λ-STATISTICAL CONVERGENCE OF ORDER α

In this paper,we introduce the concept of λ-statistical convergence of order α.Also some relations between the λ-statistical convergence of order α and strong(V,λ)-summability of order α are given.     

On ideal convergence of double sequences in probabilistic normed spaces

The notion of ideal convergence is a generalization of statistical convergence which has been intensively investigated in last few years.For an admissible ideal ∮N× N,the aim of the present paper is to introduce the concepts of ∮-convergence and ∮*-convergence for double sequences on probabilistic normed spaces(PN spaces for short).We give some relations related to these notions and find condition on the ideal ∮ for which both the notions coincide.We also define ∮-Cauchy and ∮*-Cauchy double sequences on PN spaces and show that ∮-convergent double sequences are ∮-Cauchy on these spaces.We establish example which shows that our method of convergence for double sequences on PN spaces is more general.     

系数为缺项幂级数的高阶线性微分方程解的超级

In this paper,we investigate the hyper order of the solutions of high order linear differential equations with some dominated coefficient being lacunary series,and obtain some results which improve and...     

Summing Boolean Algebras

In this paper we will study some familes and subalgebras F of P (N) that let us characterize the unconditional convergence of series through the weak convergence of subseries ∑i∈A^xi, A ∈ F. As a consequence, we obtain a new version of the Orlicz-Pettis theorem, for Banach spaces. We also study some relationships between algebraic properties of Boolean algebras and topological properties of the corresponding Stone spaces.     

Convergence Rate to Stationary Solutions for Boltzmann Equation with External Force

For the Boltzmann equation with an external force in the form of the gradient of a potential function in space variable, the stability of its stationary solutions as local Maxwellians was studied by S. Ukai et al. (2005) through the energy method. Based on this stability analysis and some techniques on analyzing the convergence rates to stationary solutions for the compressible Navier-Stokes equations, in this paper, we study the convergence rate to the above stationary solutions for the Boltzmann equation which is a fundamental equation in statistical physics for non-equilibrium rarefied gas. By combining the dissipation from the viscosity and heat conductivity on the fluid components and the dissipation on the non-fluid component through the celebrated H-theorem, a convergence rate of the same order as the one for the compressible Navier-Stokes is obtained by constructing some energy functionals.     

Convergence analysis for the Secant method based on new recurrence relations

A new convergence theorem for the Secant method in Banach spaces based on new recurrence relations is established for approximating a solution of a nonlinear operator equation. It is assumed that the divided difference of order one of the nonlinear operator is Lipschitz continuous. The convergence conditions differ from some existing ones and are easily satisfied. The results of the paper are justified by numerical examples that cannot be handled by earlier works.     

Convergence analysis for the Secant method based on new recurrence relations

A new convergence theorem for the Secant method in Banach spaces based on new recurrence relations is established for approximating a solution of a nonlinear operator equation.It is assumed that the divided difference of order one of the nonlinear operator is Lipschitz continuous.The convergence conditions differ from some existing ones and are easily satisfied.The results of the paper are justified by numerical examples that cannot be handled by earlier works.     

On the bilinear and cubic forms of some symplectic connected sums

Let ( M1 , M2 , N ) be three symplectic manifolds and suppose that we can do the symplectic connected sum of M1 and M2 along their submanifold N to obtain M1#NM2 . In this paper, we consider the bilinear and cubic forms of H* (M1#NM2 , Z) when dim M1#NM2 = 4, 6. Under some conditions, we get some relations of the bilinear and the cubic forms between M1#NM2 and M1■M2 .     

Analysis of a moving collocation method for one-dimensional partial differential equations

A moving collocation method has been shown to be very efficient for the adaptive solution of second- and fourth-order time-dependent partial differential equations and forms the basis for the two robust codes MOVCOL and MOVCOL4.In this paper,the relations between the method and the traditional collocation and finite volume methods are investigated.It is shown that the moving collocation method inherits desirable properties of both methods: the ease of implementation and high-order convergence of the traditional collocation method and the mass conservation of the finite volume method.Convergence of the method in the maximum norm is proven for general linear two-point boundary value problems.Numerical results are given to demonstrate the convergence order of the method.     

A Note on Rings and Modules Graded by Some Special Groups

In this note we prove that the prime madicals of some graded rings and the scoles of some graded modules are also graded. The results on the relations between the prime radical and the graded prime radical are also presented. Moreover, the relations between a graded ring and its initial subring are studied.     

