cyclic homology comodules and mixed complexes relating cyclic and hochschild homology one can see that any formula for hc a a will not only involve hc a and hc a but also the periodicity operator s and the hochschild groups fortunately if the map s brings in some complications it also endows hc a with a comodule structure over the cyclic homology of the ground ring k actually the comodule structure exists already on the complex level a convenient complex on which s has the form of a canonical surjection is connes s double complex with differentials b and b now the idea is to view the cyclic homology of an algebra as a composite functor

asymptotic behavior of the solution to the non isothermal phase field equation we consider the penrose fife phase field model thermodynamically consistent models of phase field type for the kinetics of phase transitions physica d 43 1990 44 62 with homogeneous neumann boundary condition to the nonlinear heat flux q 1 i e q 0 on the boundary where 0 is the temperature there is a unique h1 solution globally in time with the non empty connected compact limit set composed of stationary solutions and the linearized stable stationary solution is dynamically stable

a non isothermal phase separation with constraints and dirichlet boundary condition for temperature abstract we consider non isothermal phase separation models of the penrose fife type which were proposed in o penrose p c fife thermodynamically consistent models of phase field type for the kinetics of phase transitions physica d 43 1990 44 62 in the present paper we impose a non homogeneous dirichlet boundary condition on the nonlinear heat flux moreover we consider two cases as boundary conditions for the conserved order parameter one is the homogeneous neumann boundary condition and the other is the signorini boundary condition which is nonlinear we show the existence and uniqueness of solutions to these models

positivity of solutions of elliptic equations with nonlocal terms in this paper we study a nonlocal problem for a second order partial differential equation which depends on a parameter n we prove the existence of critical values 0 and 0 such that for all and for all non negative right hand sides our problem has nonnegative solutions we obtain a formula for 0 the maximal possible value of and find the exact value of for spherical we also study the corresponding eigenvalue problem at the end of the paper we consider the application of our results to the nonlinear system describing the distribution of temperature and potential in a microsensor

asymptotic behavior of the solution to the non isothermal phase separation abstract we consider the non isothermal phase separation models of the penrose fife type which were proposed in o penrose p c fife thermodynamically consistent models of phase field type for the kinetics of phase transitions physica d 43 1990 44 62 with homogeneous neumann boundary conditions on the nonlinear heat flux q u i e q n 0 on the boundary of a region which the material occupies here u represents the absolute temperature for this model we first show that there exists a unique solution globally in time moreover the limit set associated with the trajectory of the unique global solution is non empty connected and compact in some suitable space as well as being composed of solutions to the steady state problem for the stability of stationary solutions we show that the dynamically stable solutions to the steady state problem are characterized by linearized stable solutions to the elliptic problem with a non local term which is equivalent to our steady state problem

solutions to a penrose fife model of phase field type abstract in a recent paper sprekels and zheng study global existence of smooth solutions to a model of phase field type for the kinetics of phase transitions which was proposed by penrose and fife in this paper we study this model with constraint and show existence of solutions to that problem

on a conjecture of vorst let k be an infinite perfect field of positive characteristic such that strong resolution of singularities holds over k we prove that a localization of a d dimensional commutative k algebra r of finite type is kd 1 regular if and only if it is regular this partially affirms a conjecture of vorst

well posedness for solid liquid phase transitions with a fourth order nonlinearity abstract a phase field system which describes the evolution of both the absolute temperature and the phase variable f during first order transitions in thermal insulators is considered a thermodynamic approach is developed by regarding the order parameter as a phase field and its evolution equation as a balance law by virtue of the special form of the internal energy a third order nonlinearity g 2 f appears in the energy balance in place of the customarily constant latent heat as a consequence the bounds 0 f 1 hold whenever is positive valued in addition a nonlinear fourier law with conductivity proportional to temperature is assumed well posedness for the resulting initial and boundary value problem are then established in a suitable setting

cyclic homology cdh cohomology and negative k theory we prove a blow up formula for cyclic homology which we use to show that infinitesimal k theory satisfies cdh descent combining that result with some computations of the cdh cohomology of the sheaf of regular functions we verify a conjecture of weibel predicting the vanishing of algebraic k theory of a scheme in degrees less than minus the dimension of the scheme for schemes essentially of finite type over a field of characteristic zero

