probabilistic generation of finite simple groups ii abstract in earlier work it was shown that each nonabelian finite simple group g has a conjugacy class c such that whenever 1 x g the probability is greater than 1 10 that g x y for a random y c much stronger asymptotic results were also proved here we show that allowing equality the bound 1 10 can be replaced by 13 42 and excluding an explicitly listed set of simple groups the bound 2 3 holds we use these results to show that any nonabelian finite simple group g has a conjugacy class c such that if x 1 x 2 are nontrivial elements of g then there exists y c such that g x 1 y x 2 y similarly aside from one infinite family and a small explicit finite set of simple groups g has a conjugacy class c such that if x 1 x 2 x 3 are nontrivial elements of g then there exists y c such that g x 1 y x 2 y x 3 y we also prove analogous but weaker results for almost simple groups

the graph of the generating d tuples of a finite soluble group and the swap conjecture abstract for a d generated group g we consider the graph d g in which the vertices are the ordered generating d tuples and in which two vertices x 1 x d and y 1 y d are adjacent if and only if there exists i 1 d such that i d 2 and x i y i for each i i we prove that if g is a finite soluble then d g is connected we consider also the swap graph d g in which two generating d tuples are adjacent if they differ only by one entry proving the following if g is an arbitrary finite group and d d g 1 then d g is connected

analysis of a predator prey model with modified leslie gower and holling type ii schemes with stochastic perturbation abstract in this paper we consider a predator prey model with modified leslie gower and holling type ii schemes with stochastic perturbation we show there is a unique positive solution to the system with positive initial value and mainly investigate the long time behavior of the system condition for the system to be extinct is given and persistent condition is established at last numerical simulations are carried out to support our results

periodic solution for a non autonomous lotka volterra predator prey model with random perturbation abstract this paper studies a stochastic non autonomous lotka volterra predator prey model we prove that there exists at least one positive periodic solution under some simple and reasonable conditions in addition we obtain sufficient conditions for persistence in mean and extinction for the stochastic non autonomous system our method and results are new and the ideas could be used to study other types of non autonomous stochastic predator prey systems

new criteria on persistence in mean and extinction for stochastic competitive lotka volterra systems with regime switching abstract this paper concerns persistence in mean and extinction for stochastic competitive lotka volterra systems with regime switching by using some novel stochastic analysis techniques sufficient criteria for the partial permanence and partial extinction are established some novel sufficient conditions on persistence in mean and extinction are also obtained nontrivial examples are provided to illustrate our results

stationary distribution of stochastic population systems under regime switching abstract this paper is concerned with n species model of facultative mutualism in random environments the environment variability in this study is characterized with both white noise and color noise modeled by markovian switching we established new sufficient conditions that ensuring that the system model is positive recurrent we also showed the existence of a unique ergodic stationary distribution the presented results are demonstrated by numerical simulations

compositionality of hennessy milner logic by structural operational semantics this paper presents a method for the decomposition of hml formulas it can be used to decide whether a process algebra term satisfies a hml formula by checking whether subterms satisfy certain formulas obtained by decomposing the original formula the method uses the structural operational semantics of the process algebra the main contribution of this paper is the extension of an earlier decomposition method for the de simone format from the ph d thesis of larsen in 1986 to more general formats

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

an algorithmic introduction to numerical simulation of stochastic differential equations a practical and accessible introduction to numerical methods for stochastic differential equations is given the reader is assumed to be familiar with euler s method for deterministic differential equations and to have at least an intuitive feel for the concept of a random variable however no knowledge of advanced probability theory or stochastic processes is assumed the article is built around 10 matlab programs and the topics covered include stochastic integration the euler maruyama method milstein s method strong and weak convergence linear stability and the stochastic chain rule

