solving boundary value problems for delay differential equations by a fixed point method a general linear boundary value problem for a nonlinear system of delay differential equations dde in short is reduced to a fixed point problem v a v with a properly chosen generally nonlinear operator a the unknown fixed point v is approximated by piecewise linear function v h defined by its values v i v h t i at grid points t i i 0 1 n where n is a given positive integer and h max 1 i n t i t i 1 under suitable assumptions the existence of a fixed point of a is equivalent to existence of so called e h approximate fixed points of v h a v h which can be found by minimization of l 2 n norm of residuum v h a v h with respect to the variables v i these e h approximate fixed points are used for obtaining approximate solutions of the original boundary value problem for a system of dde numerical experiments with the boundary value problem for a system of delay differential equations of population dynamics as well as with two periodic boundary value problems one for the periodic distributed delay lotka volterra competition system and the second one modeling two coupled identical neurons with time delayed connections show an efficiency of this kind of approach

on a mutualism model with feedback controls we propose and study a mutualism model with feedback controls by applying a new differential inequality we show that the conditions which ensure the permanence of the system are the same as that of the model without feedback controls which means that the feedback control variables have no influence on the persistent property of the system our results not only improve but also complement some existing ones

permanence and extinction in nonlinear single and multiple species system with diffusion in this paper we consider the effect of diffusion on the permanence and extinction of single and multiple endangered species that live in changing patch environments average conditions are obtained for the permanence and extinction of the systems considered the results obtained in this paper generalize the main results of cui and chen the effect of diffusion on the time varying logistic population growth comput math appl 36 3 1998 1 9 permanence and extinction in logistic and lotka volterra systems with diffusion j math anal appl 258 2 2001 512 535

generalized tate curve and integral teichmuller modular forms in this paper we establish a higher genus version of the tate elliptic curve i e for a given degenerate curve we construct its universal deformation defined over the ring of formal power series of certain deformation parameters whose coefficients are in a finitely generated z algebra described by the dual graph of the degenerate curve further we study automorphic forms on the moduli space of algebraic curves which we call teichmuller modular forms by evaluating these forms on the generalized tate curve in particular we show that integral teichmuller modular forms of given degree make a finitely generated ring and we describe the structure of this ring in degree 2 and 3 cases introduction the aim of this paper is to construct a higher genus version of the tate elliptic curve over a nonlocal base ring and to study integral automor phic forms on the moduli space of algebraic curves of genus 2 by evaluating these forms on the generalized tate curve as will be stated below our results extend earlier results of the author in 10 11 12 14 and are obtained especially by using excellent works of mumford faltings and chai 22 21 3 4 the periods and 1 forms of the generalized tate curve were used in 13 to construct universal and p adic solutions of the kp kadomtsev petvyashvili hierarchy in 10 section 2 the author obtained universal power series for multiplica tive periods of curves of fixed genus g which combined with the results of 21 and 4 chapter iii allowed us to deduce the existence of a universal jacobian semi abelian scheme j univ of relative dimension g over the ring

global attractivity of positive periodic solution to periodic lotka volterra competition systems with pure delay abstract we consider a periodic lotka volterra competition system without instantaneous negative feedbacks i e pure delay systems x i t x i t r i t j 1 n a i j t x j t i j t i 1 2 n we establish some 3 2 type criteria for global attractivity of a positive periodic solution of the system which generalize the well known wright s 3 2 criteria for the autonomous delay logistic equation and thereby address the open problem proposed by both kuang y kuang global stability in delayed nonautonomous lotka volterra type systems without saturated equilibria differential integral equations 9 1996 557 567 and teng z teng nonautonomous lotka volterra systems with delays j differential equations 179 2002 538 561

conditions for global attractivity of n patches predator prey dispersion delay models abstract in this paper a nonautonomous predator prey dispersion model with functional response and continuous time delay is studied where all parameters are time dependent in this system which consists of n patches the prey species can disperse among n patches but the predator species is confined to one patch and cannot disperse it is proved the system is uniformly persistent under any dispersion rate effect furthermore the sufficient conditions are established for global attractivity of a periodic solution of the system

periodic solution and global stability for a nonautonomous competitive lotka volterra diffusion system the periodic solution and global stability for a nonautonomous competitive lotka volterra diffusion system is considered in this paper by using of brouwer fixed point theorem and constructing a suitable liapunov function under some appropriate conditions the system has a unique periodic solution which is globally stable

