blind channel equalization and spl epsiv approximation algorithms we show that a blind equalizer can be obtained without estimating any statistics based on the received data if the constellation alphabet is known the idea is to formulate the blind channel equalization problem into a quadratic optimization with binary constraints then efficient spl epsiv approximation algorithms are presented and applied to find the equalizer coefficients the proposed approach blindly equalizes the channel at symbol baud rates does not rely on estimating any statistics applies to nonminimum phase channels and converges to an spl epsiv neighborhood of a global optimum simulation results support the theoretical analysis

abstract functional differential equations and reaction diffusion systems functional differential equations and reaction diffusion systems r h martin jr and h l smith abstract several fundamental results on the existence and behavior of solutions to semilinear functional differential equations are developed in a banach space setting the ideas are applied to reaction diffusion systems that have time delays in the nonlinear reaction terms the techniques presented here include differential inequalities invariant sets and lyapunov functions and therefore they provide for a wide range of applicability the results on inequalities and especially strict inequalities are new even in the context of semilinear equations whose nonlinear terms do not contain delays several fundamental results on the existence and behavior of solutions to semilinear functional differential equations are developed in a banach space setting the ideas are applied to reaction diffusion systems that have time delays in the nonlinear reaction terms the techniques presented here include differential inequalities invariant sets and lyapunov functions and therefore they provide for a wide range of applicability the results on inequalities and especially strict inequalities are new even in the context of semilinear equations whose nonlinear terms do not contain delays suppose q is a bounded domain in rn with aq smooth and a is the laplacian operator on q also let m be a positive integer z a positive number and f fi m a continuous bounded function from 0 xc x q x c z 0 m into rm where c t 0 is the space of continuous functions from z 0 into r the purpose of this paper is to apply abstract results for semilinear functional differential equations in banach spaces to reactiondiffusion systems with time delays having the form a tu x t diau x t i t x ut x t a xeq i 1 m rdd ai x ui x t au i x t 81 x t t a x eaq u x a 0 x x 0 5 t 0 di 0 and ca q 0 o is c and i q x 0 oo r is c2 here an is the outward normal derivative on aq and if di 0 it is assumed that no boundary conditions are specified for this i also tu x t denotes the partial with respect to t whereas ut x denotes the member of c z 0 defined by 0 u x t 0 u x t 0 m our techniques provide basic existence criteria but the main point is that they can also be effectively applied to obtain estimates for solutions especially received by the editors october 7 1987 and in revised form october 7 1988 1980 mathematics subject classification 1985 revision primary 35r10 34k30

connected simple systems transition matrices and heteroclinic bifurcations given invariant sets a b and c and connecting orbits a b and b c we state very general conditions under which they bifurcate to produce an a c connecting orbit in particular our theorem is applicable in settings for which one has an admissible semiflow on an isolating neighborhood of the invariant sets and the connecting orbits and for which the conley index of the invariant sets is the same as that of a hyperbolic critical point our proof depends on the connected simple system associated with the conley index for isolated invariant sets

hopf bifurcation in a diffusive lotka volterra type system with nonlocal delay effect abstract the dynamics of a diffusive lotka volterra type model for two species with nonlocal delay effect and dirichlet boundary conditions is investigated in this paper the existence and multiplicity of spatially nonhomogeneous steady state solutions are obtained by means of lyapunov schmidt reduction the stability of spatially nonhomogeneous steady state solutions and the existence of hopf bifurcation with the changes of the time delay are obtained by analyzing the distribution of eigenvalues of the infinitesimal generator associated with the linearized system by the normal form theory and the center manifold reduction the stability and bifurcation direction of hopf bifurcating periodic orbits are derived finally our theoretical results are illustrated by a model with homogeneous kernels and one dimensional spatial domain

positive periodic solutions of n species neutral delayed lotka volterra competition system with impulsive perturbations in this paper a class of neutral delayed lotka volterra competition system with impulsive perturbations is investigated we explore the existence of positive periodic solutions of the system by using mawhin coincidence degree theory and some analytical approaches from our results we find that a part of n species of the system is driven to extinction due to competition exclusion and weak adaption to environment characterized by impulsive perturbations

