almost automorphic solutions for stochastic differential equations driven by levy noise abstract in this paper we are concerned with almost automorphic solutions for semilinear stochastic differential equations driven by levy noise on the hilbert space we present a new variant of gronwall s lemma which improves the variant of gronwall s lemma in kamenskii 2015 based on this new variant of gronwall s lemma suitable conditions on the coefficients we prove the existence and uniqueness of almost automorphic solution in distribution for some stochastic differential equations driven by levy noise on the hilbert space which improves and generalizes the results in liu 2014 subsequently by using this new variant of gronwall s lemma we investigate the existence and uniqueness of almost automorphic solution in distribution for stochastic differential equations driven by levy noise with markov switching processes under some weaker conditions in the end two examples are given to illustrate the theoretical results obtained in this paper

existence of globally attracting almost automorphic solutions to some nonautonomous higher order difference equations in this paper we introduce a new theory for asymptotically almost automorphic sequences on z which is a natural generalization of the concept of asymptotically almost periodicity for sequences due to ky fan we next make extensive use of such a newly introduced concept as well as discrete dichotomy techniques to study and establish the existence of globally attracting almost automorphic solutions to some higher order nonautonomous difference equations

modules of finite projective dimension with negative intersection multiplicities let x be the image of x in r the main object of this paper is to study modules of finite length and finite projective dimension over r one consequence of our study will be counterexamples to several conjectures concerning the behavior of intersection multiplicities for modules of finite projective dimension let denote length if s is a noetherian ring m n are finitely generated s modules l m is finite and d pdsm we may define following serre is d zs m n z m n 1 tors m n

almost automorphic mild solutions to some partial neutral functional differential equations and applications abstract the paper considers the existence and uniqueness of almost automorphic mild solutions to some classes of first order partial neutral functional differential equations sufficient conditions for the existence and uniqueness of almost automorphic mild solutions to the above mentioned equations are obtained as an application a first order boundary value problem arising in control systems is considered

on linear volterra equations in banach spaces abstract in this paper we present the basic theory for a class of volterra differential integral equations of convolution type in banach spaces we show that existence of resolvent operator for such an equation is equivalent to its wellposedness and we obtain a hille yosida theorem unfortunately this result is not easy to apply and therefore it is important to have peturbation theorems available we present a result of this type which also contains an existence theorem and show by means of several examples that it cannot be improved

bohr neugebauer type theorem for some partial neutral functional differential equations in this work we study the existence of almost periodic solutions for some partial neutral functional dierential equations using the variation of constants formula and the spectral decomposition of the phase space developed in 6 we prove that the existence of an almost periodic solution is equivalent to the existence of a bounded solution on r

weighted pseudo almost automorphic solutions of hyperbolic semilinear integro differential equations abstract in this paper we deal with weighted pseudo almost automorphic behavior of hyperbolic semilinear integro differential equations in intermediate banach spaces where the nonlinear perturbation is weighted pseudo almost automorphic type or weighted stepanov like pseudo almost automorphic type as applications some interesting examples are presented to illustrate the main findings

the macrae invariant and the first local chern character let r be a commutative noetherian ring and let m be a finitely generated module of finite projective dimension in his investigation of invariants of these modules macrae 6 constructed an invertible ideal g m associated to m which describes th part of the support of m of codimension 1 the fact that g m is invertible implies many properties of the support of m and it has recently been used by foxby 3 to prove some conjectures on intersection multiplicities of modules of finite projective dimension with modules of krull dimension one in this paper we generalize the construction of macrae to a bounded complex e of locally free sheaves on a noetherian scheme y and show that this can be used to describe the first local chern character of e a bounded complex of locally free sheavesoof finite rank will be called a perfect complex for technical reasons we assume that y is connected and quasi projective over an affine scheme let x be the support of e denoted supp e this can be defined as the set of points of y where e is not exact or equivalently as the union of the supports of the homology modules hi e we assume that x is contained in some cartier divisor locally this means that the ideal defining x contains a non zero divisor and if e is a resolution of a module our assumption follows whenever x is a proper subset of y an equivalent formulation of this condition is that x contains no points y of y such that the local ring dy has depth zero such a point will be called a point of depth zero in this situation we construct a cartier divisor g e on y generalizing the macrae invariant if y is quasi projective over a regular local ring this includes among others the case where y specr and r is a complete local ring there is a theory of local chern characters defined for perfect complexes on y for a complex e with support x as above for any scheme y together with a map of finite type f y y

