on the stochastic kuramoto sivanshinsky equation in this article we study the solution of the kuramoto sivashinsky equation on a bounded interval subject to a random forcing term we show that a unique solution to the equation exists for all time and depends continuously on the initial data

algorithmic complexity of weakly semiregular partitioning and the representation number abstract a graph g is weakly semiregular if there are two numbers a b such that the degree of every vertex is a or b the weakly semiregular number of a graph g denoted by w r g is the minimum number of subsets into which the edge set of g can be partitioned so that the subgraph induced by each subset is a weakly semiregular graph we present a polynomial time algorithm to determine whether the weakly semiregular number of a given tree is two on the other hand we show that determining whether w r g 2 for a given bipartite graph g with at most three numbers in its degree set is np complete among other results for every tree t we show that w r t 2 log 2 t o 1 where t denotes the maximum degree of t a graph g is a d d s graph if the degree of every vertex of g lies in the interval d d s a d d 1 graph is said to be semiregular the semiregular number of a graph g denoted by s r g is the minimum number of subsets into which the edge set of g can be partitioned so that the subgraph induced by each subset is a semiregular graph we prove that the semiregular number of a tree t is t 2 on the other hand we show that determining whether s r g 2 for a given bipartite graph g with g 6 is np complete in the second part of the work we consider the representation number a graph g has a representation modulo r if there exists an injective map l v g z r such that vertices v and u are adjacent if and only if l u l v is relatively prime to r the representation number denoted by r e p g is the smallest r such that g has a representation modulo r narayan and urick conjectured that the determination of r e p g for an arbitrary graph g is a difficult problem 38 in this work we confirm this conjecture and show that if n p p then for any 0 there is no polynomial time 1 n 2 approximation algorithm for the computation of representation number of regular graphs with n vertices

honey pot constrained searching with local sensory information in this paper we investigate the problem of searching for a hidden target in a bounded region of the plane using an autonomous robot which is only able to use local sensory information the problem is naturally formulated in the continuous domain but the solution proposed is based on an aggregation refinement approach in which the continuous search space is partitioned into a finite collection of regions on which we define a discrete search problem a solution to the original problem is obtained through a refinement procedure that lifts the discrete path into a continuous one we show that the discrete optimization is computationally difficult np hard but there are computationally efficient approximation algorithms for solving it the resulting solution to the continuous problem is in general not optimal but one can construct bounds to gauge the cost penalty incurred due to i the discretization of the problem and ii the attempt to approximately solve the np hard problem in polynomial time numerical simulations show that the algorithms proposed behave significantly better than naive approaches such as a random walk or a greedy algorithm c 2006 elsevier ltd all rights reserved

local exact controllability to the trajectories of the 1 d kuramoto sivashinsky equation abstract we are concerned with the boundary controllability to the trajectories of the kuramoto sivashinsky equation by using a carleman estimate we obtain the null controllability of the linearized equation around a given solution from a local inversion theorem we get the local controllability to the trajectories of the nonlinear system

technical note trading off quick versus slow actions in optimal search we consider the search for a target whose precise location is uncertain the search region is divided into grid cells and the searcher decides which cell to visit next and whether to search it quickly or slowly a quick search of a cell containing the target may damage it resulting in a failed search or it may locate the target safely if the target is not in the cell the search continues over the remaining cells if a slow search is performed on a cell then the search ends in failure with a fixed probability regardless of whether or not the target is in that cell e g because of enemy fire while performing the slow search if the slow search survives this failure possibility then the search ends in success if the target is in that cell otherwise the search continues over the remaining cells we seek to minimize the probability of the search ending in failure and consider two types of rules for visiting cells the unconstrained search in which the searcher may visit cells in any order and the constrained search in which the searcher may only visit adjacent cells e g up down left or right of cells already visited we prove that the optimal policy for the unconstrained search is to search quickly some initial set of cells with the lowest probabilities of containing the target before slowly searching the remaining cells in decreasing order of probabilities for the special case in which a quick search on a cell containing the target damages it with certainty the optimal policy is to search all cells slowly in decreasing order of probabilities we use the optimal solution of the unconstrained search in a branch and bound optimal solution algorithm for the constrained search for larger instances we evaluate heuristics and approximate dynamic programming approaches for finding good solutions

