asymptotic pattern for a partial neutral functional differential equation abstract in the present article the asymptotic speed of spread and traveling wavefronts of a partial neutral functional differential equation pnfde are investigated a variable transform yields to a partial retarded functional differential equation prfde with infinite number of constant delays the relation between the above pnfde and prfde is studied and an equivalence in a certain meaning of these two equations is verified using this equivalence we in fact obtain the existence and uniqueness of solution for the initial value problem of the pnfde we then consider the truncated system of the above prfde which is a partial retarded functional differential equation with finite number of constant delays we establish the existence of the traveling wave solution and the spreading speed for this truncated system a limit argument and the method of finite delay approximation are used to obtain the existence of the traveling wave solutions and the spreading speed for the prfde with infinite number of constant delays this leads to the existence of the traveling wave solution and the spreading speed for the considered pnfde by the above equivalence at last we confirm that the spreading speed is coincidental with the minimal wave speed for all equations an example is given to illustrate the application of our results

traveling wave solutions in n dimensional delayed reaction diffusion systems with mixed monotonicity this paper deals with the existence of traveling wave solutions for n components delayed reaction diffusion systems with mixed monotonicity based on a certain kind of mixed quasimonotonicity reaction terms of higher dimension we propose new conditions on the reaction terms and new definitions of upper and lower solutions by using schauder s fixed point theorem and a cross iteration scheme we reduce the existence of traveling wave solutions to the existence of a pair of upper and lower solutions the general results obtained will be applied to type k monotone diffusive lotka volterra systems of higher dimension

traveling waves solutions for partial neutral differential equations abstract using monotonicity techniques and the schauder fixed point theorem we study the existence of traveling waves for neutral partial differential equations in the last section we illustrate our results on the neutral versions of the kpp fisher and the kobayashi equations

convergence of conditional expectations and strong laws of large numbers for multivalued random variables on etablit des lemmes de fatou et des theoremes de convergence de lebesgue pour des esperances conditionnelles multivaluees de variables aleatoires a valeurs dans des sous ensembles fermes d un espace de banach separable

fuzzy set valued gaussian processes and brownian motions gaussian processes and brownian motion are concepts and tools in modelling important uncertain systems in many areas in view of uncertainty complexity in many real world problems we extend these tools to the case where stochastic processes can take on fuzzy sets as values in this paper we discuss fuzzy set valued gaussian processes based on the results of s li y ogura v kreinovich limit theorems and applications of set valued and fuzzy set valued random variables kluwer academic publishers dordrecht 2002 s li y ogura h t nguyen gaussian processes and martingales for fuzzy valued variables with continuous parameter inform sci 133 2001 7 21 s li y ogura f n proske m l puri central limit theorems for generalized set valued random variables j math anal appl 285 2003 250 263 n n lyashenko on limit theorems for sums of independent compact random subsets in the euclidean space j soviet math 20 1982 2187 2196 and m l puri d a ralescu the concept of normality for fuzzy random variables ann probab 13 1985 1373 1379 we also introduce the concept of fuzzy set valued brownian motion and then prove several properties of such processes

travelling wavefronts in the diffusive single species model with allee effect and distributed delay in this paper we consider the diffusive single species model with allee effect and distributed delay time special attention is paid to the existence of travelling wavefront solutions first we shall show that such fronts exist when the convolution kernel assumes the strong generic delay kernel and the delay is sufficiently small then in the non local spatial terms which account for the drift of individuals to their present position from their possible positions at previous times we shall show that such fronts still exist for the weak generic delay kernel and small delay the approach used in this paper is the geometric singular perturbation theory

probabilistic foundations for measurement modelling with fuzzy random variables we propose fuzzy random variables as a tool for modelling measurements when both aleatory and fuzzy uncertainty have to be taken into account uncertainty propagation follows the ordinary scheme for the random part and uses a t normed extension principle for the fuzzy part we concentrate on the probabilistic theoretical underpinnings of the model particularly limit theorems and discuss their implications to the model

