An exactly soluble case of the triangular ising model in a magnetic field

An anisotropic triangular Ising model in which the first- and second-order parameters and the field parameters are functionally related is solved exactly by representing the distribution of the atom patterns in terms of a suitably constructed Markov process. The probabilities of patterns, defined as the probabilities generated by this process, are a mathematically tractable alternative to the classical representation of these probabilities in terms of the partition function. The interaction and field parameters of this Ising model, its magnetization, free energy, and its nearest neighbor correlation functions, are expressed in terms of the parameters of this Markov process. Special cases are worked out in detail and numerical examples are given.     

Homology of Nilpotent Subalgebras of the Lie Superalgebra K(1,1).3

We calculate the dimensions of the second homology groups with trivial coefficients of nilpotent subalgebras of the Lie superalgebra , which is the natural superanalog of the Witt algebra. The proof is based on direct calculations of the rank of the differential. As an application, we find deformations of the maximal nilpotent subalgebra in .     

Uniqueness and asymptotic behaviour for solutions of semilinear problems with boundary blow-up

In this paper we prove uniqueness of positive solutions to logistic singular problems , , 1$">, 0$"> in , where the main feature is the fact that . More importantly, we provide exact asymptotic estimates describing, in the form of a two-term expansion, the blow-up rate for the solutions near . This expansion involves both the distance function and the mean curvature of .

     

Combinatorial analysis of Tetris-like games

We study some combinatorial properties of Tetris-like games by using Schützenberger methodology and probability generating functions. We prove that every Tetris-like game is equivalent to a finite state automaton and propose a straight foward algorithm to transform a Tetris-like game into its corresponding automaton. In this way, we can study the average number of pieces inserted during a game and the average score as a function of the player's ability and the pieces extrusion.     

非紧超凸度量空间中的一个新的极大元定理及其对抽象经济的应用

在非紧超凸度量空间中建立了一个新的极大元定理.作为应用，获得了连续选择及其不动点定理和一个Browder-Fan不动点定理.最后，新建了非紧超凸度量空间中的定性对策和抽象经济的平衡点存在定理.     

汽车保险的广义泊松过程模型

本文针对汽车保险中多车辆相撞事故的理赔建立起广义泊松过程模型,利用概率母泛函给出了其理赔总量在(0,t]内的均值与方差,并基于鞅分析方法证明了其破产概率的Lundberg不等式.     

Controlled Synthesis of CdClOH Sub-nanocones by Low-temperature Solution Process and Their Transformation into CdS Hollow Sub-nanocones

Novel CdClOH sub‐nanocone crystals were successfully synthesized on a large scale by a facile solution‐based method using polymers as crystal growth modifiers. The crystals showed cone‐like morphology. Some factors affecting the morphology and size of the product, such as reaction temperature, concentrations of polyacrylamide (PAM), and pH value of the solution, were systematically studied. Experiments implied that polymer PAM played a key role in the formation of CdClOH sub‐nanocones. A possible formation mechanism of CdClOH sub‐nanocones was suggested based on nucleation‐etching process‐recrystallization in a mild aqueous solution. Furthermore, the as‐prepared CdClOH sub‐nanocones could be further transformed into CdS hollow sub‐nanocones by an anion‐exchange reaction.     

五轴加工中心范成铣磨离轴非球面研究

离轴非球面作为非球面的一部分,是空间光学系统、天文学和高精度测量系统不可或缺的光学器件.针对空间光学对离轴非球面光学元件制造技术的重大需求,开展了离轴非球面反射镜的精密铣磨加工技术研究.分析了五轴联动范成法铣磨离轴非球面的原理,将离轴非球面所在的同轴母镜离散为一系列不同半径的球面环带,将工件坐标系建立在待加工离轴非球面...     

关于Newton级数的符号算子方法

In this paper, we present several expansions of the symbolic operator （1 ＋E）^x. Moreover, we derive some series transforms formulas and the Newton generating functions of {f（k）}.     

金属醇盐法制备Ta2O5气凝胶

 以乙醇钽为前驱物,采用金属醇盐溶胶-凝胶技术,获得了Ta₂O₅湿凝胶,分析了不同条件下的溶胶-凝胶过程,并初步探讨了凝胶过程机理。Ta₂O₅的溶胶-凝胶过程主要受到水量、催化剂用量及钽源浓度等因素的影响：体系在强酸性条件下凝胶,且随着酸性的增强,体系凝胶时间明显缩短;当水量较少时,凝胶时间随水量的增加而增加,但当水量增加到一定程度时,体系凝胶时间基本不变;实验证明,通过增大溶剂用量,体系凝胶时间延长,气凝胶理论密度降低。通过对溶胶-凝胶过程的控制,结合超临界干燥技术,获得了密度低至44 mg/cm³的Ta₂O₅气凝胶样品。