excessive measures and the existence of right semigroups and processes given a resolvent u on a lusin space e f the paper gives necessary and sufficient conditions in terms of the excessive measures that ensure the existence of a right process resp a right continuous semigroup on e f with resolvent u furthermore a notion of nonbranch points with respect to un is introduced also in terms of the excessive measures and various characterizations are given they show in particular the equivalence of this definition with those introduced and discussed by engelbert and wittmann

a mathematical model of competition for two essential resources in the unstirred chemostat a mathematical model of competition between two species for two growth limiting essential complementary resources in the unstirred chemostat is considered the existence of a positive steady state solution and some of its properties are established analytically techniques include the maximum principle the fixed point index and numerical simulations the simulations also seem to indicate that there are regions in parameter space for which a globally stable positive equilibrium occurs and that there are other regions for which the model admits bistability and even multiple positive equilibria

classical dirichlet forms on topological vector spaces the construction of the associated diffusion process given a minimal classical dirichlet form onl 2 e we construct the associated diffusion process heree is a locally convex topological vector space and is a not necessarily quasi invariant probability measure one the construction is carried out under certain assumptions one and which can be easily verified in many examples in particular we explicitly apply our results to time zero and space time quantum fields with or with out cut off

worst case analysis of an algorithm for cellular manufacturing abstract two measures for the efficiency of grouping in cellular manufacturing are discussed in this paper we first analyze the effectiveness of the first measure grouping efficiency a worst case bound is then derived for the minimum spanning tree algorithm with respect to this measure we then show a newly proposed measure grouping efficacy is not suitable from an algorithmic point of view a weighted grouping efficacy is then proposed and worst case bounds are derived with respect to this new measure we also propose several policies to improve grouping efficiency and grouping efficacy during the decomposition of larger machine cells computational results will also be presented to demonstrate the effectiveness of these measures and the worst case bounds

traces of harmonic functions and a new path space for the free quantum field the infinite dimensional ornstein uhlenbeck process associated with the free field of quantum field theory on rd is reconstructed as the traces of random harmonic functions these harmonic functions are the solutions of a generalised dirichlet problem with a random schwartz distribution as boundary data a detailed analysis of the associated trace space which is a subspace of a scaled sobolev space of negative fractional order leads to a new path space for the free field as well as to a convenient regularisation method because of the particular form of the trace space it is possible to give an explicit formula for the transition function of the process furthermore the dependence of the path space on the dimension d is discussed and a formulation of our result in terms of abstract wiener spaces is given

construction of convergent simplicial approximations of quantum fields on riemannian manifolds we construct simplicial approximations of random fields on riemannian manifolds of dimensiond we prove convergence of the fields to the continuum limit for arbitraryd in the gaussian case and ford 2 in the non gaussian case in particular we obtain convergence of the simplicial approximation to the continuum limit for quantum fields on riemannian manifolds with exponential interaction

infinite dimensional stochastic differential equations obtained by subordination and related dirichlet forms abstract new results related to the decomposition theorem of additive functionals associated to quasi regular dirichlet forms are presented a characterization of subordinate processes associated to quasi regular symmetric dirichlet forms in terms of the unique solutions of the corresponding martingale problems is obtained the subordinate of generalized ornstein uhlenbeck processes are exhibited explicitly in terms of generators dirichlet forms and unique pathwise solutions of stochastic differential equations sdes in the case where the state space is infinite dimensional as e g in euclidean quantum field theory the construction provides a characterization of the processes in terms of projections on the topological dual space and corresponding finite dimensional sdes

classical dirichlet forms on topological vector spaces closability and a cameron martin formula abstract we prove a sufficient condition for the closability of classical dirichlet forms on l 2 e which is also necessary if all components of the dirichlet form are closable here e is a locally convex topological vector space and a not necessarily quasi invariant probability measure on e the same condition is shown to imply the existence of a closed extension whose domain can be described explicitly in the special case where is quasi invariant with respect to certain vectors in e our result generalises previous theorems on closability in addition we prove a cameron martin type formula for a large class of measures if e is finite dimensional our characterisation of closability is the analogue of the corresponding one dimensional result applications to quantum fields and the connection with the well studied case of abstract wiener spaces are discussed

existence and uniqueness of solutions to stochastic functional differential equations in infinite dimensions abstract in this paper we present a general framework for solving stochastic functional differential equations in infinite dimensions in the sense of martingale solutions which can be applied to a large class of spde with finite delays e g d dimensional stochastic fractional navier stokes equations with delays d dimensional stochastic reaction diffusion equations with delays d dimensional stochastic porous media equations with delays moreover under local monotonicity conditions for the nonlinear terms we obtain the existence and uniqueness of strong solutions to spde with delays

three dimensional navier stokes equations driven by space time white noise abstract in this paper we prove existence and uniqueness of local solutions to the three dimensional 3d navier stokes n s equation driven by space time white noise using two methods first the theory of regularity structures introduced by martin hairer in 16 and second the paracontrolled distribution proposed by gubinelli imkeller perkowski in 12 we also compare the two approaches

strong uniqueness for sdes in hilbert spaces with nonregular drift we prove pathwise uniqueness for a class of stochastic dierential equations sde on a hilbert space with cylindrical wiener noise whose non linear drift parts are sums of the subdierential of a convex function and a bounded part this generalizes a classical result by one of the authors to innite dimensions our results also generalize