on travelling wavefronts of nicholson s blowflies equation with diffusion this paper is devoted to the study of nicholson s blowflies equation with diffusion a kind of time delayed reaction diffusion for any travelling wavefront with speed c c c is the minimum wave speed we prove that the wavefront is time asymptotically stable when the delay time is sufficiently small and the initial perturbation around the wavefront decays to zero exponentially in space as x but it can be large in other locations the result develops and improves the previous wave stability obtained by mei et al in 2004 the new approach developed in this paper is the comparison principle combined with the technical weighted energy method numerical simulations are also carried out to confirm our theoretical results

wave front solutions of a diffusive delay model for populations of daphnia magna abstract in this paper we consider a diffusional food limited population model incorporating a discrete time delay for the case when the delay is small we show that monotone travelling front solutions exist connecting the two uniform steady states of the model the effect of a larger delay is studied numerically suggesting that in this case travelling fronts still exist but lose their monotonicity

existence of traveling wave solutions for a reaction diffusion equation with distributed delays abstract in this paper we consider a reaction diffusion equation with distributed delays special attention is paid to the existence of traveling wave solutions for special delay kernels using the linear chain trick and the geometric singular perturbation theory we investigate a natural connection between the existence of traveling wave solutions for the reaction diffusion equation with distributed delays and the existence of traveling wave solutions for the corresponding undelayed reaction diffusion equation we show that if the corresponding undelayed reaction diffusion equation has a traveling wave solution then for any sufficiently small delay the delayed reaction diffusion equation also has a traveling wave solution

a fuzzy subgroupoid which is not a fuzzy group abstract we give an example to show that the proposition a fuzzy subgroupoid of a group must be a fuzzy group which appeared in fuzzy sets and systems 51 1992 105 109 structure and constructing of fuzzy subgroups of a group by l filep is wrong we also point out that the proof of theorem 6 in the same article is not true we give a valid proof of it

global stability of wavefronts with minimal speeds for nonlocal dispersal equations with degenerate nonlinearity abstract this paper is concerned with the global stability of wavefronts with minimal speeds for degenerate nonlocal dispersal equations by the method of super and subsolutions and a squeezing technique the wavefront with minimal speed is proved to be globally asymptotically stable with phase shift

some characterizations of fuzzy subgroups abstract we show that if a fuzzy subgroup can be written as the intersection of all its minimal fuzzy p subgroups or the intersection of all its minimal fuzzy p subgroups then some properties of the fuzzy subgroup characterize the properties of all its minimal fuzzy p subgroups or all its minimal fuzzy p subgroups and investigate interrelationships among some properties of fuzzy subgroups

travelling wave and global attractivity in a competition diffusion system with nonlocal delays in this paper we are concerned with a two competition model described by a reaction diffusion system with nonlocal delays which account for the drift of individuals to their present position from their possible positions at previous times by using the iterative technique recently developed in wang et al 2006 14 the sufficient conditions are established for the existence of travelling wave solutions connecting the semi trivial steady state to the coexistence steady state of the considered system when the domain is bounded we investigate the global attractivity of the coexistence steady state of the system under homogeneous neumann boundary conditions as well the approach used is the upper lower solutions and monotone iteration technique

a contribution to the theory of fuzzy subgroups abstract in this paper we continue our study in order to give a partial answer to the question suggested by asaad in 1991 what can be said about the structure of a group g when the information are known about the structure of a fuzzy subgroup a of g and viceversa

entire solutions in bistable reaction diffusion equations with nonlocal delayed nonlinearity this paper is concerned with entire solutions for bistable reaction diffusion equations with nonlocal delay in one dimensional spatial domain here the entire solutions are defined in the whole space and for all time t r assuming that the equation has an increasing traveling wave solution with nonzero wave speed and using the comparison argument we prove the existence of entire solutions which behave as two traveling wave solutions coming from both ends of the x axis and annihilating at a finite time furthermore we show that such an entire solution is unique up to space time translations and is liapunov stable a key idea is to characterize the asymptotic behavior of the solutions as t in terms of appropriate subsolutions and supersolutions in order to illustrate our main results two models of reaction diffusion equations with nonlocal delay arising from mathematical biology are considered