inductive synthesis of recursive processes from logical properties this paper proposes an inductive synthesis algorithm for a recursive process to synthesize a process facts which must be satisfied by the target process are given to the algorithm one by one since such facts are infinitely many in general when n facts are input to the algorithm it outputs a process which satisfies the given n facts and this generating process is repeated infinitely many times to represent facts of a process we adopt a subcalculus of calculus first we introduce a new preorder d on recursive processes based on the subcalculus to discuss its properties p dq means that p f implies q f for all formulae f in the subcalculus then its discriminative power and relationship with other preorders are also discussed finally we present the synthesis algorithm the correctness of the algorithm can be stated that the output sequence of processes by the algorithm converges to a process which cannot be distinguished from the intended one if we could know it by a given enumeration of facts in the limit a prototype system based on the algorithm is stated as well

stochastic persistence and stationary distribution in a holling tanner type prey predator model abstract in this paper we study a stochastic predator prey model with beddington deangelis type functional response and logistic growth for predators the deterministic model is already well studied and we recall some important results here we construct the stochastic model from the deterministic model by introducing multiplicative noise terms into the growth equations of prey and predator populations for the stochastic model we show that the system admits unique positive global solution starting from the positive initial value then we prove that the system is strongly persistent in mean when the intensity of environmental forcing is less than some threshold magnitudes finally we show that the system has a stationary distribution under certain parametric restrictions numerical simulations are carried out to substantiate the analytical results

periodic solution for stochastic non autonomous multispecies lotka volterra mutualism type ecosystem we give sufficient conditions for the existence of positive periodic solution we give sufficient conditions for the global attractiveness of the periodic solution we prove that all species will be extinct if the intensity of noise is large enough the results are illustrated by computer simulations the paper characterizes some qualitative dynamic properties of a stochastic non autonomous multi species mutualism model with continuous periodic parameters using khasminskii theory of stability with suitable lyapunov functions and m matrices sufficient conditions are established to guarantee existence of positive periodic solutions to the system we also provide conditions for the global attractiveness of the latter or extinction of all species for sufficiently high volatility levels results are finally supported by numerical computations

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

limit cycles for the competitive three dimensional lotka volterra system abstract in the first part of this paper it is proved that the number of limit cycles of the competitive three dimensional lotka volterra system in r 3 is finite if this system has not any heteroclinic polycycles in r 3 in the second part of this paper a 3d competitive lotka volterra system with two small parameters is discussed this system always has a heteroclinic polycycle with three saddles it is proved that there exists one parameter range in which the system is persistence and has at least two limit cycles and there exists other parameter ranges in which the system is not persistence and has at least one limit cycle

global stability of almost periodic solution of multispecies mutualism system with time delays and impulsive effects abstract this paper discusses an almost periodic multispecies lotka volterra mutualism system with time delays and impulsive effects by using the theory of comparison theorem and constructing a suitable lyapunov functional sufficient conditions which guarantee the existence and uniqueness and global asymptotical stability of almost periodic solution of this system are obtained the results of this paper is completed new an suitable example indicates the feasibility of the main results

dynamics of a stochastic heroin epidemic model abstract in this paper we investigate a stochastic heroin epidemic model by constructing suitable stochastic lyapunov functions we establish sufficient conditions for the extinction of the drug users moreover we also establish sufficient conditions for the existence of ergodic stationary distribution to the model which reveals that the drug users will persist the sensitivity analysis indicates that prevention would be more important than cure

periodic solution for a stochastic non autonomous competitive lotka volterra model in a polluted environment abstract in this paper we consider a stochastic non autonomous competitive lotka volterra model in a polluted environment we derive sufficient criteria for the existence and global attractivity of the boundary periodic solutions furthermore we obtain conditions for the existence and global attractivity of a nontrivial positive periodic solution finally we make simulations to illustrate our analytical results

