stationary distribution of stochastic population systems in this paper we consider the stochastic differential equation sde population model dx t diag x1 t xn t b ax t dt db t for n interacting species the main aim is to study the stationary distribution of the solution it is known see e g bahar and mao 2004 2 and mao 2005 6 if the noise intensity is sufficiently large then the population may become extinct with probability one our main aim here is to find out what happens if the noise is relatively small in this paper we will show the existence of a unique stationary distribution we will then develop a useful method to compute the mean and variance of the stationary distribution computer simulations will be used to illustrate our theory

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

balancing survival and extinction in nonautonomous competitive lotka volterra systems abstract we generalise and unify some recent results about extinction in n th order nonautonomous competitive lotka volterra systems for each r n we show that if the coefficients are continuous bounded by strictly positive constants and satisfy certain inequalities then any solution with strictly positive initial values has the property that n r of its components vanish whilst the remaining r components asymptotically approach a canonical solution of an r dimensional restricted system in other words r of the species being modeled survive whilst the remaining n r are driven to extinction

asymptotically periodic solutions of n competing species problem with time delays abstract a general nonautonomous lotka volterra system of integro differential equations with infinite delay is considered and sufficient conditions for uniform stability and asymptotic stability of solutions are investigated these limiting equations are used to obtain the existence of asymptotically periodic solutions of the corresponding system of equations where lower limit in the integration is zero

permanence extinction and global asymptotic stability in a stage structured system with distributed delays in this paper we consider a nonautonomous stage structured competitive system of n species population growth with distributed delays which takes into account the delayed feedback in both interspecific and intraspecific interactions we obtain by using the method of repeated replace sufficient conditions for permanence and extinction of the species the global attractivity of the unique positive equilibrium is proved in the autonomous case our results extend previous ones obtained by liu et al in nonlinear anal 51 2002 1347 1361 j math anal appl 274 2002 667 684

positive periodic solutions of n species neutral delayed lotka volterra competition system with impulsive perturbations in this paper a class of neutral delayed lotka volterra competition system with impulsive perturbations is investigated we explore the existence of positive periodic solutions of the system by using mawhin coincidence degree theory and some analytical approaches from our results we find that a part of n species of the system is driven to extinction due to competition exclusion and weak adaption to environment characterized by impulsive perturbations

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

an invariance result for capacities on wiener space we prove that tight capacities are invariant if one weakens the underlying topology as a consequence we obtain a comparison theorem about r p capacities and the corresponding notion of r p quasi continuity used in the malliavin calculus on different abstract wiener spaces ej h j with common hilbert space h furthermore we prove tightness of r p capacities of ornstein uhlenbeck semigroups with general linear drift

complete branching rules for specht modules abstract we give a combinatorial description for when the specht module of an arbitrary diagram admits a complete branching rule this description given in terms of the maximal rectangles of the diagram generalizes all previously known branching rules for specht modules such as those given by reiner and shimozono for northwest diagrams and by the present author for forest diagrams

uniqueness of diffusion generators for two types of particle systems with singular interactions abstract for two types of stochastic particle systems in r d we show non explosion in finite time by proving that their respective generators are l1 unique where is their respective invariant in these cases even symmetrizing measure we also prove the much harder l2 uniqueness in both models

dynamic analysis of stochastic virus infection model with delay effect abstract this paper mainly investigates the dynamic behavior of virus infection model with delay effect influenced by external noise first a mathematical model describing the evolution of virus under the influences of stochastic noise and delay effect is developed and necessary conditions for extinction and weak persistence are derived by ito s formula a new basic reproduction number r 0 for virus infection model with delay effect to determine whether extinction or persistence is given it is found that the delay parameter affects the new basic reproduction number r 0 and the behavior of extinction and survival of virus besides the threshold for extinction of stochastic model is smaller than the one of deterministic model in the end stochastic simulations are applied to illustrate and test the theoretical conclusions

lp uniqueness of schrodinger operators and the capacitary positive improving property abstract we prove several lp uniqueness results for schrodinger operators l v by means of the feynman kac formula using the m p capacity theory for general markov semigroups we show that the associated feynman kac semigroup is positive improving in the sense of m p capacity improving the well known one in the sense of measure using that capacitary positive improving property and two new inequalities for generalized ornstein uhlenbeck generators we show the essential self adjointness of the ground state diffusion generator l l 2 associated with two dimensional euclidean quantum fields

