on viscosity and fluctuation dissipation in exclusion processes we consider the asymmetric simple exclusion process we review some results in dimension d 3 concerning the fluctuation dissipation theorem and we prove regularity of viscosity coefficients

sufficient second order optimality conditions for semilinear control problems with pointwise state constraints second order sufficient optimality conditions are established for the optimal control of semilinear elliptic and parabolic equations with pointwise constraints on the control and the state in contrast to former publications on this subject the cone of critical directions is the smallest possible in the sense that the second order sufficient conditions are the closest to the associated necessary ones the theory is developed for elliptic distributed controls in domains up to dimension three moreover problems of elliptic boundary control and parabolic distributed control are discussed in spatial domains of dimension two and one respectively

an optimal control problem for a two prey and one predator model with diffusion abstract an optimal control problem is studied for a reaction diffusion system that models an ecosystem composed by one predator and two prey populations one proposed to maximize the total density of the three populations to do this one proves the existence of an optimal solution and one establishes first and second order optimality conditions several numerical simulations performed in both one dimensional and two dimensional isolated environments and using different holling type functional responses support the theoretical results

optimal control problem for an ecosystem with two competing preys and one predator abstract this work is devoted to the optimal control problem for an ecosystem composed of one predator and two competing preys and our goal is to maximize the total density of the three populations we first investigate the existence and uniqueness of the positive strong solution for the controlled system and find an optimal solution under given initial conditions then we establish the first order necessary optimality condition and point out that the optimal control has a bang bang form moreover the second order necessary and sufficient optimality conditions are established

schur dynamics of the schur processes abstract we construct discrete time markov chains that preserve the class of schur processes on partitions and signatures one application is a simple exact sampling algorithm for q volume distributed skew plane partitions with an arbitrary back wall another application is a construction of markov chains on infinite gelfand tsetlin schemes that represent deterministic flows on the space of extreme characters of the infinite dimensional unitary group

some results for long range exclusion processes we examine the long range exclusion process introduced by spitzer and studied by liggett and answer some of the open questions raised by liggett in particular we show the existence of equilibria corresponding to bounded dual harmonic functions and that the process can have right discontinuous paths at strictly positive times we also show that explosions when they occur do so at fixed times determined by the initial configuration finally we give an example for which the configuration with all sites occupied is not stable although the rate at which particles arrive at any given site for that configuration is infinite

asymptotic behavior of solutions for initial boundary value problems for strongly damped nonlinear wave equations abstract we study initial boundary value problems for strongly damped nonlinear wave equations by using improved integral estimates it is proven that the solutions of the problems decay to zero exponentially as time t approaches infinity under a very simple and general assumption regarding the nonlinear term

existence of solutions and optimal control for a model of tissue invasion by solid tumours abstract in this paper we study the distributed optimal control problem for the two dimensional mathematical model of cancer invasion existence of optimal state control and stability is proved and an optimality system is derived

approximate counting uniform generation and rapidly mixing markov chains the paper studies effective approximate solutions to combinatorial counting and uniform generation problems using a technique based on the simulation of ergodic markov chains it is shown that for self reducible structures almost uniform generation is possible in polynomial time provided only that randomised approximate counting to within some arbitrary polynomial factor is possible in polynomial time it follows that for self reducible structures polynomial time randomised algorithms for counting to within factors of the form 1 n are available either for all fl e r or for no fi e r a substantial part of the paper is devoted to investigating the rate of convergence of finite ergodic markov chains and a simple but powerful characterisation of rapid convergence for a broad class of chains based on a structural property of the underlying graph is established finally the general techniques of the paper are used to derive an almost uniform generation procedure for labelled graphs with a given degree sequence which is valid over a much wider range of degrees than previous methods this in turn leads to randomised approximate counting algorithms for these graphs with very good

dimension of the global attractor for strongly damped nonlinear wave equation the existence and estimate of the upper bound of the hausdorff dimension of the global attractor for the strongly damped nonlinear wave equation with the dirichlet boundary condition are considered by introducing a new norm in the phase space the gained hausdorff dimension decreases as the damping grows and remains small for large damping which conforms to physical intuition

invariant set and attractor of nonautonomous functional differential systems the paper is devoted to the invariant set and periodic attractor for nonautonomous functional differential systems some sufficient criteria of the invariant set and periodic attractor are derived particularly we have provided an estimate on existence range of periodic attractor by using the properties of nonnegative matrices and differential inequality technique

global existence and uniqueness of positive solutions and optimal control for a novel model of pest control abstractin the present paper a novel model of pest control governed by coupled sets of partial and ordinary differential equations is investigated in detail global existence and uniqueness of positive solutions to the above model are obtained also the existence of optimal control is proved and the first order and second order optimality conditions satisfied by optimal control are verified in particular the optimal control is demonstrated to be of bang bang form

