asymptotics and random sampling for bci and bck lambda terms this paper presents a bijection between combinatorial maps and a class of enriched trees corresponding to a class of expression trees in some logical systems constrained lambda terms starting from two alternative definitions of combinatorial maps the classical definition by gluing half edges and a definition by non ambiguous depth first traversal we derive non trivial asymptotic expansions and efficient random generation of logic formulae syntactic trees in the bci or bck systems

combinatorial approach to generalized bell and stirling numbers and boson normal ordering problem we consider the numbers arising in the problem of normal ordering of expressions in boson creation a and annihilation a operators a a 1 we treat a general form of a boson string a rnasn a r2as2 a r1as1 which is shown to be associated with generalizations of stirling and bell numbers the recurrence relations and closed form expressions dobinski type formulas are obtained for these quantities by both algebraic and combinatorial methods by extensive use of methods of combinatorial analysis we prove the equivalence of the aforementioned problem to the enumeration of special families of graphs this link provides a combinatorial interpretation of the numbers arising in this normal ordering problem

a diffusion model for optimal portfolio selection in the presence of brokerage fees we consider a financial market model with two assets one has deterministic rate of growth while the rate of growth of the second asset is governed by a brownian motion with drift we can shift money from one asset to another however there are losses of money brokerage fees involved in shifting money from the risky to the nonrisky asset we want to maximize the expected rate of growth of funds it is proved that an optimal policy keeps the ratio of funds in risky and nonrisky assets within a certain interval with minimal effort

average optimal singular control and a related stopping problem we observe a 2 brownian motion xt we can increase or decrease the value of the process paying r times the size of increase and l times the size of decrease holding costs are incurred continuously at a rate h zt where zt is the resulting process we consider a convex holding cost function h which is either finite everywhere or finite inside a finite interval and equal to infinity outside this interval the objective is to minimize average per unit of time expected cost it is shown that the optimal behavior is characterized by two constants a and b a b such that the optimal policy is to keep the process inside the interval a b with minimal efforts it is shown that to find the optimal interval a b one must solve a free boundary problem for the second order differential equation we give a probabilistic solution of the free boundary problem in terms of the value of a special game this game is a generalization of the optimal stopping problem there are two players observing the 2

optimal ordering policy for inventory systems with quantity dependent setup costs we consider a continuous review inventory system in which the setup cost of each order is a general function of the order quantity and the demand process is modeled as a brownian motion with a positive drift assuming the holding and shortage cost to be a convex function of the inventory level we obtain the optimal ordering policy that minimizes the long run average cost by a lower bound approach to tackle some technical issues in the lower bound approach under the quantity dependent setup cost assumption we establish a comparison theorem that enables one to prove the global optimality of a policy by examining a tractable subset of admissible policies since the smooth pasting technique does not apply to our brownian inventory model we also propose a selection procedure for computing optimal policy parameters when the setup cost is a step function

analytic functors between presheaf categories over groupoids the paper studies analytic functors between presheaf categories generalising results of a joyal 11 and r hasegawa 9 for analytic endofunctors on the category of sets we give two characterisations of analytic functors between presheaf categories over groupoids i as functors preserving filtered colimits quasi pullbacks and cofiltered limits and ii as functors preserving filtered colimits and wide quasi pullbacks the development establishes that small groupoids analytic functors between their presheaf categories and quasi cartesian natural transformations between them form a 2 category

large time behavior of an attraction repulsion chemotaxis system abstract in this study we consider an attraction repulsion chemotaxis system u t u u v u w x t 0 v t v u v x t 0 w t w u w x t 0 with homogeneous neumann boundary conditions where and are positive parameters under the critical condition that 0 we prove that the system possesses a unique global solution which is uniformly bounded in the physical domain r n n 2 3 in addition we assert that we can find 0 0 such that for all of the initial data u 0 that satisfy u 0 0 the solution of the system approaches the steady state u 0 u 0 u 0 exponentially as time tends to infinity where u 0 1 u 0

infinite dimensional linear programming approach to singularstochastic control we consider a multidimensional singular stochastic control problem with state dependent diffusion matrix and drift vector and control cost depending on the position and direction of displacement of the controlled process the objective is to minimize the total expected discounted cost we write an equivalent infinite dimensional linear programming problem on a subspace of the space conjugate to cal c bbb r n times cal c bbb r n times b where b is the unit sphere in bbb r n we write a dual linear program and prove absence of duality gap the dual program characterizes the optimal cost function as a maximal solution to the variational inequality with gradient constraints