traveling waves for competitive lotka volterra systems with spatial diffusions and spatio temporal delays abstract this paper is concerned with the existence of traveling waves for reaction diffusion equations with spatio temporal delays our approach is to use the cross iteration technique and schauder s fixed point theorem the iterative technique can be established for a class of integral operators when the reaction terms satisfy new monotonicity conditions which is different from those in previous works the results can be well applied to a two species competitive lotka volterra system with more general kernel functions in order to overcome the difficulty of spatio temporal delays we need to use a basic result from a pde textbook existence of traveling waves which connect the trivial equilibrium and the positive equilibrium indicates that there is a transition zone moving the steady state with no species to the steady state with the coexistence of two species our results can extend some existing ones for two species diffusion competitive lotka volterra systems

on the calculation of extended max and min operations between convex fuzzy sets of the real line in this paper we will identify the sets of so called sub and pseudo highest intersection points of convex fuzzy sets of the real line and will explore their properties based on the properties of these sets an algorithm for calculating extended max and min operations between two or more convex fuzzy sets of the real line with general membership functions not necessarily continuous is proposed

on the power sequence of a fuzzy matrix with convex combination of max product and max min operations in the literature the powers of a fuzzy matrix with max min max product max archimedean t norm max t norm max arithmetic mean compositions have been studied it turns out that the limiting behavior of the powers of a fuzzy matrix depends on the composition involved in this paper we consider the powers of a fuzzy matrix with convex combination of max product and max min operations we show that the powers of a fuzzy matrix a with such operations are asymptotical p period if and only if the powers of an associated boolean matrix a are p periodic moreover necessary and sufficient conditions for such a fuzzy matrix to be nilpotent are proposed

a simple computation of min and max operations for fuzzy numbers in this paper we propose a new method to implement the operations min and max for fuzzy numbers easily and quickly those considered fuzzy numbers in the operations can be of any shape

approximation by pseudo linear operators the approximation operators provided by classical approximation theory use exclusively as underlying algebraic structure the linear structure of the reals also they are all linear operators we address in the present paper the following problems need all the approximation operators be linear is the linear structure the only one which allows us to construct particular approximation operators as an answer to this problem we propose new particular pseudo linear approximation operators which are defined in some ordered semirings we study these approximations from a theoretical point of view and we obtain that these operators have very similar properties to those provided by classical approximation theory in this sense we obtain uniform approximation theorems of weierstrass type and jackson type error estimates in approximation by these operators

analytical properties and exact solutions of the lotka volterra competition system the lotka volterra competition system with diffusion is considered the painleve property of this system is investigated exact traveling wave solutions of the lotka volterra competition system are found periodic solutions expressed in terms of the weierstrass elliptic function are also given

bistable traveling waves for a competitive cooperative system with nonlocal delays abstract this paper is devoted to the study of bistable traveling waves for a competitive cooperative reaction and diffusion system with nonlocal time delays the existence of bistable waves is established by appealing to the theory of monotone semiflows and the finite delay approximations then the global stability of such traveling waves is obtained via a squeezing technique and a dynamical systems approach

convergence analysis of self adaptive equalizers a theoretical analysis of self adaptive equalization for data transmission is carried out starting from known convergence results for the corresponding trained adaptive filter the development relies on a suitable ergodicity model for the sequence of observations at the output of the transmission channel thanks to the boundedness of the decision function used for data recovery it can be proved that the algorithm is bounded strong convergence results can be reached when a perfect noiseless equalizer exists the algorithm will converge to it if the eye pattern is initially open otherwise convergence may take place towards certain other stationary points of the algorithm for which domains of attraction have been defined some of them will result in a poor error rate the case of a noisy channel exhibits limit points for the algorithm that differ from those of the classical trained algorithm the stronger the noise the greater the difference is one of the principal results of this study is the proof of the stability of the usual decision feedback algorithms once the learning period is over