ergodicity ofl2 semigroups and extremality of gibbs states we extend the classical results of holley stroock on the characterization of extreme gibbs states for the ising model in terms of the irreducibility resp ergodicity of the corresponding glauber dynamics to the case of lattice systems with unbounded linear spin spaces we first develop a general framework to discuss questions of this type using classical dirichlet forms on infinite dimensional state spaces and their associated diffusions we then describe concrete applications to lattice models with polynomial interactions i e the discretep d models of euclidean quantum field theory in addition we prove the equivalence of extremality and shift ergodicity for tempered gibbs states of these models and also discuss this question in the general framework

large deviations w r t quasi every starting point for symmetric right processes on general state spaces in the work of donsker and varadhan fukushima and takeda and that of deuschel and stroock it has been shown that the lower bound for the large deviations of the empirical distribution of an ergodic symmetric markov process is given in terms of its dirichlet form we give a short proof generalizing this principle to general state spaces that include in particular infinite dimensional and non0metrizable examples our result holds w r t quasi every starting point of the markov process moreover we show the corresponding weak upper bound w r t quasi every starting point

dirichlet operators on loop spaces essential self adjointness and log sobolev inequality for each 0 1 and potential function v rd r we consider the dirichlet form e and the associated dirichlet operator h for the gibbs measure on the loop space e c 0 1 rd 0 1 the gibbs measure is related to the gibbs state of the quantum anharmonic oscillator with the potential v via the feynman kac formula we formulate dirichlet forms in the framework of rigged hilbert spaces which are related to the loop space e we then give an approximate criterion for the essential self adjointness of dirichlet operators associated with dirichlet forms given by probability measures on hilbert spaces under appropriate conditions on the potential we apply the approximate criterion to show that the dirichlet operator h is essentially self adjoint on the domain of smooth cylinder functions in addition if the potential satisfies a uniform convexity condition we prove that the dirichlet operator h has a gap at the lower end of spectrum we also show that the gibbs measure satisfie

spde in hilbert space with locally monotone coefficients the aim of this paper is to extend the usual framework of spde with monotone coecients to include a large class of cases with merely locally monotone coecients this new framework is conceptually not more involved than the classical one but includes many more fundamental examples not included previously thus our main result can be applied to various types of spdes such as stochastic reaction diusion equations stochastic burgers type equation stochastic 2 d navier stokes equation stochastic p laplace equation and stochastic porous media equation with non monotone perturbations

the exponential stability for stochastic delay partial differential equations abstract in this paper we consider by the energy equality the exponential stability of energy solutions to a non linear stochastic functional partial differential equation with finite delay r 0 in separable hilbert spaces our method is very simple and is powerful for concrete stochastic delay partial differential equations

kolmogorov equations in infinite dimensions well posedness and regularity of solutions with applications to stochastic generalized burgers equations we develop a new method to uniquely solve a large class of heat equations so called kolmogorov equations in infinitely many variables the equations are analyzed in spaces of sequentially weakly continuous functions weighted by proper lyapunov type functions this way for the first time the solutions are constructed everywhere without exceptional sets for equations with possibly nonlocally lipschitz drifts apart from general analytic interest the main motivation is to apply this to uniquely solve martingale problems in the sense of stroock varadhan given by stochastic partial differential equations from hydrodynamics such as the stochastic navier stokes equations in this paper this is done in the case of the stochastic generalized burgers equation uniqueness is shown in the sense of markov flows

stochastic functional partial differential equations existence uniqueness and asymptotic decay property existence and uniqueness of strong solutions for a class of stochastic functional differential equations in hilbert spaces are established sufficient conditions which guarantee the transference of mean square and pathwise exponential stability from stochastic partial differential equations to stochastic functional partial differential equations are studied the stability results derived are also applied to stochastic ordinary differential equations with hereditary characteristics in particular as a direct consequence our main results improve some of those by mao shah in which it was proved that under certain conditions pathwise exponential stability is transferred from non delay equations to delay equations if the constant time lag appearing in the problem is sufficiently small while in our treatment the transference actually holds for arbitrary bounded delay variables not only in finite but in infinite dimensions

stochastic functional evolution equations with monotone nonlinearity existence and stability of the mild solutions abstract in this paper we study a class of semilinear functional evolution equations in which the nonlinearity is demicontinuous and satisfies a semimonotone condition we prove the existence uniqueness and exponentially asymptotic stability of the mild solutions our approach is to apply a convenient version of burkholder inequality for convolution integrals and an iteration method based on the existence and measurability results for the functional integral equations in hilbert spaces an ito type inequality is the main tool to study the uniqueness p th moment and almost sure sample path asymptotic stability of the mild solutions we also give some examples to illustrate the applications of the theorems and meanwhile we compare the results obtained in this paper with some others appeared in the literature

