膜与不可压缩有界流体接触时的自由振动

圆形膜与流体接触时的振动被广泛应用于工业中．推导了圆形膜在与不可压缩有界流体接触时,非对称自由振动的自振频率．鉴于膜在不可压缩、非粘性流体中振动引起的小振幅,采用速度势函数来描述流体场．使用两种方法来推导系统的自由振动频率．它们包括变分法及一种近似解法——Rayleigh商法．在用两种方法求得的自由振动频率值之间具有良好的相关性．最后,研究了流体的深度、质量密度以及径向张力对耦合系统自由振动频率的影响．     

Compact Clifford–Klein Forms of Homogeneous Spaces of SO(2, n)

A homogeneous space G/H is said to have a compact Clifford–Klein form if there exists a discrete subgroup of G that acts properly discontinuously on G/H, such that the quotient space \G/H is compact. When n is even, we find every closed, connected subgroup H of G = SO(2, n), such that G/H has a compact Clifford–Klein form, but our classification is not quite complete when n is odd. The work reveals new examples of homogeneous spaces of SO(2, n) that have compact Clifford–Klein forms, if n is even. Furthermore, we show that if H is a closed, connected subgroup of G = SL(3, R), and neither H nor G/H is compact, then G/H does not have a compact Clifford–Klein form, and we also study noncompact Clifford–Klein forms of finite volume.     

Seminormal or t-Closed Schemes and Rees Rings

We define decent schemes and canonically decent projective schemes. Forsuch schemes, total quotient schemes exist, allowing to get thenormalization, seminormalization and t-closure of a decent scheme as ascheme. We exhibit the seminormalization and t-closure of a filtration on aring. If A is a decent ring and F a regular filtration onA, the associated Rees ring R is decent andProj(R) is canonically decent. The seminormalization and t-closureof R are Rees rings and the seminormalization and t-closure ofProj(R) are gotten by using projective morphisms.     

A multifractal study of wave functions in 1-D quasicrystals

Using multifractal analysis we study extended, self-similar and non-self-similar type of wave functions in the Fibonacci model. Extended states arising due to commutation of transfer matrices for certain blocks of atoms in quasiperiodic systems are shown to have the same signature as the Bloch states in terms of the singularity spectrum withf(α)=α=1. Numerically, however, the extended states show a typical multifractal behaviour for finite chain lengths. Finite size scaling corrections yield results consistent with that obtained analytically. The self-similar states at the band edges show a multifractal behaviour and they are energy dependent in the case of blocks of atoms arranged in a Fibonacci sequence. For non-self-similar states we obtain a non-monotonic behaviour off(α) as a function of the chain length. We also show that in cases where extended states exist, the cross-over from extended to non-self-similar states in gradual.     

The transition from bursting to continuous spiking in excitable membrane models

Summary Mathematical models for excitable membranes may exhibit bursting solutions, and, for different values of the parameters, the bursting solutions give way to continuous spiking. Numerical results have demonstrated that during the transition from bursting to continuous spiking, the system of equations may give rise to very complicated dynamics. The mathematical mechanism responsible for this dynamics is described. We prove that during the transition from bursting to continuous spiking the system must undergo a large number of bifurcations. After each bifurcation the system is increasingly chaotic in the sense that the maximal invariant set of a certain two-dimensional map is topologically equivalent to the shift on a larger set of symbols. The number of symbols is related to the Fibonacci numbers.     

关于点可数覆盖

本文证明了（１）具有点可数基空间的商ｓ－像Ｘ有点可数基的充要条件是Ｘ是ｑ－空间；（２）度量空间的伪开ｓ－像若满足条件（＊），则它在伪开ｓ－映射下是保持的，（３）给出反例否定地回答了［１］和［２］中的问题．     

差商变尺度法的超线性收敛性

在文[1]的基础上,本文继续研究差商变尺度法的收敛性质,从文[1]的整体收敛性出发,进一步探讨了差商变尺度法的超线性收敛的特征,同时给出了保证超线性收敛的差商步长条件。     

A Morita type theorem for a sort of quotient categories

We consider the quotient categories of two categories of modules relative to the Serre classes of modules which are bounded as abelian groups and we prove a Morita type theorem for some equivalences between these quotient categories.     

Accuracy of Computed Eigenvectors Via Optimizing a Rayleigh Quotient

This paper establishes converses to the well-known result: for any vector such that the sine of the angle sin(u, )=O(), we have

On the construction of certain 6-dimensional symplectic manifolds with Hamiltonian circle actions

Let be a connected, compact 6-dimensional symplectic manifold equipped with a semi-free Hamiltonian action such that the fixed point set consists of isolated points or surfaces. Assume dim . In an earlier paper, we defined a certain invariant of such spaces which consists of fixed point data and twist type, and we divided the possible values of these invariants into six ``types'. In this paper, we construct such manifolds with these ``types'. As a consequence, we have a precise list of the values of these invariants.