null controllability with constraints on the state for the reaction diffusion system this paper is addressed to study the null controllability with constraints on the state for the reaction diffusion system we transform the problem into an equivalent null controllability problem with constraint on the control using a carleman inequality adapted to the constraint we prove the null controllability with constraints on the state for the reaction diffusion system holds

controlling roughening processes in the stochastic kuramoto sivashinsky equation we present a novel control methodology to control the roughening processes of semilinear parabolic stochastic partial differential equations in one dimension which we exemplify with the stochastic kuramoto sivashinsky equation the original equation is split into a linear stochastic and a nonlinear deterministic equation so that we can apply linear feedback control methods our control strategy is then based on two steps first stabilize the zero solution of the deterministic part and second control the roughness of the stochastic linear equation we consider both periodic controls and point actuated ones observing in all cases that the second moment of the solution evolves in time according to a power law until it saturates at the desired controlled value

a pseudo polynomial heuristic for path constrained discrete time markovian target search we propose a new heuristic for the single searcher path constrained discrete time markovian target search the algorithm minimizes an approximate instead of exact nondetection probability computed from the conditional probability that reflects the search history over the time windows of a fixed length l having a pseudo polynomial complexity it can solve in reasonable time the instances an order of magnitude larger than those solved in the previous studies by an asymptotic analysis relying on the fast mixing markov chain we show that the relative error of the approximation exponentially diminishes as l increases and the experimental results confirm the analysis the experiment also reveals a correlation very close to 1 between the approximate and exact nondetection probability of a search path this means that the heuristic produces near optimal search paths

induced packing of odd cycles in planar graphs an induced packing of odd cycles in a graph is a packing such that there is no edge in the graph between any two odd cycles in the packing we prove that an induced packing of k odd cycles in an n vertex graph can be found if it exists in time 2 o k 3 2 n 2 e for any constant e 0 when the input graph is planar we also show that deciding if a graph has an induced packing of two odd induced cycles is np complete

feedback control of the kuramoto sivashinsky equation abstract this work focuses on linear finite dimensional output feedback control of the kuramoto sivashinsky equation kse with periodic boundary conditions under the assumption that the linearization of the kse around the zero solution is controllable and observable linear finite dimensional output feedback controllers are synthesized that achieve stabilization of the zero solution for any value of the instability parameter the controllers are synthesized on the basis of finite dimensional approximations of the kse which are obtained through galerkin s method the performance of the controllers is successfully tested through computer simulations

on the complexity of general graph factor problems for arbitrary graphs g and h a g factor of h is a spanning subgraph of h composed of disjoint copies of g g factors are natural generalizations of l factors or perfect matchings in which g replaces the complete graph on two vertices our results show that the perfect matching problem is essentially the only instance of the g factor problem that is likely to admit a polynomial time bounded solution specifically if g has any component with three or more vertices then the existence question for g factors is np complete in all other cases the question can be resolved in polynomial time br the notion of a g factor is further generalized by replacing g by an arbitrary family of graphs this generalization forms the foundation for an extension of the traditional theory of matching this theory whose details will be developed elsewhere includes in addition to further np completeness results new polynomial algorithms and simple duality results some indication of the nature and scope of this theory are presented here

some global dynamical properties of the kuramoto sivashinsky equations nonlinear stability and attractors abstract the kuramoto sivashinsky equations model pattern formations on unstable flame fronts and thin hydrodynamic films they are characterized by the coexistence of coherent spatial structures with temporal chaos we investigate some global dynamical properties including nonlinear stability we demonstrate their low modal behavior in terms of determining modes and that the fractal dimension of all attractors is bounded by a universal constant times l 13 8 where l is a dimensionless pattern cell size in the one dimensional case such equations are indeed a paradigm of low dimensional behavior for infinite dimensional systems

observability estimate for stochastic schrodinger equations and its applications in this paper we establish a boundary observability estimate for stochastic schrodinger equations by means of the global carleman estimate our carleman estimate is based on a new fundamental identity for a stochastic schrodinger like operator applications to the state observation problem for semilinear stochastic schrodinger equations and the unique continuation problem for stochastic schrodinger equations are also addressed