uniqueness of generalized schrodinger operators and applications abstract we prove necessary and sufficient conditions on r d r 0 a e so that the operator s 2 1 w1 n has exactly one self adjoint extension on w1 p which generates a sub markovian semigroup on w1 n these conditions are shown to be always fulfilled if d 1 and are verified for a large class of functions if d 1 we also prove an infinite dimensional analogue of this result where r d is replaced by some topological vector space e and the lebesgue measure dx by a gaussian measure the role of is taken by some ornstein uhlenbeck operator with general linear drift and dom s bounded smooth cylinder functions both results are derived as special cases from a general perturbation result we also give the corresponding probabilistic version i e we prove uniqueness for the associated martingale problem we present in some detail applications to the case where is a ground state of a hamiltonian in quantum field theory settling a problem which has been open for some time furthermore we apply our results to prove uniqueness in distribution of the diffusion first constructed by g jona lasinio and p k mitter for the stochastic quantization of f 2 field theory

dynamics of a bio reactor model with chemotaxis long time dynamics of solutions to a strongly coupled system of parabolic equations modeling the competition in bio reactors with chemotaxis will be studied in particular we show that the dynamical system possesses a global attractor and that it is strongly uniformly persistent if the trivial steady state is unstable using a result of smith and waltman on perturbation of global attractors we also show that the positive steady state is unique and globally attracting

existence uniqueness and asymptotic behavior of mild solutions to stochastic functional differential equations in hilbert spaces abstract in this paper we shall consider the existence uniqueness and asymptotic behavior of mild solutions to stochastic partial functional differential equations with finite delay r 0 dx t ax t f t x t dt g t x t dw t where we assume that a is a closed densely defined linear operator and the generator of a certain analytic semigroup f c h g c l 0 2 k h are two locally lipschitz continuous functions where c c r 0 d a l 0 2 k h are two proper infinite dimensional spaces 0 w t is a given k valued wiener process and both h and k are separable hilbert spaces

restricted markov uniqueness for the stochastic quantization of p φ 2 and its applications abstract in this paper we obtain restricted markov uniqueness of the generator and uniqueness of martingale probabilistically weak solutions for the stochastic quantization problem in both the finite and infinite volume case by clarifying the precise relation between the solutions to the stochastic quantization problem obtained by the dirichlet form approach and those obtained in 10 and in 24 we prove that the solution x z where x is obtained by the dirichlet form approach in 4 and z is the corresponding o u process satisfies the corresponding shifted equation see 1 4 below moreover we obtain that the infinite volume p 2 quantum field is an invariant measure for the x y z where y is the unique solution to the shifted equation

measures of grouping efficiency in cellular manufacturing systems abstract grouping efficiency is a measure of goodness of machine part groups in cellular manufacturing systems this paper briefly presents a critical review of existing grouping measures introduces a new measure called doubly weighted grouping efficiency measure and evaluates its relative performance of with other existing measures here special emphasis is given evaluation of the goodness of clustering solutions in block diagonalization of machine part incidence matrix in order to provide information on the measures results are collected and compiled from discretely reported sources and are reported both descriptively and quantitatively categorization and generalization of these measures are made to use them for goodness of clustering in order to overcome a number of drawbacks in the previously known measures a new doubly weighted grouping efficiency measure is presented and its performance is demonstrated with respect to several efficiency measures

sobolev type fractional stochastic differential equations with non lipschitz coefficients this paper investigates the existence and uniqueness of mild solutions for a class of nonlinear fractional sobolev type stochastic differential equations in hilbert spaces in this work we used the fractional calculus semigroup theory and stochastic analysis techniques for obtaining the required result a new set of sufficient condition is established with the coefficients in the equations satisfying some non lipschitz conditions which include classical lipschitz conditions as special cases more precisely the results are obtained by means of standard picards iteration finally an example is given to illustrate the obtained theory

dynamical behavior of delayed reaction diffusion hopfield neural networks driven by infinite dimensional wiener processes in this paper we focus on the long time behavior of the mild solution to delayed reaction diffusion hopfield neural networks drdhnns driven by infinite dimensional wiener processes we analyze the existence uniqueness and stability of this system under the local lipschitz function by constructing an appropriate lyapunov krasovskii function and utilizing the semigroup theory some easy to test criteria affecting the well posedness and stability of the networks such as infinite dimensional noise and diffusion effect are obtained the criteria can be used as theoretic guidance to stabilize drdhnns in practical applications when infinite dimensional noise is taken into consideration meanwhile considering the fact that the standard brownian motion is a special case of infinite dimensional wiener process we undertake an analysis of the local lipschitz condition which has a wider range than the global lipschitz condition two samples are given to examine the availability of the results in this paper simulations are also given using the matlab

stability of semilinear stochastic evolution equations stability of moments of the mild solution of a semilinear stochastic evolution equation is studied and sufficient conditions are given for the exponential stability of the pth moment in terms of liapunov function sufficient conditions for sample continuity of the solution are also obtained and the exponential stability of sample paths is proved three examples are given to illustrate the theory

on closability of classical dirichlet forms we construct a measure on r2 such that the classical dirichlet form e f g f g d is closable but the partial dirichlet form ex f g xf xgd is not this proves the well known conjecture of m rockner

on the indices of fixed points of mappings in cones and applications abstract assume that k is a cone in a banach space and a k k is completely continuous we obtain a formula for the index in k of a fixed point of a under the assumption that a linearization exists and satisfies an invertibility condition we then use this formula to generalize some results of amann on the number of fixed points of a to the case where k has empty interior

