blind image deconvolution through bezoutians in this paper we introduce a fast algorithm for computing the univariate gcd of several polynomials not pairwise based on the generalized bezout matrix by using barnett s method this novel approach is devoted to presenting an algorithm that permits to solve the problem of blind image deconvolution by computing greatest common divisors gcd of several polynomials specifically we design a specialized algorithm for computing the gcd of bivariate polynomials of blurred images which correspond to z transforms to recover the original image all algorithms have been implemented in matlab and experimental results with synthetically blurred images are included to illustrate the effectiveness of our approach

stability of a novel stochastic epidemic model with double epidemic hypothesis abstract in this paper a novel sir disease transmission model is formulated under double epidemic hypothesis and stochastic perturbation we present the stability conditions of the disease free equilibrium of the sir model without stochastic perturbation and with stochastic perturbation we obtain the deterministic stability threshold 1 and 2 of the disease free equilibrium under which the disease free equilibrium is stochastically stable such that the disease will disappear finally leaving all the population susceptible the results show that double epidemic hypothesis and stochastic perturbation have significant effects on the dynamics behaviors of the model

the dynamics of an impulsive delay predator prey model with variable coefficients abstract in this paper we formulate a new robust two species nonautonomous predator prey model with multi delays and impulsive effects and perform a systematic mathematical and ecological study our results in this paper indicate that under the appropriate linear periodic impulsive perturbations the system is permanent and has a unique positive globally attractive semi trivial periodic solution by using the brouwer fixed point theorem we prove that if the periodic system is permanent then there is at least one positive periodic solution of the system we show that the conditions for global attractivity of the positive semi trivial periodic solution and permanence of the population of the model depend on time delay so we call it profitless in this paper the main feature is that we introduce multi delays and impulses into the predator prey model exhibit a new modeling method which is applied to investigate multi species impulsive multi delays differential equations

nonlinear stability of traveling waves to a hyperbolic parabolic system modeling chemotaxis we prove nonlinear stability of traveling waves of arbitrary amplitudes to a hyperbolic parabolic system modeling repulsive chemotaxis in contrast to the previous related results where various sm

aggregation blowup and collapse the abc s of taxis in reinforced random walks in many biological systems movement of an organism occurs in response to a diffusible or otherwise transported signal and in its simplest form this can be modeled by diffusion equations with advection terms of the form first derived by patlak bull of math biophys 15 1953 pp 311 338 however other systems are more accurately modeled by random walkers that deposit a nondiffusible signal that modifies the local environment for succeeding passages in these systems one example of which is the myxobacteria the question arises as to whether aggregation is possible under suitable hypotheses on the transition rules and the production of a control species that modulates the transition rates davis probab theory related fields 84 1990 pp 203 229 has studied this question for a certain class of random walks and here we extend this analysis to the continuum limit of such walks we first derive several general classes of partial differential equations that depend on how the movement rules are

approximate gcd and its application to ill conditioned algebraic equations abstract we describe two algorithms of approximate gcd greatest common divisor for polynomials with coefficients of floating point numbers one is for univariate polynomials and the other for multivariate polynomials the algorithms are careful extensions of the conventional euclidean algorithm and they are applied to solving ill conditioned algebraic equations ill conditioned univariate algebraic equations have multiple or close roots and we can ill conditioned system of algebraic equations which have an approprimate common divisor conventional numeric root finding methods such as newton s method give no satisfactory result for such ill conditioned systems by using an approximate gcd algorithm for multivariate polynomials the system is transformed into a well conditioned problems by a combination of algebraic and numeric methods we call such algorithms hybrid algorithms this paper shows the importance and possible fruitfulness of the hybrid algorithm

on the existence of periodic solutions of a neutral delay model of single species population growth abstract in this paper we employ some new techniques to study the existence of positive periodic solutions of the neutral delay model n t n t a t t n t b t n t t c t n t t our result gives a correct answer to the open problem 9 2 due to y kuang 1993 delay differential equations with applications in population dynamics academic press new york

solving a polynomial equation some history and recent progress the classical problem of solving an nth degree polynomial equation has substantially influenced the development of mathematics throughout the centuries and still has several important applications to the theory and practice of present day computing we briefly recall the history of the algorithmic approach to this problem and then review some successful solution algorithms we end by outlining some algorithms of 1995 that solve this problem at a surprisingly low computational cost

existence and global attractivity of positive periodic solution for a volterra model with mutual interference and beddington deangelis functional response abstract in this paper a volterra model with mutual interference and beddington deangelis functional response is investigated some sufficient conditions which guarantee the existence and global attractivity of positive periodic solution for the system are obtained furthermore our results improve the main results of paper 1

