parasite population delay model of malaria type with stochastic perturbation and environmental criterion for limitation of disease we present a stochastic delay model of an infectious disease malaria transmitted by a vectors mosquitoes after an incubation time a criterion for limitation of disease is found

completely bounded multipliers over locally compact quantum groups in this paper we consider several interesting multiplier algebras associated with a locally compact quantum groupg firstly we study the completely bounded right multiplier algebra m r cb l1 g we show that m r cb l1 g is a dual banach algebra with a natural operator predual q r l1 g and the completely isometric representation of m r cb l1 g on b l2 g studied recently by junge neufang and ruan is actually weak weak continuous secondly we study the left uniformly continuous space luc g and its banach algebra dual luc g we prove that luc g is a unital c subalgebra of l1 g if the quantum groupg is semi regular we show the connection between luc g and the quan tum measure algebra m g as well as their representations on l1 g and b l2 g finally we study the right uniformly complete qotient space ucq r l1 g and its banach algebra dual ucq r l1 g for co amenable quanum groupsg we obtain the weak homeomorphic completely isometric algebra iso morphism m r cb l1 g m g and the completely isometric isomorphism ucq r l1 g luc g

stochastic periodic solutions of stochastic differential equations driven by levy process abstract in this paper a class of periodic stochastic differential equations driven by levy processes sdeslp is studied firstly we give the existence uniqueness theorem for a large class of sdeslp then using the properties of the periodic markov processes sufficient conditions for the existence and uniqueness of periodic solution to the periodic sdeslp are given finally an example is introduced to illustrate the results developed

dynamics of the deterministic and stochastic siqs epidemic model with non linear incidence the deterministic and stochastic siqs models with non linear incidence are introduced for deterministic model the basic reproductive rate r 0 is derived moreover if r 0 1 there exists a unique endemic equilibrium which is globally asymptotically stable for stochastic model sufficient condition for extinction of the disease that is regardless of the value of r 0 is presented in addition if the intensities of the white noises are sufficiently small and r 0 1 then there exists a unique stationary distribution to stochastic model numerical simulations are also carried out to confirm the analytical results

on topological centre problems and sin quantum groups let a be a banach algebra with a faithful multiplication anda a be the quotient banach algebra of a with the left arens product we introduce a natural banach algebra which is a closed subspace of a a but equipped with a distinct multiplication with the help of this banach algebra new characteriza tions of the topological centre zt a a ofa a are obtained and a characterization of zt a a by lau and ulger for a having a bounded approximate identity is extended to all banach algebras the study of this banach algebra motivates us to introduce the notion of sin locally compact quantum groups and the concept of quotient strong arens irregularity we give characterizations of co amenable sin quan tum groups which are even new for locally compact groups our study shows that the sin property is intrinsically related to topological centre problems we also give characterizations of quotient strong arens irregularity for all quantum group algebras within the class of banach algebras introduced recently by the authors we characterize the unital ones generalizing the corresponding result of lau and ulger we study the interrelationships between strong arens irregularity and quotient strong arens irregularity revealing the complex nature of topological centre problems some open questions by lau and ulger on zt a a are also answered

stochastic dynamics and optimal control in a hybrid bioeconomic system with telephone noise and levy jumps abstract in this paper a hybrid stochastic prey predator system with double time delays and commercial exploitation is established where combined dynamic effects of telephone noise and levy jumps on stochastic population dynamics are taken into accounts existence and uniqueness of globally positive solution to the proposed system are investigated by constructing appropriate stochastic lyapunov functions existence of an ergodic and unique stationary distribution of the positive solution is discussed sufficient conditions for permanence in mean and extinction of corresponding population are derived furthermore sufficient and necessary criteria for optimal exploitation strategy are studied numerical simulations are carried out to show consistency with theoretical analysis

