persistence and extinction in stochastic delay logistic equation by incorporating ornstein uhlenbeck process abstract the persistence and extinction pe are interesting topics in mathematics this research analyzed pe of stochastic logistic equations sle by incorporating the ornstein uhlenbeck process slop and stochastic delay logistic equation sdle by incorporating the ornstein uhlenbeck process sldop firstly we proved that slop and sldop have positive solutions likewise for stochastic permanence sp weak persistence in the mean wpm non persistence in the mean npm and extinction the sufficient conditions are established for slop and sldop subsequently for numerical simulation we used 4 stage stochastic runge kutta srk4 to illustrate the effectiveness of the results

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

unified and extended form of three types of splines the three types refer to polynomial trigonometric and hyperbolic splines in this paper we unify and extend them by a new kind of spline ue spline for short defined over the space cos wt sin wt 1 t t l where l is an arbitrary nonnegative integer w is a frequency sequence w i a i a i r existing splines such as usual polynomial b splines cb splines hb splines nuat splines ah splines fb splines and the third form fb splines etc are all special cases of ue splines ue splines inherit most properties of usual polynomial b splines and enjoy some other advantageous properties for modelling they can exactly represent classical conics the catenary the helix and even the eight curve a kind of snake like curves etc

gb splines of arbitrary order explicit formulae and recurrence relations for the calculation of generalized b splines gb splines of arbitrary order are given we derive main properties of gb splines and their series i e partition of unity shape preserving properties invariance with respect to ane transformations etc it is shown that such splines have the variation diminishing property and are chebyshevian splines c 1999 elsevier science b v all rights reserved

fitting scattered data on spherelike surfaces using tensor products of trigonometric and polynomial splines a method is presented for fitting a function defined on a general smooth spherelike surfaces given measurements on the function at a set of scattered points lying ons the approximating surface is constructed by mapping the surface onto a rectangle and using a tensor product of polynomial splines with periodic trigonometric splines the use of trigonometric splines allows a convenient solution of the problem of assuring that the resulting surface is continuous and has continuous tangent planes at all points ons two alternative algorithms for computing the coefficients of the tensor fit are presented one based on global least squares and the other on the use of local quasi interpolators the approximation order of the method is established and the numerical performance of the two algorithms is compared

primary decomposition of zero dimensional ideals over finite fields gao shuhong clemson univ dept math sci clemson sc 29634 usa wan daqing univ calif irvine dept math irvine ca 92697 usa wang mingsheng acad sinica inst software informat secur lab beijing 100080 peoples r china

factoring polynomials over finite fields using differential equations and normal bases the deterministic factorization algorithm for polynomials over finite fields that was recently introduced by the author is based on a new type of linearization of the factorization problem the main ingredients are differential equations in rational function fields and normal bases of field extensions for finite fields of characteristic 2 it is known that this algorithm has several advantages over the classical berlekamp algorithm we develop the algorithm in a general framework and we show that it is feasible for arbitrary finite fields in the sense that the linearization can be achieved in polynomial time

a new tension b spline method for third order self adjoint singularly perturbed boundary value problems abstract the aim of this paper is to present a new kind of tension b spline called hyperbolic trigonometric tension b spline of order n which is generated over the space span sin t cos t sinh t cosh t 1 t t n 5 n 5 where is tension parameter this kind of b spline has most properties of usual polynomial b splines and enjoys some other advantageous properties as well also hyperbolic trigonometric tension b spline method is applied for solving self adjoint singularly perturbed problems we use some numerical examples to illustrate the accuracy and implementation of the method

permanence of hybrid competitive lotka volterra system with levy noise abstract this paper concerns stochastic permanence of a hybrid competitive lotka volterra system with levy noise sufficient conditions of stochastic permanence are obtained by combining stochastic analytical techniques with m matrix analysis

analysis of a stochastic logistic model with diffusion stochastic logistic model with diffusion and levy jumps is proposed critical value between stability and extinction for species in each patch is obtained critical value has a close relationship with levy jumps numerical simulations are introduced to validate the results taking both white noise and levy jump noise into account a stochastic logistic model with diffusion is proposed and considered under some simple assumptions the almost complete parameters analysis of the model is carried out in each case it is shown that the population in each patch is either stable in time average or extinct depending on the parameters of the model especially depending on the intensity of the levy jump noise some simulation figures are introduced to validate the theoretical results