composition of pseudo almost automorphic and asymptotically almost automorphic functions this paper is concerned with pseudo almost automorphic functions which are more general and complicated than pseudo almost periodic functions and asymptotically almost automorphic functions new results concerning the composition of pseudo almost automorphic functions are established

on the topological structure of almost automorphic and asymptotically almost automorphic solutions of differential and integral equations in abstract spaces abstract the main purpose of this paper is to deal with almost automorphic and asymptotically almost automorphic solutions of the initial value problem as well as the nonlinear volterra integral equation in banach spaces we obtain a collection of existence results of such solutions to these equations we investigate also a topological structure of such solution sets moreover we prove aronszajn type theorems for solutions of the initial value problem as well as the nonlinear volterra integral equation defined on the whole real line

stepanov like almost automorphic functions and monotone evolution equations abstract in this paper we are concerned with a new class of stepanov like almost automorphic s p a a functions with values in a banach space x this class contains the space aa x of all bochner almost automorphic functions we use the results obtained to prove the existence and uniqueness of a weak s p a a solution to the parabolic equation u t a t u f t in a reflexive banach space assuming some appropriate conditions of monotonicity coercitivity of the operators a t and s p almost automorphy of the forced term f t this result extends a known result in the case of almost periodicity an application is also given

a new approach for computing hyper singular interface stresses in iibem for solving multi medium elasticity problems in this paper a single stress integral equation is presented for solving multi medium elasticity problems and by using a newly proposed method for treating arbitrarily high order of singular boundary integrals a new method is developed for computing the stresses on the interfaces of multi media comparing to conventional multi domain boundary element methods the presented interface integral bem iibem is more efficient in computational time data preparing and program coding however a big issue is encountered in iibem when computing the stresses on interfaces since the commonly used traction recovery method in computing outer boundary stresses cannot be applied on the interfaces therefore a direct method for handling a hyper singular stress interface integral equation has to be used to obtain the interface stresses in the direct method used in the paper singularities are analytically removed by expressing the non singular part of the integration kernel as a power series in a local distance defined on a projection line plane and the stresses on the interfaces can be evaluated precisely numerical examples are given to verify the correctness of the derived boundary interface integral equations

s asymptotically ω periodic and asymptotically ω periodic solutions to semi linear cauchy problems with non dense domain abstract in this work we study the existence and uniqueness of s asymptotically periodic and asymptotically periodic solutions to a first order differential equation with linear part dominated by a hille yosida operator with non dense domain applications to partial differential equations fractional integro differential and neutral differential equations are given

asymptotically almost automorphic solutions for some integrodifferential equations with nonlocal initial conditions abstract of concern is a class of abstract semilinear integrodifferential equations with nonlocal initial conditions under some suitable hypotheses we establish some new theorems about the existence of asymptotically almost automorphic solutions to the integrodifferential equations moreover an example is given to illustrate our results

a class of linear partial neutral functional differential equations with nondense domain abstract we consider a system of linear partial neutral functional differential equations with nondense domain a natural generalized notion of solutions is provided by the integral solutions we derive a variation of constants formula which allows us to transform the integral solutions of the neutral equation to solutions of an abstract volterra integral equation the basic existence and uniqueness results are given and the solutions are shown to generate an integrated semigroup

existence and uniqueness of c n almost periodic solutions to some ordinary differential equations abstract in this paper we prove the existence and uniqueness of c n almost periodic solutions to the ordinary differential equation x t a t x t f t t r where the matrix a t r m k c is periodic and f r c k is c n almost periodic we also prove the existence and uniqueness of an ultra weak c n almost periodic solution in the case when a t a is independent of t finally we prove also the existence and uniqueness of a mild c n almost periodic solution of the semilinear hyperbolic equation x t a x t f t x considered in a banach space assuming f t x is c n almost periodic in t for each x x satisfies a global lipschitz condition and takes values in an extrapolation space f a 1 associated to a