boundedness in a quasilinear fully parabolic keller segel system of higher dimension with logistic source abstract this paper deals with the higher dimension quasilinear parabolic parabolic keller segel system involving a source term of logistic type u t u u u v g u v t v v u in 0 t subject to nonnegative initial data and homogeneous neumann boundary condition where is a smooth and bounded domain in r n n 2 and g are smooth and positive functions satisfying k s p when s s 0 1 g s a s s 2 for s 0 with g 0 0 and constants a 0 0 it is known that the model without the logistic source admits both bounded and unbounded solutions identified via the critical exponent 2 n on the other hand the model is just a critical case with the balance of logistic damping and aggregation effects for which the property of solutions should be determined by the coefficients associated in the present paper it is proved that there is 0 0 such that the problem admits global bounded classical solutions whenever 0 regardless of the size of initial data and diffusion this shows the substantial effect of the logistic source has on the behavior of solutions

a multidimensional stochastic singular control problem via dynkin game and dirichlet form the traditional difficulty with stochastic singular control is characterizing the regularities of the value function and the optimal control policy in this paper a multidimensional singular control problem is considered we found the optimal value function and the optimal control policy of this problem via a dynkin game whose solution is given by the saddle point of the cost function the existence and uniqueness of the solution to this dynkin game are proved through an associated variational inequality problem involving dirichlet form as a consequence the properties of the value function of this dynkin game imply the smoothness of the value function of the stochastic singular control problem in this way we are able to show the existence of a classical solution to this multidimensional singular control problem which was traditionally solved in the sense of viscosity solutions and this enables the application of the verification theorem to prove optimality

diffusion approximation for a controlled stochastic manufacturing system with average cost minimization we consider the problem of production control in a single machine single product unreliable manufacturing system facing a constant demand d the goal is to minimize the expected average per unit time inventory backlog costs under heavy traffic condition i e when the average production capacity is close to demand the problem is approximated by a singular stochastic control problem the approximate problem can be solved explicitly the solution is then interpreted in terms of the actual manufacturing system and a control policy for this system is derived we prove that the resulting policy is nearly optimal under the heavy traffic condition this policy is characterized by a critical level z0 that is produce at maximal rate r when inventory is less than z0 and at the demand rate d when the inventory is equal to z0 the quality of the approximate control is also discussed by comparing it to known results when they are available

aggregation vs global diffusive behavior in the higher dimensional keller segel model abstract we consider the classical parabolic parabolic keller segel system u t u u v x t 0 v t v v u x t 0 under homogeneous neumann boundary conditions in a smooth bounded domain r n it is proved that in space dimension n 3 for each q n 2 and p n one can find e 0 0 such that if the initial data u 0 v 0 satisfy u 0 l q e and v 0 l p e then the solution is global in time and bounded and asymptotically behaves like the solution of a discoupled system of linear parabolic equations in particular u v approaches the steady state m m as t where m is the total mass m u 0 of the population moreover we shall show that if is a ball then for arbitrary prescribed m 0 there exist unbounded solutions emanating from initial data u 0 v 0 having total mass u 0 m

self similarity in the combinatorics of orthogonal polynomials resume dans cet article nous construisons des structures combinatoires invariantes sous l action d une permutation donnee dans certains cas le poids de ces dernieres correspon a des polynomes orthogonaux dont on a ajuste convenablement les parametres on examine ici de ces structures associees aux polynomes de hermite laguerre krawtchouk meixner meixner pollaczek et de jacobi

instantaneous control of brownian motion a controller continuously monitors a storage system such as an inventory or bank account whose content z zt t 0 fluctuates as a 2 brownian motion in the absence of control holding costs are incurred continuously at rate h zt at any time the controller may instantaneously increase the content of the system incurring a proportional cost of r times the size of the increase or decrease the content at a cost of l times the size of the decrease we consider the case where h is convex on a finite interval and h outside this interval the objective is to minimize the expected discounted sum of holding costs and control costs over an infinite planning horizon it is shown that there exists an optimal control limit policy characterized by two parameters a and b a b roughly speaking this policy exerts the minimum amounts of control sufficient to keep zt a b for all t 0 put another way the optimal control limit policy imposes on z a lower reflecting barrier at a an