l p uniqueness for elliptic operators with unbounded coefficients in r n let a be an elliptic operator with unbounded and sufficiently smooth coefficients and let be a sub invariant measure of the operator a in this paper we give sufficient conditions guaranteeing that the closure of the operator a cc rn generates a sub markovian strongly continuous semigroup of contractions in lp rn applications are given in the case when a is a generalized schrodinger operator

global asymptotic stability in n species non autonomous lotka volterra competitive systems with infinite delays and feedback control abstract a non autonomous lotka volterra competition system with infinite delays and feedback control and without dominating instantaneous negative feedback is investigated by means of a suitable lyapunov functional sufficient conditions are derived for the global asymptotic stability of the system some new results are obtained

permanence and global stability of nonautonomous lotka volterra system with predator prey and deviating arguments by using comparison theorem and constructing suitable lyapunov functional some sufficient conditions for the permanence and global asymptotic stability of the general nonautonomous lotka volterra system with predator prey and deviating arguments are obtained

dirichlet operators a priori estimates and the uniqueness problem abstract we study the equation du dt hu 0 where h is the operator associated with the dirichlet form of quasi invariant measure on hilbert space a priori estimates of the first and second order derivatives of the solutions of the equation are obtained then these estimates are applied to the problem of essential self adjointness of the operator h on domains which consist of smooth functions

reconstruction of dynamics from an eigenstate for hamiltonians that have a formal canonical decomposition h 1 2 v x v x being a multiplication operator the definition of the dynamics by a ground state measure leads to an energy dirichlet form formulation of quantum mechanics that is more general than the operator schrodinger approach here the question of reconstruction of the dynamics from an eigenstate when the potential is not restricted to the class of multiplication operators is analyzed by explicit analysis of several examples it is found that once a particular operator class is chosen the potential and the energy form are to some extent determined by the eigenstate however depending on the type of operator the potential is chosen to be many distinct dynamics can be associated to the same fixed eigenstate the nature of the stochastic processes associated with each reconstructed dynamic is also discussed as well as a generalization of the stochastic dynamics formalism allowing for nonlocal potentials

a smooth space of tetrahedra abstract we construct a smooth symmetric compactification of the space of all labeled tetrahedra in p 3

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

lp uniqueness of non symmetric diffusion operators with singular drift coefficients i the finite dimensional case two uniqueness results for c0 semigroups on weighted lp spaces over rn generated by operators of type with singular drift are proven a key ingredient in the proofs is the verification of some kind of weak kato inequality which seems to break down exactly for those drift singularities where lp uniqueness breaks down as well

stochastic differential delay equations of population dynamics in this paper we investigate the almost surely asymptotic stability for the nonlinear stochastic differential delay equations with markovian switching some sufficient criteria on the controllability and robust stability are also established for linear stochastic differential delay equations with markovian switching

stability and attractivity of periodic solutions of parabolic systems with time delays abstract this paper is concerned with the existence stability and global attractivity of time periodic solutions for a class of coupled parabolic equations in a bounded domain the problem under consideration includes coupled system of parabolic and ordinary differential equations and time delays may appear in the nonlinear reaction functions our approach to the problem is by the method of upper and lower solutions and its associated monotone iterations the existence of time periodic solutions is for a class of locally lipschitz continuous reaction functions without any quasimonotone requirement using schauder fixed point theorem while the stability and attractivity analysis is for quasimonotone nondecreasing and mixed quasimonotone reaction functions using the monotone iterative scheme the results for the general system are applied to the standard parabolic equations without time delay and to the corresponding ordinary differential system applications are also given to three lotka volterra reaction diffusion model problems and in each problem a sufficient condition on the reaction rates is obtained to ensure the stability and global attractivity of positive periodic solutions

permanence for non autonomous food chain systems with delay in this paper we first establish a new general criterion for the permanence of kolmogorov type systems of nonautonomous functional differential equations then as applications of this criterion we study the permanence of a class of n species general nonautonomous food chain systems with delay and new sufficient condition are established