limits of galois representations in fundamental groups along maximal degeneration of marked curves i we study gal inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i actions on the fundamental groups arising in deformation of maximally degenerate marked curves and give explicit descriptions of them in terms of the principal parameters of the grothendieck teichmuller group inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 02i as a special application we present galois theoretic connections between the moduli spaces m 0 4 m 0 5 m 1 1 and m 1 2 which lead to a newtype equation satisfied by the image of gal inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 03i

periodic solutions of a predator prey system with stage structures for predator and prey abstract by using the continuation theorem of coincidence degree theory the existence of a positive periodic solution for the predator prey system with stage structures for predator and prey is established

biochemical chiral selection in the presence of instabilities chaos and noise a mathematical model is constructed to illustrate that an arbitrarily small difference in the rate constants for parallel autocatalytic reactions involving l and d isomers is sufficient to cause chiral selection in biochemical evolution it is shown that the selection is not suppressed by instabilities leading to chaos or heavy external noise

periodic solutions of abstract functional differential equations with infinite delay abstract we characterize the existence of periodic solutions for a class of abstract retarded functional differential equations with infinite delay we apply our results to the nonlinear equation x t a x t l x t n x t f t t r where a d a x x is a closed operator defined on a banach space x l is a bounded linear map n b x is a continuous function defined on an appropriate phase space b and f l p t x

almost periodic weak solutions of neutral delay differential equations with piecewise constant argument abstract in this paper we give some theorems on the almost periodic weak solutions of second order neutral delay differential equations with piecewise constant argument of the form x t px t 1 qx 2 t 1 2 f t where denotes the greatest integer function p q are nonzero constants and f t is almost periodic

stable periodic solution of a discrete periodic lotka volterra competition system abstract this paper discusses a discrete lotka volterra competition system we first obtain the persistence of the system assuming that the coefficients in the system are periodic we obtain the existence of a periodic solution moreover under some additional conditions this periodic solution is globally stable our results not only reduce to those for the scalar equation when there is no coupling but also improve and complement some in the literature

global attractivity of a positive periodic solution for a nonautonomous stage structured population dynamics with time delay and diffusion by employing the continuation theorem of coincidence degree theory the existence of a positive periodic solution for a nonautonomous stage structured population dynamics with time delay and diffusion is established further by constructing a lyapunov functional and using the result of the existence of positive periodic solution the attractivity of a positive periodic solution for above system is obtained

teichmuller groupoids and monodromy in conformal field theory we study monodromy representations of the teichmuller groupoid for the moduli space of pointed compact riemann surfaces of any genus with first order infinitesimal structure to calculate these representations using arithmetic schottky mumford uniformization theory we construct a real orbifold in the moduli space consisting of fusing and simple moves which gives tangential base points for a certain vector bundle on the moduli space with projectively flat connection we show that the monodromy of each fusing move can be expressed as a connection matrix and give the relations to the monodromy of simple moves furthermore we describe the monodromy representation associated with tsuchiya ueno yamada s conformal field theory and show that this representation can be expressed as the monodromy of the wess zumino witten model

harmless delays for uniform persistence abstract this paper studies a two dimensional predator prey system with a finite number of discrete delays our purpose is to demonstrate that the time delays are harmless for uniform persistence of the solutions of the system the results are obtained by constructing suitable persistence functionals

permanence and global attractivity of a discrete multispecies lotka volterra competition predator prey systems in this paper we propose a discrete multispecies lotka volterra competition predator prey systems for general non autonomous case sufficient conditions which ensure the permanence and the global stability of the system are obtained for periodic case sufficient conditions which ensure the existence of a globally stable positive periodic solution of the system are obtained

environmental noise impact on regularity and extinction of population systems with infinite delay abstract populations of biological species are often subject to different types of environmental noises these noises play crucial roles and have significant impact on the evolution and biodiversity to understand the effects of different types of noises on the asymptotic properties of the populations this paper reveals the influence of inherent net birth noise and the interaction noise among stochastically perturbed population systems by considering systems with infinite delays 1 this paper discovers that a the interaction noise may suppress the potential explosion and guarantee the existence of the global solution which yields regularity of the stochastic system and b the inherent net birth noise may lead to extinction of the populations 2 this paper provides sufficient conditions that ensure the stochastic persistence stochastic boundedness and asymptotic polynomial growth of the population system 3 this paper demonstrates that these asymptotic properties are completely determined by stochastic noises and are independent of other parameters