almost periodic and almost automorphic solutions of linear differential difference equations without favard s separation condition ii abstract the well known favard s theorem states that the linear differential equation 1 x a t x f t with bohr almost periodic coefficients admits at least one bohr almost periodic solution if it has a bounded solution the main assumption in this theorem is the separation among bounded solutions of homogeneous equations 2 x b t x where b h a b b t lim n a t t n if there are bounded solutions which are non separated sometimes almost periodic solutions do not exist r johnson r ortega and m tarallo v zhikov and b levitan in this paper we prove that linear differential equation 1 with levitan almost periodic coefficients has a unique levitan almost periodic solution if it has at least one bounded solution and the bounded solutions of the homogeneous equation 3 x a t x are homoclinic to zero i e lim t t 0 for all bounded solutions of 3 if the coefficients of 1 are bohr almost periodic and all bounded solutions of all limiting equations 2 are homoclinic to zero then eq 1 admits a unique almost automorphic solution the analogue of this result for difference equations is also given we study the problem of existence of bohr levitan almost periodic solutions of eq 1 in the framework of general non autonomous dynamical systems cocycles

3d multi region bem with corners and edges a novel set of auxiliary equations which supplement the fundamental boundary integral equations for the treatment of corners and edges arising in discontinuous traction problems and at zonal intersections is derived based on these equations an efficient linear 3d multi region bem algorithm is presented which can deal with arbitrarily many regions numerical examples demonstrate the effectiveness of this algorithm

pseudo almost automorphic mild solutions to semilinear integral equations in a banach space abstract in this paper we consider the existence of pseudo almost automorphic solutions of the semilinear integral equation x t t a t s a x s f s x s d s t r in a banach space x where a l 1 r a is the generator of an integral resolvent family of linear bounded operators defined on the banach space x and f r x x is a pseudo almost automorphic function the main results are proved by using integral resolvent families combined with the theory of fixed points

an efficient implementation of bem for two and three dimensional multi region elastoplastic analyses abstract boundary element methods bem have been implemented for solving multi region elastoplastic problems with the maximum efficiency a new form of newton raphson algorithm in nonlinear bem is established in which the formation of the right hand side terms in each iteration is accurately represented in this new algorithm only the equations related to the yielded nodes need gaussian elimination at each load step this advantage combined with the sub region technique now makes bem a viable tool for multi region elastoplastic analyses a combined analytical and numerical integration of boundary and volume integrals have been performed for both two and three dimensional analyses whenever the geometry of the volume cells meets the straight line or flat surface requirements the analytical integration is faster and more accurate than numerical integration the numerical results using the above formulation have been presented for some two and three dimensional practical problems commonly encountered in structural and geotechnical engineering and compared with other available solutions

a massera type theorem for almost automorphic solutions of differential equations abstract in this note we present a massera type theorem for the existence of almost automorphic solutions of periodic linear evolution equations of the form x t a t x t f t where a t is unbounded linear operator depending on t periodically and generates a periodic evolutionary process f is almost automorphic the main results are stated in terms of the almost automorphy of solutions and their carleman spectra

almost periodic solutions for abstract impulsive differential equations this paper studies the existence and uniqueness of exponentially stable almost periodic solutions for abstract impulsive differential equations in banach space the investigations are carried out by means of the fractional powers of operators we construct an example to illustrate the feasibility of our results

almost automorphic and pseudo almost automorphic mild solutions to an abstract differential equation in banach spaces in this paper we prove some existence results for almost automorphic and pseudo almost automorphic mild solutions to a class of abstract differential equations in banach spaces the main technique is based on some composition theorems combined with the contraction mapping theorem finally we present an application to a semilinear partial differential equation with dirichlet conditions

on almost automorphic type solutions of abstract integral equations a bohr neugebauer type property and some applications abstract in the present work we give some sufficient conditions to obtain a unique almost automorphic solution to abstract nonlinear integral equations which are simultaneously of advanced and delayed type and also a unique asymptotically almost automorphic mild solution to abstract integro differential equations with nonlocal initial conditions both situations are posed on banach spaces also we develop a bohr neugebauer type result for the abstract integral equations before that we introduce the notion of bounded functions develop the appropriate abstract theory and discuss the almost periodic situation as applications we study the existence of an asymptotically almost automorphic solution to integro differential equations modeling heat conduction in materials with memory and also the existence of the almost automorphic solution to semilinear parabolic evolution equations with finite delay

existence of periodic solutions of partial neutral functional differential equations with unbounded delay abstract in this article we establish a result of existence of periodic solutions for the class of quasi linear partial neutral functional differential equations with unbounded delay that can be described as the abstract functional differential equation d dt x t f t x t ax t g t x t where a is the infinitesimal generator of a strongly continuous semigroup of linear operators on a banach space and f and g are appropriate functions defined on a phase space

