exponential power series expansion for the propagator of general diffusion processes abstract the propagator of a general diffusion process is determined by expanding its exponent in a power series of a time increment t the expansion coefficients can be analytically evaluated from recursive relations we are thus able to construct a covariant short time approximation for the propagator valid to any desired precision in t attention is given both to the mathematics and its physical interpretation this allows us to shed further light on the results already known in the literature on quantum mechanics and theory of continuous markov processes

vanishing viscosity for hemivariational inequalities modeling dynamic problems in elasticity abstract in this paper we consider a mathematical model describing a dynamic linear elastic contact problem with nonmonotone skin effects the subdifferential multivalued and multidimensional reaction displacement law is employed we treat an evolution hemivariational inequality of hyperbolic type which is a weak formulation of this mechanical problem we establish a result on the existence of solutions to the cauchy problem for the hemivariational inequality this result is a consequence of an existence theorem for second order evolution inclusion for the latter using the parabolic regularization method we obtain the solution as a limit when the viscosity term tends to zero

dynamic contact problem for viscoelastic piezoelectric materials with slip dependent friction abstract in this paper we deal with a class of inequality problems for dynamic frictional contact between a piezoelectric body and a foundation the model consists of a system of the hemivariational inequality of hyperbolic type for the displacement the time dependent elliptic equation for the electric potential the friction condition is described to be the clarke subdifferential relations of nonmonotone and multivalued character in the tangential directions on the boundary the existence of a weak solution to the model is proved by embedding the problem into a class of second order evolution inclusions and by applying a surjectivity result for multivalued operators

mixed bram halmos and agler embry conditions abstract the subnormality of a hilbert space operator may be characterized either by the bram halmos conditions positivity of certain operator matrices or the agler embry conditions positivity of certain operator differences we define and consider mixed conditions involving matrices of operator differences thus yielding conditions whose extremes are the bram halmos and agler embry conditions we study these conditions for weighted shifts showing that they reduce to matrices of differences of the moments of the shifts and examine these conditions under the perturbation of a single weight of a subnormal shift

a consistent model coupling adhesion friction and unilateral contact a model considering both unilateral contact coulomb friction and adhesion is presented in the framework of continuum thermodynamics the contact zone is considered as a material boundary and the local constitutive laws are derived by choosing two specific surface potentials the free energy and the dissipation potential because of the non regular properties of these potentials convex analysis is used to derive the local behavior laws from the state and the complementary laws the adhesion is characterized by an internal variable introduced by fremond which represents the intensity of adhesion the continuous transition from a total adhesive condition to a possible pure frictional one is enforced by using elasticity coupled with damage for the interface non penetration conditions and coulomb law are strictly imposed without using any penalty the variational formulation for quasistatic problems is written as the coupling between an implicit variational inequality a variational inequality and a differential equation an increment formulation is proposed an existence result under a condition on the friction coefficient is given a numerical method is derived from the incremental formulation and various algorithms are implemented they solve a sequence of minimization problems under constraints the model is used to simulate a micro indentation experiment conducted to characterize the behavior of fiber matrix interface in a ceramic composite identification of the constitutive parameters is discussed

hemivariational inequalities modeling dynamic contact problems with adhesion abstract this paper deals with the mathematical modelling of viscoelastic frictional contact processes in mechanics which involve adhesion the model consists of a coupled system of the hemivariational inequality of hyperbolic type for the displacement and the ordinary differential equation for the bonding field the frictional forces are derived from nonconvex superpotentials through the generalized clarke subdifferential the properties of the body are described by a modified kelvin voigt constitutive law the existence of weak solution to the problem is proved by embedding it into a class of second order evolution inclusions and by applying a surjectivity result for multivalued pseudomonotone operators we also establish a result on the regularity of weak solution to the model finally examples of subdifferential boundary conditions which include the functions of d c type are provided

extremal solutions of the two dimensionall problem of moments by using the theory of the principal function of a hyponormal operator with rank one self commutator one classifies some extremal points of the solutions of the truncatedl problem of moments in two real variables these extremal elements called degenerated solutions of thel problem are proved to be in a natural bijective correspondence with the bounded quadrature domains in the complex plane the main result of the paper characterizes these degenerated solutions from three distinct perspectives complex analysis moment problems and operator theory the interplay between the three points of view each with specific techniques constitutes the main body of the paper