thermodynamically consistent models of phase field type for the kinetics of phase transitions abstract a general framework is given for the phenomenological kinetics of phase transitions in which not only the order parameter but also the temperature may vary in time and space instead of a ginzburg landau free energy functional as used in formulating the cahn hilliard equation we use the analogous entropy functional model entropy functionals and the kinetic equations resulting from them are constructed for various cases phase transitions with and without a critical point and in the former case with or without a latent heat the class considered is general enough to include the entropy functionals for the ising model in mean field approximation the van der waals fluid and a simplified version of the density functional theory of freezing a case without critical point for which the energy is conserved but the order parameter is not provides a thermodynamically consistent derivation of the phase field equations studied by caginalp fix and others and also leads in a natural way to the lyapunov functional given by langer for these equations but the treatment also suggests that a modified version of the phase field equations might provide a more realistic model of freezing

the phase field transition system with non homogeneous cauchy stefan boltzmann and homogeneous neumann boundary conditions and non constant thermal conductivity abstract the paper establishes the existence estimate uniqueness and regularity for the solution of a nonlinear parabolic system a two phase caginalp type system with non homogeneous cauchy stefan boltzmann and homogeneous neumann boundary conditions and non constant thermal conductivity it extends the already studied types of boundary conditions which makes the mathematical model to be richer and more flexible to describe the real physical phenomena including phase separation

an analysis of a phase field model of a free boundary a mathematical analysis of a new approach to solidification problems is presented a free boundary arising from a phase transition is assumed to have finite thickness the physics leads to a system of nonlinear parabolic differential equations existence and regularity of solutions are proved invariant regions of the solution space lead to physical interpretations of the interface a rigorous asymptotic analysis leads to the gibbs thompson condition which relates the temperature at the interface to the surface tension and curvature

analysis of an iterative scheme of fractional steps type associated to the reaction diffusion equation endowed with a general nonlinearity and cauchy neumann boundary conditions abstract the paper studies the existence uniqueness regularity and the approximation of solutions to the reaction diffusion equation endowed with a general nonlinear regular potential and cauchy neumann boundary conditions the convergence and error estimate results for an iterative scheme of fractional steps type associated to the nonlinear parabolic equation are also established the advantage of such method consists in simplifying the numerical computation necessary to be done in order to approximate the solution of nonlinear parabolic equation

global smooth solutions to a thermodynamically consistent model of phase field type in higher space dimensions abstract in a recent paper penrose and fife proposed a thermodynamically consistent model of phase field type for phase transition phenomena such as liquid solid phase transitions the model is based on the observation that the second law of thermodynamics postulates that the entropy functional cannot decrease along solution paths it turns out that the resulting field equations form a system of partial differential equations which is considerably more difficult than the phase field equations studied by caginalp and others for one space dimension global existence uniqueness and asymptotic behaviour of smooth solutions of the initial boundary value problem with neumann boundary data have been obtained in a recent paper by zheng in this paper we prove global existence and uniqueness in three space dimensions for the initial boundary value problem with a third boundary condition

stationary fix caginalp equation with non local term abstract we study the fix caginalp equation describing non isothermal solid liquid phase transition first we formulate a thermally closed stationary state as a nonlinear eigenvalue problem with a non local term then some results on multiple existence stability and bifurcation of the solution are proven

a phase field model with temperature dependent constraint this paper is concerned with a phase field model with temperature dependent constraint for the order parameter in the kinetic equation of the order parameter we take account of diffusion as well as undercooled superheated state which is modelled by means of a hysteresis input output relation the input is the temperature field and the output is the order parameter in this paper we shall show that there exists a solution globally in time in a physically reasonable sense when the coefficient of interfacial energy is sufficiently small

some perturbation results for the linear complementarity problem it has been shown previously that the linear complementarity problem is stable when the defining matrix is positive semidefinite and when locally the set of solutions is nonempty and bounded we enlarge the class of matrices for which this is true and also demonstrate how the boundedness condition leads to other stability type questions