attractors for random dynamical systems a criterion for existence of global random attractors for rds is established existence of invariant markov measures supported by the random attractor is proved for spde this yields invariant measures for the associated markov semigroup the results are applied to reation diffusion equations with additive white noise and to navier stokes equations with multiplicative and with additive white noise

the complexity of the optimal searcher path problem in this note we show that the problem of finding an optimal searcher path that maximizes the probability of detecting a stationary target by the end of a fixed time is np complete we also demonstrate that the problem of finding a path that minimizes mean time to detection is np hard

observability estimates and null controllability for forward and backward linear stochastic kuramoto sivashinsky equations in this paper we discuss the observability estimates and the null controllability of forward and backward linear stochastic kuramoto sivashinsky equations with random noise the key point is to establish the carleman estimates for stochastic fourth order forward and backward parabolic equations

simultaneous null controllability with constraint on the control this paper is concerned with the simultaneous null controllability with constraint on the control for a system of coupled linear heat equations first we show that by means of a change of variable a system of two linear heat equations with a same control can be rewritten in the form of a system of linear heat equations with a control function acting only in one equation then we establish an observability inequality and we state an appropriate carleman estimate adapted to the constraint that we use to prove the main result

approximate inertial manifolds for the kuramoto sivashinsky equation analysis and computations abstract we evaluate several alternative methods for the approximation of inertial manifolds for the one dimensional kuramoto sivashinsky equation kse a method motivated by the dynamics originally developed for the navier stokes equation is adapted for the kse rigorous error estimates are obtained and compared to those of other methods introduced in the literature formal relationships between these other methods and the one introduced here are established numerical bifurcation diagrams of the various approximate inertial forms for the kse are presented we discuss the correspondence between the rigorous error estimates and the accuracy of the computational results these methods can be adapted to other dissipative partial differential equations

an optimal branch and bound procedure for the constrained path moving target search problem a searcher and target move among a finite set of cells c 1 2 n in discrete time at the beginning of each time period one cell is searched if the target is in the selected cell j it is detected with probability qj if the target is not in the cell searched it cannot be detected during the current time period after each search a target in cell j moves to cell k with probability pjk the target transition matrix p pjk is known to the searcher the searcher s path is constrained in that if the searcher is currently in cell j the next search cell must be selected from a set of neighboring cells cj the object of the search is to minimize the probability of not detecting the target in t searches

a new global carleman estimate for the one dimensional kuramoto sivashinsky equation and applications to exact controllability to the trajectories and an inverse problem abstract in this paper we establish a new global carleman estimate for the linearized kuramoto sivashinsky equation which is a one parameter carleman estimate based on this estimate we can obtain the local exact controllability to the trajectories and lipschitz stability in an inverse problem for the kuramoto sivashinsky equation

stability enhancement by boundary control in the kuramoto sivashinsky equation where we refer to 0 as the anti di ussion parameter note that a more general form ut 1uxxxx 2uxx 3uux 0 can always be reduced to 1 1 by appropriate rescaling of t x and u eq 1 1 was derived independently by kuramoto et al 20 22 as a model for phase turbulence in reaction di usion systems and by sivashinsky 33 as a model for plane ame propagation describing the combined in uence of di usion and thermal conduction of the gas on stability of a plane ame front so far it has been well understood that the ks equation can also serve as a mathematical model for cellular instabilities in a variety of situations the ow of thin liquid lms on inclined planes 30 in the limit of large surface tension dendritic fronts in dilute binary alloys 31 and alfven drift waves in plasmas 23 as a nonlinear saturation mechanism of the dissipative trapped ion modes

exact controllability for stochastic transport equations this paper studies the exact controllability for stochastic transport equations by two controls one is a boundary control imposed on the drift term and the other is an internal control imposed on the diffusion term by means of the duality argument this controllability problem can be reduced to an observability problem for backward stochastic transport equations and the desired observability estimate is obtained by a new global carleman estimate also we present some results about the lack of exact controllability which show that the action of two controls is necessary to some extent this indicates that the controllability problems for stochastic pdes differ from their deterministic counterpart