solvability of dynamic antiplane frictional contact problems for viscoelastic cylinders abstract we study a mathematical model which describes the antiplane shear deformations of a cylinder in frictional contact with a rigid foundation the process is dynamic the material behavior is described with a linearly viscoelastic constitutive law and friction is modeled with a general subdifferential boundary condition we derive a variational formulation of the model which is in a form of an evolutionary hemivariational inequality for the displacement field then we prove the existence of a weak solution to the model the proof is based on an abstract result for second order evolutionary inclusions in banach spaces also we prove that under additional assumptions the weak solution to the model is unique we complete our results with concrete examples of friction laws for which our results are valid

analysis of an adhesive contact problem for viscoelastic materials with long memory abstract the goal of this paper is to study a mathematical model which describes the adhesive contact between a deformable body and a foundation the body consists of a viscoelastic material with long memory and the process is assumed to be quasistatic the adhesive contact condition on the normal plane is modeled by a version of normal compliance condition with unilateral constraint in which adhesion is taken into account the adhesive contact condition on the tangential plane is described by an adhesive clarke subdifferential condition and the evolution of the bonding field is described by an ordinary differential equation we derive the variational formulation of this problem which is a system of a variational hemivariational inequality for the displacement field and an ordinary differential equation for the bonding field then we obtain existence and uniqueness results on abstract inclusions and abstract variational hemivariational inequalities finally we apply the abstract results to prove the existence of a unique weak solution to the contact problem

solvability and continuous dependence results for second order nonlinear evolution inclusions with a volterra type operator abstract the paper deals with second order nonlinear evolution inclusions and their applications we study evolution inclusions involving a volterra type integral operator which are considered within the framework of an evolution triple of spaces first we deliver a result on the unique solvability of the cauchy problem for the inclusion by combining a surjectivity result for multivalued pseudomonotone operators and the banach contraction principle next we provide a theorem on the continuous dependence of the solution to the inclusion with respect to the operators involved in the problem finally we consider a dynamic frictional contact problem of viscoelasticity for materials with long memory and indicate how the result on evolution inclusion is applicable to the model of the contact problem

boundary hemivariational inequality of parabolic type abstract in this paper we consider a parabolic hemivariational inequality with a nonmonotone multivalued boundary condition and with a time dependent pseudomonotone operator we establish the existence of solutions for such inequality our proof is based on a known surjectivity result for operators of pseudomonotone type we present an example of semipermeability heat conduction problem to which the result applies

hemivariational inequality for viscoelastic contact problem with slip dependent friction abstract in this paper we consider a class of hyperbolic hemivariational inequalities modeling the frictional contact between a viscoelastic body and a rigid foundation the friction law is described by a multivalued subdifferential relation which includes the slip displacement dependent friction and the tresca models we establish the existence of weak solutions to the problem by using a surjectivity result for pseudomonotone mappings

dynamic bilateral contact problem for viscoelastic piezoelectric materials with adhesion abstract a model of a dynamic viscoelastic adhesive contact between a piezoelectric body and a deformable foundation is described the model consists of a system of the hemivariational inequality of hyperbolic type for the displacement the time dependent elliptic equation for the electric potential and the ordinary differential equation for the adhesion field in the hemivariational inequality the friction forces are derived from a nonconvex superpotential through the generalized clarke subdifferential the existence of a weak solution is proved by embedding the problem into a class of second order evolution inclusions and by applying a surjectivity result for multivalued operators

sub super solution method for a class of higher order evolution hemivariational inequalities abstract in this paper we extend the extremality results for the variational inequality to a higher order evolution hemivariational inequality more precisely we give an existence theorem of solution for the higher order evolution hemivariational inequality by using the sub super solution method we prove the compactness of the solution set within an order interval formed by the sub solution and super solution we also show an existence theorem of the extremal solution for the higher order evolution hemivariational inequality under consideration

coercive and semicoercive hemivariational inequalities variational inequalities have a concrete mechanical meaning they are expressions of the principle of virtual work or power in its inequality form in the case of lack of monotonicity of the underlying stress strain or reaction displacement conditions or equivalently if the corresponding energy functionals are nonconvex the variational expressions are no longer variational inequalities another type of inequality expression arises as variational formulation of the problem these expressions have been introduced in mechanics by the author and are called hemivariational inequalities the aim of this paper is the formulation of an abstract mathematical theory for coercive and semicoercive hemivariational inequalities