symmetrization techniques on unbounded domains application to a chemotaxis system on rn the authors study the parabolic elliptic system on rn u t u u v 0 v v u u 0 u0 a version of the mathematical model of chemotaxis proposed by keller and segel a differential inequality for the quantity s0u t d where u is the decreasing rearrangement of the solution u t with respect to the spatial variable is obtained as a consequence they obtain e g lp bounds of the solution u v on r2 and global in time existence of solutions under the condition r2u0 8 then the solution u v blows up in a finite time compared to the previous work of diaz diaz and nagai adv math sci appl 5 1995 no 2 659 680 mr1361010 96j 35246 where this problem has been considered on bounded domains of rn there are some additional technical difficulties connected with the regularity of the derivative u t

global well posedness for keller segel system in besov type spaces abstract the cauchy problems for keller segel system are studied using homogeneous besov spaces with the homogeneous besov spaces b p 2 n p r n which is the scaling critical case for keller segel system global solutions for small initial data are obtained in the space in addition ill posedness for keller segel system is also studied

existence of positive periodic solutions for a neutral population model with delays and impulse in this paper by using the theory of abstract continuous theorem of k set contractive operator and some analysis techniques we obtain some sufficient conditions for the existence of positive periodic solutions for a neutral population model with delays and impulse

a geometrical approach to finding multivariate approximate lcms and gcds abstract in this article we present a new approach to compute an approximate least common multiple lcm and an approximate greatest common divisor gcd of two multivariate polynomials this approach uses the geometrical notion of principal angles whereas the main computational tools are the implicitly restarted arnoldi method and sparse qr decomposition upper and lower bounds are derived for the largest and smallest singular values of the highly structured macaulay matrix this leads to an upper bound on its condition number and an upper bound on the 2 norm of the product of two multivariate polynomials numerical examples are provided

well posedness and ill posedness of a multidimensional chemotaxis system in the critical besov spaces abstract we study the cauchy problem for a multidimensional chemotaxis system in critical besov spaces b p 1 d p 2 r d b p 1 d p 1 r d d for 1 p 2 d we prove locally well posedness for large initial data and globally well posedness for small initial data of this system and more importantly we show the ill posedness in the sense that a norm inflation phenomenon occurs for p 2 d more precisely we construct a specific initial data which can be arbitrarily small in the besov spaces meanwhile the corresponding solution u can be arbitrarily large after an arbitrarily short time

computation of approximate polynomial gcds and an extension computation of approximate polynomial greatest common divisors gcds is important both theoretically and due to its applications to control linear systems network theory and computer aided design we study two approaches to the solution so far omitted by the researchers despite intensive recent work in this area correlation to numerical pade approximation enabled us to improve computations for both problems gcds and pade reduction to the approximation of polynomial zeros enabled us to obtain a new insight into the gcd problem and to devise effective solution algorithms in particular unlike the known algorithms we estimate the degree of approximate gcds at a low computational cost and this enables us to obtain certified correct solution for a large class of input polynomials we also restate the problem in terms of the norm of the perturbation of the zeros rather than the coefficients of the input polynomials which leads us to the fast certified solution for any pair of input polynomials via the computation of their roots and the maximum matchings or connected components in the associated bipartite graph

ill posedness of the navier stokes equations in a critical space in 3d abstract we prove that the cauchy problem for the three dimensional navier stokes equations is ill posed in b 1 in the sense that a norm inflation happens in finite time more precisely we show that initial data in the schwartz class s that are arbitrarily small in b 1 can produce solutions arbitrarily large in b 1 after an arbitrarily short time such a result implies that the solution map itself is discontinuous in b 1 at the origin

oscillation and stability of linear impulsive delay differential equations the main results of this paper are that the oscillation and the stability of a linear impulsive delay differential equation are equivalent respectively to the oscillation and the stability of a corresponding linear delay differential equation without impulses the results of this paper can be used to improve and derive some of the known results in the literature

fear factor in a prey predator system in deterministic and stochastic environment abstract in this article a prey predator model has been studied where apart from direct predation the prey population is affected by the fear induced from predators the basic reproduction of the prey population is reduced as a cost of fear biologically well posedness of the model system has been shown through positivity and boundedness of solutions existence criterion and stability analysis of the non negative equilibrium points have been discussed and necessary conditions for uniform persistence have been derived for corresponding non autonomous system also sufficient conditions for the existence of positive periodic solution of the non autonomous system have been established by utilizing the coincidence degree theorem we further show that the positive periodic solution is global attractor under certain conditions next we construct the stochastic model based upon the deterministic setup by perturbing the intrinsic growth rate of prey and natural mortality rate of predators it has been shown that the stochastic system admits unique positive global solution initiates from anywhere in the interior of the positive quadrant the sufficient conditions for extinction non persistence and weakly persistence of both the species have been derived along with the stochastic permanence of the system we have verified our analytical results and make a comparison between the deterministic and stochastic setup by exhaustive numerical simulations