existence of positive almost automorphic solutions to neutral nonlinear integral equations abstract this paper is concerned with neutral nonlinear delay integral equations we establish an existence theorem for positive almost automorphic solutions to the equations which extend some existing results even in the case of almost periodicity some examples are given to illustrate our results

a fast reduced order model for radial integral boundary element method based on proper orthogonal decomposition in nonlinear transient heat conduction problems abstract in order to efficiently solve nonlinear transient heat conduction problem a method combining the radial integration boundary element method ribem and the proper orthogonal decomposition pod is proposed to establish the nonlinear reduced order model and the implementation of the reduced order model makes fast numerical simulation possible in engineering field transient heat conduction problems with temperature dependent and temperature independent thermal conductivity are firstly solved by the ribem respectively and two types of snapshots are composed of these solved transient temperature fields subsequently the pod is applied in the analysis of the snapshots and then a set of optimal orthogonal basis can be obtained in the procedure of establishing the reduced order model we need to redistribute the nonlinear equations the strategy is to separate the boundary nodes defined as dirichlet condition and then the orthogonal basis is used to derive a reduced order expression for the remaining unknowns therefore the degree of freedom that needs to be solved can be greatly reduced numerical examples show that different reduced order models based on nonlinear basis and linear basis are all consistent with the full order model what is more the computational efficiency is greatly improved due to the introduction of the reduced order model

intersection multiplicities over gorenstein rings let r be a complete local ring of dimension d over a perfect field of prime characteristic p and let m be an r module of finite length and finite projective dimension s dutta showed that the equality lim n to infty frac ell f n r m p nd ell m holds when the ring r is a complete intersection or a gorenstein ring of dimension at most 3 we construct a module over a gorenstein ring r of dimension five for which this equality fails to hold this then provides an example of a nonzero todd class tau 3 r and of a bounded free complex whose local chern character does not vanish on this class

massera type theorem for almost automorphic solutions of functional differential equations of neutral type abstract in this work we study the existence of almost automorphic solutions for functional differential equations of neutral type we prove that the existence of a bounded solution on r implies the existence of an almost automorphic solution

almost automorphic solutions of nonautonomous evolution equations abstract in this paper we establish some new theorems about the existence of almost automorphic solutions to nonautonomous evolution equations u t a t u t f t and u t a t u t f t u t in banach spaces as we will see our results allow for a more general a t to some extent an example is also given to illustrate our results in addition by means of an example we show that one cannot ensure the existence of almost automorphic solutions to u t a t u t f t even if the evolution family u t s generated by a t is exponentially stable and f a a x

almost periodic and almost automorphic solutions of linear differential equations the paper is dedicated to the study problem of existence of almost periodic respectively almost automorphic recurrent solutions of linear differential equations u t a t y u t f t y y y in banach space with almost periodic respectively almost automorphic recurrent coefficients where y r is a dynamical system on the metric space y in particular we prove that if the operator a y is positive and auto adjoint then for the equation 1 u t a t y u t 0 one of the following alternative is fulfilled i there exists a complete trajectory of 1 with constant positive norm ii the trivial solution of equation 1 is uniformly asymptotically stable this problem we investigate in the framework of general linear non autonomous dynamical system we apply our general results also for the functional differential equations and difference equations

bounded and almost automorphic solutions of some nonlinear differential equations in banach spaces abstract we study some properties of bounded and almost automorphic solutions of the following nonlinear differential equation x f t x where x is a banach space and f r x x is almost automorphic with a parameter we give sufficient conditions for the existence of almost automorphic solutions when the differential equation admits at least a solution with a relatively compact range defined on the half line of positive numbers

existence and uniqueness of pseudo almost periodic solutions to some abstract partial neutral functional differential equations and applications the paper considers the existence and uniqueness of pseudo almost periodic mild solutions to some classes of first order partial neutral functional differential equations upon making some suitable assumptions existence and uniqueness results are obtained applications include both a partial integro differential equation arising in control systems and the scalar reaction diffusion equation with delay

existence of positive almost automorphic solutions to nonlinear delay integral equations abstract this paper is concerned with the existence of positive almost automorphic solutions to some nonlinear delay integral equations we first establish a new fixed point theorem for mixed monotone operator in a cone and then with its help we obtain existence theorems of positive almost automorphic solutions some examples are given to illustrate our results as one will see even in the case of almost periodicity our theorems extend some earlier results and moreover the approach dealing with the integral equation arising in an epidemic problem in this paper is also new