null controllability of some reaction diffusion systems with one control force this work is concerned with the null controllability of semilinear parabolic systems by a single control force acting on a subdomain

global carleman estimates for the linear stochastic kuramoto sivashinsky equations and their applications abstract in this paper we establish two new global carleman estimates for the linear stochastic kuramoto sivashinsky equations the first one is for the backward linear stochastic kuramoto sivashinsky equation based on this estimate and the duality argument we obtain the null controllability of the forward linear stochastic kuramoto sivashinsky equation by three controls one is an internal control in the diffusion term and the others are boundary controls the second one is for the forward linear stochastic kuramoto sivashinsky equation according to this estimate we obtain a unique continuation property for the forward linear stochastic kuramoto sivashinsky equation

on global solutions and blow up for kuramoto sivashinsky type models and well posed burnett equations abstract the initial boundary value problem ibvp and the cauchy problem for the kuramoto sivashinsky equation v t v x x x x v x x 1 2 v 2 x and other related 2 m th order semilinear parabolic partial differential equations in one dimension and in r n are considered global existence and blow up as well as l bounds are reviewed by using i classic tools of interpolation theory and galerkin methods ii eigenfunction and nonlinear capacity methods iii henry s version of weighted gronwall s inequalities iv two types of scaling blow up arguments for the ibvps existence of global solutions is proved for both dirichlet and navier boundary conditions for some related 2 m th order pdes in r n r uniform boundedness of global solutions of the cauchy problem are established as another related application the well posed burnett type equations v t v v p m v div v 0 in r n r m 1 are considered for m 1 these are the classic navier stokes equations as a simple illustration it is shown that a uniform l p r n bound on locally sufficiently smooth v x t for p n 2 m 1 implies a uniform l r n bound hence the solutions do not blow up for m 1 and n 3 this gives p 3 which reflects the famous leray prodi serrin ladyzhenskaya regularity results l p q criteria and re derives kato s class of unique mild solutions in r n truly bounded classic l 2 solutions are shown to exist in dimensions n 2 2 m 1

on approximating restricted cycle covers a cycle cover of a graph is a set of cycles such that every vertex is part of exactly one cycle an l cycle cover is a cycle cover in which the length of every cycle is in the set l the weight of a cycle cover of an edge weighted graph is the sum of the weights of its edges we come close to settling the complexity and approximability of computing l cycle covers on the one hand we show that for almost all l computing l cycle covers of maximum weight in directed and undirected graphs is mathsf apx hard most of our hardness results hold even if the edge weights are restricted to zero and one on the other hand we show that the problem of computing l cycle covers of maximum weight can be approximated within a factor of 2 for undirected graphs and within a factor of 8 3 in the case of directed graphs this holds for arbitrary sets l

dissipative quasi geostrophic dynamics under random forcing the quasi geostrophic model is a simplified geophysical fluid model at asymptotically high rotation rate or at small rossby number we consider the quasi geostrophic equation with dissipation under random forcing in bounded domains we show that global unique solutions exist for appropriate initial data unlike the deterministic quasi geostrophic equation whose well posedness is well known there seems to be no rigorous result on global existence and uniqueness of the randomly forced quasi geostrophic equation our work provides such a rigorous result on global existence and uniqueness under very mild conditions

maximum tree packing in time o n 5 2 the problem of determining the maximum number of node disjoint subtrees of a tree t on nt nodes isomorphic to a tree s on ns nodes is shown to be solvable in time o n s 3 2 nt the same asymptotic bounds are observed for the corresponding problems where topological imbedding and subgraph homeomorphism are respectively substituted for subgraph isomorphism

null controllability for forward and backward stochastic parabolic equations this paper is concerned with the null controllability for general forward and backward linear stochastic parabolic equations to develop the duality argument we establish observability estimates for linear backward and forward stochastic parabolic equations with general coefficients by means of a global carleman estimate our carleman inequality theorem 6 1 and observability estimate theorem 2 3 for backward stochastic parabolic equations are new in their forms by adding a control variable to act on the white noise we give a partial solution to the null controllability of forward stochastic heat equations which was regarded as a challenging topic see pages 99 and 108 110 in barbu rascanu and tessitore appl math optim 47 2003 pp 97 120