tightness of general c1 p capacities on banach space abstract we prove tightness of c 1 p capacities on a banach space e these capacities are defined in terms of measures on e which are not necessarily gaussian our methods are purely analytic and completely different from earlier approaches which were implemented under more restrictive assumptions

a maximum principle applied to quasi geostrophic equations we study the initial value problem for dissipative 2d quasi geostrophic equations proving local existence global results for small initial data in the super critical case decay of lp norms and asymptotic behavior of viscosity solution in the critical case our proofs are based on a maximum principle valid for more general flows

a note on stochastic semilinear equations and their associated fokker planck equations abstract the main purpose of this paper is to prove existence and uniqueness of probabilistically weak and strong solutions to stochastic differential equations sde on hilbert spaces under a new approximation condition on the drift recently proposed in 6 to solve fokker planck equations fpe extended in this paper to a considerably larger class of drifts as a consequence we prove existence of martingale solutions to the sde whose time marginals then solve the corresponding fpe applications include stochastic semilinear partial differential equations with white noise and a non linear drift part which is the sum of a burgers type part and a reaction diffusion part the main novelty is that the latter is no longer assumed to be of at most linear but of at most polynomial growth this case so far had not been covered by the existing literature we also give a direct and more analytic proof for existence of solutions to the corresponding fpe extending the technique from 6 to our more general framework which in turn requires to work on a suitable gelfand triple rather than just the hilbert state space

quantum interaction φ44 the construction of quantum field defined as a bilinear form we construct the solution t x of the quantum wave equation m2 3 0 as a bilinear form which can be expanded over wick polynomials of the free in field and where 3 t x is defined as the normal ordered product with respect to the free in field the constructed solution is correctly defined as a bilinear form on d d where d is a dense linear subspace in the fock space of the free in field on d d the diagonal of the wick symbol of this bilinear form satisfies the nonlinear classical wave equation

sub and supercritical stochastic quasi geostrophic equation in this paper we study the 2d stochastic quasi geostrophic equation on t2 for general parameter 0 1 and multiplicative noise we prove the existence of weak solutions and markov selections for multiplicative noise for all 0 1 in the subcritical case 1 2 we prove existence and uniqueness of probabilistically strong solutions moreover we prove ergodicity for the solution of the stochastic quasi geostrophic equations in the subcritical case driven by possibly degenerate noise the law of large numbers for the solution of the stochastic quasi geostrophic equations in the subcritical case is also established in the case of nondegenerate noise and 2 3 in addition exponential ergodicity is proved

stochastic analysis on product manifolds dirichlet operators on differential forms abstract we define a de rham complex over a product manifold infinite product of compact manifolds and dirichlet operators on differential forms associated with differentiable measures in particular gibbs measures which generalize the notions of bochner and de rham laplacians we give probabilistic representations for corresponding semigroups and study properties of the corresponding stochastic dynamics

a food chain model for two resources in un stirred chemostat this paper deals with a multiple food chain model in un stirred chemostat where the prey feeds on two growth limiting nonreproducing resources the conditions for existence of positive steady states are established the global bifurcation of positive solutions is considered also furthermore we obtain the conditions under which the predator possesses uniformly strong persistence or goes to extinction the techniques used in this paper include the degree theory the global bifurcation theory the semigroup theory and the maximum principle

ordinary differential equations transport theory and sobolev spaces we obtain some new existence uniqueness and stability results for ordinary differential equations with coefficients in sobolev spaces these results are deduced from corresponding results on linear transport equations which are analyzed by the method of renormalized solutions

existence and uniqueness of martingale solutions for sdes with rough or degenerate coefficients abstract in this paper we extend recent results on the existence and uniqueness of solutions of odes with non smooth vector fields to the case of martingale solutions in the stroock varadhan sense of sdes with non smooth coefficients in the first part we develop a general theory which roughly speaking allows to deduce existence uniqueness and stability of martingale solutions for l d almost every initial condition x whenever existence and uniqueness is known at the pde level in the l setting and conversely if existence and uniqueness of martingale solutions is known for l d a e initial condition then existence and uniqueness for the pde holds in the second part of the paper we consider situations where on the one hand no pointwise uniqueness result for the martingale problem is known and on the other hand well posedness for the fokker planck equation can be proved thus the theory developed in the first part of the paper is applicable in particular we will study the fokker planck equation in two somehow extreme situations in the first one assuming uniform ellipticity of the diffusion coefficients and lipschitz regularity in time we are able to prove existence and uniqueness in the l 2 setting in the second one we consider an additive noise and assuming the drift b to have bv regularity and allowing the diffusion matrix a to be degenerate also identically 0 we prove existence and uniqueness in the l setting therefore in these two situations our theory yields existence uniqueness and stability results for martingale solutions