characterization of fuzzy subgroups abstract this paper is a continuation of our earlier work abou zaid 1991 1992 asaad 1991 asaad and abou zaid 1993 1995 in order to investigate further the problem given by asaad 1991 what can be said about the structure of a fuzzy subgroup a of a group g when information is available about the structure of g and vice versa

spreading speed and wavefronts for parabolic functional differential equations with spatio temporal delays the existence of traveling wavefronts and the spreading speed for a kind of general reaction diffusion system with spatio temporal delays are investigated we obtain the conclusion that there is c 0 being the asymptotic speed of spread and the minimal speed for the system some more delicate analysis techniques have been developed to make the forms of the kernel function g t x and the function f more flexible in our paper a pair of super solution and sub solution have been constructed in order that the existence of traveling wavefronts can be guaranteed there is a biological model as an example in this article which is coincident with this system

traveling wavefronts for a time delayed non newtonian filtration equation abstract this paper is concerned with traveling wavefronts for the evolutionary p laplacian with time delay we first establish some necessary and sufficient conditions for the existence of monotone nondecreasing and nonincreasing traveling wavefronts which correspond to definite wave speeds c 1 and c 2 respectively moreover special attention is also paid to the asymptotic behavior of traveling fronts connecting two uniform steady states

traveling waves for nonlinear cellular neural networks with distributed delays abstract in this paper we will establish the existence and nonexistence of traveling waves for nonlinear cellular neural networks with finite or infinite distributed delays the dynamics of each given cell depends on itself and its nearest m left or l right neighborhood cells where delays exist in self feedback and left or right neighborhood interactions our approach is to use schauder s fixed point theorem coupled with upper and lower solutions of the integral equation in a suitable banach space further we obtain the exponential asymptotic behavior in the negative infinity and the existence of traveling waves for the minimal wave speed by the limiting argument our results improve and cover some previous works

hopf bifurcations in a reaction diffusion population model with delay effect abstract a reaction diffusion population model with a general time delayed growth rate per capita is considered the growth rate per capita can be logistic or weak allee effect type from a careful analysis of the characteristic equation the stability of the positive steady state solution and the existence of forward hopf bifurcation from the positive steady state solution are obtained via the implicit function theorem where the time delay is used as the bifurcation parameter the general results are applied to a food limited population model with diffusion and delay effects as well as a weak allee effect population model

on generalized characteristic fuzzy subgroups of a finite group abstract in 1991 asaad 2 suggested the following two questions i what can be said about the structure of a fuzzy subgroup a of a finite group g when information is known about the structure of g ii what can be said about the structure of group g when information is known about the structure of a fuzzy subgroup a of g the purpose of this paper is to continue the investigation of the above questions

on fuzzy subnormal and pronormal subgroups of a finite group abstract throughout this paper all groups are finite in 1989 asaad 2 suggested the following question knowing some information about a fuzzy subgroup a of a group g what is the structure of g and if some information is known about g what is the structure of a for example he proved that if g is a group of prime power order then g is cyclic iff there exists a fuzzy subgroup a of g such that for x y in g i if a x a y then x y and ii if a x a y then x y the aim of this paper is to continue the investigation of this question

travelling waves for a biological reaction diffusion model with spatio temporal delay in this paper we consider the reaction diffusion equations with spatio temporal delay which models the microbial growth in a flow reactor nonlocal spatial term a weighted average in space arises when the individuals have not necessarily been at the same point in space at previous time by employing linear chain technique geometric singular perturbation and the center manifold theorem we prove that the steady travelling wave does not only persist but also it looks qualitatively the same as it do with no delay at all under the introduction of delays at least for small delay

overview on the development of fuzzy random variables this paper presents a backward analysis on the interpretation modelling and impact of the concept of fuzzy random variable after some preliminaries the situations modelled by means of fuzzy random variables as well as the main approaches to model them are explained we also summarize briefly some of the probabilistic studies concerning this concept as well as some statistical applications