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

extinction in two species nonautonomous nonlinear competitive system a two species nonautonomous nonlinear competitive system is studied in this paper it is shown that if the coefficients are continuous bounded above and below by positive constants and satisfy certain inequalities then one of the components will be driven to extinction while the other one will stabilize at the certain positive solution of a nonlinear single species model our result not only generalizing but also improving the result of li and chen 2006

global stability for infinite delay lotka volterra type systems abstract in this paper sufficient conditions are established for the global stability of the saturated equilibrium of an infinite delay nonautonomous lotka volterra type system the present work is distinguished from previous work principally be allowing the system to be nonautonomous and relaxing the traditional requirement that the undelayed intraspecific competition dominates both the delayed intraspecific competition as well as the interspecific interactions we require the undelayed intraspecific competition to dominate the latter but not the former

self adjointness of some infinite dimensional elliptic operators and application to stochastic quantization we consider an operator k l in a hilbert space h where l is an ornstein uhlenbeck operator u w 1 4 h and is the invariant measure associated with l we show that k is essentially self adjoint in the space l 2 h where is the gibbs measure dx z 1 e 2u x dx an application to stochastic quantization is given

exponential stability of a competitive lotka volterra system with delays abstract in this paper the exponential stability of a two species competitive lotka volterra system with discrete delays has been studied by constructing appropriate lyapunov functional and using the linear matrix inequality lmi optimization approach a series of sufficient criteria is obtained which ensure the exponential stability of the positive equilibrium of the given lotka volterra system the results are new and improve some earlier work an illustrative example is given to demonstrate the effectiveness of the obtained results

absolute continuity of symmetric diffusions let x and y be symmetric diffusion processes with a common state space and let p m resp q be the law of x resp y with its symmetry measure m resp as initial distribution we study the consequences of the absolute continuity condition q t 1 t the density p also serves to link the dirichlet forms of x and y in a simple way our identification of l relies on notions of even and odd for additive functionals these notions complement fukushima s decomposition and the forward backward martingale decomposition of lyons and zheng

a new topological approach to the l uniqueness of operators and the l1 uniqueness of fokker planck equations abstract the usual semigroups of kernels on a polish space e are in general not strongly continuous on l e with respect to the norm topology we introduce a new topology on l e such that they become c 0 semigroups for which we can establish a simplified hille yosida theorem the new topology will allow us to introduce the uniqueness of pre generator on l e which turns out to be equivalent to the l 1 uniqueness of the associated fokker planck equation among many others and it is intimately related with the liouville properties for l 1 harmonic functions the uniqueness of several second order elliptic differential operators in l are studied 1 one dimensional diffusion operators a x f b x f 2 schrodinger operators 1 2 v 3 multi dimensional diffusion generator 1 2

global dynamics behaviors for a nonautonomous lotka volterra almost periodic dispersal system with delays abstract a nonautonomous lotka volterra dispersal system with continuous delays and discrete delays is considered by using a comparison theorem and delay differential equation basic theory we obtain sufficient conditions for the permanence of the population in every patch by constructing a suitable lyapunov functional we prove that the system is globally asymptotically stable under some appropriate conditions using almost periodic functional hull theory we get sufficient conditions for the existence uniqueness and globally asymptotical stability for an almost periodic solution this implies that the population in every patch exhibits stable almost periodic fluctuation furthermore the results show that the permanence and global stability of system and the existence and uniqueness of a positive almost periodic solution depend on the delay then we call it profitless

addendum specht modules for column convex diagrams characteristic free results for weyl modules abstract it is shown that the results in reiner and shimozono 12 have characteristic free analogues for weyl modules

a straightening algorithm for row convex tableaux abstract we produce a new basis for the schur and weyl modules associated to a row convex shape d the basis is indexed by a new class of straight tableaux which we introduce by weakening the usual requirements for standard tableaux spanning is proved via a new straightening algorithm for expanding elements of the representation into this basis for skew shapes this algorithm specializes to the classical straightening law the new straight basis is used to produce bases for flagged schur and weyl modules to provide groebner and sagbi bases for the homogeneous coordinate rings of some configuration varieties and to produce a flagged branching rule for row convex representations systematic use of supersymmetric letterplace techniques enables the representation theoretic results to be applied to representations of the general linear lie superalgebra as well as to the general linear group

