Existence of Renormalized Solutions of Nonlinear Elliptic Problems in Weighted Variable-Exponent Space

In this article, we study a general class of nonlinear degenerated elliptic problems associated with the differential inclusion $β(u)-div(a(x,Du)+F(u)) ∋ f$ in $Ω$ where $f ∈ L^1(Ω).$ A vector field $a(.,.)$ is a Carathéodory function. Using truncation techniques and the generalized monotonicity method in the framework of weighted variable exponent Sobolev spaces, we prove existence of renormalized solutions for general $L^1$-data.     

宁夏限制开发生态区农村社区发展能力评估

2020年全面建成小康社会,“十三五”是关键时期.随着全面小康目标的加速推进,“老少边穷弱”地区扶贫攻坚更加显得意义重大. 基于参与式农村评估和数理统计分析方法,以回族聚居宁夏限制开发生态区30个典型农村社区为研究对象,按居住地形对农村社区的发展能力进行评估,构建多元线性回归模型,揭示影响不同类型社区发展能力的主要因素,结合研究区实际,对区域发展提出建议. 研究发现,山地社区发展能力显著弱于川道社区;不同类型社区,影响其发展能力的因素差异显著;区位因素是决定社区发展能力的关键,包括自然区位和经济区位.本研究可为解决区域性整体脱贫提供参考,为精准扶贫,打好扶贫攻坚战建言献策.     

A Note on "Rearrangement and Matrix Product Inequalities

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Nonmonotone Interior Layer Solutions for Singularly Perturbed Semilinear Boundary Value Problems with a Turning Point

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An improved SQP algorithm for inequality constrained optimization

In this paper, the feasible type SQP method is improved. A new algorithm is proposed to solve nonlinear inequality constrained problem, in which a new modified method is presented to decrease the computational complexity. It is required to solve only one QP subproblem with only a subset of the constraints estimated as active per single iteration. Moreover, a direction is generated to avoid the Maratos effect by solving a system of linear equations. The theoretical analysis shows that the algorithm has global and superlinear convergence under some suitable conditions. In the end, numerical experiments are given to show that the method in this paper is effective.This work is supported by the National Natural Science Foundation (No. 10261001) and Guangxi Science Foundation (No. 0236001 and 0249003) of China. Acknowledgement.We would like to thank one anonymous referee for his valuable comments and suggestions, which greatly improved the quality of this paper.     

An algorithm for linear least squares problems with equality and nonnegativity constraints

We present a new algorithm for solving a linear least squares problem with linear constraints. These are equality constraint equations and nonnegativity constraints on selected variables. This problem, while appearing to be quite special, is the core problem arising in the solution of the general linearly constrained linear least squares problem. The reduction process of the general problem to the core problem can be done in many ways. We discuss three such techniques.The method employed for solving the core problem is based on combining the equality constraints with differentially weighted least squares equations to form an augmented least squares system. This weighted least squares system, which is equivalent to a penalty function method, is solved with nonnegativity constraints on selected variables.Three types of examples are presented that illustrate applications of the algorithm. The first is rank deficient, constrained least squares curve fitting. The second is concerned with solving linear systems of algebraic equations with Hilbert matrices and bounds on the variables. The third illustrates a constrained curve fitting problem with inconsistent inequality constraints.     

Adaptive synchronization of uncertain Liu system via nonlinear input

This paper addresses the adaptive synchronization for uncertain Liu system via a nonlinear input. By using a single nonlinear controller, the approach is utilized to implement the synchronization of Liu system with total parameters unknown. This method is simple and can be easily designed. What is more, it improves the existing conclusions in Ref [12]. Simulation results prove that the controller is effective and feasible in the end.     

GA-凸函数的Hadamard型不等式的推广

对GA-凸函数的Hadamard型不等式加权推广,定义了与GA-凸函数定积分有关的函数,证明了它们具有某种准线性,从而得到这些函数的单调性.     

Extreme rays for the large cone of hermitian generalized matrix functions

Given a <artwork name="GLMA31007ei1">-valued function f with domain <artwork name="GLMA31007ei2">, the symmetric group on {1,2,…, m}, we define the generalized matrix function [ f ](?), or d_f (?), in the usual way on the set of all m× m complex matrices. Letting <artwork name="GLMA31007ei3"> denote the set of all m× m positive semi-definite Hermitian matrices we consider the cone K _m whose elements are the Hermitian functions <artwork name="GLMA31007ei4"> such that [ f ]( A)≥0 for all <artwork name="GLMA31007ei5">. The extreme rays in K _m are fundamental to an understanding of the linear inequalities that result by restricting the generalized matrix functions [ f ](?) to the sets <artwork name="GLMA31007ei6">. In particular, the resolution of Lieb's permanent dominance conjecture, and certain similar conjectures such as the conjecture of Soules, will likely require identification and careful analysis of these rays. Grone, Merris, and Watkins have shown that the determinant function det(?), which is [ f ](?) if f is the signum function, is extreme in K _m for each m. We identify additional rays that are extreme for all m. In particular, we associate with each 2-term partition <artwork name="GLMA31007ei7"> of {1,2,…, m} an element <artwork name="GLMA31007ei8"> that is shown to be extreme in K _m for each m. If <artwork name="GLMA31007ei9"> is trivial, then <artwork name="GLMA31007ei10"> reduces to the determinant function; hence, our results are a natural extension of the result of Grone, Merris, and Watkins. Moreover <artwork name="GLMA31007ei11">, like det ( A), is expressible as a function of the eigenvalues of certain matrices related to A. Additional classes of extreme rays are also presented.     

On the Kolmogorov Inequality for M Φ -Norm

In this paper, we prove the Kolmogorov inequality for M | -norms generated by concave functions (with the same constants as in the Kolmogorov inequality).