dynamics for the stochastic nonlocal kuramoto sivashinsky equation dynamics for the stochastic kuramoto sivashinsky equation with a nonlocal term is studied we prove that the stochastic equation has a finite dimensional random attractor

maximum cardinality simple 2 matchings in subcubic graphs a simple 2 matching in a graph is a subset of edges m such that every node is incident with at most two edges in m a simple 2 matching is called ck restricted k 2 if it contains no cycles of length k or less we begin by considering the problem of finding maximum cardinality simple 2 matchings in subcubic graphs i e graphs whose nodes have degree at most 3 for this problem we present a min max theorem a simple polynomial time algorithm and some other results then by generalizing an approach due to vornberger we show the following for subcubic graphs the maximum cardinality c3 and c4 restricted simple 2 matching problems are polynomial time solvable there exist min max theorems for these problems and for k 5 the maximum cardinality ck restricted simple 2 matching problems are np hard

the nonnegative node weight j restricted k matching problems given a simple and undirected graph nonnegative node weights a nonnegative integer j and a positive integer k a k matching in the graph is a subgraph with no isolated nodes and with maximum degree no more than k a j restricted k matching is a k matching with each connected component having at least j 1 edges and the total node weight of a j restricted k matching is the total weight of the nodes covered by the edges in the j restricted k matching when j 1 and k 2 kaneko kaneko a 2003 a necessary and sufficient condition for the existence of a path factor every component of which is a path of length at least two j combin theory b 88 195 218 and kano et al kano m katona g kiraly z 2005 packing paths of length at least two discrete math 283 129 135 studied the problem of maximizing the number of nodes covered by the edges in a 1 restricted 2 matching in this paper we consider the problem of finding a j restricted k matching with the maximum total node weight we present a poly

stability of fredholm type integro parabolic equations linear time variant integrodifferential equations in a banach space are considered from a particular inner product conditions for solution existence and stability are derived applications to integro parabolic equations of the fredholm type are discussed

dealing with several parameterized problems by random methods abstract in this paper we apply random methods to deal with several parameterized problems for the parameterized weighted p 3 packing problem by randomly partitioning the vertices in given graph a tripartite graph can be obtained we prove that the parameterized weighted p 3 packing problem can be solved in polynomial time on tripartite graphs based on the algorithm on tripartite graphs a randomized parameterized algorithm of running time o 32 k is given for the parameterized weighted p 3 packing problem for the parameterized weighted load coloring problem by randomly partitioning the vertices in given graph into two parts and studying the structure properties of the connected components in two parts a randomized parameterized algorithm of running time o 11 32 k is presented for the parameterized claw free edge deletion problem on diamond free graphs by combining random with branching methods a parameterized algorithm of running time o 2 42 k is given

a weighted kt t free t factor algorithm for bipartite graphs for a simple bipartite graph and an integer t 2 we consider the problem of finding a minimum weight kt t free t factor which is a t factor containing no complete bipartite graph kt t as a subgraph when t 2 this problem amounts to the square free 2 factor problem in a bipartite graph for the unweighted square free 2 factor problem a combinatorial algorithm is given by hartvigsen and the weighted version of the problem is np hard for general t pap designed a combinatorial algorithm for the unweighted version and makai gave a dual integral description of kt t free t matchings for a certain case where the weight vector is vertex induced on any subgraph isomorphic to kt t for this class of weight vectors we propose a strongly polynomial algorithm to find a minimum weight kt t free t factor the algorithm adapts the unweighted algorithms of hartvigsen and pap and a primal dual approach to the minimum cost flow problem the algorithm is fully combinatorial and thus provides a dual integrality theorem which is tantamount to makai s one

restricted 2 factor polytopes the optimal k restricted 2 factor problem consists of finding in a complete undirected graph k n a minimum cost 2 factor subgraph having degree 2 at every node with all components having more than k nodes the problem is a relaxation of the well known symmetric travelling salesman problem and is equivalent to it when k n 1 we study the k restricted 2 factor polytope we present a large class of valid inequalities called bipartition inequalities and describe some of their properties some of these results are new even for the travelling salesman polytope for the case k 3 the triangle free 2 factor polytope we derive a necessary and sufficient condition for such inequalities to be facet inducing