permanence and global stability for nonautonomous n species lotka volterra competitive system with impulses and infinite delays abstract in this paper we consider a class of nonautonomous n species lotka volterra competitive systems with impulses and infinite delays by developing the methods given in teng 2002 25 we give sufficient conditions for permanence and global attractivity of the system

global asymptotic stability in n species nonautonomous lotka volterra competitive systems with infinite delays by means of lyapunov functional we have succeeded in establishing the global asymptotic stability of the positive solutions of a delayed n species nonautonomous lotka volterra type competitive system without dominating instantaneous negative feedbacks as a corollary we show that the global asymptotic stability of the positive solution is maintained provided that the delayed negative feedbacks dominate other interspecific interaction effects with delays and the mean delays are sufficiently small

borel weil theorem for configuration varieties and schur modules we present a generalization of the classical schur modules ofgl n exhibiting the same interplay among algebra geometry and combinatorics a generalized young diagramdis an arbitrary finite subset ofn n for eachd we define the schur modulesdofgl n we introduce a projective variety fdand a line bundle ld and describe the schur module in terms of sections of ld for diagrams with the northeast property i1 j1 i2 j2 d min i1 i2 max j1 j2 d which includes the skew diagrams we resolve the singularities of fdand show analogues of bott s and kempf s vanishing theorems finally we apply the atiyah bott fixed point theorem to establish a weyl type character formula of the form charsd x txwt t i j 1 xix 1j dij t wheretruns over certain standard tableaux ofd our results are valid over fields of arbitrary characteristic

uniqueness of generalized schrodinger operators part ii abstract we prove that for h 1 2 loc r d dx 0 dx a e the generalized schrodinger operator s 2 1 dom s c 0 r d has exactly one self adjoint extension on l 2 r d 2 dx which generates a sub markovian semigroup on l 2 r d 2 dx this is based on our previous work where a necessary and sufficient condition on for this to hold was proved but which was only verified to always hold if d 1 we also prove a corresponding result where r d is replaced by an infinite dimensional space and the lebesgue measure by some gaussian measure whose covariance operator has a discrete spectrum

uniform persistence in functional differential equations abstract in this paper we investigate the question of uniform persistence for retarded functional differential equations by utilizing liapunov like functions razumikhin techniques and differential inequalities we are able to establish criteria for uniform persistence analogous to those obtained by others for ordinary differential equations difference equations and reaction diffusion equations we apply these criteria to some well known biological models with delay our results indicate that the conditions which guarantee the existence of an interior equilibrium are enough to ensure uniform persistence moreover these conditions are equivalent to uniform persistence for the cases without delay as well

periodic solution and almost periodic solution for a nonautonomous lotka volterra dispersal system with infinite delay abstract this paper studies a nonautonomous lotka volterra dispersal systems with infinite time delay which models the diffusion of a single species into n patches by discrete dispersal our results show that the system is uniformly persistent under an appropriate condition the sufficient condition for the global asymptotical stability of the system is also given by using mawhin continuation theorem of coincidence degree we prove that the periodic system has at least one positive periodic solution further obtain the uniqueness and globally asymptotical stability for periodic system by using functional hull theory and directly analyzing the right functional of almost periodic system we show that the almost periodic system has a unique globally asymptotical stable positive almost periodic solution we also show that the delays have very important effects on the dynamic behaviors of the system

positive almost periodic solutions of a class of lotka volterra type competitive system with delays and feedback controls abstract in this paper we study the positive almost periodic solutions for a class of almost periodic lotka volterra type system with delays and feedback controls applying schauder s fixed point theorem a criterion on the existence of the positive almost periodic solution of the system is obtained our new criterion which improves and generalizes some well known results can be easily checked

specht series for column convex diagrams abstract we give a specht series for the specht module s d associated to a diagram d in two cases 1 when d is column convex 2 when d is the complement of a column convex diagram within a rectangular box

on the connection between schrodinger and dirichlet forms relations between schrodinger forms associated with schrodinger operators in l2 dnx rn open n 1 and the corresponding dirichlet forms are investigated various concrete examples are presented

