem is presented to illustrate a prototype example where finite deformation effects significantly impact the predicted response

nontrivial solutions for kirchhoff type problems with a parameter abstract the paper deals with the following kirchhoff type problems a b r n u 2 d x u v x u f x u in r n u h 1 r n where constants a b 0 1 is a parameter and f x u is either sublinear or superlinear at infinity under relaxed assumptions on v x we establish the existence and multiplicity results without the compactness of embedding of the working space

soliton solutions for quasilinear schrodinger equations with critical growth in this paper we establish the existence of standing wave solutions for quasilinear schrodinger equations involving critical growth by using a change of variables the quasilinear equations are reduced to semilinear one whose associated functionals are well defined in the usual sobolev space and satisfy the geometric conditions of the mountain pass theorem using this fact we obtain a cerami sequence converging weakly to a solution v in the proof that v is nontrivial the main tool is the concentration compactness principle due to p l lions together with some classical arguments used by h brezis and l nirenberg 1983 in 9