三对角行列式及其应用

利用递归方程得到了计算三对角行列式的一般方法 ,研究了三对角行列式在线性代数及组合数学中的应用 .     

二元关系的幂敛指数集

本文利用图论方法，给出了二元关系的幂敛指数集的明显表达式．     

Twisted Extensions of Spin Models

A spin model is one of the statistical mechanical models which were introduced by V.F.R. Jones to construct invariants of links. In this paper, we give a new construction of spin models of size 4n from a given spin model of size n. The process is similar to taking tensor product with a spin model of size four, but we add some sign exchange. This construction also gives symmetric four-weight spin models of the type introduced by E. Bannai and E. Bannai.     

On the generation techniques of axially symmetric stationary metrics

In the present paper, a relationship between the method of Gutsunaev-Manko and the soliton technique (for two-soliton solutions) of Belinskii-Zakharov, for generating solutions of axially symmetric stationary space-times in general relativity is discussed.     

Representation Theorems for Quantales

In this paper we prove that any quantale Q is (isomorphic to) a quantale of suitable relations on Q. As a consequence two isomorphism theorems are also shown with suitable sets of functions of Q into Q. These theorems are the mathematical background one needs in order to give natural and complete semantics for (non-commutative) Linear Logic using relations. Mathematics Subject Classification: 06D05, 06D10, 06D20, 03G25.     

Practical Method for Determining All the Minimum Solutions of Fuzzy Matrix Equation and Transitive Closure of Fuzzy Relation

In this paper,the new theory frame and practical methhod for determining all the minimumsolutions of Fuzzy matrix equation and transitive closure of Fuzzy relation is described,and it has beencarried out on the miero-computer quickly and accurately.     

Remarks on Uniformly Finitely Precomplete Positive Equivalences

The paper contains some observations on e-complete, precomplete, and uniformly finitely precomplete r. e. equivalence relations. Among these are a construction of a uniformly finitely precomplete r. e. equivalence which is neither e- nor precomplete, an extension of Lachlan's theorem that all precomplete r. e. equivalences are isomorphic, and a characterization of sets of fixed points of endomorphisms of uniformly finitely precomplete r. e. equivalences. Mathematics Subject Classification: 03D45.     

Molecular dynamics studies of thermal conductivity time correlation functions

The Green–Kubo time correlation function for the thermal conductivity in liquid argon is studied for a thermodynamic state close to the triple point by standard molecular dynamics simulations. The collective heat flux vector has been separated into contributions originated at the kinetic energy, the intermolecular potential and the pair virial function. Furthermore, the Green–Kubo time correlation functions have been broken down into partial n-body terms (n=1,2,3,4). The most important contribution to the thermal conductivity is represented by the auto correlation of the virial term. In contrast to other collective phenomena described by time correlation functions involving n-body terms, the partial Green–Kubo time correlation functions for the thermal conductivity are not affected by exponential long-time tails.     

Dissipation and large thermodynamic fluctuations

The results of recent work of Kipnis, Olla, and Varadhan on the dynamic large deviations from a hydrodynamic limit for some interacting particle models are formally extended to a general hydrodynamic situation, including non-equilibrium steady states, as a fluctuation-dissipation hypothesis. The basic conjecture is that the exponent of decay in the probability of a large thermodynamic fluctuation is given by the dissipation of the force required to produce the fluctuation. It is shown that this hypothesis leads to a nonlinear version of Onsager-Machlup fluctuation theory that had previously been proposed by Graham. A direct consequence of the theory is a dynamic variational principle for the most probable thermodynamic history subject to imposed constraints (Onsager's principle of least dissipation). Following Graham, the theory leads also to a generalized potential, analogous to an equilibrium free energy, for the nonequilibrium steady state and an associated static variational principle. Finally, a formulation of nonlinear fluctuating hydrodynamics is proposed in which the noise enters multiplicatively so as to reproduce the conjectured large-deviations theory on a formal analogy with the results of Freidlin and Wentzell for finite-dimensional systems.