slip dependent friction in dynamic elasticity the dynamic evolution with frictional contact of an elastic body is considered in modeling the contact the tresca model and a slip dependent friction law are used the existence of a solution is proved in the two dimensional case the uniqueness is proved for the one dimensional shearing problem the convergence for a vanishing viscosity of the unique solution of the viscoelastic problem to a solution of the elastic problem is obtained

on numerical approximation of a variational hemivariational inequality modeling contact problems for locking materials abstract this paper is devoted to numerical analysis of a new class of elliptic variational hemivariational inequalities in the study of a family of contact problems for elastic ideally locking materials the contact is described by the signorini unilateral contact condition and the friction is modeled by a nonmonotone multivalued subdifferential relation allowing slip dependence the problem involves a nonlinear elasticity operator the subdifferential of the indicator function of a convex set for the locking constraints and a nonconvex locally lipschitz friction potential solution existence and uniqueness result on the inequality can be found in migorski and ogorzaly 2017 in this paper we introduce and analyze a finite element method to solve the variational hemivariational inequality we derive a cea type inequality that serves as a starting point of error estimation numerical results are reported showing the performance of the numerical method

on convergence of solutions to history dependent variational hemivariational inequalities abstract the goal of the paper is to study the behavior of solutions to the history dependent variational hemivariational inequalities under perturbation of the data first we give an existence and uniqueness result which has been obtained by using previous works second we deliver a continuous dependence result when all the data are subjected to perturbations finally a quasistatic viscoelastic frictional contact problem is presented to illustrate our main results

boundary hemivariational inequality problems with doubly nonlinear operators in this paper we investigate a class of nonlinear boundary hemivariational inequality problems under suitable hypotheses the existence of solutions is established via rewriting these problems into a class of evolution inclusions and using the discretization method and the theory of pseudomonotone operators moreover the continuous dependence result of the solutions to the initial data is given

exact propagator and eigenfunctions for multistable models with arbitrarily prescribed n lowest eigenvalues the author presents a method to construct potentials for schrodinger equations with some prescribed features for which all eigenfunctions and the time dependent propagator can be explicitly calculated the prescribed features can be formulated by choosing arbitrarily the n lowest eigenvalues alternatively one can prescribe some qualitative behaviour for the potential like the number and relative depths of wells and barriers the results can also be applied to the construction of fokker planck models with prescribed properties and explicitly calculable transition probability density the method is based on ideas of supersymmetric quantum mechanics and the theory of solitons that can be traced back to the work of darboux 1894 and crum 1955

hyperexpansive completion problem via alternating sequences an application to subnormality truncations of completely alternating sequences are entirely characterized the completely hyperexpansive completion problem is solved for finite sequences of positive numbers in terms of positivity of attached matrices solutions to the problem are written explicitly for sequences of two three four five and six numbers as an application an explicit solution of the subnormal completion problem for five numbers is given

hemivariational inequality approach to the dynamic viscoelastic sliding contact problem with wear abstract the dynamic contact problem of sliding contact with wear between a viscoelastic body and a foundation is formulated as a hemivariational inequality the contact is modeled with a general normal damped response condition which is nonmonotone possibly multivalued and has the subdifferential form we establish the existence of weak solutions by using a surjectivity result for a class of pseudomonotone operators we also deliver conditions under which the solution of the evolution inclusion associated with the hemivariational inequality is unique

a quasistatic contact problem for viscoelastic materials with friction and damage abstract we consider a mathematical model which describes the frictional contact between a deformable body and a foundation the process is quasistatic the material is assumed to be viscoelastic with long memory and the frictional contact is modelled with subdifferential boundary conditions the mechanical damage of the material is described by the damage function which is modelled by a nonlinear partial differential equation we derive the variational formulation of the problem which is a coupled system of a hemivariational inequality and a parabolic equation then we prove the existence of a unique weak solution to the model the proof is based on arguments of abstract stationary inclusion and a fixed point theorem