fuzzy subgroups having the property abstract we introduce the notion of the property for a fuzzy group and characterize all finite cyclic groups in terms of this notion this property concerns the transition of the order of an element of a group from the classical to the fuzzy setting

nonlinear stability of traveling wavefronts for competitive cooperative lotka volterra systems of three species abstract this paper is concerned with nonlinear stability of traveling wavefronts for competitive cooperative lotka volterra systems of three species it is proved that all traveling wavefronts with speed c c are exponentially stable in l space by the weighted energy method and comparison principle moreover the time decay rates are obtained by weighted energy estimates

a banach lattice approach to convergent integrably bounded set valued martingales and their positive parts denote by cf x the set of all nonempty convex closed subsets of a separable banach space x let be a complete probability space and denote by l1 cf x the complete metric space of equivalence classes of a e equal integrably bounded cf x valued functions for any preassigned filtration i we describe the space of convergent integrably bounded cf x valued martingales in terms of the closure of i 1 l1 i cf x in l1 cf x in particular we provide a formula to calculate the join of two such martingales and the positive part of such a martingale our object is achieved by considering the more general setting of a near vector lattice s d endowed with a riesz metric d by means of radstrom s embedding theorem for such spaces a link is established between the space of convergent martingales in s and the space of convergent martingales in the radstrom completion r s of s this link provides information about the former space of martingales via known properties of measure free martingales in riesz normed vector lattices applicable to r s we also apply our general results to the spaces of convergent ck x valued martingales where ck x denotes the set of all nonempty convex compact subsets of x

asymptotic patterns of a structured population diffusing in a two dimensional strip abstract in this paper we derive a population model for the growth of a single species on a two dimensional strip with neumann and robin boundary conditions we show that the dynamics of the mature population is governed by a reaction diffusion equation with delayed global interaction using the theory of asymptotic speed of spread and monotone traveling waves for monotone semiflows we obtain the spreading speed c the non existence of traveling waves with wave speed 0 c c and the existence of monotone traveling waves connecting the two equilibria for c c

asymptotic behavior and traveling wave solutions for parabolic functional differential equations on presente une generalisation de la theorie des equations kpp et de diffusion bistables non lineaires on montre que des solutions onde de propagation existent pour des equations fonctionnelles paraboliques non lineaires

complete convergence for arrays of rowwise independent random variables and fuzzy random variables in convex combination spaces the aim of this study is to establish the complete convergence for arrays of rowwise independent random variables and fuzzy random variables in convex combination space our results not only generalize related previously reported results but also improve them some illustrative examples are provided

existence and nonexistence of monotone traveling waves for the delayed fisher equation abstract in this paper a new approach based on a shooting method in a half line coupled with the technique of upper lower solution pair is used to study the existence and nonexistence of monotone waves for one form of the delayed fisher equation that does not have the quasimonotonicity property a necessary and sufficient condition is provided this new method can be extended to investigate many other nonlocal and non monotone delayed reaction diffusion equations

on diffusive population models with toxicants and time delays in this article we study the global stability in reaction diffusion models for single species population growth under environmental toxicants with or without time delays the existence and uniqueness of a positive steady state solution are established in those models it is shown that as long as the magnitude of the instantaneous self limitation and toxicant effects is larger than that of the time delay effects in the model with delays the solution of both reaction diffusion systems has the same asymptotic behavior extinction or converging to the positive steady state solution depending on the growth rate of the species numerical simulations for both cases with or without time delays are demonstrated for the purpose of comparison

delay induced traveling wave fronts in reaction diffusion equations of kpp fisher type this paper explores the impact of delay on the existence of traveling wave fronts in reaction diffusion equations of kpp fisher type for two such equations one being local and the other with nonlocal effect arising from the age structure of the population we show that delay can induce slow traveling wave fronts

travelling wave fronts in reaction diffusion systems with spatio temporal delays this paper deals with the existence of travelling wave fronts in reaction diffusion systems with spatio temporal delays our approach is to use monotone iterations and a nonstandard ordering for the set of profiles of the corresponding wave system new iterative techniques are established for a class of integral operators when the reaction term satisfies different monotonicity conditions following this the existence of travelling wave fronts for reaction diffusion systems with spatio temporal delays is established finally we apply the main results to a single species diffusive model with spatio temporal delay and obtain some existence criteria of travelling wave fronts by choosing different kernels

