Partitioning a non-symmetric measure of association for three-way contingency tables

The Goodman-Kruskal tau index is a popular measure of asymmetry for two-way contingency tables where there is a one-way relationship between the variables. Numerous extensions of this index for multi-way tables have been considered in the statistical literature. These include the Gray-Williams measures, Simonetti's delta index and the Marcotorchino index.This paper looks at the partition of the Marcotorchino index for a three-way contingency table with one, two and three ordered categorical variables. Such a partition makes use of orthogonal polynomials and identifies two-way measures of asymmetry (akin to the Goodman-Kruskal tau index) and three-way measures generalisation. These partitions provide information about the structure of the asymmetric relationship between the categories in terms of location, dispersion and higher order moments.     

Representations of a class of lattice type vertex algebras

In this paper we study the representation theory for certain “half lattice vertex algebras.” In particular we construct a large class of irreducible modules for these vertex algebras. We also discuss how the representation theory of these vertex algebras are related to the representation theory of some associative algebras.     

Explicit continued fractions and quantum gravity

This paper deals with the subject of completely integrable systems, particularly Painlevé equations, monodromy and Stokes parameters, complex analysis, approximation theory, computational mathematics, and number theory. The starting point is the rather narrow question: What is the closed-form expression for the continued fraction expansions of functions having closed (explicit) form definition?     

Maximal multihomogeneity of algebraic hypersurface singularities

From the degree zero part of the logarithmic vector fields along analgebraic hypersurface singularity we identify the maximal multihomogeneity of a defining equation in form of a maximal algebraic torus in the embedded automorphism group. We show that all such maximal tori are conjugate and in one–to–one correspondence to maximal tori in the linear jet of the embedded automorphism group. These results are motivated by Kyoji Saito’s characterization of quasihomogeneity for isolated hypersurface singularities [Saito in Invent. Math. 14, 123–142 (1971)] and extend previous work with Granger and Schulze [Compos. Math. 142(3), 765–778 (2006), Theorem 5.4] and of Hauser and Müller [Nagoya Math. J. 113, 181–186 (1989), Theorem 4].     

Limit theorems and Markov approximations for chaotic dynamical systems

Summary We prove the central limit theorem and weak invariance principle for abstract dynamical systems based on bounds on their mixing coefficients. We also develop techniques of Markov approximations for dynamical systems. We apply our results to expanding interval maps, Axiom A diffeomorphisms, chaotic billiards and hyperbolic attractors.     

MgB4O7中Ce^3＋和Mn^2＋的光致发光及其能量传递

本文研究了ＭｇＢ４Ｏ７中Ｃｅ＾３＋，Ｍｎ＾２＋光致发光性质与浓度的关系，并讨论了Ｃｅ＾３＋→Ｍｎ＾２＋能量传递的机理。     

On factorial double solids with simple double points

We study when double covers of P³ ramified along nodal surfaces are not Q-factorial. In particular, we describe all the Q-factorial double covers of P³ ramified along quartic surfaces with at most seven simple double points and sextic surfaces with at most 16 simple double points.     

基态和激发态氧振动光谱的量子力学计算

利用分子势能函数的Murrell-Sorbie和PG函数形式,将时域有限差分法应用基态和激发态氧分子的振动能级的量子力学计算,计算结果令人满意.     

Studies of two interrelated series of triiridatrithia-cyclohexane and trimetallatrithia (or trioxo)-adamantane rhodium and iridium complexes

From a comparativereview on the two title series of compounds, the first part of the paper describes the most salient structural and reactivity properties of these trimetallic complexes, including metal-metal bond formation, conformational changes, enantio, and diastereomorphism. The second part presentsnew results which extend the comparison to a series of trimetallatrioxo adamantane complexes. The single crystal X-ray diffraction of the parent compound [Rh₃{μ ₃−(OCH₂)₃CCH₃}(CO)₆]—a derivative of the commercially available tripod ligand 1,1,1tris (oxomethyl)ethane—is reported together with its crystal packing which is compared to that of its sulfido analog. The paper includes a discussion of the nucleophilic and electrophilic properties of the trimetalla trioxo adamantane rhodium complexes, based on semi-empirical extended Hückel calculations Dedicated to Professor Yves Jeannin on the occasion of his 65 th birthday.     

Vanadia-silica xerogels: optical and structural properties

Vanadium doped silica gels were prepared from tetraethyl orthosilicate and three different inorganic vanadium precursors with formal oxidation states of V³⁺, V⁴⁺ and V⁵⁺ respectively. Optical and EPR studies were carried out on the dried gels to understand the changes in the oxidation state and coordination of vanadium in the doped silica gel matrix. The observed optical and EPR results provide very strong evidence to establish that irrespective of the starting material, vanadium is stabilized as vanadyl ion in the gel monoliths. EPR studies on the powdered samples corroborate the optical data on the gel samples and confirmed that the stabilized vanadyl ion is situated in a distorted octahedral geometry in these silica gels.