existence of positive periodic solutions for neutral population model with multiple delays in this paper the authors employ an abstract continuous theorem of k set contractive operator and some analysis techniques to study the existence of positive periodic solutions for a neutral delay population model with multiple delays as followsdndt n t a t b t n t j 1 nb j t n t s i t i 1 mc i t n t t i t a new result on the existence of positive periodic solutions is obtained

some results on second order neutral functional differential equations with infinite distributed delay abstract in this paper we consider two types of second order neutral functional differential equations with infinite distributed delay by choosing available operators and applying krasnoselskii s fixed point theorem we obtain sufficient conditions for the existence of periodic solutions to such equations

vector bundles on a nearly degenerate riemann surface we show that on a riemann surface x close to a maximally degenerate complex curve any semistable vector bundle of degree 0 is associated with a linear representation of the schottky group x uniformizing x further we study the relationship between the representation space of x and the moduli space of semistable bundles on x as a higher rank version of abel jacobi s theorem

quantitative stability for the first dirichlet eigenvalue in reifenberg flat domains in rn abstract in this paper we prove that if and are close enough for the complementary hausdorff distance and their boundaries satisfy some geometrical and topological conditions then 1 1 c n where 1 resp 1 is the first dirichlet eigenvalue of the laplacian in resp and is the lebesgue measure of the symmetric difference here the constant 1 could be taken arbitrary close to 1 but strictly less and c is a constant depending on a lot of parameters including dimension n and some geometric properties of the domains

stochastic lotka volterra population dynamics with infinite delay we discover in this paper that when environmental noise is strongly dependent on the population size this noise may suppress the population explosion in a finite time and guarantee the global positive solution when the environmental noise is weakly dependent on the population size the conditions that guarantee the global positive solution are independent of this environmental noise we also discuss the pth moment boundedness stochastic ultimate boundedness and moment average boundedness in time under two classes of conditions these properties are natural requirements from the biological point of view

positive periodic solutions of periodic neutral lotka volterra system with state dependent delays by using a fixed point theorem of strict set contraction some new criteria are established for the existence of positive periodic solutions of the following periodic neutral lotka volterra system with state dependent delays dxi t dt xi t ri t j 1naij t xj t j 1nbij t xj t ij t x1 t xn t j 1ncij t xj t ij t x1 t xn t i 1 2 n where ri aij bij cij c r r i j 1 2 n are periodic functions and ij ij c rn 1 r i 1 2 n are periodic functions with respect to their first arguments respectively

elliptic equations with bmo nonlinearity in reifenberg domains given p 2 8 we obtain the global w1 p estimate for the weak solution of a boundary value problem for an elliptic equation with bmo nonlinearity in a reifenberg domain assuming that the nonlinearity has sufficiently small bmo seminorm and that the boundary of the domain is sufficiently flat

a composite coincidence degree with applications to boundary value problems of neutral equations we present a topological degree theory for the nonlinear problem l i b x g x with applications to a class of boundary value problems of neutral equations where l is an unbounded fredholm operator of index zero b is condensing and g is l compact

almost periodic solutions of a discrete almost periodic logistic equation with delay abstract in this paper we consider an almost periodic discrete logistic equation with delay by constructing suitable lyapunov functional and almost periodic functional hull theory a sufficient condition is obtained for the existence of a unique almost periodic solution which is globally attractive an example together with its numerical simulation shows the feasibility of our main result

an abstract existence theorem at resonance and its applications abstract by using brouwer degree theory and a continuation theorem based on mawhin s coincidence degree an abstract existence theorem at resonance for operator equations is developed as applications of this result some sufficient conditions are given for the existence of periodic solutions of semilinear equations at resonance where the kernel of the linear part has dimension n n 2 the results due to nagle and sinkala are generalized improved and unified

spectral stability of dirichlet second order uniformly elliptic operators we prove sharp stability results for the dependence of the eigenvalues of second order uniformly elliptic linear operators with homogeneous dirichlet boundary conditions upon domain perturbation