nonlinear parabolic stochastic differential equations with additive colored noise on bf r d times bf r _ a regulated stochastic quantization we prove the existence of solutions to the nonlinear parabolic stochastic differential equation partial mathord left vphantom partial partial t right kern nulldelimiterspace partial t delta varphi v varphi eta c for polynomialsv of even degree with positive leading coefficient and c a gaussian colored noise process onr d r when c is colored enough that the gaussian solution to the linear problem has holder continuous covariance the nongaussian processes are almost surely realized by continuous functions uniqueness regularity properties asymptotic perturbation expansions and nonperturbative fluctuation bounds are obtained for the infinite volume processes these equations are a cutoff version of the parisi wu stochastic quantization procedure forp d models and the results of this paper rigorously establish the nonperturbative nature of regularization via modification of the noise process in the limit c gaussian white noise we find that the asymptotic expansion and the rigorous bounds agree for processes corresponding to the regulated stochastic quantization of super renormalizable and small coupling strictly renormalizable scalar field theories and disagree for nonrenormalizable models

coexistence solutions for a reaction diffusion system of un stirred chemostat model in this paper we study a reaction diffusion system of multiple food chain model where two predators feed on a single prey growing in an un stirred chemostat the conditions for the coexistence of steady states are determined the main technique used here is the degree theory in cones

fluctuations and their glauber dynamics in lattice systems abstract we consider a class of unbounded spin systems containing in particular anharmonic classical crystals and construct the stochastic dynamics in the space of macroscopic fluctuations starting from a given microscopic stochastic time evolution

fokker planck equations and maximal dissipativity for kolmogorov operators with time dependent singular drifts in hilbert spaces we consider a kolmogorov operator l0 in a hilbert space h related to a stochastic pde with a time dependent singular quasi dissipative drift f f t h h defined on a suitable space of regular functions we show that l0 is essentially m dissipative in the space lp 0 t h p 1 where dt dx t dx dt and the family t t 0 t is a solution of the fokker planck equation given by l0 as a consequence the closure of l0 generates a markov c0 semigroup we also prove uniqueness of solutions to the fokker planck equation for singular drifts f applications to reaction diffusion equations with time dependent reaction term are presented this result is a generalization of the finite dimensional case considered in v bogachev g da prato m rockner existence of solutions to weak parabolic equations for measures proc london math soc 3 88 2004 753 774 v bogachev g da prato m rockner on parabolic equations for measures comm partial differential equations 33 3 2008 397 418 and v bogachev g da prato m rockner w stannat uniqueness of solutions to weak parabolic equations for measures bull london math soc 39 2007 631 640 to infinite dimensions

stochastic quantization of field theory in finite and infinite volume abstract using the theory of dirichlet forms a distribution valued symmetric markov process is constructed so that it has the 4 2 measure as its invariant probability measure several properties of this process are proved and a finite to infinite volume limit theorem is established

lower bounds for an integral involving fractional laplacians and the generalized navier stokes equations in besov spaces when estimating solutions of dissipative partial differential equations in l p related spaces we often need lower bounds for an integral involving the dissipative term if the dissipative term is given by the usual laplacian lower bounds can be derived through integration by parts and embedding inequalities however when the laplacian is replaced by the fractional laplacian the approach of integration by parts no longer applies in this paper we obtain lower bounds for the integral involving by combining pointwise inequalities for with bernstein s inequalities for fractional derivatives as an application of these lower bounds we establish the existence and uniqueness of solutions to the generalized navier stokes equations in besov spaces the generalized navier stokes equations are the equations resulting from replacing in the navier stokes equations by

stochastic lagrangian particle approach to fractal navier stokes equations in this article we study the fractal navier stokes equations by using the stochastic lagrangian particle path approach in constantin and iyer comm pure appl math lxi 330 345 2008 more precisely a stochastic representation for the fractal navier stokes equations is given in terms of stochastic differential equations driven by levy processes based on this representation a self contained proof for the existence of a local unique solution for the fractal navier stokes equation with initial data in mathbb w 1 p is provided and in the case of two dimensions or large viscosity the existence of global solutions is also obtained in order to obtain the global existence in any dimensions for large viscosity the gradient estimates for levy processes with time dependent and discontinuous drifts are proved

binary jumps in continuum i equilibrium processes and their scaling limits let denote the space of all locally finite subsets configurations in rd a stochastic dynamics of binary jumps in continuum is a markov process on in which pairs of particles simultaneously hop over rd in this paper we study an equilibrium dynamics of binary jumps for which a poisson measure is a symmetrizing and hence invariant measure the existence and uniqueness of the corresponding stochastic dynamics are shown we next prove the main result of this paper a big class of dynamics of binary jumps converge in a diffusive scaling limit to a dynamics of interacting brownian particles we also study another scaling limit which leads us to a spatial birth and death process in continuum a remarkable property of the limiting dynamics is that its generator possesses a spectral gap a property which is hopeless to expect from the initial dynamics of binary jumps

the hyperbolic geometry of random transpositions turn the set of permutations of n objects into a graph g n by connecting two permutations that differ by one transposition and let t be the simple random walk on this graph in a previous paper berestycki and durrett in discrete random walks 2005 17 26 showed that the limiting behavior of the distance from the identity at time cn 2 has a phase transition at c 1 here we investigate some consequences of this result for the geometry of g n our first result can be interpreted as a breakdown for the gromov hyperbolicity of the graph as seen by the random walk which occurs at a critical radius equal to n 4 let t be a triangle formed by the origin and two points sampled independently from the hitting distribution on the sphere of radius an for a constant 0 0 whereas it is always o n thick when a 1 4 we also show that the hitting distribution of the sphere of radius an is asymptotically singular with respect to the uniform distribution finally we prove that the critical behavior of this gromov like hyperbolicity constant persists if the two endpoints are sampled from the uniform measure on the sphere of radius an however in this case the critical radius is a 1 log 2