approximation of stochastic equations driven by predictable processes a theory of stochastic differential equations driven by predictable processes in stratonovich sense is developed these driving processes include a large class of discontinuous semimartingales the theory of stochastic differential equations driven by continuous semimartingales in stratonovich sense is extended without involving lebesgue stieltjes integrals as done by meyer moreover a change of variables formula without extra terms involving the jumps of the processes holds for this theory results on approximation of driving processes are preserved

weak convergence of random p mappings and the exploration process of inhomogeneous continuum random trees we study the asymptotics of the p mapping model of random mappings on n as n gets large under a large class of asymptotic regimes for the underlying distribution p we encode these random mappings in random walks which are shown to converge to a functional of the exploration process of inhomogeneous random trees this exploration process being derived aldous miermont pitman 2004 from a bridge with exchangeable increments our setting generalizes previous results by allowing a finite number of attracting points to emerge

weighted derangements and the linearization coefficients of orthogonal sheffer polynomials the present paper is devoted to a systematic study of the combinatorial interpretations of the moments and the linearization coefficients of the orthogonal sheffer polynomials i e hermite charlier laguerre meixner and meixner pollaczek polynomials in particular we show that viennot s combinatorial interpretations of the moments can be derived directly from their classical analytical expressions and that the linearization coefficients of meixner pollaczek polynomials have an interpretation in the model of derangements analogous to those of laguerre and meixner polynomials

boundedness and decay behavior in a higher dimensional quasilinear chemotaxis system with nonlinear logistic source this paper is concerned with a class of quasilinear chemotaxis systems generalizing the prototype 0 1 ut um uv uur x t 0 vt vv u x t 0 u v 0 x t 0 u x 0 u0 x v x 0 v0 x x in a smooth bounded domain rn n2 with parameters m r1 and 0 the pde system in 0 1 is used in mathematical biology to model the mechanism of chemotaxis that is the movement of cells in response to the presence of a chemical signal substance which is in homogeneously distributed in space it is shown that if m 22nif11 n 22r n 2ifn 22rn 2n 1ifr n 22 and the nonnegative initial data u0 v0 c w1 0 then 0 1 possesses at least one global bounded weak solution apart from this it is proved that if 0 then both u t and v t decay to zero with respect to the norm in l as t

a quasilinear fully parabolic chemotaxis system with indirect signal production and logistic source abstract in this paper we study the quasilinear fully parabolic chemotaxis system with indirect signal production and logistic source u t d u u s u v f u v t v a 1 v b 1 w w t w a 2 w b 2 u under homogeneous neumann boundary conditions in a bounded and smooth domain r n n 1 where a i b i 0 i 1 2 d s c 2 0 and f r r is a smooth function generalizing the logistic source f s b s r for all s 0 with b 0 0 and r 1 we obtain the global boundedness of solutions in four cases i the self diffusion dominates the cross diffusion ii the logistic source suppresses the cross diffusion iii the logistic dampening balances the cross diffusion with 0 suitably large iv the self diffusion and the logistic source both balance the cross diffusion to some extent with 0 arbitrary as corollaries we also consider the global boundedness of solutions for the quasilinear attraction repulsion chemotaxis model with logistic source u t d u u u z u w f u z t z z u w t w w u where 0

on combinatorial differential equations abstract we analyse the solution set of first order initial value differential problems of the form dy dx x y y 0 0 in the context of combinatorial species in the sense of a joyal adv in math 42 1981 1 82 it turns out that the situation is much richer than in the case of formal power series many non isomorphic combinatorial solutions are possible for a given problem although they all have the same underlying generating series we give many examples of this phenomenon and also elaborate a combinatorial newton raphson iterative scheme for the construction of the solutions the multidimensional case is treated explicitly

linearization coefficients for boas buck polynomial sets abstract in this paper we express explicitly the linearization coefficients related to three boas buck polynomial sets using their corresponding generating functions we apply the obtained results to many classes of polynomials including some generalized hypergeometric polynomials the corresponding linearization coefficients will be expressed by means of terminating generalized kampe de feriet functions which for some cases can be reduced to hypergeometric functions or hypergeometric terms using with this purpose some known reduction formulae we obtain some well known results as particular cases as well as some new reduction formulae