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

entropy reversible diffusion processes and markov uniqueness abstract consider a symmetric bilinear form e defined on c c r d by formula in this paper we study the stochastic process associated with the smallest closed markovian extension of e c c and give a new proof of markov uniqueness i e the uniqueness of a closed markovian extension based on purely probabilistic arguments we also give another purely analytic one as a consequence we show that all invariant measures are reversible provided they are of finite energy the problem of uniqueness of such measures is also partially solved

uniqueness of gibbs states for quantum lattice systems we prove uniqueness of euclidean gibbs states for certain quantum lattice systems with unbounded spins we use dobrushin s uniqueness criterion the necessary estimates for the vasershtein distance between the corresponding one point conditional distributions with boundary conditions differing only at one side are obtained by proving a log sobolev inequality on the infinite dimensional single spin loop spaces some important classes of concrete examples to which all this applies are discussed

permanence for a class of periodic time dependent competitive system with delays and dispersal in a patchy environment in this paper we study m species time delayed competitive lotka volterra type dispersal system with periodic coefficients in n patches by utilizing analytic method sufficient and realistic conditions on permanence and the existence of periodic solution are established the theoretical results are confirmed by a special example and numerical simulations

stochastic delay lotka volterra model we reveal in this paper that the environmental noise will not only suppress a potential population explosion in the stochastic delay lotka volterra model but will also make the solutions to be stochastically ultimately bounded to reveal these interesting facts we stochastically perturb the delay lotka volterra model x t diag x1 t xn t b ax t into the ito form dx t diag x1 t xn t b ax t dt x t dw t and show that although the solution to the original delay equation may explode to infinity in a finite time with probability one that of the associated stochastic delay equation does not we also show that the solution of the stochastic equation will be stochastically ultimately bounded without any additional condition on the matrix a

dirichlet operators a priori estimates and uniqueness problems ii abstract we study some basic properties of the dirichlet operator in weighted l p spaces we work under rather general assumptions on weights that destroy minimal local sobolev regularity of the form domain

permanence extinction and balancing survival in nonautonomous lotka volterra system with delays in this paper the periodic n species lotka volterra competition systems with time delays are considered the sufficient conditions are derived for the permanence extinction and balancing survival of the system some known results are improved and unified further our results suggest that under some conditions the introduction and the variance of the time delays will be either harmless or useless conjecture about the effect of time delays on some global behaviors of the system is advanced

non self adjoint jacobi matrices with a rank one imaginary part we develop direct and inverse spectral analysis for finite and semi infinite non self adjoint jacobi matrices with a rank one imaginary part it is shown that given a set of n not necessarily distinct nonreal numbers in the open upper lower half plane uniquely determines an n n jacobi matrix with a rank one imaginary part having those numbers as its eigenvalues counting algebraic multiplicity algorithms of reconstruction for such finite jacobi matrices are presented a new model complementing the well known livsic triangular model for bounded linear operators with a rank one imaginary part is obtained it turns out that the model operator is a non self adjoint jacobi matrix we show that any bounded prime non self adjoint linear operator with a rank one imaginary part acting on some finite dimensional respectively separable infinite dimensional hilbert space is unitarily equivalent to a finite respectively semi infinite non self adjoint jacobi matrix this obtained theorem strengthens a classical result of stone established for self adjoint operators with simple spectrum we establish the non self adjoint analogs of the hochstadt and gesztesy simon uniqueness theorems for finite jacobi matrices with nonreal eigenvalues as well as an extension and refinement of these theorems for finite non self adjoint tri diagonal matrices to the case of mixed eigenvalues real and nonreal a unique jacobi matrix unitarily equivalent to the operator of integration ff x 2i xlf t dt in the hilbert space l2 0 l is found as well as spectral properties of its perturbations and connections with the well known bernoulli numbers we also give the analytic characterization of the weyl functions of dissipative jacobi matrices with a rank one imaginary part