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

a fully abstract denotational semantics for the calculus of higher order communicating systems abstract in this paper we study the calculus of higher order communicating systems chocs thomsen proc of popl 89 acm 1989 pp 143 154 inform comput 116 1 1995 38 57 in a denotational setting we present a construction of a denotational semantics for chocs which resides in a domain constructed using the standard constructions of separated sum cartesian product the plotkin power domain constructor and recursively defined domains we show under mild restrictions that the denotational semantics and the operational semantics of chocs are fully abstract we have previously proved using bisimulation arguments that processes as first class objects are powerful enough to simulate recursion however the proof is very long and tedious to demonstrate the power of the denotational approach we use it to obtain a very simple proof of the simulation of recursion result

testing equivalences for processes abstract given a set of processes and a set of tests on these processes we show how to define in a natural way three different equivalences on processes these equivalences are applied to a particular language ccs we give associated complete proof systems and fully abstract models these models have a simple representation in terms of trees

the ergodic property and positive recurrence of a multi group lotka volterra mutualistic system with regime switching abstract in this paper we consider a stochastic multi group lotka volterra mutualistic system under regime switching it is well known that the population is forced to expire when the perturbation is sufficiently large the main aim here is to investigate its ergodic property and positive recurrence by stochastic lyapunov functions under small perturbation which can be used to explain some recurring phenomena in practice and thus provide a good description of permanence the mean of the stationary distribution is estimated simulations are also carried out to confirm our analytical 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

asymptotic behavior of a stochastic non autonomous predator prey system with jumps in this paper a two species stochastic non autonomous food chain predator prey system with jumps is proposed and studied the asymptotic properties of the system are examined sufficient conditions for extinction non persistence in the mean weak persistence in the mean and weak persistence of the system are established results show that levy jumps are disadvantageous for the persistence of the populations furthermore we also show that the solution is stochastically ultimate bounded under certain conditions some examples together with numerical simulations are introduced to illustrate our main results

analysis of a stochastic autonomous mutualism model abstract an autonomous lotka volterra mutualism system with random perturbations is investigated under some simple conditions it is shown that there is a decreasing sequence k which has the property that if 1 1 then all the populations go to extinction i e lim t x i t 0 1 i n if k 1 k 1 then lim t x j t 0 j k 1 n whilst the remaining k populations are stable in the mean i e lim t t 1 0 t x i s d s a positive constant i 1 k if n 1 then all the species are stable in the mean sufficient conditions for stochastic permanence and global asymptotic stability are also established

duality for modal m logics abstract the modal calculi are extensions of propositional modal logics with least and greatest fix point operators they have significant expressive power being capable to encode properly temporal notions alien to standard modal systems we focus here on kozen s 21 calculi both finitary and infinitary based on an extension of the classical modal duality to the case of positive modal algebras that we present we prove a stone type duality for positive modal calculi which specializes to a duality for the boolean modal logics thus we extend while also improving on results published in 3 the main improvements are 1 extension to the negation free case 2 a presentation of the algebraic models of the logics in a syntax free manner 3 an explicit duality for the case of the finitary calculus missing in 3 and 4 a completeness result for the negation free or not finitary modal calculus in kripke semantics the special case of completeness for the boolean calculus is an improvement over that presented in 3 but weaker than the theorem of 35 the duality presented here seems to be closer to abramsky s domain theory in logical form 1 as the latter is based on a more general duality for distributive lattices and it has the potential to extensions for modal calculi on a non classical intuitionistic relevant prepositional basis yielding appropriate completeness theorems

full abstractness for a functional concurrent language with higher order value passing we study an applied typed call by value calculus which in addition to the usual types for higher order functions contains an extra type called proc for processes the constructors for terms of this type are similar to those found in standard process calculi such as ccs we first give an operational semantics for this language in terms of a labelled transition system which is then used to give a behavioural preorderbased on contexts the expression n dominates m if in every appropriate context if m can produce a boolean value then so can n

model checking mobile processes we introduce a temporal logic for the polyadic calculus based on fixed point extensions of hennessy milner logic features are added to account for parametrisation generation and passing of names including the use following milner of dependent sum and product to account for unlocalised input and output and explicit parametrisation on names using abstraction and application the latter provides a single name binding mechanism supporting all parametrisation needed a proof system and decision procedure is developed based on stirling and walker s approach to model checking the modal calculus using constants one difficulty for both conceptual and efficiency based reasons is to avoid the explicit use of the rule for parametrised processes a key idea following hennessy and lin s approach to deciding bisimulation for certain types of value passing processes is the relativisation of correctness assertions to conditions on names based on this idea a proof system and a decision procedure are obtained for arbitrary calculus processes with finite control calculus correlates of ccs finite state processes avoiding the use of parallel composition in recursively defined processes