a note on persistence and extinction of a randomized food limited logistic population model this paper addresses the issue of the asymptotic behavior for a non autonomous randomized food limited logistic population model several sufficient conditions are formulated and proved for p moment persistence and extinction of the population as well as in sense of almost sure results show that food limited assumption has an influence on the convergence rate of the solution to the equilibria for the deterministic and stochastic model some previously known results are improved numerical simulations are provided to support the results

competitive lotka volterra population dynamics with jumps abstract this paper considers competitive lotka volterra population dynamics with jumps the contributions of this paper are as follows a we show that a stochastic differential equation sde with jumps associated with the model has a unique global positive solution b we discuss the uniform boundedness of the p th moment with p 0 and reveal the sample lyapunov exponents c using a variation of constants formula for a class of sdes with jumps we provide an explicit solution for one dimensional competitive lotka volterra population dynamics with jumps and investigate the sample lyapunov exponent for each component and the extinction of our n dimensional model

on competitive lotka volterra model in random environments focusing on competitive lotka volterra model in random environments this paper uses regime switching diffusions to model the dynamics of the population sizes of n different species in an ecosystem subject to the random changes of the external environment it is demonstrated that the growth rates of the population sizes of the species are bounded above moreover certain long run average limits of the solution are examined from several angles a partial stochastic principle of competitive exclusion is also derived finally simple examples are used to demonstrate our findings

a separation property of positive definite functions on locally compact groups and applications to fourier algebras abstract for a closed subgroup h of a locally compact group g consider the property that the continuous positive definite functions on g which are identically one on h separate points in g h from points in h we prove a structure theorem for almost connected groups having this separation property for every closed subgroup also when a pair g h has this separation property there are interesting consequences in the ideal theory of the fourier algebra of g

global existence of bifurcated periodic solutions in a commensalism model with delays abstract this paper is concerned with a commensalism model with a discrete delay and a distributed delay by linearizing the system at the positive equilibrium and analyzing the associated characteristic equation the asymptotic stability of the interior equilibrium is investigated it is found that the interior equilibrium is asymptotically stable when the discrete delay is less than a certain critical value and unstable when the discrete delay is greater than this critical value by regarding the delay as the bifurcation parameter the existence of hopf bifurcation is also considered furthermore the properties of hopf bifurcation are determined in particular the global existence of bifurcated periodic solutions is established by applying the topological global hopf bifurcation theorem which shows that the local hopf bifurcations imply the global ones after the second critical value of parameter finally numerical simulations supporting the theoretical analysis are also included

torsion free genus zero congruence subgroups of psl2 ℝ we study and classify all the conjugacy classes of the genus zero congruence subgroups of psl2 r with no elliptic elements we show that it suffices to classify those inside the modular group and determine them completely we also discuss an application to modular curves

periodic solutions and stationary distribution of mutualism models in random environments abstract this paper is concerned with mutualism models in random environments for the periodic mutualism model disturbed by white noise using has minskii theory of periodic solution we show that this model admits a nontrivial positive periodic solution then sufficient conditions for the existence and global attractivity of the boundary periodic solutions are established for the mutualism model disturbed by both white noise and telephone noise sufficient conditions for positive recurrence and the existence of ergodic stationary distribution of the solution are established finally examples are introduced to illustrate the results developed

fuchsian groups automorphic functions and schwarzians in this paper a close connection is established between the geometry of certain genus zero fuchsian groups and the analytic properties of the automorphic forms obtained by applying a certain differential operator to the hauptmoduls of the groups

ergodicity and bifurcations for stochastic logistic equation with non gaussian levy noise abstract in this paper we will prove that the local rds generated by the stochastic logistic equation with non gaussian levy noise is continuous linear and crude cocycle by basing on multiplicative ergodic theorem then we determine all invariant measures of the local rds generated by the stochastic logistic equation with non gaussian levy noise and we calculate the lyapunov exponent for each of these measures furthermore we will show that the stochastic logistic equation with non gaussian levy noise admits a d bifurcations which is significantly different from the classical brownian motion process