wavefronts and global stability in a time delayed population model with stage structure we formulate and study a one dimensional single species diffusive delay population model the time delay is the time taken from birth to maturity without diffusion the delay differential model extends the well known logistic differential equation by allowing delayed constant birth processes and instantaneous quadratically regulated death processes this delayed model is known to have simple global dynamics similar to that of the logistic equation through the use of a sub supersolution pair method we show that the diffusive delay model continues to generate simple global dynamics this has the important biological implication that quadratically regulated death processes dramatically simplify the growth dynamics we also consider the possibility of travelling wavefront solutions of the scalar equation for the mature population connecting the zero solution of that equation with the positive steady state our main finding here is that our fronts appear to be all monotone regardless of the size of the delay this is in sharp contrast to the frequently reported findings that delay causes a loss of monotonicity with the front developing a prominent hump in some other delay models

reaction diffusion systems with time delays monotonicity invariance comparison and convergence in a recent paper we have obtained differential inequality results developed comparison theorems and established invariance criteria for mild solutions of abstract functional differential equations in a banach space the primary application for these results is to reaction diffusion systems in which the reaction nonlinearity contains time delays in the present paper we apply these results to reaction diffusion systems with time delays of the form u t d u f x u t x x u u n 0 x where is a bounded open set in r n with smooth boundary u r n d diag d 1 d n with d i 0

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

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

the optimum combination of block codes and receivers for arbitrary channels a determination is made of the combinations of transmitted block codewords and matching receiver filters that maximize the signal to noise ratio at the detector with arbitrary channel impulse response and arbitrary noise spectrum this permits representing the channel as a set of parallel uncoupled subchannels with uncorrelated noise the representation is used to calculate the capacity of an arbitrary block coded time discrete channel it is shown that substantial coding gains compared to symbol by symbol processing can be achieved the block code used can be concatenated with trellis coded modulation so that the two coding gains are additive

sufficient output conditions for identifiability in blind equalization the problem of input identifiability in blind deconvolution is considered where the input belongs to a known discrete alphabet input identifiability is an algorithm independent property which does not necessarily imply channel identifiability sufficient conditions for input identifiability are derived in terms of algebraic relations on the observed output it is shown how these new results relate to and unify other known sufficient conditions

blind identification of fir systems excited by discrete alphabet inputs an algorithm for the identification of finite impulse response fir system parameters from output measurements for systems excited by discrete alphabet inputs is described the approach taken is algebraic it does not rely directly on the statistical properties of the measurements but rather it essentially solves the nonlinear equations appearing in the problem by converting them to equivalent linear equations using the discrete alphabet property of the input signal the proposed algorithm was tested by computer simulations and some of these simulations are illustrated

finite alphabet source recovery in polynomial systems consider a parameterised system whose output vector is a polynomial function of the elements of both the source vector and the parameter vector assume there are only a finite number of possible source vectors source recovery endeavours to determine the source vector given only the output vector and in particular without knowledge of the parameter vector this paper after proving both the decidability and implementability of source recovery focuses on the task of deriving necessary and sufficient conditions for source recovery to be feasible although it is difficult to derive a condition which is readily verifiable for most systems this paper derives a relatively simple condition for source recovery to be feasible in bilinear and other affine in parameter systems an application of this result to wireless communications is given it is proved that guard intervals in transmission systems enable the receiver to recover the source symbols using only a single received block and without knowledge of the channel parameters

stability of planar waves in a lotka volterra system this paper is concerned with the large time behavior of disturbed planar fronts in the lotka volterra system in r n n 2 we first show that the large time behavior of the disturbed fronts can be approximated by that of the mean curvature flow with a drift term for all large time up to t and then we prove that the planar front is asymptotically stable in l r n under ergodic perturbations which include quasi periodic and almost periodic ones as special cases

the multitone channel the maximum bit rate of multitone qam quadrature amplitude modulation over a general linear channel is found first the overall bit rate for an awgn channel with a two level transfer function is maximized using a multitone qam system the power distribution between the tones and the number of bits symbol per tone is optimized for a given symbol error rate extending these results to the general channel it is shown that the optimum power division for multitone signals is similar to the water pouring solution of information theory furthermore multitone qam performance is about 9 db worse than the channel capacity independent of the channel characteristics the multitone results throughout are compared to those of an equivalent single tone linearly equalized system the comparison shows that the multitone system is useful for some channels e g those with deep nulls in the transfer function the maximum bit error rate over a twisted pair channel which is performance dominated by near end crosstalk next is also found