Weak convergence of the sequential empirical processes of residuals in TAR models

This paper studies the weak convergence of the sequential empirical process K n of the residuals in the threshold autoregressive(TAR)model of order p.Under some mild conditions,it is shown that K n converges weakly to a Kiefer process plus a random variable which converges to a multivariate normal.This differs from that given by Bai(1994)for a stationary autoregressive and moving average(ARMA)model.     

Generalized statistical convergence and statistical core of double sequences

In this paper we extend the notion of A-statistical convergence to the （λ,μ）statistical convergence for double sequences x =（xjk）. We also determine some matrix transformations and establish some core theorems related to our new space of double sequences Sλ,μ.     

ZEROS OF ENTIRE SOLUTIONS TO COMPLEX LINEAR DIFFERENCE EQUATIONS＊

In this article,we study the complex oscillation problems of entire solutions to homogeneous and nonhomogeneous linear difference equations,and obtain some relations of the exponent of convergence of z...     

On Absolute Nörlund Spaces and Matrix Operators

In a more recent paper, the second author has introduced a space |C_α|_k as the set of all series by absolute summable using Ces`aro matrix of order α -1. In the present paper we extend it to the absolute N?rlund space |N_p~θ|_k taking N?rlund matrix in place of Ces`aro matrix, and also examine some topological structures, α-β-γ-duals and the Schauder base of this space. Further we characterize certain matrix operators on that space and determine their operator norms, and so extend some well-known results.     

ON THE DISTRIBUTION OF THE VALUES OF MEROMOPHIC FUNCTIONS OF INFINITE ORDER

<正> ⅠNTRODUCTIONIn 1896,Borel established the well known theorem relative tothe distribution of moduli of values for an integral function f(z) offinlite positive order O“The exponent of convergence of the moduliof the zeros of f(z)-α is equal to Q for every constant α exceptpossiibly one value of α at most.”Afterwards he proved a moregeneral theorem in replacing a by an integral function π(z) of orderless than o. Concerning the distribution of argulnents o[" values fora meromorphic fumctionf(z) of finite positive order, Viliron discoveredin 1929 the existence of what he called “direction of Borel” and     

Euler多项式的若干对称恒等式

Using the generating functions, we prove some symmetry identities for the Euler polynomials and higher order Euler polynomials, which generalize the multiplication theorem for the Euler polynomials. Also we obtain some relations between the Bernoulli polynomials, Euler polynomials, power sum, alternating sum and Genocchi numbers.     

g-Besselian frames in Hilbert spaces

In this paper, we introduce the concept of a g-Besselian frame in a Hilbert space and discuss the relations between a g-Besselian frame and a Besselian frame. We also give some characterizations of g-Besselian frames. In the end of this paper, we discuss the stability of g-Besselian frames. Our results show that the relations and the characterizations between a g-Besselian frame and a Besselian frame are different from the corresponding results of g-frames and frames.     

Convergence error estimates of the Crank-Nicolson scheme for solving decoupled FBSDEs

In this work, we theoretically analyze the convergence error estimates of the Crank-Nicolson(C-N) scheme for solving decoupled FBSDEs. Based on the Taylor and It-Taylor expansions, the Malliavin calculus theory(e.g.,the multiple Malliavin integration-by-parts formula), and our new truncation error cancelation techniques, we rigorously prove that the strong convergence rate of the C-N scheme is of second order for solving decoupled FBSDEs, which fills the gap between the second-order numerical and theoretical analysis of the C-N scheme.     

Convergence of Vortex Methods for Initial Boundary Value Problems

In this paper we study the vortex methods for the Euler equation of incompressible flow with initial and boundary conditions. Second order extrapolation scheme is applied to calculate the motion of vortex blobs near boundary. Under some corresponding conventional hypotheses second order convergence result is proved, which achieves the same precision as that of the pure initial value problems and can be generalized to any higher order without difficulty. The convergence of the vortex-in-cell method where the stream functions are approximated by the finite element method is also proved.     

A NEW CHARACTERIZATION OF Qp^# FUNCTIONS

A new characterization of Q#p is given, which implies immediately a known result. Also, the authors consider a class Np of bounded characteristic with order p, 0 < p < ∞, in the unit disk and give some relationship between it and other classes of meromorphic functions. This paper answers partly a question mentioned by Aulaskari and Lappan.