some properties of pseudo almost automorphic functions and applications to abstract differential equations abstract this paper is concerned with some properties of pseudo almost automorphic functions which are more general and complicated than pseudo almost periodic functions using these properties we establish an existence and uniqueness theorem for pseudo almost automorphic mild solutions to semilinear differential equations in a banach space

almost automorphic solutions of non autonomous difference equations abstract in the present paper we study the non autonomous difference equations given by u k 1 a k u k f k and u k 1 a k u k g k u k for k z where a k is a given non singular n n matrix with elements a i j k 1 i j n f z e n is a given n 1 vector function g z e n e n and u k is an unknown n 1 vector with components u i k 1 i n we obtain the existence of a discrete almost automorphic solution for both the equations assuming that a k and f k are discrete almost automorphic functions and the associated homogeneous system admits an exponential dichotomy also assuming the function g satisfies a global lipschitz type condition we prove the existence and uniqueness of an almost automorphic solution of the nonlinear difference equation

resolvent operators for integral equations in a banach space conditions are given which ensure the existence of a resolvent operator for an integrodifferential equation in a banach space the resolvent operator is similar to an evolution operator for nonautonomous differential equations in a banach space as in the finite dimensional case this operator is used to obtain a variation of parameters formula which can be used to obtain results concerning the asymptotic behaviour of solutions and weak solutions

complete second order linear differential equations with almost periodic solutions abstract this paper characterizes equations of the type u t bu t au t 0 in a banach space where a b are densely defined closed linear operators and whose solutions are all almost periodic

existence of pseudo almost automorphic mild solutions to stochastic fractional differential equations abstract fractional stochastic differential equations have gained considerable importance due to their application in various fields of science and engineering this paper is concerned with the square mean pseudo almost automorphic solutions for a class of fractional stochastic differential equations in a hilbert space the main objective of this paper is to establish the existence and uniqueness of square mean pseudo almost automorphic mild solutions to a linear and semilinear case of these equations a new set of sufficient conditions is obtained to achieve the required result by using the stochastic analysis theory and fixed point strategy finally an example is provided to illustrate the obtained theory

wellposedness and wave propagation for a class of integrodifferential equations in banach space in recent years there has been an increasing interest in the mathematical treatment of problems which originate in the theory of viscoelastic materials in such problems the constitutive relations for these materials incorporate the history of the strain or the strain rate and in the linear theory lead to linear volterra integrodifferential equations with infinite memory in a banach space x the purpose of this paper is to examine the problems of wellposedness and wave propagation for one such equation in particular we are concerned with equations of the form x t 4 x r j f t s x s ds al

pseudo almost automorphic mild solutions to nonautonomous differential equations and applications abstract in this paper we introduce a new concept of bi almost automorphic functions and obtain new existence and uniqueness theorems for pseudo almost automorphic mild solutions to several nonautonomous differential equations moreover two examples are given to illustrate the general theorems

self sustained oscillations in a ring array of coupled lossless transmission lines abstract in this paper we derive a neutral difference differential system with diffusion which arises from a ring array of coupled lossless transmission lines we investigate the problem of self sustained oscillations of the considered transmission lines and apply a global hopf bifurcation theorem to establish the existence of multiple large amplitude phase locked periodic solutions in the corresponding neutral system

square mean pseudo almost automorphic process and its application to stochastic evolution equations abstract this paper introduces the concept of the square mean pseudo almost automorphy for a stochastic process also it introduces the properties on the completeness and the composition of the space that consists of such processes with appropriate settings and by virtue of the theory of the semigroups of the operators to an evolution family the banach fixed point theorem and the stochastic analysis techniques this paper investigates the existence the uniqueness and the global stability of the square mean pseudo almost automorphic solutions for a general class of stochastic evolution equations finally this paper provides an illustrative example to justify the practical usefulness of the established theoretical results

existence of positive pseudo almost periodic solutions to a class of neutral integral equations abstract in this work a new fixed point theorem in partially ordered banach spaces is established and then used to prove the existence of positive pseudo almost periodic solutions to a class of neutral integral equations our existence theorem extends some recent results due to e ait dads p cieutat l lhachimi positive pseudo almost periodic solutions for some nonlinear infinite delay integral equations mathematical and computer modelling 49 2009 721 739 to a more general class of integral equations