blind equalization by direct examination of the input sequences this paper presents a novel approach to blind equalization deconvolution which is based on direct examination of possible input sequences in contrast to many other approaches it does not rely on a model of the approximative inverse of the channel dynamics to start with the blind equalization identifiability problem for a noise free finite impulse response channel model is investigated a necessary condition for the input which is algorithm independent for blind deconvolution is derived this condition is expressed in an information measure of the input sequence a sufficient condition for identifiability is also inferred which imposes a constraint on the true channel dynamics the analysis motivates a recursive algorithm where all permissible input sequences are examined the exact solution is guaranteed to be found as soon as it is possible an upper bound on the computational complexity of the algorithm is given this algorithm is then generalized to cope with time varying infinite impulse response channel models with additive noise the estimated sequence is an arbitrary good approximation of the maximum a posteriori estimate the proposed method is evaluated on a rayleigh fading communication channel the simulation results indicate fast convergence properties and good tracking abilities

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

persistence of wavefronts in delayed nonlocal reaction diffusion equations we develop a perturbation argument based on existing results on asymptotic autonomous systems and the fredholm alternative theory that yields the persistence of traveling wavefronts for reaction diffusion equations with nonlocal and delayed nonlinearities when the time lag is relatively small this persistence result holds when the nonlinearity of the corresponding ordinary reaction diffusion system is either monostable or bistable we then illustrate this general result using five different models from population biology epidemiology and bio reactors

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

dynamical analysis of a logistic equation with spatio temporal delay this paper is concerned with a logistic equation with spatio temporal delay the local asymptotic behavior of positive constant steady state solution of the equation is considered in particular by using the iterative technique sufficient conditions are established for the existence of traveling wave front solution connecting the zero and the positive constant steady state solution finally numerical simulations supporting the theoretical analysis are also included

combined coding and training for unknown isi channels the traditional method of sending a training signal to identify a channel followed by data may be viewed as a simple code for the unknown channel results in blind sequence detection suggest that performance similar to this traditional approach can be obtained without training however for short packets and or time recursive algorithms significant error floors exist due to the presence of sequences that are indistinguishable without knowledge of the channel in this paper we reconsider training signal design in light of recent results in blind sequence detection specifically we consider the tradeoff between the complexity of receiver processing and the amount of training overhead required more generally we design training codes which combine modulation and training in order to design these codes we find an expression for the pairwise error probability of the joint maximum likelihood jml channel and sequence estimator this expression motivates a pairwise distance for the jml receiver based on principal angles between the range spaces of data matrices the general code design problem generalized sphere packing is formulated as the clique problem associated with an unweighted undirected graph we provide optimal and heuristic algorithms for this clique problem for both long and short packets we demonstrate that significant improvements are possible by jointly considering the design of the training modulation and receiver processing

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

totally blind channel identification by exploiting guard intervals blind identification techniques estimate the impulse response of a channel by exploiting known finite alphabet or statistical properties of the transmitted symbols alternatively oversampling the output is known to introduce dependencies also exploitable for channel identification this paper proves the feasibility of estimating the channel by relying instead on the short sequences of zeros known as guard intervals or zero padding introduced between transmitted blocks by a number of communication protocols since no property of the transmitted information symbols is assumed the method is called totally blind channel identification it is proved that totally blind channel identification requires only two received blocks to estimate the channel

an efficient computational algorithm for min max operations abstract this paper describes an efficient computational algorithm for evaluating min max operations and the derivatives of min max functions which are common computation problems in the training of many types of fuzzy neural networks analysis and simulation are used to assess the efficiency of the computational algorithm developed in this paper