a generalized cyclotomic identity abstract in this paper we prove a generalization of the cyclotomic identity for each group g satisfying suitable finiteness conditions we prove this generalized cyclotomic identity by counting coloured g set structures the cyclotomic identity corresponds to taking g the free abelian group of rank one for the free abelian group of rank two for example we get an analogous identity involving the generating function of the partition function interalia we show that studying g set structures gives a unified and conceptually simple approach to other classical combinatorial identities not to the author s knowledge previously linked in the literature

dynkin games via dirichlet forms and singular control of one dimensional diffusions we consider a zero sum game of optimal stopping in which each of the opponents has the right to stop a one dimensional diffusion process there are two types of costs the first is accumulated continuously at the rate h xt where xt is the current position of the process the second is a cost associated with the stopping of the process it is given by the function f1 x for the first player and the function f2 x for the second player where x is the position of the process when the stopping option is exercised we study the solution of the free boundary problem associated with this game via dirichlet forms on the appropriate functional space integrating the value function of the game we get a solution to another free boundary problem which yields the optimal return function for a singular stochastic control problem

application of an adams type inequality to a two chemical substances chemotaxis system abstract this paper deals with positive solutions of the fully parabolic system u t u u v in 0 1 v t v v w in 0 2 w t w w u in 0 under homogeneous neumann boundary conditions or mixed boundary conditions no flux and dirichlet conditions in a smooth bounded domain r n n 4 with positive parameters 1 2 0 and nonnegative smooth initial data u 0 v 0 w 0 in the lower dimensional case n 3 it is proved that for all reasonable initial data solutions of the system exist globally in time and remain bounded in the case n 4 it is shown that in the radially symmetric setting solutions to the neumann boundary value problem of the system exist globally in time and remain bounded if u 0 l 1 8 2 as to the mixed boundary value problem we will establish global existence and boundedness of solutions if u 0 l 1 8 2 without radial symmetry the key ingredients are a lyapunov functional and an adams type inequality a lyapunov functional of the above problems will be constructed and the constant 8 2 is deduced from the critical constant in the adams type inequality this result is regarded as a generalization of the well known 8 problem in the keller segel system to higher dimensions

boundedness in a quasilinear parabolic parabolic keller segel system with logistic source abstract we consider a quasilinear parabolic parabolic keller segel system involving a source term of logistic type 0 1 u t u u u v g u x t 0 t v t v v u x t 0 t with nonnegative initial data under neumann boundary condition in a smooth bounded domain r n n 1 here and are supposed to be smooth positive functions satisfying c 1 s p and c 1 s q s c 2 s q when s s 0 with some s 0 1 and we assume that g is smooth on 0 fulfilling g 0 0 and g s a s s 2 for all s 0 with constants a 0 and 0 within this framework it is proved that whenever q 1 for any sufficiently smooth initial data there exists a unique classical solution which is global in time and bounded our result is independent of p

optimal policies for brownian inventory systems with a piecewise linear ordering cost we consider a stochastic inventory system with general piecewise linear ordering cost the cumulative demand is modeled as a brownian motion process the ordering cost function is neither convex nor concave it may not be monotone and it is not even necessarily continuous and it includes most ordering cost functions studied in the literature e g economies of scale or dis economies of scale all unit discount or incremental discount and multiple setup costs as special cases in addition to ordering cost the system incurs the usual holding shortage cost and the objective is to minimize the average system cost per unit of time despite the complexity in the ordering cost function we show that an optimal control policy is very simple it is either an s s policy or a one sided singular control policy

une theorie combinatoire des series formelles abstract this paper presents a combinatorial theory of formal power series the combinatorial interpretation of formal power series is based on the concept of species of structures a categorical approach is used to formulate it a new proof of cayley s formula for the number of labelled trees is given as well as a new combinatorial proof due to g labelle of lagrange s inversion formula polya s enumeration theory of isomorphism classes of structures is entirely renewed recursive methods for computing cycle index polynomials are described a combinatorial version of the implicit function theorem is stated and proved the paper ends with general considerations on the use of coalgebras in combinatorics

addition theorems via continued fractions we show connections between a special type of addition formulas and a theorem of stieltjes and rogers we use different techniques to derive the desirable addition formulas we apply our approach to derive special addition theorems for bessel functions and confluent hypergeometric functions we also derive several additions theorems for basic hypergeometric functions applications to the evaluation of hankel determinants are also given

