非线性抛物组非均匀网格差分解的唯一性和稳定性

１．引言 １．对一维非线性抛物组,在文献山中已构造一般非均匀网格差分格式,其中差分逼近的组合系数对不同的网格点和不同的网格层可以不同,并且运用不动点原理证明了差分解的存在性和收敛性．在非均匀网格差分格式中差分逼近的组合系数为常数的情形,文献［２］证明了具有有界二阶差商的离散向量解的存在性、唯一性和稳定性．本文将对文献［１］中构造的一般非均匀网格差分格式,证明所得到的差分解的唯一性和稳定性． 考虑如下非线性抛物组其中是未知的ｍ－维向量函数是给定的矩阵函数,ｊ（ｘ,ｔ,ｕ,ｐ）。是给定的ｍ－维向量函数…     

Bifurcation and disaggregation in urban/regional spatial modelling: A technical note

Using the Lowry-Garin model as an example, we illustrate the complexity of bifurcation and aggregation issues in urban/regional spatial systems. As a first step, a disaggregate version of the Lowry-Garin model is formulated. Then the general conditions for bifurcation are identified in terms of disaggregate labor-force participation rate, population-serving ratio and accessibility indices. Physical interpretation of these conditions is also given.     

Stability analysis of nonautonomous difference systems with delaying arguments

We present sufficient conditions for the stability of the nonautonomous difference system , k∈Z⁺, with m?1, when the (n×n)-matrices Aj(⋅) are slowly varying coefficients. The proposed approach is based on the generalization of the “freezing” method for ordinary differential equations. The stability conditions are formulated in terms of the corresponding Cauchy's function.     

一类复差分方程组的亚纯解(英文)

本文研究了一类复差分方程组的增长性的问题.利用亚纯函数的Nevanlinna值分布理论,得到了有关复差分方程组的亚纯解的一个重要结果,将复差分方程的某些结果推广到复差分方程组中.     

超导故障限流器的研究现状及其应用

超导故障限流器(Superconducting Fault Current Limiter,SFCL)是利用超导体的基本特性,有效限制电力系统故障短路电流,提高电网安全性和稳定性的一种新型电力设备。文中在综合大量文献的基础上,对超导故障限流器进行了一种较为系统的分类。基于该种分类,结合目前国内外的研究现状,就电阻型、磁屏蔽型、饱和铁芯电抗器型、桥路型SFCL的工作原理作了详细的分析介绍,还给出了它们在电力系统中的安装位置。最后,对超导故障限流器的研究中存在的问题及其发展趋势做了说明。     

基于平面通量展开的三维Pin by Pin输运SP3计算

基于Pin by Pin输运SP3计算是下一代反应堆物理计算方法中一个重要的研究方向.节块法一般采用高阶通量和中子源展开以适应较大的节块尺寸,因此对于Pin by Pin计算来说效率偏低.由于反应堆堆芯不均匀性更多发生在径向,本文提出一种径向基于二维平面通量展开结合轴向常规节块法的综合方法进行三维Pin by Pin输...     

Memory Effects in High-Dimensional Systems Faithfully Identified by Hilbert–Schmidt Speed-Based Witness

A witness of non-Markovianity based on the Hilbert–Schmidt speed (HSS), a special type of quantum statistical speed, has been recently introduced for low-dimensional quantum systems. Such a non-Markovianity witness is particularly useful, being easily computable since no diagonalization of the system density matrix is required. We investigate the sensitivity of this HSS-based witness to detect non-Markovianity in various high-dimensional and multipartite open quantum systems with finite Hilbert spaces. We find that the time behaviors of the HSS-based witness are always in agreement with those of quantum negativity or quantum correlation measure. These results show that the HSS-based witness is a faithful identifier of the memory effects appearing in the quantum evolution of a high-dimensional system with a finite Hilbert space.     

Thermodynamics of a Fluid of Hard D-dimensional Spheres: Percus-Yevick and Carnahan-Starling-like Results for D = 4 and 5

Abstract

The equations of state (EOS) of four and five dimensional hyperspheres have been calculated using Leutheusser's ansatz. In five dimensions these, and the correlation functions, are compared with the results obtained from the analytic solution of the Percus—Yevick (PY) approximation. It is shown that the ansatz reproduces extremely well the PY results. However, in both approximations neither the virial, Z_v , nor the compressibility, Z_c , EOS reproduce well the available molecular dynamics (MD) results. Yet a linear combination of Z_v and Z_c , following the Carnahan—Starling EOS for hard spheres, are in excellent agreement with the MD results in four and five dimensions.     

A cohomological obstruction for global quasi-bi-Hamiltonian fields

We introduce the notion of integrating factor for a 1-form which is an inner product of a vector fields and a 2-form, and the notion of weakly bi-Hamiltonian field also, which is locally quasi-bi-Hamiltonian. A cohomological class in some first cohomology space is associated to such vector fields when this is weakly bi-Hamiltonian and defined relatively to the above 1-form. This class is a cohomological obstruction to the existence of a global integrating factor for the 1-form.