a system of evolution hemivariational inequalities modeling thermoviscoelastic frictional contact abstract in this paper we prove the existence and uniqueness of the weak solution for a dynamic thermoviscoelastic problem which describes frictional contact between a body and a foundation we employ the kelvin voigt viscoelastic law include the thermal effects and consider the general nonmonotone and multivalued subdifferential boundary conditions the model consists of the system of the hemivariational inequality of hyperbolic type for the displacement and the parabolic hemivariational inequality for the temperature the existence of solutions is proved by using a surjectivity result for operators of pseudomonotone type the uniqueness is obtained for a large class of operators of subdifferential type satisfying a relaxed monotonicity condition

variational methods for non differentiable functionals and their applications to partial differential equations the interest in extending the theory of nonlinear partial differential equations pde to pde with discontinuous nonlinearities dnde has been increasing daily the reasons are twofold 1 many free boundary problems may be reduced to boundary value problems of dnde cf chang 16 71 chang and jiang 9 and fleishman and mahar 121 2 sometimes in dealing with a pde problem it is beneficial to put the original pde into a large category for instance dnde cf chang 7 simply speaking a dnde is as follows

on k hyperexpansive operators abstract this paper considers the k hyperexpansive hilbert space operators t those satisfying 0 p n n p t p t p 0 1 n k and the k expansive operators those satisfying the above inequality merely for n k it is known that if t is k hyperexpansive then so is any power of t we prove the analogous result for t assumed merely k expansive turning to weighted shift operators we give a characterization of k expansive weighted shifts and produce examples showing the k expansive classes are distinct for a weighted shift w that is k expansive for all k that is completely hyperexpansive we obtain results for k hyperexpansivity of back step extensions of w in addition we discuss the completely hyperexpansive completion problem which is parallel to stampfli s subnormal completion problem

dynamic contact problem for viscoelastic piezoelectric materials with normal damped response and friction in this paper we deal with a class of inequality problems for dynamic frictional contact between a piezoelectric body and a foundation the model consists of a system of the hemivariational inequality of hyperbolic type for the displacement the time dependent elliptic equation for the electric potential the contact is modeled by a general normal damped response condition and a friction law which are nonmonotone possibly multivalued and have the subdifferential form the existence of a weak solution to the model is proved by embedding the problem into a class of second order evolution inclusions and by applying a surjectivity result for multivalued operators

numerical analysis of a hyperbolic hemivariational inequality arising in dynamic contact in this paper a fully dynamic viscoelastic contact problem is studied the contact is assumed to be bilateral and frictional where the friction law is described by a nonmonotone relation between the tangential stress and the tangential velocity a weak formulation of the problem leads to a second order nonmonotone subdifferential inclusion also known as a second order hyperbolic hemivariational inequality we study both semidiscrete and fully discrete approximation schemes and bound the errors of the approximate solutions under some regularity assumptions imposed on the true solution optimal order error estimates are derived for the linear element solution this theoretical result is illustrated numerically

weak solvability of a fractional viscoelastic frictionless contact problem abstract the goal of this paper is to study a quasistatic frictionless contact problem for a viscoelastic body in which the constitutive equation is modeled with the fractional kelvin voigt law and the contact condition is described by the clarke subdifferential of a nonconvex and nonsmooth functional the variational formulation of this problem is provided in the form of a fractional hemivariational inequality in order to solve this inequality we apply the rothe method and prove that the associated abstract volterra inclusion has at least one solution

statistical replacement for systems with delta correlated fluctuations nonlinear systems with stochastic parameters are approximated by simpler systems using a method that we call statistical replacement this method is an extension of the previously developed agree which was restricted to systems with additive fluctuations statistical replacement incorporates the distinctions between globally stable thermodynamically closed systems and thermodynamically open systems that can be unstable

decay of energy for second order boundary hemivariational inequalities with coercive damping abstract in this article we consider the asymptotic behavior of solutions to second order evolution inclusions with the boundary multivalued term u t a t u t b u t j t u t 0 and u t a t u t b u t j t u t 0 where a is a possibly nonlinear coercive and pseudomonotone operator b is linear continuous symmetric and coercive is the trace operator and j is a locally lipschitz integral functional with denoting the clarke generalized gradient taken with respect to the second variable for both cases we provide conditions under which the appropriately defined energy decays exponentially to zero as time tends to infinity we discuss assumptions and provide examples of multivalued laws that satisfy them