stochastic lotka volterra models with multiple delays abstract this paper investigates the asymptotic behavior of the stochastic lotka volterra model with multiple delays by using certain matrix techniques some results on nonexplosion boundedness and pathwise estimation of the model are investigated

stability in distribution of a stochastic predator prey system with s type distributed time delays abstract this paper concerns the dynamics of a stochastic predator prey lotka volterra system with s type distributed time delays sufficient conditions for the stability in distribution of the solutions sds to the system are obtained the results show that the dynamic scenarios of the sds are completely characterized by two parameters 1 2 among which 1 is just related to the environmental noise while 2 is closely related to both time delays and environmental noises if 2 0 then the distributions of prey predator converge weakly to a unique ergodic invariant distribution ueid if 1 0 2 then the predator goes to extinction while the distributions of prey converge weakly to a ueid if 0 1 then both the predator and prey go to extinction

cpo models for compact gsos languages in this paper we present a general way of giving denotational semantics to a class of languages equipped with an operational semantics that fits the gsos format of bloom istrail and meyer the canonical model used for this purpose will be abramsky s domain of synchronization trees and the denotational semantics automatically generated by our methods will be guaranteed to be fully abstract with respect to the finitely observable part of the bisimulation preorder in the process of establishing the full abstraction result we also obtain several general results on the bisimulation preorder including a complete axiomatization for it and give a novel operational interpretation of gsos languages

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

asymptotic behaviour of the stochastic lotka volterra model this paper examines the asymptotic behaviour of the stochastic extension of a fundamentally important population process namely the lotka volterra model the stochastic version of this process appears to have far more intriguing properties than its deterministic counterpart indeed the fact that a potential deterministic population explosion can be prevented by the presence of even a tiny amount of environmental noise shows the high level of difference which exists between these two representations

modal logics for communicating systems abstract simple modal logics for milner s sccs and ccs are presented we offer sound and complete axiomatizations of validity relative to these calculi as models also we present compositional proof systems for when a program satisfies a formula these involve proof rules which are like gentzen introduction rules except that there are also introduction rules for the program combinators of sccs and ccs the compositional rules for restriction or hiding and parallel combinators arise out of a simple semantic strategy

the effects of time dependent delays on global stability of stochastic lotka volterra competitive model abstract in this paper a stochastic lotka volterra competitive model with time dependent delays is investigated sufficient conditions for global asymptotic stability of the positive equilibrium are established the obtained result demonstrates that time dependent delays have important impacts on the global asymptotic stability of the positive equilibrium of the considered system

the criteria for globally stable equilibrium in n dimensional lotka volterra systems abstract in this paper a set of sufficient conditions are obtained for the existence of a globally asymptotically stable equilibrium point in various submodels of the classic n dimensional lotka volterra system the submodels are the following systems competition cooperative or predator prey chain system and competition cooperative or predator prey model between one and multispecies the criteria in this paper are in explicit forms of the parameters and thus are easily verifiable

on the long time behavior of non autonomous lotka volterra models with diffusion via the sub supertrajectory method abstract in this paper we study in detail the geometrical structure of global pullback and forwards attractors associated to non autonomous lotka volterra systems in all the three cases of competition symbiosis or prey predator in particular under some conditions on the parameters we prove the existence of a unique nondegenerate global solution for these models which attracts any other complete bounded trajectory thus we generalize the existence of a unique strictly positive stable stationary solution from the autonomous case and we extend to lotka volterra systems the result for scalar logistic equations to this end we present the sub supertrajectory tool as a generalization of the now classical sub supersolution method in particular we also conclude pullback and forwards permanence for the above models