the optimal search for a moving target when the search path is constrained a search is conducted for a target moving in discrete time among a finite number of cells according to a known markov process the searcher must choose one cell in which to search in each time period the set of cells available for search depends upon the cell chosen in the last time period the problem is to find a searcher path i e a sequence of search cells that maximizes the probability of detecting the target in a fixed number of time periods we formulate the problem as a partially observable markov decision process and present a finite time horizon pomdp solution technique which is simpler than the standard linear programming methods

matching and weighted p2 packing algorithms and kernels parameterized algorithms and kernelization algorithms are presented for the weighted p 2 packing problem which is a generalization of the famous graph matching problem the parameterized algorithms are based on the following new techniques and observations 1 new study on structure relationship between graph matchings in general graphs and p 2 packings in bipartite graphs 2 an effective graph bi partitioning algorithm and 3 a polynomial time algorithm for a constrained weighted p 2 packing problem in bipartite graphs the kernelization algorithms are based on the following new techniques 1 the application of graph matching in kernelization 2 a crown reduction structure for weighted problems these techniques lead to randomized and deterministic parameterized algorithms that significantly improve the previous best upper bounds for the problem for both weighted and unweighted versions for the kernelization algorithm by using a weighted version of crown reduction a kernel of size o k 2 is presented where k is the given parameter of the problem

the np completeness of edge coloring we show that it is np complete to determine the chromatic index of an arbitrary graph the problem remains np complete even for cubic graphs

discrete sequential search with positive switch cost suppose one object is hidden in one of n boxes according to a known probability distribution p1 pn the boxes are to be searched sequentially the probability of overlooking the object if we search box k and if the object is in box k is denoted by qk the cost of a search of box k amounts to ck if we decide to search box k directly after box k we have to pay some extra cost called switch cost tk k the problem is under some reasonable assumptions to construct a strategy with minimal expected cost if t 0 the problem has a well known solution unfortunately there are many reasons which establish the conjecture that there does not exist an easy construction rule for optimal strategies in the general case we give necessary and sufficient conditions for the existence of optimal strategies which are ultimately periodic u p since we state bounds on the length not only of the transient phase but also of the period of optimal u p strategies we may construct these optimal strategies by comparing finitely many strategies if optimal u p strategies exist we prove some other results to reduce the number of strategies which we have to compare at last we present a numerical example

local exact controllability to the trajectories of the swift hohenberg equation abstract this paper is addressed to study the local exact controllability to the trajectories of the swift hohenberg equation we first establish a new global carleman estimate for the fourth order parabolic operator and we consider the exact controllability to the trajectories of the linearized system then by local inversion theorem we show that the same result holds for the swift hohenberg equation

nonlocal models for nonlinear dispersive waves abstract considered herein are model equations for the unidirectional propagation of small amplitude nonlinear dispersive long waves such as those governed by the classical korteweg de vries equation of special interest are physical situations in which the linear dispersion relation is not appropriately approximated by a polynomial so that the operator modelling dispersive effect is nonlocal particular cases in view here are the benjamin ono equation and the intermediate long wave equation which arise in internal wave theory and smith s equation which governs certain types of continental shelf waves the initial value problem for these equations is shown to be globally well posed in the classical sense including continuous dependence upon the initial data and in certain cases upon the modelling of nonlinear and dispersive effects whilst the results are stated for the specific equations listed above the techniques utilized are seen to have a considerable range of generality as regards application to nonlinear dispersive evolution equations particularly worthy of note is our theorem implying that solutions of the intermediate long wave equation converge strongly to solutions of the korteweg de vries equation or to solutions of the benjamin ono equation in appropriate asymptotic limits

global stabilization of the kuramoto sivashinsky equation via distributed output feedback control abstract this work addresses the problem of global exponential stabilization of the kuramoto sivashinsky equation kse subject to periodic boundary conditions via distributed static output feedback control under the assumption that the number of measurements is equal to the total number of unstable and critically stable eigenvalues of the kse and a necessary and sufficient stability condition is satisfied linear static output feedback controllers are designed that globally exponentially stabilize the zero solution of the kse the controllers are designed on the basis of finite dimensional approximations of the kse which are obtained through galerkin s method the theoretical results are confirmed by computer simulations of the closed loop system

