Jordan标准形定理的初等变换证明

本文对 Jordan标准形定理给出了一种使用初等变换的证明 ,直观意义明显、易于理解 ,可用于线性代数教学 .     

Stability problem of a circular sandwich ring under uniform external pressure

The solution of the stability problem of a circular sandwich ring under uniform external pressure is given in a refined statement. The need to determinate the precritical stresses in load-bearing layers in the refined statement with regard to the transverse compression of the core is established, which is the basis for the detection of the mixed flexural buckling forms (BFs) with more than two half-waves along the circumferential coordinate (n>2). It is found that sandwich structures with a determining parameter of transverse compression corresponding to the limit of transition from the mixed BFs to synphasic ones are the most efficient from the weight viewpoint. Translated from Mekhanika Kompozitnykh Materialov, Vol. 36, No. 3, pp. 317–328, May–June, 2000.     

Hermite and Smith normal form algorithms over Dedekind domains

We show how the usual algorithms valid over Euclidean domains, such as the Hermite Normal Form, the modular Hermite Normal Form and the Smith Normal Form can be extended to Dedekind rings. In a sequel to this paper, we will explain the use of these algorithms for computing in relative extensions of number fields.

     

一类间接控制系统的绝对稳定性问题

利用厄米特二次型和若当标准形理论研究了一般间接控制系统的绝对稳定性问题,给出了绝对稳定性的代数形式的判别准则。所得到的结果是新的和有用的。     

Fuzzy线性映射

在基本Fuzzy点空间上提出了Fuzzy线性映射的概念,证明了Fuzzy线性映射的表示定理,讨论了Fuzzy线性映射的合成、可逆及保持Fuzzy集合的线性运算等相关性质。     

A necessary condition for the minimum of a quadratic form under rearrangements

A necessary condition is derived for a quadratic form p^tGp to be minimal among all permutations of the nonnegative nontrivial vector p. The quadratic form arises from the stability problem of a fixed-fixed taut string loaded with masses at equidistant points.     

Analysis of the Electronic Vibrational Spectra of Bisanthene by Calculating Normal Modes

At 4.2 K, the quasiline fluorescence and fluorescence-excitation spectra (in the region of the S ₁ S ₀- and S ₂ S ₀ transitions) of bisanthene in n-hexane have been obtained. Using the MO/M8ST method, the calculation of the A _g normal modes in the S ₀, S ₁, and S ₂ electronic states was carried out for the bisanthene molecule; the relative intensities of the transitions in the corresponding vibronic spectra were also calculated. The analysis of the results of calculations and experiment made it possible to draw conclusions on the form of the modes for a number of normal vibrations which are active in the bisanthene vibronic spectra.     

LOCALIZED PATTERNS OF THE CUBIC-QUINTIC SWIFT-HOHENBERG EQUATIONS WITH TWO SYMMETRY-BREAKING TERMS

Homoclinic snake always refers to the branches of homoclinic orbits mbox{near} a heteroclinic cycle connecting a hyperbolic or non-hyperbolic equilibrium and a periodicorbit in a reversible variational system. In this paper, the normal form of a Swift-Hohenberg equation with two different symmetry-breaking terms (non-reversible term and non-k-symmetry term) are investigated by using multiple scale method, and their bifurcation diagrams are initially studied by numerical simulations. Typically, we predict numerically the existence of so-called round-snakes and round-isolas upon particular two symmetric-breaking perturbations.     

Quasilinear Schrödinger equations with unbounded or decaying potentials

We study the existence of nonnegative and nonzero solutions for the following class of quasilinear Schrödinger equations: where V and Q are potentials that can be singular at the origin, unbounded or vanishing at infinity. In order to prove our existence result we used minimax techniques in a suitable weighted Orlicz space together with regularity arguments and we need to obtain a symmetric criticality type result.