the product replacement algorithm and kazhdan s property t a problem of great importance in computational group theory is to generate nearly uniformly distributed random elements in a finite groupg a good example of such an algorithm should start at any given set of generators use no prior knowledge of the structure of g and in a polynomial number of group operations return the desired random group elements see bb2 then these random elements can be used further to determine the structure of g in a pioneer paper bb1 babai found such an algorithm which provably generates nearly uniformly distributed random elements in o log g group multiplications too many for practical applications a different heuristic the product replacement algorithm was designed by leedham green and soicher lg and studied by celler et al in clmno in spite of the fact that very little theoretical justification was known practical experiments showed excellent performance so it quickly became the most popular practical algorithm to generate random group elements and was included in the two most frequently used group algebra packages gap sc and magma bcp a systematic and quantitative approach was carried out by diaconis and saloffcoste ds1 ds2 see also bb2 cg but their results did not reveal the mystery of the truly outstanding performance of the algorithm the aim of this paper is to propose a conceptual explanation based on kazhdan s property t from representation theory of lie groups and to improve some of the previous estimates on the running time the product replacement algorithm works as follows clmno given a finite group g let k g be the set of k tuples g g1 gk of elements of g such that g1 gk g we call elements of k g the generating k tuples given a generating k tuple g1 gk define a move on it in the following way choose uniformly a pair i j such that 1 i 6 j k then apply one of the following four operations with equal probability

bisimulation and divergence abstract behavioural preorders based on the idea of bisimulation but refining the notion of bisimulation equivalence and providing explicit treatments of the phenomenon of divergence in communicating systems are investigated particular study is made of these preorders in the context of milner s calculus of communicating systems the precongruence relations generated by the preorders are characterized and axiomatized on the classes of finite closed terms and sequential terms a verification technique based on the theory of the preorders is introduced and illustrated

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

global stability problem for coupled systems of differential equations on networks the global stability problem of equilibria is investigated for coupled systems of differential equations on networks using results from graph theory we develop a systematic approach that allows one to construct global lyapunov functions for large scale coupled systems from building blocks of individual vertex systems the approach is applied to several classes of coupled systems in engineering ecology and epidemiology and is shown to improve existing results

d wise generation of prosolvable groups abstract let g be a topological group for 2 d n denote by d g the largest m for which there exists an m tuple of elements of g such that any of its d entries generate g topologically we obtain a lower bound for d g in the case when g is a prosolvable group our result implies in particular that if g is d generated then the difference d g d tends to infinity when the smallest prime divisor of the order of g tends to infinity one of the aim of the paper is to draw the attention to an intriguing question in linear algebra whose solution would allow to improve our bounds and determine the precise value for d g in several relevant cases for example when d 2 and g is a prosolvable group

on hybrid competitive lotka volterra ecosystems abstract this paper is concerned with competitive lotka volterra model in random environments it uses regime switching diffusion to model the dynamic of population sizes of n different species in a ecosystem subject to the random changes of the external environment we show that the positive solution of the associated stochastic differential equation does not explode in finite time with probability 1 moreover we demonstrate that the solution is stochastically bounded continuous and has finite moments furthermore we obtain certain asymptotic results regarding large time behavior and present some numerical experimental results

connectivity of the product replacement graph of simple groups of bounded lie rank abstract the product replacement algorithm is a practical algorithm for generating random elements of a finite group the algorithm can be described as a random walk on a graph whose vertices are the generating k tuples of the group for a fixed k we show that there is a function c r such that for any finite simple group of lie type with lie rank r the product replacement graph of the generating k tuples is connected for any k c r the proof uses results of larsen and pink m j larsen r pink finite subgroups of algebraic groups preprint 1998 and does not rely on the classification of finite simple groups

stationary distribution and periodic solutions for stochastic holling leslie predator prey systems abstract the stochastic autonomous and periodic predator prey systems with holling and leslie type functional response are investigated for the autonomous system we prove that there exists a unique stationary distribution which is ergodic by constructing a suitable lyapunov function under relatively small white noise the result shows that stationary distribution doesn t rely on the existence and the stability of the positive equilibrium in the undisturbed system furthermore for the corresponding non autonomous system we show that there exists a positive periodic markov process under relatively weaker condition finally numerical simulations illustrate our theoretical results