on the existence uniqueness and regularity of solutions to the phase field system with a general regular potential and a general class of nonlinear and non homogeneous boundary conditions abstract this paper studies a caginalp phase field transition system endowed with a general regular potential as well as a general class in both unknown functions of nonlinear and non homogeneous depending on time and space variables boundary conditions we first prove the existence uniqueness and regularity of solutions to the allen cahn equation subject to the nonlinear and non homogeneous dynamic boundary conditions the existence uniqueness and regularity of solutions to the caginalp system in this new formulation are also proved this extends previous works concerned with regular potential and nonlinear boundary conditions allowing the present mathematical model to better approximate the real physical phenomena especially phase transitions

continuity properties of the karush kuhn tucker point set in quadratic programming problems we obtain necessary and sufficient conditions for the set of the karush kuhn tucker points in a canonical quadratic programming problem to be upper semicontinuous or lower semicontinuous with respect to the problem parameters

applications of degree theory to linear complementarity problems in this paper we consider two applications of degree theory to linear complementarity problems in the first application we study the stability of an lcp at a solution point specifically we prove the stability of an lcp corresponding to a p0 matrix at an isolated solution using a recent degree formula due to stewart 1991 we strengthen a stability result of gowda and pang 1992 in the second application we use the same degree formula of stewart to describe the number of solutions of lcpm q when m is a negative almost n matrix this analysis leads to a lipschitzian characterization of the solution map i q solm q corresponding to a nondegenerate negative matrix

non linear system for non isothermal diffusive phase separation abstract an evolution system which extends the cahn hilliard model to non isothermal situations subject to convex constraints for solutions is studied the problem can be considered as representing a simple model of non isothermal phase separation driven by diffusive mechanisms a variational formulation of the problem is introduced using t dependent subdifferential operator techniques in hilbert spaces existence and uniqueness of weak solutions are proved

on solution stability of the linear complementarity problem in the paper 5 c d ha introduced the notion of stability of a linear complementarity problem at a solution point and established several sufficient conditions for stability to hold in the present paper we derive some new stability results which significantly improve ha s results included in these new results are i a complete characterization of the stability condition under a nonsingularity assumption and ii further characterizations of solution stability in the case of a linear complementarity problem with a fully semimonotone matrix

variational inequalities for a system of elliptic parabolic equations abstract we create a general framework for mathematical study of variational inequalities for a system of elliptic parabolic equations in this paper we establish a solvability theorem concerning the existence of solutions for the vector valued elliptic parabolic variational inequality with time dependent constraint moreover we give some applications of the system for example time dependent boundary obstacle problem and time dependent interior obstacle problem

bass nk groups and cdh fibrant hochschild homology the k theory of a polynomial ring r t contains the k theory of r as a summand for r commutative and containing q we describe k r t k r in terms of hochschild homology and the cohomology of kahler differentials for the cdh topology we use this to address bass question whether kn r kn r t implies kn r kn r t1 t 2 the answer to this question is affirmative when r is essentially of finite type over the complex numbers but negative in general

a class of nonlinear elliptic parabolic equations with time dependent constraints on etudie les equations d evolutions non lineaires de la forme f t du t dt t v t v t bu t 0 t t dans un espace de hilbert h ou t est la sous differentielle d une fonction convexe t definie sur h b est un operateur monotone maximal dans h on considere l existence et l unicite des solutions ainsi que des estimations a priori

structural and stability properties of p 0 nonlinear complementarity problems we consider p0 nonlinear complementarity problems and study the connectedness and stability of the solutions by applying degree theory and the mountain pass theorem to a smooth reformulation of the complementarity problem we show that the solution set is connected and bounded if a bounded isolated component of the solution set exists and that a solution is locally unique if and only if it is globally unique furthermore we prove that a solution is stable in ha s sense if and only if it is globally unique while the complementarity problem is stable if and only if the solution set is bounded

on degeneracy in linear complementarity problems abstract let m be an n n matrix and q an n th order vector then the linear complementarity problem lcp q m is defined as follows determine x 0 such that w mx q 0 and x t w 0 a vector x which satisfies these conditions is called a solution of the problem and a solution for which x i w i 0 for at least one value of i is termed degenerate if the solutions of lcp q m are nondegenerate and their number is odd even we say that the solution set has odd even parity and murty has shown that this parity is determined uniquely by m in this paper the idea of parity is extended to degenerate solutions and through these to solution sets containing both degenerate and nondegenerate solutions these results are then used to give a generalization of lemke s method and to analyse the stability of certain degenerate solutions of linear complementarity problems