optimal control for an age dependent competitive species model in a polluted environment in this paper a new age dependent toxicant population model in an environment with small toxicant capacity is formulated and the optimal control problem for this kind hybrid system is investigated the existence and uniqueness of nonnegative solution of this model is obtained by using a fixed point theorem the optimality conditions for the control problem are given by means of tangent normal cone techniques in nonlinear functional analysis the existence of optimal control policy is carefully verified by using of ekeland s variational principle

on the dimension of the global attractor for the damped sine gordon equation this article gives a more precise estimate on the dimension of the global attractor for the damped sine gordon equation the gained hausdorff dimension remains small for large damping which conforms to physics

l_2 rates of convergence for attractive reversible nearest particle systems the critical case reversible nearest particle systems are certain one dimensional interacting particle systems whose transition rates are determined by a probability density beta n with finite mean on the positive integers the reversible measure for such a system is the distribution nu of the stationary renewal process corresponding to this density in an earlier paper we proved under certain regularity conditions that the system converges exponentially rapidly in l 2 nu if and only if the system is supercritical this in turn is equivalent to beta n having exponential tails in this paper we consider the critical case and give moment conditions on beta n which are separately necessary and sufficient for the convergence of the process in l 2 nu at a specified algebraic rate in order to do so we develop conditions on the generator of a general markov process which correspond to algebraic l 2 convergence of the process the use of these conditions is also illustrated in the context of birth and death chains on the positive integers

optimal control strategies for a new ecosystem governed by reaction diffusion equations abstract an optimal control problem for a new ecosystem described by reaction diffusion equations is studied in this contribution different from the classical prey predator law the phenomenon that the growth of predator population gradually reduces due to the after effects of prey population is ubiquitous in the real world such as allelopathy phenomenon in planktonic ecosystems to model this relationship between predator and prey populations together with diffusion behaviors a novel model with general holling type functional response is presented after that the existence and uniqueness of the global positive strong solution to the ecosystem is obtained by the method of semigroups of operators on this basis an optimal control problem of the ecosystem is considered the existence of optimal control strategy is proved by using minimal sequence then the first order necessary optimality condition is obtained and the corresponding optimal control is found to be of on off form furthermore the second order necessary condition for optimal control and sufficient condition for local optimal control are all established finally a numerical example is offered to demonstrate the applications of the results obtained in this work

the convergence result for critical reversible nearest particle systems we consider critical reversible nearest particle systems we assume that the associated renewal measure has large moments as well as some regularity conditions it is shown that such processes started from a nontrivial ergodic translation invariant distribution converge in distribution to the upper invariant measure

slow droplet driven relaxation of stochastic ising models in the vicinity of the phase coexistence region we consider the stochastic ising models glauber dynamics corresponding to the infinite volume basic ising model in arbitrary dimensiond 2 with nearest neighbor interaction and under a positive external magnetic fieldh under minimal assumptions on the rates of flip so that all the common choices are included we obtain results which state that when the system is at low temperaturet the relaxation time when the evolution is started with all the spins down blows up whenh 0 as exp t hd 1 the precise results are lower and upper bounds of this form moreover after a time which does not scale withh and before a time which also grows as an exponential of a multiple of 1 hd 1 ash 0 the law of the state of the process stays whenh is small close to the minus phase of the same ising model without an external field these results may be considered as a partial vindication of a conjecture raised by aizenman and lebowitz in connection to the metastable behavior of these stochastic ising models

on the splitting up method for rough partial differential equations abstract this article introduces the splitting method to systems driven by rough paths the focus is on nonlinear partial differential equations with rough noise but we also cover rough differential equations applications to stochastic partial differential equations arising in control theory and nonlinear filtering are given

finite fractal dimension of random attractor for stochastic non autonomous strongly damped wave equation abstract in this paper we first prove the existence of a random attractor for stochastic non autonomous strongly damped wave equations with additive white noise then we apply a criteria to obtain an upper bound of fractal dimension of the random attractor of considered system

kernel sections for non autonomous strongly damped wave equations we prove the existence of compact kernel sections for the process generated by a non autonomous strongly damped wave equation with homogeneous dirichlet boundary condition we show that the upper bound of the hausdorff dimension of sections decreases as the damping grows for large strong damping

on a prey predator reaction diffusion system with holling type iii functional response in this paper we study a prey predator model defined by an initial boundary value problem whose dynamics is described by a holling type iii functional response we establish global existence and uniqueness of the strong solution we prove that if the initial data are positive and satisfy a certain regularity condition the solution of the problem is positive and bounded on the domain q 0 t x w and then we deduce the continuous dependence on the initial data a numerical approximation of the system is carried out with a spectral method coupled with the fourth order runge kutta time solver the biological relevance of the comparative numerical results is also presented

