The solvable radical of Sylow factorizable groups

Let G be a finite group. A complete Sylow product of G is a product of Sylow subgroups of G, one for each prime divisor of |G|. We shall call G a Sylow factorizable group if it is equal to at least one of its complete Sylow products. We prove that if G is a Sylow factorizable group then the intersection of all complete Sylow products of G is equal to the solvable radical of G. We generalize the concepts and the result to Sylow products which involve an arbitrary subset of the prime divisors of |G|. Received: 26 January 2005     

Bayesian estimation of keyword confidence in Chinese Continuous speech recognition

In a syllable-based speaker-independent Chinese continuous speech recognition system based on classical Hidden Markov Model(HMM),a Bayesian approach of keyword confidence estimation is studied,which utilizes both acoustic layer scores and syllable-based statistical language model(LM) score.The Maximum a posteriori(MAP) confidence measure is proposed,and the forward-backward algorithm calculating the MAP confidence scores is deduced.The performance of the MAP confidence measure is evaluated in keyword spotting application and the experiment results show that the MAP confidence scores provide high discriminability for keyword candidates.Furthermore,the MAP confidence measure can be applied to various speech recognition applications.     

Laplacians and the Cheeger Inequality for Directed Graphs

We consider Laplacians for directed graphs and examine their eigenvalues. We introduce a notion of a circulation in a directed graph and its connection with the Rayleigh quotient. We then define a Cheeger constant and establish the Cheeger inequality for directed graphs. These relations can be used to deal with various problems that often arise in the study of non-reversible Markov chains including bounding the rate of convergence and deriving comparison theorems.Received September 8, 2004     

Orbital formal normal forms for general Bogdanov-Takens singularity

We solve completely the problem of classification of germs of complex planar vector fields with nilpotent singularity with respect to formal orbital equivalence.     

Bi12TiO20纳米粉体的制备及其光吸收特性研究

以钛酸四丁酯和硝酸铋为原料 ,利用化学溶液分解法制备了Bi12 TiO2 0 纳米多晶粉体 .采用XRD和TEM对其结构和形貌进行了表征 .结合热重 差热 (TG DTA)分析 ,探讨了Bi12 TiO2 0 晶相的形成机理 .通过UV Vis漫反射谱的测定 ,研究了Bi12 TiO2 0 纳米晶粉体的光吸收特性 .结果显示 ,从组成为化学计量比的前驱液中可以很容易制得纯Bi12 TiO2 0 纳米晶粉体 ,该Bi12 TiO2 0 纳米晶粉体呈现了在很宽的波长范围内 (5 6 0～ 385nm )对光的吸收的特性 .     

Ihara zeta functions of digraphs

After defining and exploring some of the properties of Ihara zeta functions of digraphs, we improve upon Kotani and Sunada’s bounds on the poles of Ihara zeta functions of undirected graphs by considering digraphs whose adjacency matrices are directed edge matrices.     

On the bidirectional vortex and other similarity solutions in spherical coordinates

The bidirectional vortex refers to the bipolar, coaxial swirling motion that can be triggered, for example, in cyclone separators and some liquid rocket engines with tangential aft-end injectors. In this study, we present an exact solution to describe the corresponding bulk motion in spherical coordinates. To do so, we examine both linear and nonlinear solutions of the momentum and vorticity transport equations in spherical coordinates. The assumption will be that of steady, incompressible, inviscid, rotational, and axisymmetric flow. We further relate the vorticity to some power of the stream function. At the outset, three possible types of similarity solutions are shown to fulfill the momentum equation. While the first type is incapable of satisfying the conditions for the bidirectional vortex, it can be used to accommodate other physical settings such as Hill’s vortex. This case is illustrated in the context of inviscid flow over a sphere. The second leads to a closed-form analytical expression that satisfies the boundary conditions for the bidirectional vortex in a straight cylinder. The third type is more general and provides multiple solutions. The spherical bidirectional vortex is derived using separation of variables and the method of variation of parameters. The three-pronged analysis presented here increases our repertoire of general mean flow solutions that rarely appear in spherical geometry. It is hoped that these special forms will permit extending the current approach to other complex fluid motions that are easier to capture using spherical coordinates.     

Equivariant fixed-point indices of iterated maps

We describe an equivariant version (for actions of a finite group G) of Dold’s index theory, [10], for iterated maps. Equivariant Dold indices are defined, in general, for a G-map U → X defined on an open G-subset of a G-ANR X (and satisfying a suitable compactness condition). A local index for isolated fixed-points is introduced, and the theorem of Shub and Sullivan on the vanishing of all but finitely many Dold indices for a continuously differentiable map is extended to the equivariant case. Homotopy Dold indices, arising from the equivariant Reidemeister trace, are also considered.      

On semi cover-avoiding subgroups of finite groups

A subgroup H of a finite group G is said to have the semi cover-avoiding property in G if there is a normal series of G such that H covers or avoids every normal factor of the series. In this paper, some new results are obtained based on the assumption that some subgroups have the semi cover-avoiding property in the group.