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

sharp precision in hensel lifting for bivariate polynomial factorization popularized by zassenhaus in the seventies several algorithms for factoring polynomials use a so called lifting and recombination scheme concerning bivariate polynomials we present a new algorithm for the recombination stage that requires a lifting up to precision twice the total degree of the polynomial to be factored its cost is dominated by the computation of reduced echelon solution bases of linear systems we show that our bound on precision is asymptotically optimal

the asymptotic solution of a class of third order boundary value problems arising in the theory of thin film flows this paper studies boundary and interior layer phenomena exhibited by solutions of certain singularly perturbed third order boundary value problems which govern the motion of thin liquid films subject to viscous capillary and gravitational forces precise conditions specifying where and when the third order derivative terms in the differential equations can be neglected are derived and improved estimates for the actual solutions in terms of solutions of the lower order models are constructed the paper also contains a technique for replacing a third order problem with an asymptotically equivalent second order one that may have wider applicability

overlapping schwarz methods for isogeometric analysis based on generalized b splines abstract generalized b splines gb splines are a special class of tchebycheff b splines that are smooth piecewise function with sections in more general spaces gb splines allow for an exact representation of conic sections as well as transcendental curves and thus they become very attractive for geometrical modeling and numerical simulation in this paper we present overlapping schwarz preconditioners for elliptic problems discretized with isogeometric analysis based on gb splines an h analysis of the proposed preconditioners shows an optimal convergence rate bound that is scalable in the number of subdomains and that is linear in the ratio between subdomain and overlap sizes numerical results in two and three dimensional tests confirm this analysis and also illustrate the good convergence properties of the preconditioner with respect to the discretization parameters the domain deformation and the jumping coefficients

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

mathematical models of population interactions with dispersal ii differential survival in a change of habitat abstract the paper considers a model of dispersing populations in the form of a system of nonlinear ordinary differential equations dispersal pressure is density dependent and a parameter measures the barrier strength the model also incorporates a transition probability to allow for a risk in changing habitats for the two dimensional case the region in parameter space for existence of a stable equilibrium solution is exactly determined bounded in part by a branch of a hyperbola for the n dimensional case similar but less complete results are obtained

stochastic population dynamics driven by levy noise abstract this paper considers stochastic population dynamics driven by levy noise the contributions of this paper lie in that a using the khasminskii mao theorem we show that the stochastic differential equation associated with our model has a unique global positive solution b applying an exponential martingale inequality with jumps we discuss the asymptotic pathwise estimation of such a model

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

permanence and asymptotic behaviors of stochastic predator prey system with markovian switching and levy noise abstract this paper concerns the dynamics of a stochastic predator prey system with markovian switching and levy noise first the existence and uniqueness of global positive solution to the system is proved then by combining stochastic analytical techniques with m matrix analysis sufficient conditions of stochastic permanence and extinction are obtained furthermore for the stochastic permanence case by means of four constants related to the stationary probability distribution of the markov chain and the parameters of the subsystems both the superior limit and the inferior limit of the average in time of the sample path of the solution are estimated finally our conclusions are illustrated through an example

quintic b spline method for solving second order linear and nonlinear singularly perturbed two point boundary value problems in this paper we have studied a numerical scheme to solve second order singularly perturbed two point linear and nonlinear boundary value problems the boundary layer of this type of problems exhibits at one end left or right point of the domain due to the presence of perturbation parameter the quintic b spline method and suitable piecewise uniform shishkin mesh have been used linear and nonlinear second order singularly perturbed boundary value problems have been solved by the present method the convergence analysis is also provided and the method is shown to have uniform convergence of fourth order numerical results have demonstrated the efficiency of the present method