weighted pseudo almost automorphic solutions to a semilinear fractional differential equation with stepanov like weighted pseudo almost automorphic nonlinear term in this paper we investigate some existence results of weighted pseudo almost automorphic solutions to a semilinear fractional differential equation in banach spaces with stepanov like weighted pseudo almost automorphic nonlinear term our main results are based upon ergodicity and composition theorems of stepanov like weighted pseudo almost automorphic functions combined with fixed point techniques

stepanov like pseudo almost periodicity and its applications to some nonautonomous differential equations abstract the paper revisits the concept of s p pseudo almost periodicity recently introduced by the author in particular we study the existence of pseudo almost periodic solutions to some nonautonomous differential equations in the case when the semilinear forcing term is both continuous and s p pseudo almost periodic for p 1 applications include the existence of pseudo almost periodic solutions to the heat equation with a forcing term which is s p pseudo almost periodic and jointly continuous

asymptotic periodicity for some evolution equations in banach spaces abstract this work deals with the existence and uniqueness of pseudo almost periodic and asymptotically periodic mild solutions to some evolution equations in banach spaces

existence of asymptotically almost automorphic solutions to some abstract partial neutral integro differential equations abstract the paper establishes the existence and uniqueness of asymptotically almost automorphic mild solution to an abstract partial neutral integro differential equation with unbounded delay an example is given to illustrate our results

pseudo almost automorphic solutions of some nonlinear integro differential equations in this paper we discuss the existence and uniqueness of a pseudo almost automorphic solution of an integro differential equation in a banach space x we achieve our results using the methods of fractional powers of operators and the banach fixed point theorem these results are new and complement the existing ones

mappings of higher order and nonlinear equations in some spaces of almost periodic functions abstract in the first part of the paper we examine mappings of higher order from a general point of view that is in normed spaces of bounded real valued functions defined on r particular attention is paid to the relation of such mappings with the so called autonomous superposition operators next we investigate mappings of higher order in banach spaces of almost periodic functions and their perturbations we also give necessary and sufficient conditions guaranteeing that a nonautonomous superposition operator acts in the space of almost periodic functions in the sense of levitan and is uniformly continuous in the banach space of bounded almost periodic functions in the sense of levitan we discuss mappings of higher order and a convolution operator some applications to nonlinear differential and integral equations are given

on evolutionary volterra equations with state dependent delay abstract in this work we study topological properties of the solution set of abstract volterra equations with state dependent delay particularly we ensure that such a set is a nonempty compact and connected set as application we consider our abstract results in the framework of integro differential equations coming from viscoelasticity theory

existence results for some damped second order volterra integro differential equations abstract in this paper we make a subtle use of operator theory techniques and the well known schauder fixed point principle to establish the existence of pseudo almost automorphic solutions to some second order damped integro differential equations with pseudo almost automorphic coefficients in order to illustrate our main results we will study the existence of pseudo almost automorphic solutions to a structurally damped plate like boundary value problem

element differential method and its application in thermal mechanical problems summary in this paper a new numerical method element differential method edm is proposed for solving general thermal mechanical problems the key point of the method is the direct differentiation of the shape functions of lagrange isoparametric elements used to characterize the geometry and physical variables a set of analytical expressions for computing the first and second order partial derivatives of the shape functions with respect to global coordinates are derived based on these expressions a new collocation method is proposed for establishing the system of equations in which the equilibrium equations are collocated at nodes inside elements and the traction equilibrium equations are collocated at interface nodes between elements and outer surface nodes of the problem attributed to the use of the lagrange elements which can guarantee the variation of physical variables consistent through all elemental nodes edm has higher stability than the traditional collocation method the other main features of edm are that no mathematical or mechanical principles are required to set up the system of equations and no integrals are involved to form the coefficients of the system a number of numerical examples of two and three dimensional problems are given to demonstrate the correctness and efficiency of the proposed method

almost automorphic solutions to nonautonomous semilinear evolution equations in banach spaces abstract this paper is concerned with almost automorphy of the solutions to a nonautonomous semilinear evolution equation u t a t u t f t u t in a banach space with a stepanov like almost automorphic nonlinear term we establish a composition theorem for stepanov like almost automorphic functions furthermore we obtain some existence and uniqueness theorems for almost automorphic solutions to the nonautonomous evolution equation by means of the evolution family and the exponential dichotomy some results in this paper are new even if a t is time independent

