Potts models with magnetic field: Arithmetic,geometry, and computation

We give a sheaf theoretic interpretation of Potts models with external magnetic field, in terms of constructible sheaves and their Euler characteristics. We show that the polynomial countability question for the hypersurfaces defined by the vanishing of the partition function is affected by changes in the magnetic field: elementary examples suffice to see non-polynomially countable cases that become polynomially countable after a perturbation of the magnetic field. The same recursive formula for the Grothendieck classes, under edge-doubling operations, holds as in the case without magnetic field, but the closed formulae for specific examples like banana graphs differ in the presence of magnetic field. We give examples of computation of the Euler characteristic with compact support, for the set of real zeros, and find a similar exponential growth with the size of the graph. This can be viewed as a measure of topological and algorithmic complexity. We also consider the computational complexity question for evaluations of the polynomial, and show both tractable and NP-hard examples, using dynamic programming.     

Invariants of Characteristics of Some Systems of Partial Differential Equations

We introduce the notion of an invariant of characteristics for a system of first-order partial differential equations. We prove that the existence of invariants is connected with passiveness of some systems. We describe a few methods for construction of new invariants from those already known. We give a scheme for application of the invariants to reduction and integration of systems of partial differential equations. As an application we consider the equation of gas dynamics.     

Investigation of thin-film electroluminescent structures on rough subsrates

Results of experimental investigations of the volt-brightness characteristics, frequency dependences of brightness, and the directional radiation pattern of electroluminescent MSDM, MSCM, and MSDCM emitters, where M stands for the first transparent and second nontransparent electrodes, S is a semiconductor, D is a thin-film dielectric, and C is a silicone-based composite liquid dielectric with a powdered segnetoelectric filler, developed on conventional “smooth” and rough glass substrates are presented. It is shown that electroluminescent structures on rough surfaces have a brightness approximately two times higher than that of similar structures developed on a “smooth” substrate. Ul’yanovsk State University, 42, L. Tolstoi St., Ul’yanovsk, 432700, Russia. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 64, No. 4, pp. 507–512, July–August, 1997.     

非线性控制系统的最小实现

对于那些由代数微分方程描述的具有输入输出关系的非线性控制系统，本文采用两种方法讨论了其最小实现问题：一种方法是直接计算系统的特征列；另一种方法则采用了本原元定理．两种方法给出的最小实现所需的状态变量最小数目是相等的．文中的大量代数与微分运算则可利用数学机械化来完成     

在可交换四元数空间中的双曲方程的特征边值问题

讨论了一阶和二阶双曲复方程的特征边值问题.对其中两种线性方程,分别在不同的情况下获得通解和可解条件.而对于拟线性的二阶双曲复方程,证明了解的存在性和唯一性.     

代数体函数的定理

本文定义并研究了代数体函数的加法．结合杨乐的方法,将仪洪勋联系重值的亚纯函数唯一性定理推广到多值的代数体函数．     

Euler characteristic and related measures for random geometric sets

By an elementary calculation we obtain the exact mean values of Minkowksi functionals for a standard model of percolating sets. In particular, a recurrence theorem for the mean Euler characteristic recently put forward is shown to be incorrect. Related previous mathematical work is mentioned. We also conjecture bounds for the threshold density of continuum percolation, which are associated with the Euler characteristic.     

确定线性偏微分方程组可积系统的对合特征集方法

基于Ritt-Wu特征集方法和Riquier-Janet理论,给出一种将线性微分方程组化成简单标准形式的有效算法．该算法通过消去冗余和添加可积条件获得线性微分方程组的完全可积系统(有形式幂级数解)或不相容判定．该算法不仅适用于常系数的线性偏微分方程组,而且对于变系数(以函数为系数)仍然有效．作者还给出了完全可积系统判定定理及其严格证明．     

FeCoB-SiO2磁性纳米颗粒膜的微波电磁特性

采用交替沉积磁控溅射工艺制备了超薄多层的FeCoB SiO2 磁性纳米颗粒膜 .利用x射线衍射仪、扫描探针显微镜、透射电子显微镜分析了薄膜的微结构和形貌特征 .采用振动样品磁强计、四探针法、微波矢量分析仪及谐振腔法测量薄膜试样的磁电性能和微波复磁导率 .重点对SiO2 介质相含量、薄膜微结构对电磁性能产生重要影响的机理做了分析和探讨 .结果表明 :这类FeCoB SiO2 磁性纳米颗粒膜具有良好的软磁性能和高频电磁性能 ,2GHz时的磁导率 μ′高于 70 ,可以应用于高频微磁器件或微波吸收材料的设计     

Directed Motion of a Molecular Motor Based on the Four-State Model with Unequal Substeps

A periodic one-dimensional four-state hopping model is proposed. In the model, the substeps betweenarbitrary adjacent states are unequal, and an explicit solution of the master equation is first obtained for the probabilitydistribution as a function of the time and position for any initial distribution with all the transients included. Next, thetransient behaviors in the initial period of time and the characteristic time to reach the steady state for the molecularmotor are discussed. Finally, we compare the steady state results to experiments and illustrate qualitatively the kineticbehaviors of a molecular motor under external load F.