stability of a three species stochastic delay predator prey system with levy noise abstract this work is concerned with a three species stochastic delay prey mesopredator superpredator system with levy noise we will characterize the complete dynamic scenarios of stability in distribution of solution sds by three parameters 1 2 3 which depend on the interaction and levy noise

optimal control of harvesting for single population the aim of this paper is to study the optimal harvesting policies for single population model that is to say we assume that the objective of the harvester is to find a harvesting plan making the harvesting yield maximum or maintaining the constant yield and making the terminal population level maximum when the harvesting has happened in a rigid time interval

on a stochastic logistic equation with impulsive perturbations a stochastic logistic model with impulsive perturbations is proposed and investigated first we give a new definition of a solution of an impulsive stochastic differential equation isde which is more convenient for use than the existing one using this definition we show that our model has a global and positive solution and obtain its explicit expression then we establish the sufficient conditions for extinction non persistence in the mean weak persistence persistence in the mean and stochastic permanence of the solution the critical value between weak persistence and extinction is obtained in addition the limit of the average in time of the sample path of the solution is estimated by two constants afterwards the lower growth rate and the upper growth rate of the solution are estimated finally sufficient conditions for global attractivity are established

approximation properties for group algebras and group von neumann algebras let g be a locally compact group let c g resp vn g be the c algebra resp the von neumann algebra associated with the left regular representation i of g let a g be the fourier algebra of g and let moa g be the set of completely bounded multipliers of a g with the completely bounded norm moa g is a dual space and we say that g has the approximation property ap if there is a net ua of functions in a g with compact support such that ua a 1 in the associated weak topology in particular g has the ap if g is weakly amenable a g has an approximate identity that is bounded in the completely bounded norm for a discrete group f we show that f has the ap x c f has the slice map property for subspaces of any c algebra x vn jt has the slice map property for a weakly closed subspaces of any von neumann algebra property se the semidirect product of weakly amenable groups need not be weakly amenable we show that the larger class of groups with the ap is stable with respect to semidirect products and more generally this class is stable with respect to group extensions we also obtain some results concerning crossed products for example we show that the crossed product m a g of a von neumann algebra m with property s by a group g with the ap also has property s

optimal harvesting policy for general stochastic logistic population model abstract we consider some optimal harvesting policies for a general stochastic logistic population model for two management objectives that are maximum sustainable yield and the maximum retained profits the optimal harvesting policies are obtained meanwhile the optimal harvest effort the maximum of expectation of sustainable yield or retained profits and the corresponding variance are given

noise suppresses exponential growth under regime switching consider a given system under regime switching whose solution grows exponentially and suppose that the system is subject to environmental noise in some regimes can the regime switching and the environmental noise work together to make the system change significantly the answer is yes in this paper we will show that the regime switching and the environmental noise will make the original system whose solution grows exponentially become a new system whose solutions will grow at most polynomially in other words we reveal that the regime switching and the environmental noise will suppress the exponential growth

linear relations among the fourier coefficients of modular forms on groups γ0 n of genus zero and their applications we study the linear relations among the fourier coefficients of modular forms on the group 0 n of genus zero applying these linear relations congruence properties of hecke eigenforms replicable properties of hauptmoduln and congruences of representation numbers of the sums of n squares can be obtained the eta quotient expression of the unique normalized modular form n z of weight 12 on 0 n with a zero of maximum order at is listed

optimal harvesting of a stochastic mutualism model with levy jumps in this letter a stochastic mutualism model with levy jumps and harvesting is considered under some simple assumptions sufficient and necessary criteria for the existence of optimal harvesting policy are established the optimal harvesting effort and the maximum of sustainable yield are also obtained the effects of random noises on the optimal harvesting of the model are discussed and some numerical simulations are introduced to illustrate the main results

