Generalization of the Gibbsian relation for dilute systems

The Gibbsian relation is of fundamental importance to the thermodynamics of nonequilibrium systems. In this paper, we shall present an analytical derivation and several generalizations of this relation for dilute, nonequilibrium and certain highly nonequilibrium, systems. Our analysis will beindependent of the collision dynamics, because it will be based on the general kinetic equation witharbitrary collision integrals. Consequently, our analysis can provide athermodynamic derivation and several generalizations of the Gibbsian relation. Our distribution functions can also admit some arbitrary, nonequilibrium and highly nonequilibrium, forms. With the help of the generalized Gibbsian relation and a fundamental axiom to be postulated, the entropy production rates and the generalized forces and fluxes will be studied for our highly nonequilibrium systems. The second law of thermodynamics will be postulated and verified in specific cases. Onsager's reciprocity relations will be discussed.     

Nonlinear characteristics of the quantitative relationship between the glass‐transition temperature and the structure of homopolymers

Fuzzy set theory was used to study the relationship between the glass‐transition temperature (T_g) and structure of homopolymers. The method can map the relationship and give the T_g for 235 polymers with a standard deviation of 8 K (the confidence bound was 90%). The entropy of the fuzziness was used to quantitatively describe the interactions among groups. The method was used to predict the T_g of 10 polymers not included in the 235 polymers, with a standard deviation of 9 K (the confidence bound was 90%). The study demonstrates again that fuzzy set theory can be effectively used to investigate the quantitative structure–property relationship of polymers. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 2164–2169, 2002     

光子晶体光纤的基模分析

简化了光子晶体光纤的模式计算公式，计算了六角晶格光子晶体光纤的色散关系，对不同空气柱半径的色散作了比较，发现随着空气柱半径的增加，模式折射率变小，波导模式色散的零色散点向长波方向移动。     

A Short Proof of Krattenthaler Formulas

With an effort to investigate a unified approach to the Lagrange inverse Krattenthaler established operator method we finally found a general pair of inverse relations, called the Krattenthaler forumlas. The present paper presents a very short proof of this formula via Lagrange interpolation. Further, our method of proof declares that the Krattenthaler result is unique in the light of Lagrange interpolation. Received April 9, 1999, Accepted December 7, 2000     

Design of group decisions II. In spaces of partial order fuzzy relations

For the case of initial data in the problem of group choice represented as fuzzy partial orderings two problems are solved: (1) design of a set group decisions which satisfy the Pareto unanimity principlle and stay ‘halfway’ between initial relations and (2) design of a unique group decision.     

Kramers-Kronig type of dispersion relation in nonlinear optics

The applicability of Kramers-Kronig (K-K) relation under nearly sharp resonant transition regime in narrow-gap semiconductors has been established and consequently, a generalized dispersion relation for nonlinear optical susceptibility of a dielectric is derived. This relation can be employed in the study of nonlinear optical processes in solids as well as in plasmas over a wide frequency spectrum.     

A Unified Approach to the Proportional Relation for Discrete-Time Single-Server Queues

It is well known that a simple relation called proportional relation holds for some queueing models, that is, the stationary queue length distribution of one system can be expressed as the product of a constant and the distribution of another system which is different only in the buffer capacity. Recently, the proportional relation has been verified for various discrete-time single-server queues with correlated arrivals, where it has been also shown that the proportional constant can be expressed in terms of the distribution of one system. This implies that the stationary queue length distribution of one system can be completely expressed in terms of the distribution of the other system. In this paper, we consider a generalized model of discrete-time single-server queue, which covers all previous ones, and give a simple and unified proof to the proportional relation as well as the expression of the proportional constant.     

Constant tolerance intersection graphs of subtrees of a tree

A chordal graph is the intersection graph of a family of subtrees of a host tree. In this paper we generalize this. A graph G=(V,E) has an (h,s,t)-representation if there exists a host tree T of maximum degree at most h, and a family of subtrees {S_v}_v∈V of T, all of maximum degree at most s, such that uv∈E if and only if |S_u∩S_v|?t. For given h,s, and t, there exist infinitely many forbidden induced subgraphs for the class of (h,s,t)-graphs. On the other hand, for fixed h?s?3, every graph is an (h,s,t)-graph provided that we take t large enough. Under certain conditions representations of larger graphs can be obtained from those of smaller ones by amalgamation procedures. Other representability and non-representability results are presented as well.     

Sun's Log-concavity Conjecture on the Catalan–Larcombe–French Sequence

Let {P_n}n≥0 denote the Catalan-Larcombe-French sequence,which naturally came from the series expansion of the complete elliptic integral of the first kind.In this paper,we prove the strict log-concavity of the sequence {P_n~(1/n)}_n≥1,which was originally conjectured by Z.W.Sun.We also obtain the strict log-concavity of the sequence {V_n~(1/n)}_n≥1,where {V_n}_n≥0 is the Fennessey-LarcombeFrench sequence arising from the series expansion of the complete elliptic integral of the second kind.     

A result on combinatorial curvature for embedded graphs on a surface

Let G be an infinite graph embedded in a surface such that each open face of the embedding is homeomorphic to an open disk and is bounded by finite number of edges. For each vertex x of G, we define the combinatorial curvature