periodic solution for a two species nonautonomous competition lotka volterra patch system with time delay abstract by using the continuation theorem of coincidence degree theory the existence of a positive periodic solution for a two species nonautonomous competition lotka volterra patch system with time delay x 1 t x 1 t r 1 t a 1 t x 1 t b 1 t y t d 1 t x 2 t x 1 t x 2 t x 2 t r 2 t a 2 t x 2 t d 2 t x 1 t x 2 t y t y t r 3 t a 3 t x 1 t b 3 t y t t 0 k s y t s ds is established where ri t ai t i 1 2 3 di t i 1 2 bi t i 1 3 and t are all positive periodic continuous functions with period w 0 is a nonnegative constant and k s is a continuous nonnegative function on 0

on permanence and global stability in a general gilpin ayala competition predator prey discrete system abstract in this paper we propose a discrete multispecies general gilpin ayala competition predator prey model by using new difference inequality and developing the analysis technique of chen and zhou y chen z zhou stable periodic solution of a discrete periodic lotka volterra competition system j math anal appl 277 2003 358 366 sufficient conditions are established for the permanence and the global stability an example shows the feasibility of our results

uniform persistence and periodic solutions for a discrete predator prey system with delays abstract in this paper we deal with a discrete predator prey system with delay we first give a sufficient condition for the uniform persistence of the system assuming that the coefficients in the system are periodic by generalizing the yoshizawa s theorem on the existence of periodic solution for ordinary differential equations to the difference equations with delays we obtain the existence of a periodic solution basing on the uniform persistence result

mapping class group action versus galois action on profinite fundamental groups let x be an algebraic curve of genus g n punctured defined over a number field k then the profinite or the pro l completion of the topological fundamental group of x admits two actions the action of the profinite completion of the mapping class group of the orientable surface of topological type g n and the action of the absolute galois group of k this paper compares these two in the profinite case it is shown that the intersection of the images of these two actions is trivial if x is affine and its fundamental group is nonabelian on the contrary in the pro l case there are many curves such that the image of the galois action contains the image of the mapping class group action it is proved that the set of points corresponding to such curves is dense in the moduli space of g n curves

permanence criteria for general delayed discrete nonautonomous n species kolmogorov systems and its applications in this paper the permanence for the general nonautonomous n species discrete kolmogorov systems with delays is studied by using the method of multiple discrete lyapunov like functionals a quite general sufficient condition is established as application of this result new sufficient conditions are obtained to ensure the permanence of all species for the discrete nonautonomous pure delayed n species lotka volterra competitive systems and food chain systems particularly as special cases a series of new sufficient conditions on the permanence for the discrete nonautonomous pure delayed lotka volterra two species competitive systems predator prey systems and three species food chain systems and the discrete autonomous pure delayed lotka volterra competition systems and food chain systems are obtained

an existence result for a class of shape optimization problems given a bounded open subset of rn we prove the existence of a minimum point for a functional f defined on the family a of all quasiopen subsets of under the assumption that f is decreasing with respect to set inclusion and that f is lower semicontinuous on a with respect to a suitable topology related to the resolvents of the laplace operator with dirichlet boundary condition applications are given to the existence of sets of prescribed volume with minimal kth eigenvalue or with minimal capacity with respect to a given elliptic operator

potential estimates of superquadratic elliptic systems with vmo coefficients in reifenberg domains abstract the purpose of this paper is to study an inhomogeneous dirichlet problem of a superquadratic nonlinear elliptic system with vmo coefficients in reifenberg flat domains we derive pointwise potential estimates for weak solution to the dirichlet problem as a consequence we derive global integrability estimates for solutions with respect to lorentz and morrey norms

global dynamics behaviors for a nonautonomous lotka volterra almost periodic dispersal system with delays abstract a nonautonomous lotka volterra dispersal system with continuous delays and discrete delays is considered by using a comparison theorem and delay differential equation basic theory we obtain sufficient conditions for the permanence of the population in every patch by constructing a suitable lyapunov functional we prove that the system is globally asymptotically stable under some appropriate conditions using almost periodic functional hull theory we get sufficient conditions for the existence uniqueness and globally asymptotical stability for an almost periodic solution this implies that the population in every patch exhibits stable almost periodic fluctuation furthermore the results show that the permanence and global stability of system and the existence and uniqueness of a positive almost periodic solution depend on the delay then we call it profitless

stable periodic solution of a discrete periodic lotka volterra competition system with a feedback control this paper discusses a discrete lotka volterra competition system with feedback controls we first obtain the persistence of the system assuming that the coefficients in the system are periodic we obtain the existence of a periodic solution moreover under some additional conditions this periodic solution is globally stable