boundedness in a quasilinear parabolic parabolic keller segel system with subcritical sensitivity abstract we consider the quasilinear parabolic parabolic keller segel system u t d u u s u v x t 0 v t v v u x t 0 under homogeneous neumann boundary conditions in a convex smooth bounded domain r n with n 1 it is proved that if s u d u c u with 2 n and some constant c 0 for all u 1 then the classical solutions to the above system are uniformly in time bounded provided that d u satisfies some technical conditions such as algebraic upper and lower growth resp decay estimates as u this boundedness result is optimal according to a recent result by the second author winkler 2010 27 which says that if s u d u c u for u 1 with c 0 and some 2 n n 2 then for each mass m 0 there exist blow up solutions with mass u 0 m in addition this paper also proves a general boundedness result for quasilinear non uniformly parabolic equations by modifying the iterative technique of moser alikakos alikakos 1979 1

impulse control of brownian motion the constrained average cost case when a manufacturer places repeated orders with a supplier to meet changing production requirements he faces the challenge of finding the right balance between holding costs and the operational costs involved in adjusting the shipment sizes we consider an inventory whose content fluctuates as a brownian motion in the absence of control at any moment a controller can adjust the inventory level by any positive or negative quantity but incurs both a fixed cost and a cost proportional to the magnitude of the adjustment the inventory level must be nonnegative at all times and continuously incurs a linear holding cost the objective is to minimize long run average cost we show that control band policies are optimal for the average cost brownian control problem and explicitly calculate the parameters of the optimal control band policy this form of policy is described by three parameters q q s 0 q q s when the inventory falls to zero rises to s the controller expedites curtails shipments to return it to q q employing apparently new techniques based on methods of lagrangian relaxation we show that this type of policy is optimal even with constraints on the size of adjustments and on the maximum inventory level we also extend these results to the discounted cost problem

optimal consumption for general diffusions with absorbing and reflecting barriers two stochastic control problems of the storage or inventory type are considered for general diffusion processes in the absorption problem a diffusion process is controlled by subtracting a nondecreasing withdrawal process the controlled process is absorbed if it reaches zero the objective function to be maximized is the expected discounted value of the withdrawals plus a discounted penalty for absorption in the reflection problem the process can be controlled by subtracting a withdrawal process and adding a deposit process and the controlled process must be nonnegative one seeks to maximize an expected discounted weighted difference in withdrawals and deposits the value function is computed and a necessary and sufficient condition for the existence of an optimal policy is given when they exist optimal policies are found to be the minimal processes which keep the controlled process inside an interval

optimal correction problem of a multidimensional stochastic system abstract we consider a stochastic dynamic system which is governed by a multidimensional diffusion process with constant drift and diffusion coefficients the correction corresponds to an additive input which is under control there is no limit on the rate of input into the system the objective is to minimize the expected cumulative cost associated with the position of the system and the amount of control exerted it is proved that hamilton jacobi bellman s equation of the problem has a solution which corresponds to the optimal cost of the problem an existence of optimal policy is proved

functors of white noise associated to characters of the infinite symmetric group the characters of the infinite symmetric group are extended to multiplicative positive definite functions on pair partitions by using an explicit representation due to versik and kerov the von neumann algebra generated by the fields with f in an infinite dimensional real hilbert space is infinite and the vacuum vector is not separating for a family depending on an integer n 1 an exclusion principle is found allowing at most identical particles on the same state the algebras are type factors functors of white noise are constructed and proved to be non equivalent for different values of n

optimal inventory control with jump diffusion and nonlinear dynamics in the demand in this paper we consider an inventory control problem with a nonlinear evolution and a jump diffusion demand model this work extends the earlier inventory model proposed by benkherouf and johnson math methods oper res 76 2012 pp 377 393 by including a general jump process however as those authors note their techniques are not applicable to models with demand driven by jump diffusion processes with drift therefore the combination of diffusion and general compound poisson demands is not completely solved from the dynamic programming principle we transform the problem into a set of quasi variational inequalities q v i the difficulty arises when solving the q v i because the second derivative and integration term appear in the same inequality our technique is to construct a set of coupled auxiliary functions then an analytical study of the q v i implies the existence and uniqueness of an s s policy