stability of the linear complementarity problem at a solution point in this paper we study the behavior of a solution of the linear complementarity problem when data are perturbed we give characterizations of strong stability of the linear complementarity problem at a solution in the case of stability we give sufficient and necessary conditions

the k theory of toric varieties recent advances in computational techniques for k theory allow us to describe the k theory of toric varieties in terms of the k theory of fields and simple cohomological data

robustness and nondegenerateness for linear complementarity problems in this paper the main focus is on a stability concept for solutions of a linear complementarity problem a solution of such a problem is robust if it is stable against slight perturbations of the data of the problem relations are investigated between the robustness the nondegenerateness and the isolatedness of solutions it turns out that an isolated nondegenerate solution is robust and also that a robust nondegenerate solution is isolated since the class of linear complementarity problems with only robust solutions or only nondegenerate solutions is not an open set attention is paid to garcia s classgn of linear complementarity problems the nondegenerate problems ingn form an open set

infinitesimal cohomology and the chern character to negative cyclic homology there is a chern character from k theory to negative cyclic homology we show that it preserves the decomposition coming from adams operations at least in characteristic zero

k regularity cdh fibrant hochschild homology and a conjecture of vorst it is a well known fact that algebraic if theory is homotopy invariant as a functor on regular schemes if x is a regular scheme then the natural map kn x kn x x 1 is an isomorphism for all n ez this is false in general for nonregular schemes and rings to express this failure bass introduced the terminology that for any contravari ant functor v defined on schemes a scheme x is called v regular if the pullback maps v x v x x ar are isomorphisms for all r 0 if x spec i we also say that r is p regular thus regular schemes are ifn regular for every n in contrast it was observed as long ago as in 2 that a nonreduced affine scheme can never be k regular in particular if a is an artinian ring that is a o dimensional noetherian ring then a is regular that is reduced if and only if a is ifi regular in 17 vorst conjectured that for an affine scheme x of finite type over a field f and of dimension d regularity and k i regularity are equivalent vorst proved this conjecture for d 1 by proving that regularity implies normality in this paper we prove vorst s conjecture in all dimensions provided the char acteristic of the ground field f is zero in fact we prove a stronger statement we say that x is regular in codimension n in x note that for all n z if a ring r is ifn regular then it is kn i regular this is proved in 17 for n 1 and in 6 4 4 for n kh x where k x is the algebraic if theory spectrum of x and kh x is the homotopy if theory of x defined in 19 we write fk r for fk spec r theorem 0 1 let r be a commutative ring which is essentially of finite type over a field f of characteristic 0 then the following hold a if tk r is n connected then r is regular in codimension khi x is an isomorphism for i n and a surjection for i n 1 so that fk x

stability analysis of variational inequalities and nonlinear complementarity problems via the mixed linear complementarity problem and degree theory this paper is concerned with the mixed linear complementarity problem and the role it and its variants play in the stability analysis of the nonlinear complementarity problem and the karush kuhn tucker system of a variational inequality problem under a nonsingular assumption the mixed linear complementarity problem can be converted to the standard problem in this case the rich theory of the latter can be directly applied to the former in this work we employ degree theory to derive some sufficient conditions for the existence of a solution to the mixed linear complementarity problem in the absence of the nonsingularity property next we extend this existence theory to the mixed nonlinear complementarity problem and establish a main stability result under a certain degree theoretic assumption concerning the linearized problem we then specialize this stability result and its consequences to the parametric variational inequality problem under the assumption of a unique set of multipliers finally we

nonlinear degenerate parabolic equations with neumann boundary condition abstract we study neumann problem for a class of nonlinear degenerate parabolic pde a typical nonlinearity we have in mind is for instance u 1 u u 0 we establish a necessary and sufficient condition on given data for existence of solution

non isothermal phase transition models with neumann boundary conditions abstract we study the systems of nonlinear parabolic pdes for penrose fife models of non isothermal phase transitions both models with conserved and non conserved order parameters are studied with neumann boundary conditions imposed on the systems in multi dimensional spatial domain