A parametric representation of linguistic hedges in Zadeh’s fuzzy logic

This paper proposes a model for the parametric representation of linguistic hedges in Zadeh’s fuzzy logic. In this model each linguistic truth-value, which is generated from a primary term of the linguistic truth variable, is identified by a real number r depending on the primary term. It is shown that the model yields a method of efficiently computing linguistic truth expressions accompanied with a rich algebraic structure of the linguistic truth domain, namely De Morgan algebra. Also, a fuzzy logic based on the parametric representation of linguistic truth-values is introduced.     

X分形晶格上Gauss模型的临界性质

采用实空间重整化群变换的方法,研究了2维和d(d>2)维X分形晶格上Gauss模型的临界性质.结果表明:这种晶格与其他分形晶格一样,在临界点处,其最近邻相互作用参量也可以表示为K=bqiqi(qi是格点i的配位数,bqi是格点i上自旋取值的Gauss分布常数)的形式;其关联长度临界指数v与空间维数d(或分形维数df)有关.这与Ising模型的结果存在很大的差异. 关键词： X分形晶格 重整化群 Gauss模型 临界性质     

Difference discrete connection and curvature on cubic lattice Dedicated to Professor Sheng GONG on the occasion of his 75th birthday

In a way similar to the continuous case formally, we define in different but equivalent manners the difference discrete connection and curvature on discrete vector bundle over the regular lattice as base space. We deal with the difference operators as the discrete counterparts of the derivatives based upon the differential calculus on the lattice. One of the definitions can be extended to the case over the random lattice. We also discuss the relation between our approach and the lattice gauge theory and apply to the discrete integrable systems.     

一类平面七次多项式系统赤道环的稳定性与极限环分支

本文研究一类平面七次多项式系统赤道环的稳定性和极限环分支，给出了系统的前12个奇点量公式，可积性条件及在赤道附近存在3个极限环的条件，较为精细地指出了极限环的存在位置。     

Numerical analysis of the Toda lattice equations

Numerical solutions to three systems of integrable evolutionary equations from the Toda lattice hierarchy are analyzed. These are the classical Toda lattice, the second local dispersive flow, and the second extended dispersive flow. Special attention is given to the properties of soliton solutions. For the equations of the second local flow, two types of solitons interacting in a special manner are found. Solutions corresponding to various initial data are qualitatively outlined.     

关于PFI-代数与剩余格

本文提出了一种强FI代数-PFI代数,并且深入研究了它的性质,借此进一步揭示了FI-代数和剩余格之间更加密切的联系,进而以FI-代数为基本框架建立了R0-代数、正则剩余格等逻辑系统的结构特征(包括对隅结构)及其相互关系．这种以FI-代数为基础来统一处理剩余格和R0-代数的方法,同样适合于格蕴涵代数和MV代数等代数结构,而且从中更能清楚地看出它们之间的密切联系,也将有助于对相应形式逻辑系统与模糊推理的研究．     

Measurements of edge-uncolorability

Cubic bridgeless graphs with chromatic index four are called uncolorable. We introduce parameters measuring the uncolorability of those graphs and relate them to each other. For k=2,3, let c_k be the maximum size of a k-colorable subgraph of a cubic graph G=(V,E). We consider r₃=|E|−c₃ and . We show that on one side r₃ and r₂ bound each other, but on the other side that the difference between them can be arbitrarily large. We also compare them to the oddness ω of G, the smallest possible number of odd circuits in a 2-factor of G. We construct cyclically 5-edge connected cubic graphs where r₃ and ω are arbitrarily far apart, and show that for each 1c<2 there is a cubic graph such that ωcr₃. For k=2,3, let ζ_k denote the largest fraction of edges that can be k-colored. We give best possible bounds for these parameters, and relate them to each other.     

Little Grothendieck's theorem for sublinear operators

Let SB(X,Y) be the set of the bounded sublinear operators from a Banach space X into a Banach lattice Y. Consider π₂(X,Y) the set of 2-summing sublinear operators. We study in this paper a variation of Grothendieck's theorem in the sublinear operators case. We prove under some conditions that every operator in SB(C(K),H) is in π₂(C(K),H) for any compact K and any Hilbert H. In the noncommutative case the problem is still open.     

Steady-state analytical solutions for the lattice boltzmann equation

A general class of analytical solutions of the lattice Boltzmann equation is derived for two-dimensional, steady-state unidirectional flows. A subset of the solutions that verifies the corresponding Navier-Stokes equations is given. It is pointed out that this class includes, e.g., the Couette and the Poiseuille flow but not, e.g., the basic Kolmogorov flow. For steady-state non-unidirectional flows, first and second order solutions of the lattice Boltzmann equation are derived. Practical consequences of the analysis are mentioned. Differences between the technique applied here and those used in some earlier works are emphasized.     

A Note on Cactus Trees: Variational vs. Recursive Approach

In this article we deal with the variational approach to cactus trees (Husimi trees) and the more common recursive approach, that are in principle equivalent for finite systems. We discuss in detail the conditions under which the two methods are equivalent also in the analysis of infinite (self-similar) cactus trees, usually investigated to the purpose of approximating ordinary lattice systems. Such issue is hardly ever considered in the literature. We show (on significant test models) that the phase diagram and the thermodynamic quantities computed by the variational method, when they deviates from the exact bulk properties of the cactus system, generally provide a better approximation to the behavior of a corresponding ordinary system. Generalizing a property proved by Kikuchi, we also show that the numerical algorithm usually employed to perform the free energy minimization in the variational approach is always convergent.