a search game when a search path is given abstract in this paper we investigate a search game in discrete time and space a searcher is given a search path in advance and his look on the path is determined by a randomized look strategy a target selects a path from some options the searcher gains a value on the detection of the target but expends search cost by the look a pay off function of the game for the searcher is the expected reward which is defined as the expected value minus the expected search cost first we show a recursive relation for the conditional optimal look strategy of the searcher given a target path we prove its np completeness though it looks simple and clarify some characteristics of the solution then our original continuous game is converted to a matrix game from these facts we consider a relationship between the game and the one sided optimizing problem and examine some examples

p attracting and p invariant sets for a class of impulsive stochastic functional differential equations in this paper a nonlinear and nonautonomous impulsive stochastic functional differential equation is considered by establishing an l operator differential inequality and stochastic analysis technique we obtain the p attracting set and p invariant set of the impulsive stochastic functional differential equation an example is also discussed to illustrate the efficiency of the obtained results

kolmogorov equation associated to a stochastic kuramoto sivashinsky equation abstract this paper investigates the relation between the kolmogorov operator associated to a stochastic kuramoto sivashinsky equation and the infinitesimal generator for the corresponding transition semigroup we prove that the infinitesimal generator is the closure of kolmogorov operator in the space of continuous functions with k th polynomial growth with respect to convergence topology and the space l 2 h respectively the proof depends on various estimates on the solution invariant measure and transition semigroup as a product we also obtains smoothing properties of the transition semigroup

null controllability with constraints on the state for the linear stochastic kuramoto sivashinsky equation abstract this paper is addressed to study the null controllability with constraints on the state for the linear stochastic kuramoto sivashinsky equation we transform the problem into an equivalent null controllability problem with constraint on the control using a carleman inequality adapted to the constraints we prove the null controllability with constraints on the state for the linear stochastic kuramoto sivashinsky equation holds

optimal strategy of route and look for the path constrained search problem with reward criterion abstract a target is moving among a finite number of cells k 1 k in discrete time t 1 t knowing probability of the target s path selection a searcher is searching for the target with constraints that he can move from cell i to one of the adjacent cells i i the searcher detects the target with the probability pi on the look into cell i in which both the target and the searcher are there he gains a value v t on the detection of the target at time t but expends cost c0 i t on the search in cell i at t the searcher selects his route and determines whether he looks into his current cell on the route or not in this paper our purpose is to find an optimal strategy for the route and the look of the searcher which maximizes the expected reward defined as the expected value minus the expected cost the problem is formulated as an integer programming problem for solving the problem we use a branch and bound procedure with an upper bound estimation

discounted mean bound for the optimal searcher path problem with non uniform travel times we consider an extension of the optimal searcher path problem osp where a searcher moving through a discretised environment may now need to spend a non uniform amount of time travelling from one region to another before being able to search it for the presence of a moving target in constraining not only where but when the search of each cell can take place the problem more appropriately models the search of environments which cannot be easily partitioned into equally sized cells an existing osp bounding method in literature the mean bound is generalised to provide bounds for solving the new problem in a branch and bound framework the main contribution of this paper is an enhancement discounted mean dmean which greatly tightens the bound for the new and existing problems alike with almost no additional computation we test the new algorithm against existing osp bounding methods and show it leads to faster solution times for moving target search problems

a global attracting set for the kuramoto sivashinsky equation new bounds are given for the l2 norm of the solution of the kuramoto sivashinsky equation partial t u x t partial x 2 partial x 4 u x t u x t partial x u x t for initial data which are periodic with periodl there is no requirement on the antisymmetry of the initial data the result is mathop lim sup limits t to infty left u cdot t right 2 leqslant const l 8 5

large deviation for the nonlocal kuramoto sivashinsky spde abstract in this paper we establish a large deviation principle for the weak solution to a nonlocal kuramoto sivashinsky stochastic partial differential equation with small noise perturbation the key technique is an application of the contraction principle