quasilinear approximations for the propagator of the fokker planck equation abstract four novel classes of the approximate fokker planck propagators are developed by means of a decoupling operator treatment for a small time increment t these are correct at least through second order t the propagators have an ornstein uhlenbeck form thus leading to novel discrete path integrals with a linear reference system their ambiguities are characterized by an arbitrary function of the time increment and by a matrix and a vector field which may be both time and state dependent the efficiency of the treatment used is very sensitive to the choice of these functions several forms of which are proposed the power of the treatment is illustrated by a physically meaningful fokker planck equation relevant to laser physics being used as the global approximations the approximate propagators obtained are shown to provide a correct description of a bistable system in the entire time domain a scaling theory of suzuki including its unified version emerges from them in a very natural way another attractive feature of our general treatment when compared to the others known in the literature is that it allows for equations with singular diffusion matrices two of which a kramers equation and a colored noise problem are considered

a class of evolution variational inequalities with memory and its application to viscoelastic frictional contact problems abstract in this paper we consider the first order evolution variational inequality involving two history dependent operators a result on existence and uniqueness of solution is proved we illustrate the applicability of this result by considering a dynamic frictional contact problem for viscoelastic material with the normal compliance contact condition with memory and coulomb s law of dry friction

evolution hemivariational inequality for a class of dynamic viscoelastic nonmonotone frictional contact problems in this paper we consider a class of hyperbolic hemivariational inequalities modeling the frictional contact between a viscoelastic body and a rigid foundation the friction condition is described by a multivalued subdifferential relation which includes both the slip displacement and the slip rate dependent friction and the tresca models the existence of weak solutions to the problem is proved by exploiting a surjectivity result for a class of pseudomonotone mappings

a characterization of k hyponormality via weak subnormality abstract an operator t acting on a hilbert space h is said to be weakly subnormal if there exists an extension t acting on k h such that t t f t t f for all f h when such partially normal extensions exist we denote by m p n e t the minimal one on the other hand for k 1 t is said to be k hyponormal if the operator matrix t j t i i j 1 k is positive we prove that a 2 hyponormal operator t always satisfies the inequality t t t t t 2 t t and as a result t is automatically weakly subnormal thus a hyponormal operator t is 2 hyponormal if and only if there exists b such that ba a t and t a 0 b is hyponormal where a t t 1 2 more generally we prove that t is k 1 hyponormal if and and only if t is weakly subnormal and m p n e t is k hyponormal as an application we obtain a matricial representation of the minimal normal extension of a subnormal operator as a block staircase matrix

nonlinear second order evolution inclusions with noncoercive viscosity term abstract in this paper we deal with a second order nonlinear evolution inclusion with a nonmonotone noncoercive viscosity term using a parabolic regularization approximation of the problem and a priori bounds that permit passing to the limit we prove that the problem has a solution

hyponormal operators with rank two self commutators abstract in this paper it is shown that if t l h satisfies i t is a pure hyponormal operator ii t t is of rank two and iii ker t t is invariant for t then t is either a subnormal operator or the putinar s matricial model of rank two more precisely if t ker t t has a rank one self commutator then t is subnormal and if instead t ker t t has a rank two self commutator then t is either a subnormal operator or the kth minimal partially normal extension t k k of a k 1 hyponormal operator t k which has a rank two self commutator for any k z hence in particular every weakly subnormal or 2 hyponormal operator with a rank two self commutator is either a subnormal operator or a finite rank perturbation of a k hyponormal operator for any k z

operator theory and algebraic geometry on presente des resultats en theorie des operateurs multivariable dont les demonstrations se relient a des techniques issues de la geometrie algebrique

on the existence of solutions for nonlinear parabolic problems with nonmonotone discontinuities abstract in this paper we consider a nonlinear parabolic problem with a discontinuous nonmonotone nonlinearity we assume the existence of an upper solution and a lower solution such that using results from the theory of pseudomonotone operators and from the theory of multivalued analysis together with truncation and penalization techniques we show that there exists at least one solution x t z such that t z x t z t z a e on t z

diffusion in a potential field path integral approach abstract within the framework of the path integral formalism we develop a simple method to solve the fokker planck diffusion problems in a potential field including the decay of an unstable state unlike previous approaches it yields a unified treatment of all time regimes and is legitimate for any value of the diffusion coefficient an attractive feature of our method is that it provides numerical results in regions where there are no analytical solutions in particular being valid for an arbitrary shape of the potential it is very useful for studying a diffusion problem near and in the critical point where the standard treatments break down moreover our method after a simple transformation permits to obtain also the first passage times of the process

