权为任意正实数的Poincare级数（II）解析的情形

设ｒ为一个正实数，１＜ｒ＜２，是一个Ｈ－群，υ：Γ→Ｃ是一个乘子系（定义见文［８］）．本文在［８］的基础上讨论了Ｐｏｉｎｃａｒｅ级数的存在性．令Ｐ＿（ｎｒ）（ｚ，υ，Ａ＿ｊ，Γ，ｋ＿ｊ）＝Ｐ＿（ｎｒ）（ｚ，０，υ，Γ，ｋ＿ｊ）．这里Ｐ＿（ｎｒ）（ｚ，ｓ，Ａ＿ｊ，Γ，ｋ＿ｊ）如文［８］中定义．我们有：定理｛Ｐ＿（ｎｒ）（ｚ，υ，Ａ＿ｊ，Γ，ｋ＿ｊ）｝ｎ＋ｋ＿Ｋ＞０是群Γ的，权为ｒ的具有乘子系υ的全纯歧点型模形式，且它们张成歧点型模形式所成的空间．应用这个结果，我们证明了一些模形式的性质并推导出一个重要的恒等式．该恒等式在半整权模形式的Ｆｏｕｒｉｅｒ系数估计中有极重要的地位．     

ZERO SET OF SOBOLEV FUNCTIONS WITH NEGATIVE POWER OF INTEGRABILITY

§1. Introduction Let ? ? Rn (n ≥1) be an open set, p ≥1. We consider functions u ∈W1 (?), such ,pthat, for some α> 0, |u|? < ∞. α (1.1) ?When p = 1, it is also natural to consider u ∈BV (?) which satis?es (1.1). For any u ∈W1 (?), p ≥1 or u ∈BV (?), we de?ne its zero set by …     

POINCAR BIFURCATION FOR QUADRATIC SYSTEMS WITH A CENTER REGION AND AN UNBOUNDED TRIANGULAR REGION

In this paper, we discuss the Poincare bifurcation for a class of quadratic systems with an unbounded triangular region and a center region. It is proved, by Poincare bifurcation, that inside the center region quadratic system perturbed by quadratic polynomial perturbation may generate three limit cycles.     

A topological horseshoe in a fractional-order Qi four-wing chaotic system

A fractional-order Qi four-wing chaotic system is present based on the Grunwald-Letnikov denition. The existence of topological horseshoe in a fractional chaotic system is analyzed by utilizing topological horseshoe theory. A Poincare section is properly chosen to obtain the Poincare map which is proved to be semi-conjugate to a 2-shift map, implying that the fractional-order Qi four-wing chaotic system exhibits chaos.     

VANISHING THEOREMS FOR ACH KAHLER MANIFOLDS AND HARMONIC MAPS

We discuss a class of complete Kaihler manifolds which are asymptotically complex hyperbolic near infinity. The main result is vanishing theorems for the second L2 cohomology of such manifolds when it has positive spectrum. We also generalize the result to the weighted Poincare inequality case and establish a vanishing theorem provided that the weighted function p is of sub-quadratic growth of the distance function. We also obtain a vanishing theorem of harmonic maps on manifolds which satisfies the weighted Poincare inequality.     

Poincaré线性连续统直觉概念的公式化(英文)

本文研究了Poincaré著名注记中“内束”观念的数学表述法问题,通过构建Poincaré连续统模型,得到了这一问题的一种解答。文中还论述了有关数理哲学及方法论问题;文末特别指出了须继续研究的数学问题。     

Bifurcations of rough heteroclinic loop with two saddle points

The bifurcation problems of rough 2-point-loop are studied for the case p11 > λ11, p21 < λ21, P11p21 <λ111λ21. where - pi1 < 0 and λi1 > 0 are the pair of principal eigenvalues of unperturbed system at saddle point pi, i = 1,2. Under the transversal and nontwisted conditions, the authors obtain some results of the existence of one 1-periodic orbit, one 1-periodic and one 1-homoclinic loop, two 1-periodic orbits and one 2-fold 1-periodic orbit. Moreover, the bifurcation surfaces and the existence regions are given, and the corresponding bifurcation graph is drawn.     

Covariant and dynamical reduction for principal bundle field theories

Reduction for field theories with symmetry can be done either covariantly—that is, on spacetime—or dynamically—that is, after spacetime is split into space and time. The purpose of this article is to show that these two reduction procedures are, in an appropriate sense, equivalent for a class of field theories whose fields take values in a principal bundle. One can think of this class of field theories as including examples such as a “sea of rigid bodies” with and appropriate interbody coupling potential.     

THE POINCAR BIFURCATION OF A CUBIC HAMILTONIAN SYSTEM WITH HOMOCLINIC LOOP

In this paper, we discuss the Poincare bifurcation of a cubic Hamiltonian system with homoclinic loop. We prove that the system can generate at most seven limit cycles after a small perturbation of general cubic polynomials.     

Hilbert模形式与一类Dirichlet级数的特殊值

在文［２］中，Ｗ．Ｋｏｈｎｎ对权为ｋ和ｌ的任意二个歧点型模形式ｆ和ｇ（其变换群是全模群ＳＬ＿２（Ｚ））定义了一类Ｄｉｒｉｃｈｌｅｔ级数Ｌ＿（ｆ，ｇ，ｎ）（ｓ），利用Ｌ＿（ｆ，ｇ；ｎ）（ｓ）（为整数），可构造一个线性映射Ｗ＿ｇ：Ｓ＿ｋ→Ｓ＿（ｋ－ｌ）．并且讨论了Ｌ＿（ｆ，ｇ；ｎ）的一些特征值．在本文中，我们将［２］中的结果推广到Ｈｉｌｂｅｒｔ模形式的情况，并得到类似的结论．