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

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

convergence of dirichlet forms and associated schrodinger operators abstract we study the convergence of local dirichlet forms and associated schrodinger operators conditions are given for n in order that the schrodinger operators n n associated with dirichlet forms u x 2 n 2 x dx generate contraction semigroups which converge strongly in l2 r d moreover conditions are given which permit one to identify the limit contraction semigroups and schrodinger operators

the essential self adjointness of generalized schrodinger operators a necessary and sufficient condition is given for the generalized schrodinger operator a 12 i 1n di di to be essentially self adjoint in l2 dx under general assumptions on and for arbitrary domains in rn in particular if is strictly positive and locally lipschitz continuous on rn then a is essentially self adjoint examples of non essential self adjointness and a complete discussion of the one dimensional case are also given these results have applications to the problem of the essential self adjointness of quantum hamiltonians and to the uniqueness problem of markov processes

on the uniqueness problem for dirichlet operators abstract strong uniqueness in l 2 and in l 1 for dirichlet operators in finite dimensional spaces is studied

permanence in kolmogorov type systems of nonautonomous functional differential equations abstract in this paper we establish some general results on the permanence of the n species kolmogorov type nonautonomous functional differential system formula i 1 2 n these results are applied to the n species lotka volterra type systems with distributed delays that is when f i t x t are linear functions of x t our method consists of constructing n liapunov like functions which can be regarded as boundary functions of some compact region inside the positive cone in r n

the space of triangles vanishing theorems and combinatorics abstract we consider compactifications of pn 3 ij the space of triples of distinct points in projective space one such space is a singular variety of configurations of points and lines another is the smooth compactification of fulton and macpherson and a third is the triangle space of schubert and semple we compute the sections of line bundles on these spaces and show that they are equal as gl n representations to the generalized schur modules associated to bad generalized young diagrams with three rows borel weil theorem on the one hand this yields weyl type character and dimension formulas for the schur modules on the other a combinatorial picture of the space of sections cohomology vanishing theorems play a key role in our analysis

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

absolute continuity of the invariant measures for some stochastic pdes we consider a free system and an interacting systems having invariant measures and respectively under suitable assumptions we prove an explicit formula relating with and implying the absolute continuity of with respect to we apply our result to a reaction diffusion equation and to the burgers equation

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

almost periodic solution for n species lotka volterra competitive system with delay and feedback controls abstract in this paper a n species lotka volterra competition system with delay and feedback controls is investigated by means of the theory of comparison theorem and suitable lyapunov functional some sufficient conditions for the existence and uniqueness of almost positive periodic solutions of this system is obtained

some new results of nonautonomous lotka volterra competitive systems with delays abstract in this paper we improve and generalize the results of montes de oca and zeeman j math anal appl 192 1995 360 370 proc amer math soc 124 1996 3677 3687 to general n species nonautonomous lotka volterra type competitive systems with finite or infinite delays we establish a series of criteria under which a part of the n species of the systems is driven to extinction while the remaining part of the n species is persistent or uniformly persistent or coexists globally asymptotically stable

profitless delays for a nonautonomous lotka volterra predator prey almost periodic system with dispersion abstract this paper studies a nonautonomous lotka volterra almost periodic predator prey dispersal system with discrete and continuous time delays which consists of two patches the prey species can disperse among two patches but the predator species is confined to one patch and cannot disperse by using comparison theorem and delay differential equation basic theory we prove the system is uniformly persistent under some appropriate conditions further by constructing suitable lyapunov functional we show that the system is globally asymptotically stable under some appropriate conditions by using a new method and almost periodic functional hull theory we show that the almost periodic system has a unique globally asymptotical stable strictly positive almost periodic solution the conditions for the permanence global stability of system and the existence uniqueness of positive almost periodic solution depend on delays so time delays are profitless finally ecological conclusions and a particular case are given these results are basically an extension of the known results for nonautonomous lotka volterra systems

laplace operators on the cone of radon measures abstract we consider the infinite dimensional lie group g which is the semidirect product of the group of compactly supported diffeomorphisms of a riemannian manifold x and the commutative multiplicative group of functions on x the group g naturally acts on the space m x of radon measures on x we would like to define a laplace operator associated with a natural representation of g in l 2 m x here is assumed to be the law of a measure valued levy process a unitary representation of the group cannot be determined since the measure is not quasi invariant with respect to the action of the group g consequently operators of a representation of the lie algebra and its universal enveloping algebra in particular a laplace operator are not defined nevertheless we determine the laplace operator by using a special property of the action of the group g a partial quasi invariance we further prove the essential self adjointness of the laplace operator finally we explicitly construct a diffusion process on m x whose generator is the laplace operator