dynamic hemivariational inequalities in contact mechanics abstract this paper gives a review of results on the existence and uniqueness of solutions to some mechanical contact problems the second order evolution problems with a general normal compliance response condition and a normal damped response one in viscoelasticity are discussed finally a new result for a problem which includes the slip displacement dependent friction and the tresca model is provided

existence of non subnormal polynomially hyponormal operators in 1950 p r halmos motivated in part by the successful development of the theory of normal operators introduced the notions of subnormality and hyponormality for bounded hilbert space operators an operator t is subnormal if it is the restriction of a normal operator to an invariant subspace t is hyponormal if t t tt it is a simple matrix calculation to verify that subnormality implies hyponormality but the converse is false one reason is that subnormality is invariant under polynomial calculus indeed analytic functional calculus while hyponormality is not if one then defines t to be polynomially hyponormal when p t is hyponormal for every polynomial p e c z the following question arises naturally

existence results for evolution hemivariational inequalities of second order abstract in this paper we consider evolution hemivariational inequalities of second order with a time dependent pseudomonotone operator and nonmonotone multivalued perturbations we present the existence of solutions for such inequality the proof profits from a result on the surjectivity of operators of pseudomonotone type we discuss some examples which indicate the practical importance of our theoretical findings

unstable state dynamics treatment of colored noise the diffusion of a particle set near an unstable point in a bistable potential is considered the scaling theory of fluctuations proposed originally for onedimensional systems driven by gaussian white noise is extended to arbitrary dimensions the merits and drawbacks of the scaling theory are discussed by taking a model problem in one dimension it is shown in passing that the saddle point approximation enables one to get analytic expressions for various moments of the stochastic process the two different methods to include asymptotic fluctuations which are absent in the usual scaling solution are shown to be equivalent an alternate way of including asymptotic fluctuations is attempted by solving the associated fokker planck equation using the fer formula the reason for the failure of this method is traced after this it is argued that the unified scaling theory should be applicable for treatment of colored noise as well for the scaling assumption is independent of the statistical property of the driving noise explicit monte carlo simulation of a model onedimensional system driven by exponentially correlated gaussian noise is performed and compared with the scaling solution to bolster this point the agreement is very good

linear analysis of quadrature domains iii the linear data of a quadrature domain introduced in the first paper in this series is further investigated the matricial structure of all hyponormal operators with finite rank self commutators which is inductively constructed from such linear data is discussed in particular a conservation law of a determinantal function in the iterative process of defining these matrices is exploited the spectrum of the determining left upper corner of some of these operators is analyzed in connection with the existence of generalized quadrature formulas on planar domains

numerical estimation of the path integral and the diffusion in an anharmonic oscillator abstract the solution of the fokker planck equation given in the form of the path integral is estimated by the contribution from paths around the most probable path a numerical procedure for this estimation is given and applied to the regression of an anharmonic oscillator under a random force from unstable positions to a stable position

solution of fokker planck equation using trotter s formula solution of fokker planck equation using trotter s formula is discussed the method is illustrated on the linear fokker planck equation and the ornstein uhlenbeck solution is obtained for the case of a general nonlinear fokker planck equation the method yields an integral representation amenable to approximations in the lowest order approximation suzuki s scaling result emerges physical interpretation and limitations of the approximations are also discussed

modelling of nonconvex nonsmooth energy problems dynamic hemivariational inequalities with impact effects nonconvex nonsmooth energy functions lead to hemivariational inequalities the subjects of the present paper are dynamic hemivariational inequalities without and with impact effects first some existence and approximation results are obtained for dynamic hemivariational inequalities without impact effects then for the case of impact a new type of variational expressions has been obtained including variations of the time and the place of impact and the corresponding dynamic hemivariational inequalities have been formulated

existence of antiperiodic solutions for hemivariational inequalities in this paper we consider the problem of existence of antiperiodic solutions for first order and second order hemivariational inequalities with a pseudomonotone operator we first give the surjectivity result and then prove a existence of antiperiodic solutions for hemivariational inequalities with the surjectivity result