the combinatorics of a class of representation functions abstract in the study of the irreducible representations of the unitary group u n one encounters a class of polynomials defined on n 2 indeterminates z ij 1 i j n which may be arranged into an n n matrix array z z ij these polynomials are indexed by double gelfand patterns or equivalently by pairs of column strict young tableaux of the same shape using the double labeling property one may define a square matrix d z whose elements are the double indexed polynomials these matrices possess the remarkable group multiplication property d xy d x d y for arbitrary matrices x and y even though these matrices may be singular for z u u n these matrices give irreducible unitary representations of u n these results are known but not always fully proved from the extensive physics literature on representation of the unitary groups where they are often formulated in terms of the boson calculus and the multiplication property is unrecognized the generality of the multiplication property is the key to understanding group representation theory from the purview of combinatorics the combinatorial structure of the general polynomials is expected to be intricate and in this paper we take the first step to explore the combinatorial aspects of a special class which can be defined in terms of the set of integral matrices with given row and column sums these special polynomials are denoted by l z where and are integral vectors representing the row sums and column sums of a class of integral matrices we present a combinatorial interpretation of the multiplicative properties of these polynomials we also point out the connections with macmahon s master theorem and schwinger s inner product formula which is essentially equivalent to macmahon s master theorem finally we give a formula for the double pfaffian which is crucial in the studies of the generating function of the 3 n j coefficients in angular momentum theory we also review the background of the general polynomials and give some of their properties

object grammars and bijections a new systematic approach for the specification of bijections between sets of combinatorial objects is presented it is based on the notion of object grammars object grammars give recursive descriptions of objects and generalize context free grammars the study of a particular substitution in these object grammars confirms once more the key role of dyck words in the domain of enumerative and bijective combinatorics

the q t gaussian process the q t fock space fq t h introduced in this paper is a deformation of the q fock space of bozejko and speicher the corresponding creation and annihilation operators now satisfy the commutation relation aq t f aq t g qaq t g aq t f f g htn turn mathjax off a defining relation of the chakrabarti jagannathan deformed quantum oscillator algebra the moments of the deformed gaussian element sq t h aq t h aq t h are encoded by the joint statistics of crossings and nestings in pair partitions the q 0 t specialization yields a natural single parameter deformation of the full boltzmann fock space of free probability with the corresponding semicircular measure variously encoded via the rogers ramanujan continued fraction the t airy function the t catalan numbers of carlitz riordan and the first order statistics of the reduced wigner process

positive effects of repulsion on boundedness in a fully parabolic attraction repulsion chemotaxis system with logistic source abstract in this paper we study the global boundedness of solutions to the fully parabolic attraction repulsion chemotaxis system with logistic source u t u u v u w f u v t v v u w t w w u subject to homogeneous neumann boundary conditions in a bounded and smooth domain r n n 1 where and are positive constants and f r r is a smooth function generalizing the logistic source f s a b s for all s 0 with a 0 b 0 and 1 it is shown that when the repulsion cancels the attraction i e the solution is globally bounded if n 3 or n min n 2 4 n n 2 6 n 17 n 2 3 n 4 4 with n 2 therefore due to the inhibition of repulsion to the attraction in any spatial dimension the exponent is allowed to take values less than 2 such that the solution is uniformly bounded in time

cayley continuants in 1858 cayley considered a particular kind of tridiagonal determinants or continuants by a direct inspection of the first cases he conjectured an identity expressing these determinants in terms of certain other determinants considered by sylvester in 1854 then cayley proved the conjectured identity by induction but as he wrote he felt unsatisfied with his proof the main aim of this paper is to give a straightforward proof of cayley s identity using the method of formal series moreover we use this method and umbral calculus techniques to obtain several other identities cayley continuants appear in several contexts and in particular in enumerative combinatorics mittag leffler polynomials meixner polynomials of the first kind the falling and the raising factorials are just few instances of these continuants they can be interpreted in terms of weighted permutations moreover as we prove in this paper they also appear in the context of hankel determinants generated by certain catalan like numbers

bounded variation singular stochastic control and dynkin game we consider a bounded variation singular stochastic control problem with value v in a general situation with control of a diffusion and nonlinear cost functional defined as solution to a backward stochastic differential equation bsde associated with this is a dynkin game with value u we establish the well known relation frac partial partial x v u for this general situation a saddle point for the dynkin game is given by the pair of first action times of an optimal control the methods are from stochastic analysis and include a priori estimates pathwise construction and comparison theorems for forward stochastic differential equations fsde and bsde

