Some new results for demimartingales

Harremoёs obtained some new maximal inequalities for non-negative martingales. In this paper, we get some new maximal and minimal inequalities for non-negative demimartingales which generalize the results of Harremoёs. We also obtain an inequality for non-negative demimartingales which generalizes the result of Iksanov and Marynych. Finally we obtain a strong law of large numbers, strong growth rate and integrability of supremum for demimartingales which generalize and improve the result of Chow.     

Constructing Restricted Patterson Measures for Geometrically Infinite Kleinian Groups

In this paper, we study exhaustions, referred to as p-restrictions, of arbitrary nonelementary Kleinian groups with at most finitely many bounded parabolic elements. Special emphasis is put on the geometrically infinite case, where we obtain that the limit set of each of these Kleinian groups contains an infinite family of closed subsets, referred to as p-restricted limit sets, such that there is a Poincaré series and hence an exponent of convergence δp, canonically associated with every element in this family. Generalizing concepts which are well known in the geometrically finite case, we then introduce the notion of p-restricted Patterson measure, and show that these measures are non-atomic, δp-harmonic, δp-subconformal on special sets and δp-conformal on very special sets. Furthermore, we obtain the results that each p-restriction of our Kleinian group is of δp-divergence type and that the Hausdorff dimension of the p-restricted limit set is equal to δp.     

A Note on Harnack Type Inequality for the Gaussian Curvature Flow

In this short note we present a new Harnack expression for the Gaussian curvature flow, which is modeled from the shrinking self similiar solutions. As applications we give alternate proofs of Chow’s Harnack inequality and entropy estimate.     

<Emphasis Type="Italic">∂</Emphasis>-operations and <Emphasis Type="Italic">H</Emphasis><Subscript><Emphasis Type="Italic">V</Emphasis></Subscript>-fields

The hyperoperations, called theta-operations （δ）, are motivated from the usual property, which the derivative has on the derivation of a product of functions. Using any map on a set, one can define δ-operations. In this paper, we continue our study on the δ-operations on groupoids, rings, fields and vector spaces or on the corresponding hyperstructures. Using δ-operations one obtains, mainly, Hwstructures, which form the largest class of the hyperstructures. For representation theory of hyperstructures, by hypermatrices, one needs special Hv-rings or Hy-fields, so these hyperstructures can be used. Moreover, we study the relation of these δ-structures with other classes of hyperstructures, especially with the Hv-structures.     

A Class of Generalized Hausdorff Means

In the research of divergent series the important idea is that choose a suitable trasformation have to be of regularity, of sequence of partial sum of the series. The Hausdorff transformation is H=δμδ in matrix form, in which μ is any diagonal transformation and δ is so-called δ-transformation. In this paper, we construct a class of generalized Housdorff transformation using the Gould-Hsu inverse series, and give necessary and sufficient condition of that it shou ld be regular.     

Boundedness and Asymptotic Stability of Multistep Methods for Generalized Pantograph Equations

In this paper, we deal with the boundedness and the asymptotic stability of linear and one-leg multistep methods for generalized pantograph equations of neutral type, which arise from some fields of engineering. Some criteria of the boundedness and the asymptotic stability for the methods are obtained.     

On Split δ-Jordan Lie Triple Systems

The aim of this article is to study the structures of arbitrary split δ-Jordan Lie triple systems, which are a generalization of split Lie triple systems. By developing techniques of connections of roots for this kind of triple systems, we show that any of such δ-Jordan Lie triple systems T with a symmetric root system is of the form ■with U a subspace of T0 and any I[α] a well described ideal of T, satisfying■ .     

THE EXISTENCE AND STABILITY OF ALMOST PERIODIC SOLUTION

By using the ordinary dichotomy and theory of stability,we study the nonli- near differential equation and obtain some sufficient conditions which guarantee the existence and stability of almost periodic solution for the nonlinear diffe- rential equation.     

On a classical theorem on the diameter and minimum degree of a graph

In this work, we obtain good upper bounds for the diameter of any graph in terms of its minimum degree and its order, improving a classical theorem due to Erd¨os, Pach, Pollack and Tuza.We use these bounds in order to study hyperbolic graphs(in the Gromov sense). To compute the hyperbolicity constant is an almost intractable problem, thus it is natural to try to bound it in terms of some parameters of the graph. Let H(n, δ_0) be the set of graphs G with n vertices and minimum degree δ_0, and J(n, Δ) be the set of graphs G with n vertices and maximum degree Δ. We study the four following extremal problems on graphs: a(n, δ_0) = min{δ(G) | G ∈ H(n, δ_0)}, b(n, δ_0) = max{δ(G) |G ∈ H(n, δ_0)}, α(n, Δ) = min{δ(G) | G ∈ J(n, Δ)} and β(n, Δ) = max{δ(G) | G ∈ J(n, Δ)}. In particular, we obtain bounds for b(n, δ_0) and we compute the precise value of a(n, δ_0), α(n, Δ) andβ(n, Δ) for all values of n, δ_0 and Δ, respectively.     