on the algebraic identifiability of finite impulse response channels driven by linearly precoded signals it is common in wireless communications to perform some form of linear precodingoperation on the source signal prior to transmission over a channel although the traditional reason for precoding is to improve the performance of the communication system this paper draws attention to the fact that the receiver can identify the impulse response of the channel without any prior knowledge of the transmitted signal simply by solving a system of polynomial equations since different precoders lead to different systems of equations this paper addresses the fundamental issue of determiningwhich classes of linear precoders lead to a system of equations havinga unique solution in doingso basic properties of polynomial equations which are useful for studyingother identifiability issues commonly encountered in eng ineeringand the applied sciences are presented 2004 elsevier b v all rights reserved

approximation by max min operators a general theory and its applications abstract in this study we obtain a general approximation theorem for max min operators including many significant applications we also study the error estimation in this approximation by using holder continuous functions the main motivation for this work is the paper by bede et al 2008 12 as a special case of our results we explain how to approximate nonnegative continuous functions of one and two variables by means of the max min shepard operators we also study the approximation by the max min bernstein operators furthermore to verify the theory we display graphical illustrations

multidimensional signal sets through the shell construction for parallel channels the authors derive a procedure to send r bits on m parallel channels a decomposition of the best constellation in z sup m 1 2 1 2 is given in terms of the cross products of lower dimensional shells of points the proposed scheme can be used with good known coset codes to provide an alternate method of coded modulation the results indicate that one can get good shaping gains for low encoder complexity the method is also generalized for channels with unequal gains the authors also find a significant performance advantage at fixed shaping gain in certain cases with respect to the recent voronoi constellations in terms of peak to average power and constellation expansion

periodic solutions of a neutral impulsive predator prey model with beddington deangelis functional response with delays in this paper we consider a neutral predator prey model with the beddington deangelis functional response and impulsive effect sufficient conditions are obtained for the existence of positive periodic solutions by a systematic qualitative analysis some known results in the literature are generalized

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

baseband trellis codes with a spectral null at zero a method is described for modifying classical n dimensional trellis codes to provide baseband codes that combine a spectral null at dc with significant coding gain the information rate of the classical code is decreased by one bit and this extra redundancy is used to keep the running digital sum bounded equivalently if the rate is held constant then twice as many signal points are needed causing a power penalty of 6 n db baseband trellis codes are presented for several information rates together with complete spectral plots and performance comparisons a method of constructing baseband codes with multiple spectral nulls is also described

discrete multiple tone modulation with coset coding for the spectrally shaped channel a discrete approach to multiple tone modulation is developed for digital communication channels with arbitrary intersymbol interference isi and additive gaussian noise multiple tone modulation is achieved through the concatenation of a finite block length modulator based on discrete fourier transform dft code vectors and high gain coset or trellis codes symbol blocks from an inverse dft idft are cyclically extended to generate isi free channel output symbols that decompose the channel into a group of orthogonal and independent parallel subchannels asymptotic performance of this system is derived and examples of asymptotic and finite block length coding gain performance for several channels are evaluated at different values of bits per sample this discrete multiple tone technique is linear in both the modulation and the demodulation and is free from the effects of error propagation that often afflict systems employing bandwidth optimized decision feedback plus coset codes

the max product generalized sampling operators convergence and quantitative estimates abstract in this paper we study the max product version of the generalized sampling operators based upon a general kernel function in particular we prove pointwise and uniform convergence for the above operators together with a certain quantitative jackson type estimate based on the first order modulus of continuity of the function being approximated the proof of the proposed results are based on the definition of the so called generalized absolute moments by the proposed approach the achieved approximation results can be applied for several type of kernels not necessarily duration limited such as the sinc function the fejer kernel and many others examples of kernels with compact support for which the above theory holds can be given for example by the well known central b splines

vector coding for partial response channels a linear technique for combining equalization and coset codes on partial response channels with additive white gaussian noise is developed the technique vector coding uses a set of transmit filters or vectors to partition the channel into an independent set of parallel intersymbol interference isi free channels for any given finite or infinite block length the optimal transmit vectors for such channel partitioning are shown to be the eigenvectors of the channel covariance matrix for the specified block length and the gains of the individual channels are the eigenvalues an optimal bit allocation and energy distribution are derived for the set of parallel channels under an accurate extension of the continuous approximation for power in optimal multidimensional signal sets for constellations with unequal signal spacing in different dimensions examples are presented that demonstrate performance advantages with respect to zero forcing decision feedback methods that use the same coset code on the same partial response channel only resampling the channel at an optimal rate and assuming no errors in the feedback path will bring the performance of the decision feedback methods up to the level of the vector coded system