global stability and stochastic permanence of a non autonomous logistic equation with random perturbation abstract this paper discusses a randomized non autonomous logistic equation d n t n t a t b t n t d t t d b t where b t is a 1 dimensional standard brownian motion in d q jiang n z shi a note on non autonomous logistic equation with random perturbation j math anal appl 303 2005 164 172 the authors show that e 1 n t has a unique positive t periodic solution e 1 n p t provided a t b t and t are continuous t periodic functions a t 0 b t 0 and 0 t a s 2 s d s 0 we show that this equation is stochastically permanent and the solution n p t is globally attractive provided a t b t and t are continuous t periodic functions a t 0 b t 0 and min t 0 t a t max t 0 t 2 t by the way the similar results of a generalized non autonomous logistic equation with random perturbation are yielded

sufficient and necessary conditions of stochastic permanence and extinction for stochastic logistic populations under regime switching in this paper we prove that a stochastic logistic population under regime switching controlled by a markov chain is either stochastically permanent or extinctive and we obtain the sufficient and necessary conditions for stochastic permanence and extinction under some assumptions in the case of stochastic permanence we estimate the limit of the average in time of the sample path of the solution by two constants related to the stationary probability distribution of the markov chain and the parameters of the subsystems of the population model finally we illustrate our conclusions through two examples

optimal harvesting of a stochastic delay logistic model with levy jumps the optimal harvesting problem of a stochastic time delay logistic model with levy jumps is considered in this article we first show that the model has a unique global positive solution and discuss the uniform boundedness of its pth moment with harvesting then we prove that the system is globally attractive and asymptotically stable in distribution under our assumptions furthermore we obtain the existence of the optimal harvesting effort by the ergodic method and then we give the explicit expression of the optimal harvesting policy and maximum yield

a note on nonautonomous logistic equation with random perturbation abstract this paper discusses a randomized nonautonomous logistic equation d n t n t a t b t n t d t t d b t where b t is 1 dimensional standard brownian motion we show that e 1 n t has a unique positive t periodic solution e 1 n p t provided a t b t and t are continuous t periodic functions a t 0 b t 0 and 0 t a s 2 s d s 0

dynamics of a stochastic holling ii one predator two prey system with jumps abstract in this paper a stochastic holling ii one predator two prey system with jumps is investigated firstly the properties of the solution such as the existence and uniqueness of the global positive solution stochastic ultimate boundedness and the pathwise estimation are studied then we mainly establish the sufficient conditions for the extinction and persistence in the mean of the solution results show that positive jump noise is advantageous to the system while negative jump noise is disadvantageous finally a numerical example is introduced to illustrate the results

modelling and analysis of a harvested prey predator system incorporating a prey refuge the present paper deals with a prey predator model incorporating a prey refuge and independent harvesting in either species our study shows that using the harvesting efforts as controls it is possible to break the cyclic behaviour of the system and drive it to a required state the possibility of existence of bionomic equilibria has been considered the problem of optimal harvest policy is then solved by using pontryagin s maximal principle

on uniformization of burnside s curve y2 x5 x the main objects of uniformization of the curve y2 x5 x are studied its burnside s parametrization corresponding schwarz s equation and accessory parameters as a result we obtain the first examples of solvable fuchsian equations on torus and exhibit number theoretic integer q series for uniformizing functions relevant modular forms and analytic series for holomorphic abelian integrals a conjecture of whittaker for hyperelliptic curves and its hypergeometric reducibility are discussed we also consider the conversion between burnside s and whittaker s uniformizations

optimal harvesting of a stochastic delay competitive lotka volterra model with levy jumps abstract this paper systematically investigates the optimal harvesting of a stochastic delay competitive lotka volterra model with levy jumps under some simple assumptions the sufficient conditions for extinction and stable in the time average of each species are established the stability in distribution of this model is proved under our assumptions finally the sufficient and necessary criteria for the existence of optimal harvesting policy are established and the explicit expression of the optimal harvesting effort and the maximum of sustainable yield are also obtained and some numerical simulations are introduced to demonstrate the theoretical results