Some Estimation Problems for Linear Model of Time Series,

If{X(n),n≥1}are random variables which satisfy following linear modelwhere α_j,λ_j,l≤j≤n are unknown constants andis real stationary sequence.In thispaper we discuss the estimation of λ_j,α_j and introduce δ-separated periodgram maximum estimatorλ_j for λ_j.Under some moderate conditions we prove the following consistence and asymptotionormality for these estimators,as the size     

THE EXISTENCE, UNIQUENESS AND STABILITY OF ALMOST PERIODIC SOLUTION FOR A CLASS OF NONLINEAR SYSTEM

In this paper, we study the problems on the existence, uniqueness and stability of almost periodic solution for a class of nonlinear system. Using fixed point theorem and Lyapunov functional, the sufficient conditions are given which guarantee the existence, uniqueness and stability of almost periodic solution for the system.     

ON STABLE PERTURBATIONS OF THE STIFFLY WEIGHTED PSEUDOINVERSE AND WEIGHTED LEAST SQUARES PROBLEM

In this paper we study perturbations of the stiffly weighted pseudoinverse （W^1/2 A）^＋W^1/2 and the related stiffly weighted least squares problem, where both the matrices A and W are given with W positive diagonal and severely stiff. We show that the perturbations to the stiffly weighted pseudoinverse and the related stiffly weighted least squares problem are stable, if and only if the perturbed matrices A = A ＋ δA satisfy several row rank preserving conditions.     

ON MAXWELL EQUATIONS WITH THE TRANSPARENT BOUNDARY CONDITION

In this paper we show the well-posedness and stability of the Maxwell scattering problem with the transparent boundary condition. The proof depends on the well-posedness of the time-harmonic Maxwell scattering problem with complex wave numbers which is also established.     

ON THE ALMOST PERIODIC SOLUTIONS OF HIGHER DIMENSIONAL NONAUTONOMOUS SYSTEMS

By means of the properties of almost periodic system and Lyapunov function, we give some criteria which guarantee the existence and uniqueness and stability of almost periodic solutions of higher dimensional nonautonomous system. The result is more convenient and effective than the related result in[1].     

Two-group SIR epidemic model with stochastic perturbation

A stochastic two-group SIR model is presented in this paper.The existence and uniqueness of its nonnegative solution is obtained,and the solution belongs to a positively invariant set.Furthermore,the globally asymptotical stability of the disease-free equilibrium is deduced by the stochastic Lyapunov functional method if R0 ≤ 1,which means the disease will die out.While if R0 1,we show that the solution is fluctuating around a point which is the endemic equilibrium of the deterministic model in time average.In addition,the intensity of the fluctuation is proportional to the intensity of the white noise.When the white noise is small,we consider the disease will prevail.At last,we illustrate the dynamic behavior of the model and their approximations via a range of numerical experiments.     

Stability of viscous contact wave for compressible navier-stokes system of general gas with free boundary

In this paper, we study the large time behavior of solutions to the nonisentropic Navier-Stokes equations of general gas, where polytropic gas is included as a special case, with a free boundary. First we construct a viscous contact wave which approximates to the contact discontinuity, which is a basic wave pattern of compressible Euler equation, in finite time as the heat conductivity tends to zero. Then we prove the viscous contact wave is asymptotic stable if the initial perturbations and the strength of the contact wave are small. This generalizes our previous result [6] which is only for polytropic gas.     

A PERTURBATION ANALYSIS FOR THE PROJECTION OF A STIFFLY SCALED MATRIX

In this paper we study the perturbation bound of the projection (WA )(WA ), where both the matrices A and W are given with W positive diagonal and severely stiff. When the perturbed matrix A=A δA satisfy several row rank preserving conditions, we derive a new perturbation bound of the projection.     

GLOBAL BEHAVIOR IN A RATIONAL RECURSIVE SEQUENCE

In this paper, we study the global stability, and the periodic character of the rational recursive sequence. We show that the positive equilibrium of the sequence is a global attractor with a basin which depends on certain conditions posed on the coefficients.     

ON EQUILIBRIA AND PERIODIC ORBITS OF COOPERATIVE SYSTEMS IN R~3

In the paper we present new criteria for existence of equilibria and periodic orbits for 3-dimensional systems which are cooperative. Particular attention is given to the relations of equilibria, cycle K and stable manifold of K. Meanwhile, the results of Hirsch [1, Theorem 9] and Jiang [2] are improved.     

带有脉冲控制的生物系统种群持久存在性问题研究

In this paper,on the basis of the theories and methods of ecology and ordinary differential equations,an ecological model with an impulsive control strategy is established.By using the theories of impulsive equations,small amplitude perturbation skills and compar-ison technique,we get the condition which guarantees the global asymptotical stability of the prey-x-eradication and predator-y-eradication periodic solution.It is proved that the system is permanent.Furthermore,numerical simulations are also illustrated which agree well with our theoretical analysis.All these results may be useful in study of the dynamic complexity of ecosystems.