the effect of diffusion on the time varying logistic population growth abstract in this paper we consider the effect of diffusion on the species that live in changing patches environment different from the former studies 1 4 we pay attention to the more important situation in conservation biology that species live in a weak patches environment in the sense that species in some of the isolated patches will be extinct without the contribution from other patches we obtain an interesting result the identical species can persist for some diffusion rates and can also vanish for another set of restriction on diffusion rates

permanence for a discrete time lotka volterra type food chain model with delays abstract considered is a delayed discrete time lotka volterra type food chain model sufficient conditions are established for the permanence and the feasibility of the obtained results are illustrated with an example

uniform persistence in functional differential equations abstract in this paper we investigate the question of uniform persistence for retarded functional differential equations by utilizing liapunov like functions razumikhin techniques and differential inequalities we are able to establish criteria for uniform persistence analogous to those obtained by others for ordinary differential equations difference equations and reaction diffusion equations we apply these criteria to some well known biological models with delay our results indicate that the conditions which guarantee the existence of an interior equilibrium are enough to ensure uniform persistence moreover these conditions are equivalent to uniform persistence for the cases without delay as well

periodic solution and almost periodic solution for a nonautonomous lotka volterra dispersal system with infinite delay abstract this paper studies a nonautonomous lotka volterra dispersal systems with infinite time delay which models the diffusion of a single species into n patches by discrete dispersal our results show that the system is uniformly persistent under an appropriate condition the sufficient condition for the global asymptotical stability of the system is also given by using mawhin continuation theorem of coincidence degree we prove that the periodic system has at least one positive periodic solution further obtain the uniqueness and globally asymptotical stability for periodic system by using functional hull theory and directly analyzing the right functional of almost periodic system we show that the almost periodic system has a unique globally asymptotical stable positive almost periodic solution we also show that the delays have very important effects on the dynamic behaviors of the system

permanence and stability of equilibrium for a two prey one predator discrete model in this letter a predator prey system of two prey one predator discrete model is investigated it is proved that the system is permanence under some appropriate conditions by jacobian matrix method a sufficient and necessary condition is derived for the local asymptotic stability of a equilibrium of the system meanwhile we give a suitable example for supporting our theoretical result

spectral stability estimates for the dirichlet and neumann laplacian in rough domains abstract in this paper we establish new quantitative stability estimates with respect to domain perturbations for all the eigenvalues of both the neumann and the dirichlet laplacian our main results follow from an abstract lemma stating that it is actually sufficient to provide an estimate on suitable projection operators whereas this lemma could be applied under different regularity assumptions on the domain here we use it to estimate the spectrum in lipschitz and in so called reifenberg flat domains our argument also relies on suitable extension techniques and on an estimate on the decay of the eigenfunctions at the boundary which could be interpreted as a boundary regularity result

four periodic solutions of a generalized delayed predator prey system by using the continuation theorem of coincidence degree theory the existence conditions of four periodic solutions for the delayed predator prey system is established

almost periodic solutions of single population model with hereditary effects the main purpose of this paper is to show how the coincidence degree theory can be used to obtain almost periodic solutions for single population model with almost periodic coefficients some sufficient conditions are obtained for checking the existence uniqueness and stability of almost periodic solution the analysis generalizes the results corresponding to the periodic case of the single population model

a periodic predator prey chain system with impulsive perturbation a periodic predator prey chain system with impulsive effects is considered by using the global results of rabinowitz and standard techniques of bifurcation theory the existence of its trivial semi trivial and nontrivial positive periodic solutions is obtained it is shown that the nontrivial positive periodic solution for such a system may be bifurcated from an unstable semi trivial periodic solution furthermore the stability of these periodic solutions is studied

on a subgroup of the grothendieck teichmuller group acting on the tower of profinite teichmuller modular groups you may make an article published by springer verlag available on your personal home page provided the source of the published article is cited and springer verlag is mentioned as copyright holder you are requested to create a link to the published article in link springer s internet service the link must be accompanied by the following text the original publication is available on link http link springer de please use the appropriate url and or doi for the article in link articles disseminated via link are indexed abstracted and referenced by many abstracting and information services bibliographic networks subscription agencies library networks and consortia

permanence and extinction analysis for a delayed periodic predator prey system with holling type ii response function and diffusion abstract in this paper it is studied that two species predator prey lotka volterra type dispersal system with delay and holling type ii response function in which the prey species can disperse among n patches while the density independent predator species is confined to one of the patches and cannot disperse sufficient conditions of integrable form for the boundedness permanence extinction and the existence of positive periodic solution are established respectively