central limit theorems for generalized set valued random variables abstract we give central limit theorems for generalized set valued random variables whose level sets are compact both in r d or in a banach space under milder conditions than those obtained recently by the latter two authors

traveling wavefronts for delayed reaction diffusion systems via a fixed point theorem abstract by using schauder s fixed point theorem we prove some existence results for traveling wavefronts of reaction diffusion systems with quasimonotonicity reactions more precisely we reduce the existence of traveling wavefronts to the existence of an admissible pair of supersolution and subsolution which are easy to construct in practice finally to illustrate our main results we study the existence of traveling wavefronts for a delayed predator prey model with diffusion as well as the reaction diffusion system with the well known belousov zhabotinskii reaction and the obtained results improve the existing ones

environmental periodicity and time delays in a food limited population model abstract sufficient conditions are obtained for the existence of a globally attracting positive periodic solution of the food limited population system modelled by the equation n t r t k t n t m k t c t r t n t m where m is a nonnegative integer and k r c are continuous positive periodic functions of period

groups and fuzzy subgroups ii abstract in 1991 asaad has suggested the following question what can be said about the structure of a group g when information is known about the structure of a fuzzy subgroup a of g and vice versa the purpose of this paper is to continue the investigation of the above mentioned question

travelling waves for delayed reaction diffusion equations with global response we develop a new approach to obtain the existence of travelling wave solutions for reaction diffusion equations with delayed non local response the approach is based on an abstract formulation of the wave profile as a solution of an operational equation in a certain banach space coupled with an index formula of the associated fredholm operator and some careful estimation of the nonlinear perturbation the general result relates the existence of travelling wave solutions to the existence of heteroclinic connecting orbits of a corresponding functional differential equation and this result is illustrated by an application to a model describing the population growth when the species has two age classes and the diffusion of the individual during the maturation process leads to an interesting non local and delayed response for the matured population

strong laws of large numbers for independent fuzzy set valued random variables abstract in this paper we shall present strong laws of large numbers slln s for independent not necessary identically distributed fuzzy set valued random variables whose base space is a separable banach space or an euclidean space in the sense of the extended hausdorff metric d h we apply the method to the sequence of independent identically distributed fuzzy set valued random variables to give a simple proof of slln s

fuzzy orders relative to fuzzy subgroups abstract in this paper we introduce the notion of fuzzy orders of the elements of a group and show that most of the basic properties of orders of elements in the group theory are valid in the theory of fuzzy groups where ordinary orders of elements are replaced by fuzzy orders of elements reports of further development of the subject will follow in subsequent essays

convergence of set valued sub and supermartingales in the kuratowski mosco sense the purpose of this paper is to prove some convergence theorems of closed and convex set valued sub and supermartingales in the kuratowski mosco sense to get submartingale convergence theorems we give sufficient conditions for the kudo aumann integral and hiai umegaki conditional expectation to be closed both for compact convex set valued random variables and for closed convex set valued random variables we also give an example of a bounded closed convex set valued random variable whose kudo aumann integral is not closed

on the uniform stability for a food limited population model with time delay in this paper we provide sufficient conditions which guarantee the uniform stability as well as asymptotic stability of the positive equilibrium for a food limited population model with time delay

traveling wave solutions in a delayed diffusive competition system abstract in this paper we first investigate the existence of traveling wave fronts in a delayed diffusive competition system by constructing a pair of upper and lower solutions then we consider the asymptotic behavior of traveling wave solutions at the minus plus infinity by means of the bilateral laplace transform finally the monotonicity and uniqueness up to the translation of traveling wave solutions are also obtained by the strong comparison principle and the sliding method