global asymptotic behavior of a chemostat model with two perfectly complementary resources and distributed delay a model of the chemostat involving two species of microorganisms competing for two perfectly complementary growth limiting nutrients is considered the model incorporates distributed time delay in the form of integral differential equations in order to describe the time involved in converting nutrient to biomass the delays are included in the nutrient and species concentrations simultaneously a general class of monotone increasing functions is used to describe nutrient uptake sufficient conditions based on biologically meaningful parameters in the model are given that predict competitive exclusion for certain parameter ranges and coexistence for others we prove that the global asymptotic attractivity of steady states of the model is similar to that of the corresponding model without time delays however our results indicate that when the inherent delays are in fact large ignoring them may result in incorrect predictions

two inequalities for symmetric diffusion semigroups underγ3 0 abstract from the meyer bakry inequality we deduce two inequalities one is an extension of the gagliardo nirenberg inequality for multiplication of sobolev functions the other extends an inequality due to maz ya for composition of nonnegative sobolev functions

a pointwise estimate for fractionary derivatives with applications to partial differential equations this article emphasizes the role played by a remarkable pointwise inequality satisfied by fractionary derivatives in order to obtain maximum principles and lp decay of solutions of several interesting partial differential equations in particular there are applications to quasigeostrophic flows in two space variables with critical viscosity that model the eckman pumping see baroud ch n plapp b b she z s swinney h l 2002 phys rev lett 88 114501 and constantin p 2002 phys rev lett 89 184501

brownian motions on metric graphs brownian motions on a metric graph are defined their generators are characterized as laplace operators subject to wentzell boundary at every vertex conversely given a set of wentzell boundary conditions at the vertices of a metric graph a brownian motion is constructed pathwise on this graph so that its generator satisfies the given boundary conditions

dirichlet forms and dirichlet operators for gibbs measures of quantum unbounded spin systems essential self adjointness and log sobolev inequality for each 0 1 we consider the dirichlet form mu gamma and the associated dirichlet operator h mu gamma for the gibbs measure of quantum unbounded spin systems interacting via superstable and regular potential the gibbs measure is related to the gibbs state of the system via a functional euclidean integral procedure the configuration space for the spin systems is given by omega e mathbb z v e left omega in c left left 0 1 right mathbb r d right omega left 0 right omega left 1 right right we formulate dirichlet forms in the framework of rigged hilbert spaces which are related to the space under appropriate conditions on the potential we show that the dirichlet operator h mu left gamma right is essentially self adjoint on the domain of smooth cylinder functions we give sufficient conditions on the potential so that the corresponding gibbs measure is uniformly log concave ulc this property gives the spectral gap of the dirichlet operator h mu left gamma right at the lower end of the spectrum furthermore we prove that under the conditions of ulc the unique gibbs measure satisfies the log sobolev inequality ls we use an approximate argument used in the study of the same subjects for loop spaces which in turn is a modification of the method originally developed by s albeverio yu g kondratiev and m rockner

uniqueness and the global markov property for euclidean fields the case of general exponential interaction the uniqueness and the global markov property for the regular gibbs measure corresponding to the interaction u lambda varphi lambda int limits lambda d 2 x int d varrho alpha e alpha varphi 0 x for 0 d a probability measure with support in 2 sqrt pi 2 sqrt pi is proved

attractors for 2d navier stokes models with delays abstract the existence of an attractor for a 2d navier stokes system with delay is proved the theory of pullback attractors is successfully applied to obtain the results since the abstract functional framework considered turns out to be nonautonomous however on some occasions the attractors may attract not only in the pullback sense but in the forward one as well also this formulation allows to treat in a unified way terms containing various classes of delay features constant variable distributed delays etc as a consequence some results for the autonomous model are deduced as particular cases of our general formulation

green s and dirichlet spaces associated with fine markov processes this is the second paper in a series devoted to green s and dirichlet spaces in the first paper we have investigated green s space k and the dirichlet space h associated with a symmetric markov transition function pt x b now we assume that p is a transition function of a fine markov process x and we prove that a the space h can be built from functions which are right continuous along almost all paths b the positive cone k in k can be identified with a cone m of measures on the state space c the positive cone h in h can be interpreted as the cone of green s potentials of measures m to every measurable set b in the state space e there correspond a subspace k b of k and a subspace h b of h the orthogonal projections of k onto k and of h onto h b can be expressed in terms of the hitting probabilities of b by the markov process x as the main tool we use additive functionals of x corresponding to measures m

a competition model for two resources in un stirred chemostat abstract this paper studies a un stirred chemostat with two species competing for two growth limiting non reproducing resources we determine the conditions for positive steady states of the two species and then consider the global attractors of the model in addition we obtain the conditions under which the two populations uniformly strongly persist or go to extinction since the diffusion mechanism with homogeneous boundary conditions inhibits the growth of the organism species it can be understood that the coexistence will be ensured by proportionally smaller diffusions for the two species in particular it is found that both instability and bi stability subcases of the two semitrivial steady states are included in the coexistence region the two populations will go to extinction when both possess large diffusion rates if just one of them spreads faster with the other one diffusing slower then the related semitrivial steady state will be globally attracting the techniques used for the above results consist of the degree theory the semigroup theory and the maximum principle

