POSITIVE SOLUTIONS TO m-POINT BOUNDARY VALUE PROBLEM OF NONLINEAR FRACTIONAL DIFFERENTIAL EQUATION WITH p-LAPLACIAN

In this paper,we are concerned with the existence of positive solutions to an m-point boundary value problem with p-Laplacian of nonlinear fractional differential equation.By means of Krasnosel'skii fixed-point theorem on a convex cone and Leggett-Williams fixed-point theorem,the existence results of solutions are obtained.     

THE INTERIOR LAYER SOLUTION TO NONLOCAL REACTION DIFFUSION EQUATIONS

An initial boundary value problem of semilinear nonlocal reaction diffusion equations is considered.Under some suitable conditions,using the asymptotic theory,the existence and asymptotic behavior of the interior layer solution to the initial boundary value problem are studied.     

SYNCHRONIZATION OF TWO COUPLED HINDMARSH-ROSE NEURONS BY A PACEMAKER

This paper considers the synchronization of two coupled Hindmarsh-Rose neurons by a pacemaker.Based on the stability theory of differential equations,the complete synchronization of this pacemaker neuron model is reached.Moreover,we also show that pacemaker can enhance or induce synchronization.Numerical simulations are given to illustrate the main results.     

ON THE NUMBER OF LIMIT CYCLES OF A POLYNOMIAL DIFFERENTIAL SYSTEM

In this paper, we employ qualitative analysis and methods of bifurcation theory to study the maximum number of limit cycles for a polynomial system with center in global bifurcation.     

EXISTENCE OF POSITIVE SOLUTIONS TO SINGULAR SUBLINEAR SEMIPOSITONE NEUMANN BOUNDARY VALUE PROBLEM

The existence of positive solutions to a singular sublinear semipositone Neumann boundary value problem is considered. In this paper,the nonlinearity term is not necessary to be bounded from below and the function q(t) is allowed to be singular at t = 0 and t = 1.     

GLOBAL STABILITY OF AN SVIR EPIDEMIC MODEL WITH VACCINATION

In this paper, an SIR epidemic model with vaccination for both the newborns and susceptibles is investigated, where it is assumed that the vaccinated individuals have the temporary immunity. The basic reproduction number determining the extinction or persistence of the infection is found. By constructing a Lyapunov function, it is proved that the disease free equilibrium is globally stable when the basic reproduction number is less than or equal to one, and that the endemic equilibrium is globally stable wh...     

Archimedean operator-theoretic Positivstellensätze

We prove a general archimedean positivstellensatz for hermitian operator-valued polynomials and show that it implies the multivariate Fejer-Riesz theorem of Dritschel-Rovnyak and positivstellensätze of Ambrozie-Vasilescu and Scherer-Hol. We also obtain several generalizations of these and related results. The proof of the main result depends on an extension of the abstract archimedean positivstellensatz for ?-algebras that is interesting in its own right.     

Idempotents and the multiplicative group of some totally bounded rings

In this paper, we extend some results of D.Dolzan on finite rings to profinite rings, a complete classification of profinite commutative rings with a monothetic group of units is given. We also prove the metrizability of commutative profinite rings with monothetic group of units and without nonzero Boolean ideals. Using a property of Mersenne numbers, we construct a family of power 2^ℵ0 commutative non-isomorphic profinite semiprimitive rings with monothetic group of units.     

Numerical treatment of solving singular integral equations by using Sinc approximations

In this paper we propose numerical treatment for singular integral equations. The methods are developed by means of the Sinc approximation with smoothing transformations. Such approximation is an effective technique against the singularities of the equations, and achieves exponential convergence. Therefore the methods improve conventional results where only polynomial convergence have been reported. The resulting algebraic system is solved by least squares approximation and leap frog algorithm. Estimation of errors of the approximate solution is presented. Some experimental tests are presented to show the efficient of the proposed methods.     

Quasirecognition by prime graph of finite simple groups L n (2) and U n (2)

Let G be a finite group. The prime graph ??(G) of G is defined as follows. The vertices of ??(G) are the primes dividing the order of G and two distinct vertices p, p?? are joined by an edge if G has an element of order pp??. Let L=L _n (2) or U _n (2), where n?R17. We prove that L is quasirecognizable by prime graph, i.e. if G is a finite group such that ??(G)=??(L), then G has a unique nonabelian composition factor isomorphic to L. As a consequence of our result we give a new proof for the recognition by element orders of L _n (2). Also we conclude that the simple group U _n (2) is quasirecognizable by element orders.