permanence for a class of periodic time dependent competitive system with delays and dispersal in a patchy environment in this paper we study m species time delayed competitive lotka volterra type dispersal system with periodic coefficients in n patches by utilizing analytic method sufficient and realistic conditions on permanence and the existence of periodic solution are established the theoretical results are confirmed by a special example and numerical simulations

nonautonomous lotka volterra systems with delays abstract the paper studies the general nonautonomous lotka volterra multispecies systems with finite delays the ultimate boundedness permanence global attractivity and existence and uniqueness of strictly positive solutions positive periodic solutions and almost periodic solutions are obtained these results are basically an extension of the known results for nonautonomous lotka volterra multispecies systems without delay to systems with delay

permanence and extinction in logistic and lotka volterra systems with diffusion abstract in this paper we consider the effect of diffusion on the permanence and extinction of single and multiple endangered species that live in changing patch environments differing from former studies our discussion includes the important situation in conservation biology in which species live in a weak patchy environment in the sense that species will become extinct in some of the isolated patches for the single population model we show that identical species can persist for some diffusion rates and can also vanish for another set of restrictions on the diffusion rates although the single endangered species will vanish in some isolated patches without contributions from other patches furthermore we consider the existence uniqueness and global stability of the positive periodic solution for prey predator systems we can make both the prey and the predator species permanent by choosing the diffusion rates appropriately even if the prey species has a negative intrinsic growth rate in some patches moreover we introduce an exotic competitive species y into the habitat occupied by the native species x competitive permanence and competitive exclusion both are considered the implications of these results are significant for the conservation of endangered species

four positive periodic solutions to two species parasitical system with harvesting terms by using mawhin s continuation theorem of coincidence degree theory we establish the existence of four positive periodic solutions for two species parasitical system with harvesting terms an example is given to illustrate the effectiveness of our results

permanence extinction and balancing survival in nonautonomous lotka volterra system with delays in this paper the periodic n species lotka volterra competition systems with time delays are considered the sufficient conditions are derived for the permanence extinction and balancing survival of the system some known results are improved and unified further our results suggest that under some conditions the introduction and the variance of the time delays will be either harmless or useless conjecture about the effect of time delays on some global behaviors of the system is advanced

asymptotic periodicity for some evolution equations in banach spaces abstract this work deals with the existence and uniqueness of pseudo almost periodic and asymptotically periodic mild solutions to some evolution equations in banach spaces

existence and global attractivity of positive periodic solutions for delay lotka volterra competition patch systems with stocking abstract by means of mawhin s continuation theorem of coincidence degree and lyapunov functional a set of easily verifiable criteria are established for the existence and global attractivity of positive periodic solutions for delay lotka volterra competition patch system with stocking x 1 t h 1 t x 1 t a 1 t b 1 t x 1 t c 1 t y t d 1 t x 2 t 1 x 1 t s 1 t x 2 t h 2 t x 2 t a 2 t b 2 t x 2 t d 2 t x 1 t 2 x 2 t s 2 t y t h 3 t y t a 3 t b 3 t y t t 0 k s y t s ds c 3 t x 1 t s 3 t some known results are generalized and improved

relative pro l completions of mapping class groups abstract fix a prime number l in this paper we develop the theory of relative pro l completion of discrete and profinite groups a natural generalization of the classical notion of pro l completion and show that the pro l completion of the torelli group does not inject into the relative pro l completion of the corresponding mapping class group when the genus is at least 2 see theorem 1 below as an application we prove that when g 2 the action of the pro l completion of the torelli group t g 1 on the pro l fundamental group of a pointed genus g surface is not faithful the choice of a first order deformation of a maximally degenerate stable curve of genus g determines an action of the absolute galois group g q on the relative pro l completion of the corresponding mapping class group we prove that for all g all such representations are unramified at all primes l when the first order deformation is suitably chosen this proof was communicated to us by mochizuki and tamagawa

divergence form operators in reifenberg flat domains we study the boundary regularity of solutions of elliptic operators in divergence form with c 0 coefficients or operators which are small perturbations of the laplacian in non smooth domains we show that as in the case of the laplacian there exists a close relationship between the regularity of the corresponding elliptic measure and the geometry of the domain

