Besov-Morrey spaces: Function space theory and applications to non-linear PDE

This paper is devoted to the analysis of function spaces modeled on Besov spaces and their applications to non-linear partial differential equations, with emphasis on the incompressible, isotropic Navier-Stokes system and semi-linear heat equations. Specifically, we consider the class, introduced by Hideo Kozono and Masao Yamazaki, of Besov spaces based on Morrey spaces, which we call Besov-Morrey or BM spaces. We obtain equivalent representations in terms of the Weierstrass semigroup and wavelets, and various embeddings in classical spaces. We then establish pseudo-differential and para-differential estimates. Our results cover non-regular and exotic symbols. Although the heat semigroup is not strongly continuous on Morrey spaces, we show that its action defines an equivalent norm. In particular, homogeneous BM spaces belong to a larger class constructed by Grzegorz Karch to analyze scaling in parabolic equations. We compare Karch's results with those of Kozono and Yamazaki and generalize them by obtaining short-time existence and uniqueness of solutions for arbitrary data with subcritical regularity. We exploit pseudo-differential calculus to extend the analysis to compact, smooth, boundaryless, Riemannian manifolds. BM spaces are defined by means of partitions of unity and coordinate patches, and intrinsically in terms of functions of the Laplace operator.

     

The asymptotic behaviors of a stage-structured autonomous predator-prey system with time delay

In this paper, we consider an autonomous predator-prey Lotka-Volterra system in which individuals in the population may belong to one of two classes: the immatures and the matures, the age to maturity is represented by a time delay. By using eigenvalue analysis, principal term analyze method, reduction to absurdity, and iterative method, we obtain some simple conditions for global asymptotic stability of the unique positive equilibrium point. Moreover, a condition that the prey population in the system get extinction and the predator population in the system get permanence will be obtained. Meanwhile the theorems extend the corresponding conclusions in which there have no two stage structures.     

农户信用评估系统的设计与运用研究

农户信用评估的研究对推动农村消费信用的发展，促进农村经济良好运行十分重要。本在构造农户信用评估的指标体系的基础上，提出了农户信用评估神经网络模型的算法，利用实际搜集到的农户资料进一步建立了农户信用评估模型，继而构造了农户信用评估系统，并举例说明了该系统的实际运用，以期能为农村经济发展中的农户信用评价及相关研究提供一丝基础性启发。     

Gauss-Manin connections for arrangements, III Formal connections

We study the Gauss-Manin connection for the moduli space of an arrangement of complex hyperplanes in the cohomology of a complex rank one local system. We define formal Gauss-Manin connection matrices in the Aomoto complex and prove that, for all arrangements and all local systems, these formal connection matrices specialize to Gauss-Manin connection matrices.

     

BEPCII直线加速器相控系统设计研究

为了补偿由于各种因素引起的微波相位漂移,BEPCII直线加速器需要建立微波相位反馈控制系统.能量最大法将用来确定每台功率源的最佳相位.沿直线加速器速调管长廊铺设相位稳定同轴线提供相位参考.现在已经完成了关键部件,如PAD单元、IfA 单元的开发.搭建了相控最小系统对系统进行了验证.     

Excess molar enthalpies of binary mixtures of 1-hexene with some cyclic and aromatic hydrocarbons at 298.15 K

Microcalorimetric measurements of excess molar enthalpies, at 298.15 K, are reported for the four binary systems formed by mixing 1-hexene with the cycloalkanes: cyclohexane and methylcyclohexane, and with the aromatic hydrocarcons: benzene and toluene. Smooth Redlich-Kister representations of the results are presented. It was found that the Liebermann-Fried model also provided good representations of the results.     

NCD系统的数学理论

无索赔折扣系统(No Claim Discount system,简记为NCD系统)是世界各国机动车辆险中广泛采用的一种经验费率厘定机制.本文尝试建立了NCD系统严谨的数学理论, 重点讨论了NCD系统的数学建模和稳态分析.此外,作为本文必要的数学前提,首先在第2节着重探讨了随机矩阵间的随机优序关系,并将所得结论运用至齐次不可约且遍历的马尔科夫链的研究中,这些内容也有其独立的数学上的兴趣.     

非Chetaev型变质量非完整系统的Lie对称性与Noether对称性

研究非Chetaev型变质量非完整系统的Lie对称性与Noether对称性以及其间的 关系,给出Lie对称性导致Noether对称性以及Noether对称性导致Lie对称性的条件.     

社会经济管理系统和谐性模型的构建与分析

本文从非线性自然观的视野。引用与分析了社会经济系统功能模型与效应模型。构建了系统和谐状态模型与和谐状态可信度模型，形象地说明了企业系统的和谐既是一个随机不确定状态。又是企业和谐力量与不和谐力量相互抗争干涉的过程。依据协同学原理提出了企业系统和谐演进的机制，表明企业系统的和谐发展是子系统和谐协同的过程。即子系统竞争合作的过程。文中所构建的模型，从理论上清晰地说明了企业系统和谐有序运行的机理，为如何构建和谐企业。提供了建设性的思考。     

Robust Speed Control of a Low Damped Electromechanical System Based on CRONE Control: Application to a Four Mass Experimental Test Bench

Robust speed control of a low damped electromechanical system with backlash is studied, controlled load angular speed being not measured. The proposed control strategy combines a Luenberger observer (load angular speed and load torque disturbance estimations) and a robust CRONE controller. The observer provides estimation of the load angular speed and of the disturbance torque applied on the load. Through the computation of only three independent parameters (as many as a PID controller), the CRONE controller permits to ensure the robust speed control of the load in spite of plant parametric variations and speed observation errors. The proposed control strategy is applied to a four mass experimental test bench.