spatial structures and periodic travelling waves in an integro differential reaction diffusion population model an integro differential reaction diffusion equation is proposed as a model for populations where local aggregation is advantageous but intraspecific competition increases as global populations increase it is claimed that this is inherently more realistic than the usual kind of reaction diffusion model for mobile populations three kinds of bifurcation from the uniform steady state solution are considered i to steady spatially periodic structures ii to periodic standing wave solutions and iii to periodic travelling wave solutions these correspond to aggregation and motion of populations

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

new trellis codes based on lattices and cosets a new technique is proposed for constructing trellis codes which provides an alternative to ungerboeck s method of set partitioning the new codes use a signal constellation consisting of points from an n dimensional lattice lambda with an equal number of points from each coset of a sublattice lambda one part of the input stream drives a generalized convolutional code whose outputs are cosets of lambda while the other part selects points from these cosets several of the new codes are better than those previously known

traveling wave fronts for generalized fisher equations with spatio temporal delays we study the existence of traveling wave fronts for a reaction diffusion equation with spatio temporal delays and small parameters the equation reduces to a generalized fisher equation if small parameters are zero we present two results in the first one we deal with the equation with very general kernels and show the persistence of fisher wave fronts for all sufficiently small parameters in the second one we deal with some particular kernels with which the nonlocal equation can be reduced to a system of singularly perturbed odes and we are then able to apply the geometric singular perturbation theory and phase plane arguments to this system to show the existence of the minimal wave speed the existence of a continuum of wave fronts and the global uniqueness of the physical wave front with each wave speed

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

existence and stability of time periodic traveling waves for a periodic bistable lotka volterra competition system abstract this paper is concerned with the time periodic lotka volterra competition diffusion system u t d 1 t u x x u r 1 t a 1 t u b 1 t v v t d 2 t v x x v r 2 t a 2 t u b 2 t v x r t 0 where d i t r i t a i t b i t c 2 r are t periodic functions 0 1 i 1 2 under certain conditions the system admits two stable semi trivial periodic solutions p t 0 and 0 q t and a unique coexistence periodic solution u 0 t v 0 t which is unstable and satisfies 0 u 0 t p t and 0 v 0 t q t for t 0 t in this paper we prove that the system admits a time periodic traveling wave solution u x t v x t u x c t t v x c t t connecting two periodic solutions p t 0 and 0 q t as x where c is the wave speed by using a dynamical method we show that the time periodic traveling wave solution u x c t t v x c t t is asymptotically stable and unique modulo translation for front like initial values

approximation of fuzzy numbers by max product bernstein operators in this paper firstly we extend to an arbitrary compact interval the definition of the nonlinear bernstein operators of max product kind by proving that their order of uniform approximation is the same as in the particular case of the unit interval then similarly to the particular case of the unit interval we will prove that these operators preserve the quasi concavity too since these properties will help us to generate in a simple way fuzzy numbers of the same support it turns out that these results are very suitable in the approximation of fuzzy numbers moreover these operators approximate the non degenerate segment core with a good order of approximation in addition in the case when the fuzzy numbers are given in parametric form the bernstein max product operator generates a sequence of fuzzy numbers whose widths expected intervals ambiguities and values approximate with a convergent rate the width the expected interval the ambiguity and the value of the approximated fuzzy number finally we obtain a quantitative approximation with respect to a well known integral type metric for some subclasses of functions leading to applications to the approximation of some subclasses of fuzzy numbers

traveling curved fronts of bistable lotka volterra competition diffusion systems in r 3 this paper is concerned with the existence and other qualitative properties of three dimensional traveling curved fronts for bistable lotka volterra competition diffusion systems in r 3 it is first shown that there exists a traveling front of convex polyhedral shape to such systems which is asymptotically stable then by taking the limits of such solutions as lateral surfaces go to infinity one proves the existence as well as the uniqueness of a three dimensional traveling curved front for any given g c s 1 with min 0 2 g 0