高阶椭圆算子Dirichlet本征值的下界

设Ω是R^m(m≥2）中的一个有界区域,其边界足够光滑,考察2p(p≥1）阶椭圆算子（－1）^p ∑│α│＝│β│＝pa^α(Aαβa^β)在Dirichlet边界条件下的本征值问题,给出了其本征值的一个下界,该下界除与维数m有关外仅依赖于区域Ω的体积。     

Banach空间二阶非线性奇异微分方程的解

文中讨论了Banach空间中一类右端具有奇异性的二阶非线性微分方程的边值问题,利用不动点方法,获得了该边值问题解的存在性定理.最后还给出了相应的例子.     

Certain subclasses of p-valently analytic functions involving a generalized fractional differintegral operator

By making use of the principle of subordination between analytic functions and the generalized fractional differintegral operator, we introduce and investigate some new subclasses of p-valently analytic functions in the open unit disk. Such results as inclusion relationships, integral-preserving properties, convolution properties, subordination and superordination properties, and sandwich theorems for these classes are derived.     

Operators on Soft Inner Product Spaces

In the present paper, self-adjoint operator and completely continuous operator on soft inner product spaces have been introduced and some basic properties of such operators are studied.     

A separation theorem for the weak s-convex orders

The present paper extends to higher degrees the well-known separation theorem decomposing a shift in the increasing convex order into a combination of a shift in the usual stochastic order followed by another shift in the convex order. An application in decision making under risk is provided to illustrate the interest of the result.     

Finite Difference/Collocation Method for Two-Dimensional Sub-Diffusion Equation with Generalized Time Fractional Derivative

In this paper, we propose a finite difference/collocation method for two-dimensional time fractional diffusion equation with generalized fractional operator. The main purpose of this paper is to design a high order numerical scheme for the new generalized time fractional diffusion equation. First, a finite difference approximation formula is derived for the generalized time fractional derivative, which is verified with order $2-\alpha$ $(0<\alpha<1)$. Then, collocation method is introduced for the two-dimensional space approximation. Unconditional stability of the scheme is proved. To make the method more efficient, the alternating direction implicit method is introduced to reduce the computational cost. At last, numerical experiments are carried out to verify the effectiveness of the scheme.     

A Survey for the Spectrum of Triangles over Sequence Spaces

Abstract

In the present paper, we summarize the recent literature concerning the spectrum and fine spectrum with respect to Goldberg’s classification of some operators represented by an infinite matrix over certain sequence spaces.     

Term rank preservers of Boolean matrices

We obtain some characterizations of linear operators that preserve the term rank of Boolean matrices. That is, a linear operator over Boolean matrices preserves the term rank if and only if it preserves the term ranks 1 and k(≠1) if and only if it preserves the term ranks 2 and l(≠2). Other characterizations of term rank preservers are given.