local model checking for infinite state spaces bradtield j and c stirling local model checking for infinite spaces theoretical computer science 96 1992 157 174 we present a sound and complete tableau proof system for establishing whether a set of elements of an arbitrary transition system model has a property expressed in a slight extension of the modal mu calculus the proof system we believe offers a very general verification method applicable to a wide range of computational systems in the last twenty years many approaches to program verification have been developed hoare s partial correctness logic for simple while programs gave an early sound and relatively complete proof system this approach was subsequently extended to total correctness and to richer classes of programs dynamic logics offered a more abstract view of hoare logics especially in their propositional versions pnueli pioneered the use of propositional temporal logics as more general program logics capable of describing crucial properties of perpetual concurrent systems a variety of temporal logics have been studied particularly branching and linear time many useful decidability and expressiveness results relating logics and automata have been obtained as well as sound and complete axiomatizations of validity a slightly earlier tradition in the study of correctness was given by the work on program schemes where second order logics were advocated especially in the form of the mu calculus due to de bakker de roever and park an elegant generalization of propositional dynamic and temporal logics drawing on this tradition is the propositional modal mu calculus due to pratt and kozen the modal mu calculus has been shown to include propositional

a modal characterization of observational congruence on finite terms of ccs we propose a translation method of finite terms of ccs into formulas of a modal language representing their class of observational congruence for this purpose we define a modal language and a function associating with any finite term of ccs a formula of the language satisfied by the term furthermore this function is such that two terms are congruent if and only if the corresponding formulas are equivalent the translation method consists in associating with operations on terms action operations on the corresponding formulas this work is a first step towards the definition of a modal language with modalities expressing both possibility and inevitability and which is compatible with observational congruence

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

crowns and factorization of the probabilistic zeta function of a finite group abstract we employ the concept of crown to study the generalized euler factors of the probabilistic zeta function of finite groups

a logic for the description of nondeterministic programs and their properties we present a logic called synchronization tree logic stl for the specification and proof of programs described in a simple term language obtained from a constant nil by using a set a of unary operators a binary operator and recursion the elements of a represent names of actions represents non deterministic choice and nil is the program preforming no action the language of formulas of the logic proposed contains the term language used for the description of programs i e programs are formulas of the logic this provides a uniform frame to deal with programs and their properties as the verification of anassertion t f t is a program f is a formula is reduced to the proof of the validity of the formula t f we propose a sound and under some conditions complete deductive system for synchronization tree logics and discuss their relation with modal logics used for the specification of programs

a unified approach for studying the properties of transition systems abstract in this paper a systematic method for generating comparing and proving the properties of transition systems is presented it is assumed that any property of a system can be defined by giving a set of target states and a type of reachability ten different types of reachability are proposed by appropriately choosing the set of target states a family of ten potentially different properties is generated the main conclusion is that the reachability types and therefore the system properties can be characterized by simple relations involving the set of the possible initial states and fixed points of certain continuous predicate trasformers depending on the set of target states as a consequence in order to prove a given property it is sufficient to compute iteratively greatest or least fixed points of continuous predicate transformers some examples are presented which show how the results can be applied to prove the properties of concurrent systems represented by non deterministic models

coexistence and exclusion of stochastic competitive lotka volterra models abstract this work derives sufficient conditions for the coexistence and exclusion of a stochastic competitive lotka volterra model the conditions obtained are close to necessary in addition convergence in distribution of positive solutions of the model is also established a number of numerical examples are given to illustrate our results

stochastic lotka volterra systems with levy noise abstract this paper is concerned with stochastic lotka volterra models perturbed by levy noise firstly stochastic logistic models with levy noise are investigated sufficient and necessary conditions for stochastic permanence and extinction are obtained then three stochastic lotka volterra models of two interacting species perturbed by levy noise i e predator prey system competition system and cooperation system are studied for each system sufficient and necessary conditions for persistence in the mean and extinction of each population are established the results reveal that firstly both persistence and extinction have close relationships with levy noise secondly the interaction rates play very important roles in determining the persistence and extinction of the species

