Weak stability of almost regular contact foliations

We prove that on a compact manifold, a contact foliation obtained by a smallC ¹ perturbation of an almost regular contact flow has at least two closed characteristics. This solves the Weinstein conjecture for contact forms which areC ¹-close to almost regular contact forms.Supported in part by NSF Grant DMS 90-01861     

Ekeland变分原理的推广及其应用

本文给出一般形式的Ekeland变分原理,并讨论泛函强制性条件与一般形式的 (PS)’条件之间的关系.     

Finite arithmetic subgroups ofGL n,III

LetG be an algebraic group inGL _n (C) defined over Q, andK an algebraic number field with the maximal orderO _k . If the groupG(O _k ) of rational points ofG inM _n (O _k ) is a finite group and if it satisfies a certain condition, which is satisfied, for example, whenK is a nilpotent extension of Q and 2 is unramified, thenG(O _k ) is generated by roots of unity inK andG(Z). Dedicated to the memory of Professor K G Ramanathan     

A Characterization for Geodsic Spheres in Space Forms

We use the maximum principle for second-order elliptic operators to establish a sufficient condition for a compact hypersurface in a space form to be a geodesic sphere in terms of a pinching for the s-mean curvature.     

Quasilinear systems with memory kernels

We consider a quasilinear integrodifferential system in non-normal form. Such a system is a generalization of a phase-field model with memory and includes, as a particular case, the system describing the combustion of a material with memory. In this paper, we study both the direct and the inverse problems. Our fundamental tools are: the theory of analytic semigroups, optimal regularity results and fixed point arguments.     

单位球面上的子流形有关截曲率的Pinching定理

设M是单位球面上不含脐点的子流形,Moebius形式Φ消失,本文讨论M 关于Mobius度量的截曲率的Pinching问题.     

On the Proper Form of the Amplitude Modulation Equations for Resonant Systems

The complex amplitude modulation equations of a discrete dynamicalsystem are derived under general conditions of simultaneous internal andexternal resonances. Alternative forms of the real amplitude and phaseequations are critically discussed. First, the most popular polar formis considered. Its properties, known in literature for a multitude ofspecific problems, are here proven for the general case. Moreover, thedrawbacks encountered in the stability analysis of incomplete motions(i.e. motions containing some zero amplitudes) are discussed as aconsequence of the fact the equations are not in standard normal form.Second, a so-called Cartesian rotating form is introduced, which makesit possible to evaluate periodic solutions and analyze their stability,even if they are incomplete. Although the rotating form calls for theenlargement of the space and is not amenable to analysis of transientmotions, it systematically justifies the change of variables sometimesused in literature to avoid the problems of the polar form. Third, amixed polar-Cartesian form is presented. Starting from the hypothesisthat there exists a suitable number of amplitudes which do not vanish inany motion, it is proved that the mixed form leads to standard formequations with the same dimension as the polar form. However, if suchprincipal amplitudes do not exist, more than one standard form equationshould be sought. Finally, some illustrative examples of the theory arepresented.     

A Rational Triplic Form for the Exponential

The theory of the power series solution is applied to the Hamburger DE to derive an improper fraction triplic form, E₂ ^N(x), for e^x on the real line. E₂ ^N turns out to be a simpler equivalent to the vertical sequence P₂ ^N of the related Padé table P_M ^N and with comparable summation features.     

关于Riemann流形中的2-调和子流形

讨论了黎曼流形中的 2-调和子流形,获得了这类子流形的第二基本形式模长平方和Ricci曲率的pinching定理:设M是n+p维黎曼流形N的具有平行平均曲率向量的n维 2-调和子流形,如果N的截面曲率的上、下确界分别记为KN和KN,则当M的第二基本形式模长平方s[ (n-1)KN-KN+nH2 ]时,M是极小子流形。