the periodic solutions for general periodic impulsive population systems of functional differential equations and its applications in this paper the general periodic impulsive population systems of functional differential equations are investigated by using the method of poincare map and horn s fixed point theorem we prove that the ultimate boundedness of all solutions implies the existence of periodic solutions as applications of this result the existence of positive periodic solutions for the general periodic impulsive kolmogorov type population dynamical systems are discussed we further prove that as long as the system is permanent there must exist at least one positive periodic solution in addition the permanence and existence of positive periodic solutions are discussed for the periodic impulsive single species logistic models and the periodic impulsive n species lotka volterra competitive models with delays

global dynamics of a hyperbolic parabolic model arising from chemotaxis we prove global existence and qualitative behavior of classical solutions for a hyperbolic parabolic system describing chemotaxis on bounded domains it is shown that classical solutions to the initial boundary value problem of the one dimensional model exist globally in time for large initial data and the solutions converge to constant equilibrium states exponentially in time which rigorously demonstrates the collapsing of cell populations in chemotaxis moreover similar results are established for the multidimensional model when the initial data are small

global existence and finite time blow up for a class of semilinear pseudo parabolic equations abstract in this paper we study a class of semilinear pseudo parabolic equations by introducing a family of potential wells we prove the invariance of some sets global existence nonexistence and asymptotic behavior of solutions with initial energy j u 0 d moreover we obtain finite time blow up with high initial energy j u 0 d by comparison principle

an elementary proof of barnett s theorem about the greatest common divisor of several univarlate polynomials abstract this articule provides a new proof of barnett s theorem giving the degree of the greatest common divisor of several univariate polynomials with coefficients in a field in terms of the rank of a well defined matrix the new proof is elementary and self contained no use of jordan form or invariant factors and it is based on some easy to state properties of subresultants moreover this proof allows one to generalize barnett s results to the case when the considered polynomials have their coefficients in an integral domain

existence theorem for periodic solutions of higher order nonlinear differential equations abstract we study the existence of periodic solutions to differential equations of the form l x g t x x x m f t with l x x m a m 1 x m 1 a 1 x

global existence in critical spaces for compressible navier stokes equations we investigate global strong solutions for isentropic compressible fluids with initial data close to a stable equilibrium we obtain the existence and uniqueness of a solution in a functional setting invariant by the scaling of the associated equations more precisely the initial velocity has the same critical regularity index as for the incompressible homogeneous navier stokes equations and one more derivative is needed for the density we point out a smoothing effect on the velocity and a l 1 decay on the difference between the density and the constant reference state the proof lies on uniform estimates for a mixed hyperbolic parabolic linear system with a convection term

computing greatest common divisors and squarefree decompositions through matrix methods the parametric and approximate cases abstract barnett s method through bezoutians is a purely linear algebra method allowing to compute the degree of the greatest common divisor of several univariate polynomials in a very compact way two different uses of this method in computer algebra are introduced here firstly we describe an algorithm for parameterizing the greatest common divisor of several polynomials in k x y being x a parameter taking values in an real field k secondly we consider the problem of computing the approximate greatest common divisor with limited accuracy for several univariate polynomials following corless et al r m corless p m gianni b m trager s watt the singular value decomposition for polynomial systems in acm international symposium on symbolic and algebraic computation 1995 pp 195 207 given a family of polynomials whose coefficients are imperfectly known we describe an algorithm for computing their approximate greatest common divisor by using as main tools barnett s method and singular value decomposition computations furthermore we show how to use this algorithm in order to obtain the approximate squarefree decomposition of a given polynomial with imperfectly known coefficients

global well posedness for compressible navier stokes equations with highly oscillating initial velocity in this paper we prove global well posedness for compressible navier stokes equations in the critical functional framework with the initial data close to a stable equilibrium this result allows us to construct global solutions for the highly oscillating initial velocity the proof relies on a new estimate for the hyperbolic parabolic system with convection terms 2010 wiley periodicals inc

boundedness for impulsive delay differential equations and applications to population growth models abstract in this paper criteria on uniform ultimate boundedness are derived for impulsive delay differential equations using lyapunov functions and razumikhin techniques it should be noted that the boundedness criteria establish global existence of solutions as well as boundedness without assuming a priori that solutions can necessarily be continued to infinity those criteria are then used to obtain permanence results for population growth models some examples are discussed to illustrate the theorems

existence of positive periodic solution of an impulsive delay logistic model abstract in this paper we use the continuation theory for k set contractions to study the existence of positive periodic solutions of the impulsive delay logistic model x t r t x t 1 x t k t t t k x t k x t k b k x t k k 1 2 the sufficient conditions of the existence of positive periodic solution are obtained