the power of the future perfect in program logics the expressiveness of branching time tense temporal logics whose eventually operators are relativised to general paths into the future is investigated these logics are interpreted in models obtained by generalising the usual notion of transition system to allow infinite transitions it is shown that the presence of formulae expressing the future perfect enables one to prove that the expressiveness of the logic can be characterised by a notion of bisimulation on the generalised transition systems the future perfect is obtained by adding a past tense operator to the language finally the power of various tense languages from the literature are investigated in this framework

algebraic laws for nondeterminism and concurrency since a nondeterministic and concurrent program may in general communicate repeatedly with its environment its meaning cannot be presented naturally as an input output function as is often done in the denotational approach to semantics in this paper an alternative is put forth first a definition is given of what it is for two programs or program parts to be equivalent for all observers then two program parts are said to be observation congruent if they are in all program contexts equivalent the behavior of a program part that is its meaning is defined to be its observation congruence class the paper demonstrates for a sequence of simple languages expressing finite terminating behaviors that in each case observation congruence can be axiomatized algebraically moreover with the addition of recursion and another simple extension the algebraic language described here becomes a calculus for writing and specifying concurrent programs and for proving their properties

asymptotic properties of hybrid diffusion systems in response to the increasing needs for control and optimization of hybrid systems this work is concerned with such asymptotic properties as recurrence also known as weak stochastic stability in the literature and ergodicity of regime switching diffusions using liapunov functions necessary and sufficient conditions for positive recurrence are developed then ergodicity of positive recurrent regime switching diffusions is obtained by constructing cycles using the associated discrete time markov chains

calculi for synchrony and asynchrony abstract a calculus for distributed computation is studied based upon four combinators a central idea is an abelian group of actions which models the interfaces between components of a distributed computing agent using a notion of bisimulation congruence relations are defined over computing agents and thence an algebraic theory is derived the calculus models both synchronous and asynchronous computation in particular it is shown that the author s calculus of communicating systems 1980 which is an asynchronous model is derivable from the calculus presented here

existence of periodic solutions for a periodic mutualism model on time scales abstract by using mawhin s continuation theorem of coincidence degree theory sufficient criteria are obtained for the existence of periodic solutions of the mutualism model x t r 1 t k 1 t 1 t exp y t 2 t y t 1 exp y t 2 t y t exp x t 1 t x t y t r 2 t k 2 t 2 t exp x t 1 t x t 1 exp x t 1 t x t exp y t 2 t y t where r i k i i c t r i k i i 1 2 i i c t r t i 1 2 r i k i i i i i 1 2 are functions of period 0

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

asymptotic stability of a stochastic may mutualism system abstract this paper deals with a mutualism system in random environments in which the cooperation of two species is guaranteed depending on increasing the carrying capacity of each other mathematically we obtain the existence and uniqueness of a stable stationary distribution by means of markov semigroup theory and fokker planck equation in addition we prove that densities of the distributions for the solutions converge in l 1 to an invariant density under appropriate conditions numerical simulations are also presented to illustrate the theoretical results

termination deadlock and divergence in this paper a process algebra that incorporates explicit representations of successful termination deadlock and divergence is introduced and its semantic theory is analyzed both an operational and a denotational semantics for the language is given and it is shown that they agree the operational theory is based upon a suitable adaptation of the notion of bisimulation preorder the denotational semantics for the language is given in terms of the initial continuous algebra that satisfies a set of equations e ci e it is shown that ci e is fully abstract with respect to our choice of behavioral preorder several results of independent interest are obtained namely the finite approximability of the behavioral preorder and a partial completeness result for the set of equations e with respect to the preorder

proof systems for satisfiability in hennessy milner logic with recursion abstract an extension of hennessy milner logic with recursion is presented a recursively specified formula will have two standard interpretations a minimal one and a maximal one minimal interpretations of formulas are useful for expressing liveness properties of processes whereas maximal interpretations are useful for expressing safety properties we present sound and complete proof systems for both interpretations for when a process satisfies a possibly recursive formula the rules of the proof systems consist of an introduction rule for each possible structure of a formula and are intended to extend the work of stirling and winskel moreover the proof systems may be presented directly in prolog to yield a decision procedure for verifying when a finite state process satisfies a specification given as a possibly recursive formula