B(X)上保持约当积的固定点的满射

设B(X)是维数大于等于3的复Banach空间X上有界线性算子全体构成的代数.设A∈B(X),若Ax=x,则称x∈X是算子A的固定点.Fix(A)表示A的所有固定点的集合.本文刻画了B(X)上保持算子的Jordan积的固定点的满射.     

Equi-attraction and backward compactness of pullback attractors for point-dissipative Ginzburg-Landau equations

A new concept of an equi-attractor is introduced, and defined by the minimal compact set that attracts bounded sets uniformly in the past, for a non-autonomous dynamical system. It is shown that the compact equi-attraction implies the backward compactness of a pullback attractor. Also, an eventually equi-continuous and strongly bounded process has an equi-attractor if and only if it is strongly point dissipative and strongly asymptotically compact. Those results primely strengthen the known existence result of a backward bounded pullback attractor in the literature. Finally, the theoretical criteria are applied to prove the existence of both equi-attractor and backward compact attractor for a Ginzburg-Landau equation with some varying coefficients and a backward tempered external force.     

A new idea to construct the fractal interpolation function

The aim of this paper is to present a new idea to construct the nonlinear fractal interpolation function, in which we exploit the Matkowski and the Rakotch fixed point theorems. Our technique is different from the methods presented in the previous literatures.     

Very weak solutions to elliptic equations with singular convection term

We study Dirichlet problem for a nonlinear equation with a drift term. Despite the presence of the singular convection term, we establish existence and uniqueness of a solution in spaces larger than the natural one.     

A globally linearly convergent method for pointwise quadratically supportable convex–concave saddle point problems

We study the Proximal Alternating Predictor–Corrector (PAPC) algorithm introduced recently by Drori, Sabach and Teboulle [8] to solve nonsmooth structured convex–concave saddle point problems consisting of the sum of a smooth convex function, a finite collection of nonsmooth convex functions and bilinear terms. We introduce the notion of pointwise quadratic supportability, which is a relaxation of a standard strong convexity assumption and allows us to show that the primal sequence is R-linearly convergent to an optimal solution and the primal-dual sequence is globally Q-linearly convergent. We illustrate the proposed method on total variation denoising problems and on locally adaptive estimation in signal/image deconvolution and denoising with multiresolution statistical constraints.     

Investigations of Viscous Dissipation in Stagnation Point Flow Past a Stretchable Riga Wall: Modern Analysis of Heat Transport

This article scrutinizes the features of viscous dissipation in the stagnation point flow past through a linearly stretched Riga wall by implementing Cattaneo-Christov heat flux model. Viscous dissipation is carried out in Cattaneo-Christov diffusion analysis for the first time in this letter. As a result of Cattaneo-Christov model, some extra terms of viscous dissipation are appeared in the energy equation. These extra terms of viscous dissipation are missing in the literature. On the utilization of suitable transformations, the equations governing the problem are reduced under the boundary layer approximation into the non-linear and dimensionless ordinary differential equations. Convergent approach is utilized to solve the dimensionless governing equations. The solution thus acquired is used to highlight the effects of emerging parameters on velocity distribution and fluid's temperature through the graphs. Features of the drag force (or skin friction co-efficient) are graphically interpreted. It is noticed that the presence of modified Hartman number helps to reduce the fluid's temperature but enhances the velocity profile. Further an enlargement in the value of thermal time relaxation parameter helps to decrease the temperature distribution.     

基于波普尔证伪思想视角下的化学课堂教学

结合实例介绍了基于波普尔证伪思想视角下的化学课堂教学，具体教学形式包括：教学预设与生成不一致时，用证实或证伪进行验证；教学设计中埋下教学冲突，给学生创造出证伪机会；充分利用实验探究功能，通过证伪提升原理认识；引导学生自主合作学习时，相互质疑、讨论、释疑、证伪。波普尔证伪思想对化学教学具有一定的启示作用：发展学生的批判思维是化学教学的应有之义；培育学生的创新意识是化学教学的重要职责。     

Singular Hamiltonian elliptic systems with critical exponential growth in dimension two

We will focus on the existence of nontrivial solutions to the following Hamiltonian elliptic system where are numbers belonging to the interval [0, 2), V is a continuous potential bounded below on by a positive constant and the functions f and g possess exponential growth range established by Trudinger–Moser inequalities in Lorentz–Sobolev spaces. The proof involves linking theorem and a finite‐dimensional approximation.