pyramidal traveling fronts in a nonlocal delayed diffusion equation abstract recently there have been great progresses on the study of nonplanar traveling wave solutions of reaction diffusion equations in this paper we study the pyramidal traveling fronts of nonlocal delayed diffusion equation in r n with n 2 by using the comparison principle and establishing super and subsolution since the effect of nonlocal delay we show that nonlocal delayed diffusion equation in n dimensional space has a pyramidal traveling front u t x v x x n s t toward x n axis for each s c 0 in particular two dimensional traveling curved front and three dimensional pyramidal fronts for nonlocal delayed diffusion equation in r 2 and r 3 are also established respectively moreover we also extend our results to generally nonlocal delayed reaction diffusion equation

traveling waves for a time delayed newtonian filtration equation abstract this paper deals with traveling wave solutions for a degenerate parabolic equation with time delay we first establish the necessary and sufficient conditions to the existence of monotone nonincreasing and nondecreasing traveling wave solutions which correspond to a unique wave speed c respectively it will be shown that the traveling wave may be a semi finite or infinite traveling wave under different exponents furthermore we give an accurate estimation on the convergent rate for the semi finite or infinite traveling waves

fuzzy subgroups of nilpotent groups in 1991 asaad has suggested the following question what can be said about the structure of a group g when information is known about the structure of a fuzzy subgroup a of g and vice versa this question has been partially investigated in fuzzy sets and systems39 1991 323 328 the purpose of this paper is to continue more investigations for the above mentioned question

spreading speeds and traveling wavefronts for second order integrodifference equations this paper is concerned with the spreading speeds and traveling wavefronts for second order integrodifference equations by introducing an auxiliary integrodifference system the spreading speed is established for the integrodifference equation it is shown that the spreading speed coincides with the minimal wave speed for monotonic traveling wavefronts furthermore we prove that the traveling wavefronts are stable by applying the squeezing technique finally we analyze the different effects of the delay term appearing in the integrodifference equation from the viewpoint of ecology

asymptotic stability of traveling wave fronts in nonlocal reaction diffusion equations with delay abstract this paper is concerned with the asymptotic stability of traveling wave fronts of a class of nonlocal reaction diffusion equations with delay under monostable assumption we prove that the traveling wave front is exponentially stable by means of the technical weighted energy method when the initial perturbation around the wave is suitable small in a weighted norm the exponential convergent rate is also obtained finally we apply our results to some population models and obtain some new results which recover complement and or improve a number of existing ones

traveling wavefronts in diffusive and cooperative lotka volterra system with delays existence of traveling wave front solutions is established for diffusive and cooperative lotka volterra system with delays the result is an extension of an existing result for delayed logistic scaler equation to systems and is somewhat parallel to the existing result for diffusive and competitive lotka volterra systems without delay the approach used in this paper is the upper lower solution technique and the monotone iteration recently developed by wu and zou j dynam differential equations 13 2001 651 687 for delayed reaction diffusion systems without the so called quasimonotonicity 2002 elsevier science usa all rights reserved

a phase plane discussion of convergence to travelling fronts for nonlinear diffusion the paper is concerned with the asymptotic behavior as t of solutions u x t of the equation u t u xx f left u right 0 x in left infty infty right in the case f 0 f 1 0 with f u non positive for u 0 sufficiently close to zero and f u non negative for u 1 sufficiently close to 1 this guarantees the uniqueness but not the existence of a travelling front solution u u x ct u 0 u and it is shown in essence that solutions with monotonic initial data converge to a translate of this travelling front if it exists and to a stacked combination of travelling fronts if it does not the approach is to use the monotonicity to take u and t as independent variables and p ux as the dependent variable and to apply ideas of sub and super solutions to the diffusion equation for p

existence and stability of traveling wave fronts in reaction advection diffusion equations with nonlocal delay this paper is concerned with the existence uniqueness and globally asymptotic stability of traveling wave fronts in the quasi monotone reaction advection diffusion equations with nonlocal delay under bistable assumption we construct various pairs of super and subsolutions and employ the comparison principle and the squeezing technique to prove that the equation has a unique nondecreasing traveling wave front up to translation which is monotonically increasing and globally asymptotically stable with phase shift the influence of advection on the propagation speed is also considered comparing with the previous results our results recovers and or improves a number of existing ones in particular these results can be applied to a reaction advection diffusion equation with nonlocal delayed effect and a diffusion population model with distributed maturation delay some new results are obtained