topological centers of certain dual algebras let a be a banach algebra with a bounded approximate identity let z1 and z2 be respectively the topological centers of the algebras a and a a in this paper for weakly sequentially complete banach algebras in particular for the group and fourier algebras l1 g and a g we study the sets z1 z2 the relations between them and with several other subspaces of a or a

module maps on duals of banach algebras and topological centre problems we study various spaces of module maps on the dual of a banach algebra a and relate them to topological centres we introduce an auxiliary topological centre zt a a for the left quotient banach algebra a a of a our results indicate that zt a a is indispensable for investigating properties of module maps over a and for understanding some asymmetry phenomena in topological centre problems as well as the interrelationships between different arens irregularity properties for the class of banach algebras of type m introduced recently by the authors we show that strong arens irregularity can be expressed both in terms of automatic normality of a module maps on a and through certain commutation relations this in particular generalizes the earlier work on group algebras by ghahramani and mcclure 1992 13 and by ghahramani and lau 1997 12 we link a module map property over a to the space wap a of weakly almost periodic functionals on a generalizing a result by lau and ulger 1996 34 for banach algebras with a bounded approximate identity we also show that for a locally compact quantum group g the quotient strong arens irregularity of l1 g can be obtained from that of m g and can be characterized via the canonical c0 g module structure on luc g

multipliers of the fourier algebras of some simple lie groups and their discrete subgroups for any amenable locally compact group g the space of multipliers ma g of the fourier algebra a g coincides with the space b g of functions on g that are linear combinations of continuous positive definite functions we prove that ma g b g 0 for many non amenable connected groups more specifically we prove that moa g b g 0 for the classical complex lie groups and the general lorentz groups soo n 1 n 2 moa g is a certain subspace of ma g which we call the space of completely bounded multipliers of a g unlike ma g the space moa g has nice stability properties with respect to direct products of groups it is known that the fourier algebra of the free group on n generators n 2 2 admits an unbounded approximate unit pn which is bounded in the multiplier norm we extend this result to any closed subgroup of the general lorentz group soo n 1 moreover we show that for these groups pn can be chosen to be bounded with respect to the moa g norm by a duality argument we obtain that the reduced c algebra of every discrete subgroup of soo n 1 has the completely bounded approximation property in particular this property holds for c f2 the reduced c algebra of the free group on two generators we also prove

dynamical analysis and optimal control in a hybrid stochastic double delayed bioeconomic system with impulsive contaminants emission and levy jumps abstract in this paper a hybrid stochastic double delayed prey predator bioeconomic system with impulses and levy jumps is established where commercial harvesting on each population and impulsive contaminants emission from surrounding environment on each population growth are taken into account sufficient conditions for persistence in the mean and extinction of interacting population are investigated the asymptotical stability in distribution of the proposed system is studied furthermore optimal price control strategy and maximum of expectation of sustainable yield are discussed numerical simulations are carried out to illustrate theoretical analysis

module homomorphisms and topological centres associated with weakly sequentially complete banach algebras abstract this paper is a contribution to the theory of weakly sequentially complete banach algebras a we require them to have bounded approximate identities and for the most part to be ideals in their second duals so that examples are the group algebras l 1 g for compact groups g or the fourier algebras a g for discrete amenable groups g in section 2 we present our main result that the topological centre or set of weak bicontinuous elements of a is identifiable with a as a corollary we deduce in section 3 that each left a module homomorphism from a to a a can be realized as right translation by an element of a these conclusions generalise recent advances in the subject in section 4 we take a special algebra l 1 s for a commutative discrete semigroup s and show that if its second dual has an identity then that identity must lie in l 1 s