compact almost automorphic solutions to semilinear cauchy problems with non dense domain in this work we study the existence and uniqueness of compact almost automorphic solutions to a first order differential equation with a linear part dominated by a hille yosida type operator with non dense domain

compact almost automorphic solutions to integral equations with infinite delay abstract given a l 1 r and the generator a of an l 1 integrable resolvent family of linear bounded operators defined on a banach space x we prove the existence of compact almost automorphic solutions of the semilinear integral equation u t t a t s a u s f s u s d s for each f r x x compact almost automorphic in t for each x x and satisfying lipschitz and holder type conditions in the scalar linear case we prove that a l 1 r positive nonincreasing and log convex is sufficient to obtain the existence of compact almost automorphic solutions

almost automorphic solutions for abstract functional differential equations for abstract linear functional differential equations with an almost automorphic forcing term we establish a result on the existence of almost automorphic solutions which extends the classical theorem due to massera on the existence of periodic solutions for linear periodic ordinary differential equations

interface integral bem for solving multi medium elasticity problems in this paper boundary integral equations for multi medium elasticity problems are derived from the boundary domain integral equations for single medium elasticity problems with varying shear modulus the new formulations derived make up for the lack of boundary integral equations in solving multi medium problems using the boundary element method the effect of nonhomogeneity between adjacent materials is embodied by the interface integrals appearing in the integral equation and including the differences of adjacent material properties comparing to conventional multi domain boundary element methods the presented interface integral bem iibem approach is more efficient in computational time data preparing and program coding numerical examples are given to verify the correctness of the derived boundary interface integral equations

almost periodic and pseudo almost periodic solutions to fractional differential and integro differential equations abstract we study the existence of almost periodic resp pseudo almost periodic mild solutions for fractional differential and integro differential equations in the case when the forcing term belongs to the class of stepanov almost resp stepanov like pseudo almost periodic functions

a new composition theorem for square mean almost automorphic functions and applications to stochastic differential equations abstract in this paper we establish a new composition theorem for square mean almost automorphic functions under conditions which are different from lipschitz conditions in the literature we apply this new composition theorem together with schauder s fixed point theorem to investigate the existence of square mean almost automorphic mild solutions for a stochastic differential equation in a real separable hilbert space finally an interesting corollary is also given for the sub linear growth cases

numerical equivalence defined on chow groups of noetherian local rings in the present paper we define a notion of numerical equivalence on chow groups or grothendieck groups of noetherian local rings which is an analogue of that on smooth projective varieties under a mild condition it is proved that the chow group modulo numerical equivalence is a finite dimensional vector space as in the case of smooth projective varieties numerical equivalence on local rings is deeply related to that on smooth projective varieties for example if grothendieck s standard conjectures are true then a vanishing of chow group of local rings modulo numerical equivalence can be proven using the theory of numerical equivalence the notion of numerically roberts rings is defined it is proved that a cohen macaulay local ring of positive characteristic is a numerically roberts ring if and only if the hilbert kunz multiplicity of a maximal primary ideal of finite projective dimension is always equal to its colength numerically roberts rings satisfy the vanishing property of intersection multiplicities we shall prove another special case of the vanishing of intersection multiplicities using a vanishing of localized chern characters

almost periodicity in frechet spaces in this paper we deal with almost periodic functions with values in a frechet space we apply obtained results to prove the existence of solutions of the initial value problem as well as the volterra integral equation in this class of functions we also introduce and investigate asymptotically almost periodic functions with values in a frechet space

existence of pseudo almost automorphic solutions to some abstract differential equations with sp pseudo almost automorphic coefficients abstract this paper introduces and studies the notion of s p pseudo almost automorphy or stepanov like pseudo almost automorphy which generalizes in a natural fashion the concept of pseudo almost automorphy that was recently introduced in the literature by liang xiao and zhang we next obtain the existence of pseudo almost automorphic solutions to some differential equations with s p pseudo almost automorphic coefficients

pseudo almost periodicity of some nonautonomous evolution equations with delay abstract this paper is concerned with pseudo almost periodicity of the solutions to the nonautonomous evolution equation with delay u t a t u t f t u t h some sufficient conditions which ensure the existence and uniqueness of pseudo almost periodic mild solutions to the evolution equation with delay are given an example is shown to illustrate our results

existence results for partial neutral functional differential equations with unbounded delay abstract we prove the existence of mild solutions for a partial neutral functional integrodifferential equation with unbounded delay using the leray schauder alternative