formes de dirichlet generales et densite des variables aleatoires reelles sur l espace de wiener abstract it is shown that the main properties of dirichlet spaces can be proved without the classical local compacity hypothesis to this purely measurable framework we extend the functional calculus and the energy image density property these results are then applied to the ornstein uhlenbeck semi group on wiener space where it is obtained that the real random variables which are solutions of lipschitzian stochastic differential equations always have probability densities after perhaps an initial deterministic phase

on the contraction property of energy forms on infinite dimensional space abstract we prove that certain energy forms on infinite dimensional space with polynomial domain have the contraction or dirichlet property some consequences are discussed

a system of resource based growth models with two resources in the unstirred chemostat abstract models of single species growth in the unstirred chemostat on two growth limiting nonreproducing resources are considered for the case of two complementary resources the existence and uniqueness of a positive steady state solution is established it is also proved that the unique positive solution is globally attracting for the system with regard to nontrivial nonnegative initial values for the case of two substitutable resources the existence of a positive steady state solution is determined for a range of the parameter m n techniques include the maximum principle monotone method and global bifurcation theory the longtime behavior of the corresponding limiting system is given for a range of m n in the special case of m n the uniqueness and global attractivity of the positive steady state solution of the original system is established

the existence and uniqueness of the solution for stochastic functional differential equations with infinite delay abstract this paper is devoted to build the existence and uniqueness theorem of solutions to stochastic functional differential equations with infinite delay short for isfdes at phase space bc 0 r d under the uniform lipschitz condition the linear growth condition is weaked to obtain the moment estimate of the solution for isfdes furthermore the existence and uniqueness theorem of the solution for isfdes is derived and the estimate for the error between approximate solution and accurate solution is given on the other hand under the linear growth condition the uniform lipschitz condition is replaced by the local lipschitz condition the existence and uniqueness theorem is also valid for isfdes on t 0 t moreover the existence and uniqueness theorem still holds on interval t 0 where t 0 r is an arbitrary real number

the maximum principle and the global attractor for the dissipative 2d quasi geostrophic equations the long time behavior of the solutions to the two dimensional dissipative quasi geostrophic equations is studied we obtain a new positivity lemma which improves a previous version of a cordoba and d cordoba 10 and 11 as an application of the new positivity lemma we obtain the new maximum principle i e the decay of the solution in l p for any p 2 when f is zero as a second application of the new positivity lemma for the sub critical dissipative case with open image in new window the existence of the global attractor for the solutions in the space h s for any s 2 1 is proved for the case when the time independent f is non zero therefore the global attractor is infinitely smooth if f is this significantly improves the previous result of berselli 2 which proves the existence of an attractor in some weak sense for the case 1 the global attractor exists in h s for any s 0 and the estimate of the hausdorff and fractal dimensions of the global attractor is also available

on a system of reaction diffusion equations arising from competition in an unstirred chemostat a system of reaction diffusion equations modeling two species competition in an unstirred chemostat is considered the asymptotic behavior of solutions is given as a function of the parameters and it is determined when neither one or both competing populations survive techniques include the maximum principle theory of uniform persistence in infinite dimensional dynamical systems and the theory of strongly order preserving semidynamical system

machine part cell formation using biclustering abstract cellular manufacturing is the cornerstone of many modern flexible manufacturing techniques taking advantage of the similarities between parts in order to decrease the complexity of the design and manufacturing life cycle part machine grouping pmg problem is the key step in cellular manufacturing aiming at grouping parts with similar processing requirements or similar design features into part families and by grouping machines into cells associated to these families the pmg problem is np complete and the different proposed techniques for solving it are based on heuristics in this paper a new approach for solving the pmg problem is proposed which is based on biclustering biclustering is a methodology where rows and columns of an input data matrix are clustered simultaneously a bicluster is defined as a submatrix spanned by both a subset of rows and a subset of columns although biclustering has been almost exclusively applied to dna microarray analysis we present that biclustering can be successfully applied to the pmg problem we also present empirical results to demonstrate the efficiency and accuracy of the proposed technique with respect to related ones for various formations of the problem

ergodicity for the stochastic dynamics of quasi invariant measures with applications to gibbs states the convex set maof quasi invariant measures on a locally convex spaceewith given shift radon nikodym derivatives i e cocycles a atk k k0 t ris analyzed the extreme points of maare characterized and proved to be non empty a specification of lattice type is constructed so that macoincides with the set of the corresponding gibbs states as a consequence via a well known method due to dynkin and follmer a unique representation of an arbitrary element in main terms of extreme ones is derived furthermore the corresponding classical dirichlet forms e d e and their associated semigroups t t t 0onl2 e are discussed under a mild positivity condition it is shown that mais extreme if and only if e d e is irreducible or equivalently t t t 0is ergodic this implies time ergodicity of associated diffusions applications to gibbs states of classical and quantum lattice models as well as those occuring in euclidean quantum field theory are presented in particular it is proved that the stochastic quantization of a guerra rosen simon gibbs state on d r2 ininfinite volumewith polynomial interaction is ergodic if the gibbs state is extreme i e is a pure phase which solves a long standing open problem