controllability to the trajectories of phase field models by one control force in this article we study the controllability to the trajectories of 2 2 nonlinear parabolic systems for control forces acting on a single equation of the system this result which in particular applies to caginalp s phase field model actually extends those obtained for the semilinear heat equations the proof relies on kakutani s fixed point theorem and makes use of an observability estimate for the associated linearized system

controllability of a 4 4 quadratic reaction diffusion system we consider a 4 4 nonlinear reaction diffusion system posed on a smooth domain of r n n 1 with controls localized in some arbitrary nonempty open subset of the domain this system is a model for the evolution of concentrations in reversible chemical reactions we prove the local exact controllability to stationary constant solutions of the underlying reaction diffusion system for every n 1 in any time t 0 a specificity of this control system is the existence of some invariant quantities in the nonlinear dynamics the proof is based on a linearization which uses return method and an adequate change of variables that creates crossed diffusion which will be used as coupling terms of second order the controllability properties of the linearized system are deduced from carleman estimates a kakutani s fixed point argument enables to go back to the nonlinear parabolic system then we prove a global controllability result in large time for 1 n 2 thanks to our local controllabillity result together with a known theorem on the asymptotics of the free nonlinear reaction diffusion system

large deviations for stochastic nonlinear beam equations abstract we establish a large deviation principle for the solutions of stochastic partial differential equations for nonlinear vibration of elastic panels also called stochastic nonlinear beam equations

independent packings in structured graphs packing a maximum number of disjoint triangles into a given graph g is np hard even for most classes of structured graphs in contrast we show that packing a maximum number of independent that is disjoint and nonadjacent triangles is polynomial time solvable for many classes of structured graphs including weakly chordal graphs asteroidal triple free graphs polygon circle graphs and interval filament graphs these classes contain other well known classes such as chordal graphs cocomparability graphs circle graphs circular arc graphs and outerplanar graphs our results apply more generally to independent packings by members of any family of connected graphs

laminarizing effects of dispersion in an active dissipative nonlinear medium abstract the kuramoto sivashinsky equation has become a popular prototype for systems which exhibit spatial temporal chaos we show here that a linear dispersion term h xxx tends to arrest such irregular behavior in favor of spatially periodic cellular structures as is consistent with prior numerical and experimental observations the study includes a normal form analysis and a numerical investigation of periodic and solitary stationary wave solutions of the equation it is shown that by 1 1 the infinite families of stationary periodic waves of the kuramoto sivashinsky equation each ending in a solitary wave have been annihilated successively such that only a lone family of periodic waves consisting of one hump kdv pulses for 3 7 remains as the only periodic stationary wave attractors of the system these periodic waves have much larger domains of attraction than the strange attractors and hence tend to dominate spatial temporal chaos in an extended domain with significant dispersion

dynamics of a nonlocal kuramoto sivashinsky equation abstract in this paper we study the effects of a nonlocal term on the global dynamics of the kuramoto sivashinsky equation we show that the equation possesses a family of maximal attractors parameterized by the mean value of the initial data the dimension of the attractor is estimated as a function of the coefficient of the nonlocal term and the width of the periodic domain

existence and finite dimensionality of the global attractor for a class of nonlinear dissipative equations in this work we discuss the cauchy problem for a class of nonlinear dissipative equations as well as the existence of a global attractor and we estimate its dimension in the sense of the hausdorff or fractal dimension

internal controllability of the kawahara equation on a bounded domain abstract in this paper we consider the kawahara equation posed on a bounded interval with a distributed control first we establish a carleman estimate for the kawahara equation with internal observation then applying this carleman estimate we can show that the kawahara equation is null controllable furthermore we prove the null controllability with constraints on the state for the kawahara equation

exact controllability for stochastic schrodinger equations abstract this paper is addressed to studying the exact controllability of stochastic schrodinger equations by two controls one is a boundary control and the other is an internal control in the diffusion term by means of the duality argument the control problem is converted into an observability problem for backward stochastic schrodinger equations and the desired observability estimate is obtained by a global carleman estimate at last we give a result about the lack of exact controllability which shows that the action of two controls is necessary