analysis of autonomous lotka volterra competition systems with random perturbation abstract this paper discusses a randomized n species lotka volterra competition system we show that this system is stable in time average under certain conditions furthermore there is a stationary distribution of this system if extra conditions are satisfied also we give the extinction condition of this system finally numerical simulations are carried out to support our results

asymptotic properties of stochastic hybrid gilpin ayala system with jumps this paper focuses on studying the dynamics of the stochastic gilpin ayala model under regime switching with jumps the aim is to analyze what happens under the perturbations of regime switching and jumps some asymptotic properties are investigated and sufficient conditions for stochastic permanence extinction non persistence in the mean and weak persistence are provided the critical value among the extinction non persistence in the mean and weak persistence is obtained our results demonstrate that the dynamics of the model have close relations with the jumps and the stationary distribution of the markov chain

dynamics of a stochastic holling tanner predator prey model abstract in the paper we study a stochastic holling tanner predator prey system first by constructing a suitable stochastic lyapunov function we establish sufficient conditions for the existence of a unique ergodic stationary distribution of the positive solutions to the system after that sufficient causes for extinction of the predator population is obtained meanwhile we also obtain the threshold between persistence and extinction of the predator population at last some examples and numerical simulations are provided to illustrate our theoretical results

mapping ideals of quantum group multipliers abstract we study the dual relationship between quantum group convolution maps l 1 g l g and completely bounded multipliers of g for a large class of locally compact quantum groups g we completely isomorphically identify the mapping ideal of row hilbert space factorizable convolution maps with m c b l 1 g yielding a quantum gilbert representation for completely bounded multipliers we also identify the mapping ideals of completely integral and completely nuclear convolution maps the latter coinciding with l 1 b g where b g is the quantum bohr compactification of g for quantum groups whose dual has bounded degree we show that the completely compact convolution maps coincide with c b g our techniques comprise a mixture of operator space theory and abstract harmonic analysis including fubini tensor products the non commutative grothendieck inequality quantum eberlein compactifications and a suitable notion of inner co amenable quantum group that we introduce and for which we exhibit examples from the bicrossed product construction our main results are new even in the setting of group von neumann algebras v n g for quasi sin locally compact groups g

analysis of a stochastic non autonomous food limited lotka volterra cooperative model in this paper a stochastic non autonomous food limited lotka volterra cooperative model is proposed and investigated sufficient conditions are formulated and verified for p moment persistence and extinction of the system results demonstrate that cooperative coefficients have important effects on the convergence rate of the solution to the equilibria of the stochastic model some numerical simulations are introduced to support the analytical results

relations in a quantized elastica in the previous article matsutani s 2002 j geom phys 43 146 62 we showed the hyperelliptic solutions of a loop soliton as a study of a quantized elastica using the results this paper studies relations between the quantized elastica and integrals of its schwarz derivative the winding effects in the quantized elastica problems and some other related relations

optimal harvesting policy of logistic population model in a randomly fluctuating environment abstract in this paper we investigate the optimal harvest policy of a stochastic logistic population model the value of this study lies in two aspects mathematically we establish a stochastic threshold theorem to govern whether the population persists or not in the case of population persistence we prove the existence uniqueness and global asymptotic stability of the invariant density of the fokker planck equation associated with the sde model and we further show the relation between these two models in addition we give the unique optimal harvesting effort and the corresponding maximum of expectation of sustainable yield which gives us the profile of the optimal harvesting policy of the sde model ecologically we find that big harvesting effort or big intensity of noise will lead the population to extinct risk almost surely in addition we find that under a fixed randomness strategy and proper harvesting the maximum sustainable yield increases systematically as the harvesting effort increases but overexploitation will reduce the level of maximize sustainable yield and eventually make the whole population extinct with probability one hence in order to obtain the optimal harvesting policy we must decrease the harvesting effort and the intensity of noise furthermore we find that our parameter perturbation method in this paper is more beneficial to the exploitation of renewable resources than the classical one given by beddington and may 1977 the results show that different perturbation method can exhibit different stochastic population dynamics