non symmetric dirichlet forms on semifinite von neumann algebras abstract the theory of non symmetric dirichlet forms is generalized to the non abelian setting also establishing the natural correspondences among dirichlet forms sub markovian semigroups and sub markovian resolvents within this context some results on the allowed functional calculus for closed derivations on hilbert algebras are obtained examples of non symmetric dirichlet forms given by derivations on hilbert algebras are studied

asymptotic coupling and a general form of harris theorem with applications to stochastic delay equations there are many markov chains on infinite dimensional spaces whose one step transition kernels are mutually singular when starting from different initial conditions we give results which prove unique ergodicity under minimal assumptions on one hand and the existence of a spectral gap under conditions reminiscent of harris theorem the first uses the existence of couplings which draw the solutions together as time goes to infinity such asymptotic couplings were central to mattingly and sinai in comm math phys 219 3 523 565 2001 mattingly in comm math phys 230 3 461 462 2002 hairer in prob theory relat field 124 345 380 2002 bakhtin and mattingly in commun contemp math 7 553 582 2005 on which this work builds as in bakhtin and mattingly 2005 the emphasis here is on stochastic differential delay equations harris celebrated theorem states that if a markov chain admits a lyapunov function whose level sets are small in the sense that transition probabilities are uniformly bounded from below then it admits a unique invariant measure and transition probabilities converge towards it at exponential speed this convergence takes place in a total variation norm weighted by the lyapunov function a second aim of this article is to replace the notion of a small set by the much weaker notion of a d small set which takes the topology of the underlying space into account via a distance like function d with this notion at hand we prove an analogue to harris theorem where the convergence takes place in a wasserstein like distance weighted again by the lyapunov function this abstract result is then applied to the framework of stochastic delay equations in this framework the usual theory of harris chains does not apply since there are natural examples for which there exist no small sets except for sets consisting of only one point this gives a solution to the long standing open problem of finding natural conditions under which a stochastic delay equation admits at most one invariant measure and transition probabilities converge to it

dynamical behavior of nonautonomous stochastic reaction diffusion neural network models this brief investigates nonautonomous stochastic reaction diffusion neural network models with s type distributed delays first the existence and uniqueness of mild solution are studied under the lipschitz condition without the linear growth condition due to the existence of a nonautonomous reaction diffusion term and the infinite dimensional wiener process the criteria for the well posedness of the models are established based on the evolution system theory then the s type distributed delay which is an infinite delay is handled by the truncation method and sufficient conditions for the global exponential stability are obtained by constructing a simple lyapunov krasovskii functional candidate finally neural network examples and an illustrative example are given to show the applications of the obtained results

on the small time behavior of ornstein uhlenbeck processes with unbounded linear drifts in this paper we study the small time behavior of ornstein ulenbeck processes with unbounded linear drifts on hilbert spaces the large deviations estimates are obtained the general theory of dirichlet forms lyons zheng s decompositions and the convolution representation of the processes play an important role

specifications and martin boundaries for scr p phi _2 random fields it is shown thatp 2 gibbs states in the sense of guerra rosen and simon are given by a specification the construction of the specification is based on finding a proper version of the interaction density given by the polynomialp the existence of this version follows from the fact that all powers of the solution of a dirichlet problem for an open bounded setu with boundary data given by a distribution are integrable onu as a consequence the martin boundary theory for specifications can be applied top 2 random fields it follows that anyp 2 gibbs state can be represented in terms of extreme gibbs states in certain cases the extreme gibbs states are characterized in terms of harmonic functions it follows in particular that for any given boundary condition introduced so far the associated cutoffp 2 measure has a representation as an integral over harmonic functions

nonlinear functional differential equations of monotone type in hilbert spaces abstract in this paper we study a class of semilinear functional evolution equations with finite delay in which the nonlinearity satisfies the weak condition of demicontinuity with respect to functional variable and also a semimonotone condition we will prove the existence uniqueness and measurability of the mild solutions based on an extension of the analogous results for non delay initial value problems on banach spaces and a version of recently developed random schauder s fixed point theorem this will be done first for the generalized solutions and then we follow an approximating procedure to obtain the same results for the mild solutions

potential theory of infinite dimensional levy processes abstract we study the potential theory of a large class of infinite dimensional levy processes including brownian motion on abstract wiener spaces the key result is the construction of compact lyapunov functions i e excessive functions with compact level sets then many techniques from classical potential theory carry over to this infinite dimensional setting thus a number of potential theoretic properties and principles can be proved answering long standing open problems even for the brownian motion on abstract wiener space as e g formulated by r carmona in 1980 in particular we prove the analog of the known result that the cameron martin space is polar in the levy case and apply the technique of controlled convergence to solve the dirichlet problem with general not necessarily continuous boundary data

martingale and stationary solutions for stochastic navier stokes equations we prove the existence of martingale solutions and of stationary solutions of stochastic navier stokes equations under very general hypotheses on the diffusion term the stationary martingale solutions yield the existence of invariant measures when the transition semigroup is well defined the results are obtained by a new method of compactness