poincare inequalities uniform domains and extension properties for newton sobolev functions in metric spaces in the setting of metric measure spaces equipped with a doubling measure supporting a weak p poincare inequality with 1 p 1 we obtain a near characterization of n1 p extension domains with loc

dynamic behaviors of a delay differential equation model of plankton allelopathy in this paper we consider a modified delay differential equation model of the growth of n species of plankton having competitive and allelopathic effects on each other we first obtain the sufficient conditions which guarantee the permanence of the system as a corollary for periodic case we obtain a set of delay dependent condition which ensures the existence of at least one positive periodic solution of the system after that by means of a suitable lyapunov functional sufficient conditions are derived for the global attractivity of the system for the two dimensional case under some suitable assumptions we prove that one of the components will be driven to extinction while the other will stabilize at a certain solution of a logistic equation examples show the feasibility of the main results

global stability of discrete population models with time delays and fluctuating environment the global stability of a discrete population model of volterra type is studied the model incorporates time delays and allows for a fluctuating environment by linearization of the model at positive solutions and construction of liapunov functionals sufficient conditions are obtained to ensure a positive solution of the model is stable and attracts all positive solutions

permanence in kolmogorov type systems of nonautonomous functional differential equations abstract in this paper we establish some general results on the permanence of the n species kolmogorov type nonautonomous functional differential system formula i 1 2 n these results are applied to the n species lotka volterra type systems with distributed delays that is when f i t x t are linear functions of x t our method consists of constructing n liapunov like functions which can be regarded as boundary functions of some compact region inside the positive cone in r n

positive periodic solutions of neutral lotka volterra system with periodic delays in this paper several sufficient conditions are investigated for the existence of positive periodic solutions of a general neutral lotka volterra system with unbounded delays by using the theory of coincidence degree our results extend and improve existing results and have further applications in population dynamics

permanence and global attractivity of the discrete gilpin ayala type population model in this paper we propose a discrete gilpin ayala competition model and a discrete gilpin ayala type multispecies competition predator model for general nonautonomous case sufficient conditions which ensure the permanence and the global stability of the system are obtained for periodic case sufficient conditions which ensure the existence of an unique globally stable positive periodic solution of the system are obtained an example together with its numeric simulations shows the feasibility of the main results

permanence of a discrete n species food chain system with time delays in this paper a discrete n species food chain system with time delays is considered by applying the comparison theorem of difference equation sufficient conditions are obtained for the permanence of the system

a necessary and sufficient condition for permanence of a lotka volterra discrete system with delays abstract in this paper we consider the permanence of the following lotka volterra discrete competition system with delays k1 k2 l1 and l2 x n 1 x n exp r1 1 x n k1 1y n k2 y n 1 y n exp r2 1 2x n l1 y n l2 we show the system is permanent for all nonnegative integers k1 k2 l1 and l2 if and only if 1

some new results of nonautonomous lotka volterra competitive systems with delays abstract in this paper we improve and generalize the results of montes de oca and zeeman j math anal appl 192 1995 360 370 proc amer math soc 124 1996 3677 3687 to general n species nonautonomous lotka volterra type competitive systems with finite or infinite delays we establish a series of criteria under which a part of the n species of the systems is driven to extinction while the remaining part of the n species is persistent or uniformly persistent or coexists globally asymptotically stable

profitless delays for a nonautonomous lotka volterra predator prey almost periodic system with dispersion abstract this paper studies a nonautonomous lotka volterra almost periodic predator prey dispersal system with discrete and continuous time delays which consists of two patches the prey species can disperse among two patches but the predator species is confined to one patch and cannot disperse by using comparison theorem and delay differential equation basic theory we prove the system is uniformly persistent under some appropriate conditions further by constructing suitable lyapunov functional we show that the system is globally asymptotically stable under some appropriate conditions by using a new method and almost periodic functional hull theory we show that the almost periodic system has a unique globally asymptotical stable strictly positive almost periodic solution the conditions for the permanence global stability of system and the existence uniqueness of positive almost periodic solution depend on delays so time delays are profitless finally ecological conclusions and a particular case are given these results are basically an extension of the known results for nonautonomous lotka volterra systems

global stability and asymptotically periodic solution for nonautonomous cooperative lotka volterra diffusion system two asymptotically cooperative lotka volterra populations in the two patch system with diffusion were considered in this paper each population could diffuse independently and discretely between its intrapatch and interpatch by means of constructing a suitable liapunov function we obtained that the systems had a unique asymptotically periodic solution which was globally asymptotically stable