the c algebra generated by operators with compact support on a locally compact group abstract let g be a locally compact group and vn g be the von neumann algebra generated by the left regular representation of g let ucb denote the c subalgebra generated by operators in vn g with compact support when g is abelian ucb corresponds to the space of bounded uniformly continuous functions on the dual group of g in this paper we prove among other things that for a large class of locally compact groups which include the heisenberg group the ax b group and the motion group the centre of the banach algebra ucb is the fourier stieltjes algebra b g

asymptotic behaviors of stochastic periodic differential equation with markovian switching some asymptotic behaviors of hybrid stochastic periodic differential equations are investigated in this paper firstly by constructing the space of the periodic functions with probability measure values we prove that the solution processes converge to a stochastic process with periodic distribution under the conditions of the existence and uniqueness tightness of the transition probability and global attractivity of the solutions for stochastic periodic differential equations with markovian switching then we give the definition of stochastic periodic solution of stochastic periodic differential equations which can be regarded as the stochastic counterpart of the periodic solution for the deterministic systems for the stochastic periodic logistic equation we firstly give the expression of the unique explicit solution and other properties such as p moment boundedness global attractivity and asymptotic stability in distribution we then prove the existence uniqueness and stability of the unique stochastic periodic solution finally we simulate the sample trajectory of stochastic periodic logistic equation the results show a certain degree of periodicity in fact it is a simulation result for the mixture of periodicity and randomness

optimal control strategy for an impulsive stochastic competition system with time delays and jumps abstract driven by both white and jump noises a stochastic delayed model with two competitive species in a polluted environment is proposed and investigated by using the comparison theorem of stochastic differential equations and limit superior theory sufficient conditions for persistence in mean and extinction of two species are established in addition we obtain that the system is asymptotically stable in distribution by using ergodic method furthermore the optimal harvesting effort and the maximum of expectation of sustainable yield esy are derived from hessian matrix method and optimal harvesting theory of differential equations finally some numerical simulations are provided to illustrate the theoretical results

geometry of c algebras and the bidual of their projective tensor product abstract given c algebras a and b consider the banach algebra a b where denotes the projective banach space tensor product if a and b are commutative this is the varopoulos algebra v a b we write v a for v a a it has been an open problem for almost 40 years to determine precisely when a b is arens regular see e g 33 48 49 we solve this classical question for arbitrary c algebras indeed we show that a b is arens regular if and only if a or b has the phillips property note that a has the latter property if and only if it is scattered and has the dunford pettis property a further equivalent condition is that a has the schur property or again equivalently the enveloping von neumann algebra a is finite atomic i e a direct sum of matrix algebras hence arens regularity of a b is entirely encoded in the geometry of the c algebras in case a and b are von neumann algebra we conclude that a b is arens regular if and only if a or b is finite dimensional we also show that this characterization does not generalize to the class of non selfadjoint dual even commutative operator algebras specializing to commutative c algebras a and b we obtain that v a b is arens regular if and only if a or b is scattered we further describe the centre z v a showing that it is banach algebra isomorphic to a e h a where e h denotes the extended haagerup tensor product we deduce that v a is strongly arens irregular if and only if a is finite dimensional hence v a is neither arens regular nor strongly arens irregular if and only if a is non scattered this is the case e g for a l

noise expresses exponential growth under regime switching consider a given system under regime switching whose solution grows at most polynomially and suppose that the system is subject to environmental noise in some regimes can regime switching and the environmental noise work together to make the system change significantly the answer is yes in this paper we will show that the regime switching and the environmental noise will make the original system whose solution grows at most polynomially become a new system whose solution will grow exponentially in other words we reveal that regime switching and the environmental noise will express the exponential growth