optimal control for age dependent population hybrid system in a polluted environment in this paper we study an optimal control problem for an age dependent population hybrid system in a polluted environment namely we establish a new toxicant population model with age dependence in a small content of the environment by fixed point theorem we obtain the existence and uniqueness of nonnegative solution of the toxicant population model with age dependence we employ tangent normal cone techniques in nonlinear functional analysis to deduct the optimality conditions for control problem the existence of optimal control policy is carefully verified by means of ekeland s variational principle

critical phenomena for spitzer s reversible nearest particle systems motivated by several results and open problems concerning harris basic contact process we consider the relationship between the critical behavior of the finite and infinite versions of spitzer s reversible nearest particle systems we show that the critical values for the finite and infinite systems agree but that the behavior of the two systems at the common critical value can differ the nash williams recurrence criterion for reversible markov chains is an important tool used in the proofs of the main results and we give a new treatment of that theory finally we compute several critical exponents for the nearest particle systems

a primal dual active set strategy for optimal boundary control of a nonlinear reaction diffusion system this paper is concerned with optimal boundary control of an instationary reaction diffusion system in three spatial dimensions this problem involves a coupled nonlinear system of parabolic differential equations with bilateral as well as integral control constraints we include the integral constraint in the cost by a penalty term whereas the bilateral control constraints are handled explicitly first and second order conditions for the optimization problem are analyzed a primal dual active set strategy is utilized to compute optimal solutions numerically the algorithm is compared to a semismooth newton method

incomplete determinantal processes from random matrix to poisson statistics we study linear statistics of a class of determinantal processes which interpolate between poisson and gue ginibre statistics in dimension 1 or 2 these processes are obtained by performing an independent bernoulli percolation on the particle configuration of a log gas confined in a general potential we show that depending on the expected number of deleted particles there is a universal transition for mesoscopic linear statistics namely at small scales the point process behave according to random matrix theory while at large scales it needs to be renormalized because the variance of any linear statistic diverges the crossover is explicitly characterized as the superposition of a h 1 or h 1 2 correlated gaussian noise depending on the dimension and an independent poisson process the proof consists in computing the limits of the cumulants of linear statistics using the asymptotics of the correlation kernel of the process

second order necessary and sufficient optimality conditions for optimization problems and applications to control theory this paper deals with a class of nonlinear optimization problems in a function space where the solution is restricted by pointwise upper and lower bounds and by finitely many equality and inequality constraints of functional type second order necessary and sufficient optimality conditions are established where the cone of critical directions is arbitrarily close to the form which is expected from the optimization in finite dimensional spaces the results are applied to some optimal control problems for ordinary and partial differential equations

optimal control of a nutrient phytoplankton zooplankton fish system we consider the mathematical formulation analysis and numerical solution of an optimal control problem for a nonlinear nutrient phytoplankton zooplankton fish reaction diffusion system we study the existence of optimal solutions derive an optimality system and determine optimal solutions in the original spatially homogeneous formulation m scheffer oikos 62 1991 pp 271 282 the dynamics of plankton were investigated as a function of parameters for nutrient levels and fish predation rate on zooplankton in our paper the model is spatially extended and the parameter for fish predation treated as a multiplicative control variable the model has implications for the biomanipulation of food webs in eutrophic lakes to help improve water quality in order to illustrate the control of irregular spatiotemporal dynamics of plankton in the model we implement a semi implicit in time finite element method with mass lumping and present the results of numerical experiments in two space dimensions

limiting behavior for strongly damped nonlinear wave equations in this paper we investigate both the existence and the limiting behavior for the equation utt aut au t u ut where a is a sectorial operator is periodic in t and satisfies certain regularity and growth assumptions in most results on limiting behavior we will assume a has compact resolvent we consider the equation as an abstract ode defined on a paired space x x 0 1 with regard to the limiting behavior one of our principal results will be to show that if there is a bounded set in one of the spaces considered for which all points or trajectories enter into and remain then there is a set j consisting of very smooth functions defined on all of the spaces considered which is the maximum compact invariant set uniformly asymptotically stable connected and having very strong attractivity properties in all these spaces we will often show it attracts all points in a bounded set uniformly we will give a few sharper results for the case where a the work is motivated by recent papers of webb and fitzgibbon and applies techniques found in recent papers by the author

optimal control of a competitive system with age structure we investigate optimal control of a first order partial differential equation pde system representing a competitive population model with age structure the controls are the proportions of the populations to be harvested and the objective functional represents the profit from harvesting the existence and unique characterization of the optimal control pair are established