factoring multivariate polynomials via partial differential equations a new method is presented for factorization of bivariate polynomials over any field of characteristic zero or of relatively large characteristic it is based on a simple partial differential equation that gives a system of linear equations as in berlekamp s and niederreiter s algorithms for factoring univariate polynomials the dimension of the solution space of the linear system is equal to the number of absolutely irreducible factors of the polynomial to be factored and any basis for the solution space gives a complete factorization by computing gcd s and by factoring univariate polynomials over the ground field the new method finds absolute and rational factorizations simultaneously and is easy to implement for finite fields local fields number fields and the complex number field the theory of the new method allows an effective hilbert irreducibility theorem thus an efficient reduction of polynomials from multivariate to bivariate

stochastic population dynamics under regime switching ii this is a continuation of our paper q luo x mao stochastic population dynamics under regime switching j math anal appl 334 2007 69 84 on stochastic population dynamics under regime switching in this paper we still take both white and color environmental noise into account we show that a sufficient large white noise may make the underlying population extinct while for a relatively small noise we give both asymptotically upper and lower bound for the underlying population in some special but important situations we precisely describe the limit of the average in time of the population

direct methods for primary decomposition leti be an ideal in a polynomial ring over a perfect field we given new methods for computing the equidimensional parts and radical ofi for localizingi with respect to another ideal and thus for finding the primary decomposition ofi our methods rest on modern ideas from commutative algebra and are direct in the sense that they avoid the generic projections used by hermann 1926 and all others until now

dynamics of a leslie gower holling type ii predator prey system with levy jumps abstract this paper is concerned with a stochastic predator prey system with modified leslie gower and holling type ii schemes with levy jumps first we prove there is a unique positive solution to the system with a positive initial value then we establish the sufficient conditions for stability in mean and extinction of the system finally we introduce some numerical simulations to support the main results the results shows that the levy jumps can change the properties of the population systems significantly

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

analysis on stochastic delay lotka volterra systems driven by levy noise abstract in this paper two types of stochastic lotka volterra systems i e competition system and predator prey system with time delays and levy noise are discussed for each model we establish sufficient and necessary criteria for stability in time average and extinction of each population the thresholds between stability in time average and extinction of each model are obtained some recent results are improved and extended significantly these results point out that i time delays are harmless for stability in time average and extinction of our model ii both stability in time average and extinction have close relationships with levy noise iii the interaction rates play significant roles in determining the stability in time average and extinction of the populations

dynamics of a stochastic one prey two predator model with levy jumps levy noise of one species increases extinction risk of this species and its predator levy noise of one species has no impact on the extinction or not of its prey in some cases levy noises do not effect the stability in distribution of the model this paper is concerned with a one prey two predator model with both white noises and levy noises we first carry out the almost complete parameters analysis for the model in each case we show that each species is either persistent in the mean or extinct depending on some critical values then we establish the sufficient criteria for stability in distribution of the model finally we use some numerical examples to demonstrate the analytical findings

the existence of periodic solutions for discrete time coupled systems on networks with time varying delay abstract this paper deals with the existence of periodic solutions for discrete time coupled systems on networks with time varying delay dcsntd based on coincidence degree theory graph theory and lyapunov method a systematic method is given to study the existence of periodic solutions for dcsntd a lyapunov type theorem and a coefficient type criterion are derived respectively furthermore we apply this novel approach to research the existence of periodic solutions for discrete time coupled oscillators with time varying delay finally a numerical simulation is presented to illustrate the effectiveness and feasibility of our results

singular perturbations of boundary value problems for a class of third order nonlinear ordinary differential equations abstract this article shows the existence uniqueness and asymptotic estimates of solutions of the singularly perturbed boundary value problems for a class of the third order nonlinear ordinary differential equations with a small parameter e 0 ey x y y e satisfying the condition y 0 0 y 1 0 y 1 0 or y 0 0 y 1 0 y 1 0

a remark on stochastic logistic model with diffusion stochastic logistic system with diffusion is proposed and studied almost sufficient and necessary conditions for stability in time average and extinction are established some numerical examples are introduced to support the main results

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