persistence and extinction in stochastic non autonomous logistic systems this paper studies two widely used stochastic non autonomous logistic models for the first system sufficient conditions for extinction non persistence in the mean weak persistence and stochastic permanence are established the critical number between weak persistence and extinction is obtained for the second system sufficient criteria for extinction non persistence in the mean weak persistence in the mean strong persistence in the mean and stochastic permanence are established the critical number between weak persistence in the mean and extinction is obtained it should be pointed out that this research is systematical and complete in fact the behaviors of the two models in every coefficient cases are cleared up by the results obtained in this paper

amenability of hopf von neumann algebras and kac algebras abstract let m be a hopf von neumann algebra the operator predualm ofmis a completely contractive banach algebra with multiplicationm m m m we call m operator amenableif the completely contractive banach algebram isoperator amenable i e for every operatorm bimodulev every completely bounded derivation fromm into the dualm bimodulev is inner there is a weaker notion of amenability introduced by d voiculescu we say that a hopf von neumann algebra m isvoiculescu amenableif there exists a left invariant mean onm we show that if a hopf von neumann algebra m is operator amenable then it is voiculescu amenable for kac algebras there is astrong voiculescu amenability we show that for discrete kac algebras these amenabilities are all equivalent in fact if we letk m be a discrete kac algebra and letk m be its compact dual kac algebra then the following are equivalent 1 kis operator amenable 2 kis voiculescu amenable 3 the von neumann algebramis hyperfinite 4 kis strong voiculescu amenable 5 kis operator amenable 6 m has a bounded approximate identity

stability of a stochastic delay commensalism model with levy jumps abstract in this work a stochastic delay commensalism system with levy jumps is formulated and studied sharp sufficient conditions for stability in distribution of the model are established the results show that levy jumps can change the stability of the model

global stability of two group sir model with random perturbation abstract in this paper we discuss the two group sir model introduced by guo li and shuai h b guo m y li z shuai global stability of the endemic equilibrium of multigroup sir epidemic models can appl math q 14 2006 259 284 allowing random fluctuation around the endemic equilibrium we prove the endemic equilibrium of the model with random perturbation is stochastic asymptotically stable in the large in addition the stability condition is obtained by the construction of lyapunov function finally numerical simulations are presented to illustrate our mathematical findings

population dynamical behavior of lotka volterra system under regime switching in this paper we investigate a lotka volterra system under regime switching dx t diag x 1 t x n t b r t a r t x t dt s r t db t where b t is a standard brownian motion the aim here is to find out what happens under regime switching we first obtain the sufficient conditions for the existence of global positive solutions stochastic permanence and extinction we find out that both stochastic permanence and extinction have close relationships with the stationary probability distribution of the markov chain the limit of the average in time of the sample path of the solution is then estimated by two constants related to the stationary distribution and the coefficients finally the main results are illustrated by several examples

existence uniqueness and global asymptotic stability of positive solutions of a predator prey system with holling ii functional response with random perturbation abstract this paper discusses a randomized two species predator prey system with holling ii functional response we show that the positive solution of the associated stochastic delay differential equation does not explode to infinity in a finite time in addition the existence uniqueness and global asymptotic stability of the positive solutions are studied

analysis of a general stochastic non autonomous logistic model with delays and levy jumps abstract in this paper a general stochastic non autonomous logistic model with delays and levy jumps is proposed and studied sufficient criteria for extinction non persistence in the mean and weak persistence of the model are established the threshold between weak persistence and extinction is also obtained finally numerical simulations are introduced to illustrate the theoretical analysis results our results illustrate that both persistence and extinction have close relationships with time dependent delay and levy noise

optimal harvesting of a stochastic commensalism model with time delay abstract this article is concerned with a two species stochastic delay commensalism model with harvesting firstly sufficient and necessary criteria for extinction and persistence of each species are established then sufficient and necessary criteria for the existence of a unique optimal harvesting policy are obtained and the explicit form of the optimal harvesting policy is given finally some influences of stochasticity on extinction persistence and optimal harvesting policy are illustrated with several simulations