a calculus for the random generation of labelled combinatorial structures a systematic approach to the random generation of labelled combinatorial objects is presented it applies to structures that are decomposable i e formally specifiable by grammars involving set sequence and cycle constructions a general strategy is developed for solving the random generation problem with two closely related types of methods for structures of size n the boustrophedonic algorithms exhibit a worst case behaviour of the form o n log n the sequential algorithms have worst case o n2 while offering good potential for optimizations in the average case the complexity model is in terms of arithmetic operations and both methods appeal to precomputed numerical table of linear size that can be computed in time o n2 a companion calculus permits systematically to compute the average case cost of the sequential generation algorithm associated to a given specification using optimizations dictated by the cost calculus several random generation algorithms of the sequential type are developed most of them have expected complexity 1 2n log n and are thus only slightly superlinear the approach is exemplified by the random generation of a number of classical combinatorial structures including cayley trees hierarchies the cycle decomposition of permutations binary trees functional graphs surjections and set partitions

impulse control of multidimensional jump diffusions this paper studies regularity properties of the value function for an infinite horizon discounted cost impulse control problem where the underlying controlled process is a multidimensional jump diffusion with possibly infinite activity jumps surprisingly despite these jumps we obtain the same degree of regularity as for the diffusion case at least when the jump satisfies certain integrability conditions

boundedness in quasilinear keller segel systems of parabolic parabolic type on non convex bounded domains abstract this paper deals with the quasilinear fully parabolic keller segel system u t d u u s u v x t 0 v t v v u x t 0 under homogeneous neumann boundary conditions in a bounded domain r n with smooth boundary n n the diffusivity d u is assumed to satisfy some further technical conditions such as algebraic growth and d 0 0 which says that the diffusion is allowed to be not only non degenerate but also degenerate the global in time existence and uniform in time boundedness of solutions are established under the subcritical condition that s u d u k u e for u 0 with 2 n k 0 and e 0 when d 0 0 this paper represents an improvement of tao and winkler 17 because the domain does not necessarily need to be convex in this paper in the case r n and d 0 0 uniform in time boundedness is an open problem left in a previous paper 7 this paper also gives an answer to it in bounded domains

smooth fit principle for impulse control of multidimensional diffusion processes value functions of impulse control problems are known to satisfy quasi variational inequalities qvis a bensoussan and j l lions impulse control and quasivariational inequalities heyden son philadelphia 1984 translation of controle impulsionnel et inequations quasi variationnelles gauthier villars paris 1982 this paper proves the smooth fit c 1 property of the value function for multidimensional controlled diffusions using a viscosity solution approach we show by examples how to exploit this regularity property to derive explicitly optimal policy and value functions

regularity of the value function for a two dimensional singular stochastic control problem it is desired to control a two dimensional brownian motion by adding a possibly singularly continuous process to it so as to minimize an expected infinite horizon discounted running cost the hamilton jacobi bellman characterization of the value function v is a variational inequality which has a unique twice continuously differentiable solution the optimal control process is constructed by solving the skorokhod problem of reflecting the two dimensional brownian motion along a free boundary in the nabla v direction

boundedness of solutions to a quasilinear parabolic parabolic keller segel system with a logistic source abstract we study global solutions of a class of chemotaxis systems generalizing the prototype u t u u u v a u b u r x t 0 v t v v u x t 0 in a bounded domain r n n 1 with smooth boundary u u 1 u u u 1 1 and the parameters r 1 a 0 b 0 and r it is proved that if 0 max r 1 2 n or b is big enough if r 1 then the classical solutions to the above system are uniformly in time bounded our results improve the results of wang et al 2014 28 and cao 2014 3 and also enlarge the range of the results of tao and winkler 2012 25 and ishida et al 2014 14

boundedness of the attraction repulsion keller segel system a b s t r a c t this paper considers the initial boundary value problem of the attraction repulsion keller segel model describing aggregation of microglia in the central nervous system in alzheimer s disease due to the interaction of chemoattractant and chemorepellent if repulsion dominates over attraction we show the global existence of classical solution in two dimensions and weak solution in three dimensions with large initial data u x 0 u0 x v x 0 v 0 x w x 0 w 0 x x