entire solutions in monostable reaction diffusion equations with delayed nonlinearity abstract entire solutions for monostable reaction diffusion equations with nonlocal delay in one dimensional spatial domain are considered a comparison argument is employed to prove the existence of entire solutions which behave as two traveling wave solutions coming from both directions some new entire solutions are also constructed by mixing traveling wave solutions with heteroclinic orbits of the spatially averaged ordinary differential equations and the existence of such a heteroclinic orbit is established using the monotone dynamical systems theory key techniques include the characterization of the asymptotic behaviors of solutions as t in term of appropriate subsolutions and supersolutions two models of reaction diffusion equations with nonlocal delay arising from mathematical biology are given to illustrate main results

bistable wavefronts in a diffusive and competitive lotka volterra type system with nonlocal delays abstract a diffusive lotka volterra type model with nonlocal delays for two competitive species is considered the existence of a traveling wavefront analogous to a bistable wavefront for a single species is proved by transforming the system with nonlocal delays to a four dimensional system without delay furthermore in order to prove the asymptotic stability up to translation of bistable wavefronts of the system the existence regularity and comparison theorem of solutions of the corresponding cauchy problem are first established for the systems on r by appealing to the theory of abstract functional differential equations the asymptotic stability up to translation of bistable wavefronts are then proved by spectral methods in particular we also prove that the spreading speed is unique by upper and lower solutions technique from the point of view of ecology our results indicate that the nonlocal delays appeared in the interaction terms are not sensitive to the invasion of species of spatial isolation

fuzzy random variables abstract in this paper we define the concepts of fuzzy random variable and the expectation of a fuzzy random variable the new definition of expectation generalizes the integral of a set valued function we derive some properties of these new concepts by considering a suitable generalization of the hausdorff metric we derive the lebesgue dominated convergence type theorem

gaussian processes and martingales for fuzzy valued random variables with continuous parameter abstract the purpose of this paper is to discuss fuzzy valued gaussian processes and martingales with continuous parameter we mainly obtain a representation theorem for fuzzy valued gaussian processes after proving a new embedding theorem based on previous results about set valued and fuzzy valued martingales cf s li y ogura j fuzzy math 4 1996 905 s li y ogura fuzzy sets and systems 101 1999 453 s li y ogura ann probab 26 1998 1384 1402 s li y ogura in proc ifsa 97 vol 4 1997 pp 9 13 s li y ogura in c bertoluzza m a gil d a ralescu eds statistical modeling analysis and management of fuzzy data physica in press y ogura s li fuzzy sets and systems in press we prove optional sampling theorems for set valued and fuzzy valued martingales with continuous parameter

groups and fuzzy subgroups abstract the purpose of this paper is to deal with the following two problems 1 what can be said about the structure of a fuzzy subgroup a of a group g when information is known about the structure of g 2 what can be said about the structure of a group g when information is known about the structure of a fuzzy subgroup a of g

limit theorems for fuzzy random variables a strong law of large numbers and a central limit theorem are proved for independent and identically distributed fuzzy random variables whose values are fuzzy sets with compact levels the proofs are based on embedding theorems as well as on probability techniques in banach space

traveling waves for time delayed reaction diffusion equations with degenerate diffusion abstract this paper is concerned with time delayed reaction diffusion equations with degenerate diffusion when the term for birth rate is a nonlocal integral with a heat kernel the family of minimum wave speeds corresponding to all the degenerate diffusion coefficients is proved to admit a uniform positive infimum however when the term for birth rate is local there is no positive infimum of all the minimum wave speeds this difference indicates that the nonlocal effect plays a role as laplacian such that a positive lower bound independent of the degenerate diffusion exists for the minimum wave speeds the approach adopted for the proof is the monotone technique with the viscosity vanishing method the degeneracy of diffusion for the equation causes us essential difficulty in the proof a number of numerical simulations are also carried out at the end of the paper which further numerically confirm our theoretical results