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51.
In this paper, we consider hypersurfaces in the unit lightlike sphere. The unit sphere can be canonically embedded in the lightcone and de Sitter space in Minkowski space. We investigate these hypersurfaces in the framework of the theory of Legendrian dualities between pseudo‐spheres in Minkowski space. 相似文献
52.
In this paper, bifurcation of limit cycles for the degenerate equilibrium to a three- dimensional system is investigated. Firstly, we use formal series to calculate the focal values at the high-order critical point on center manifold. Then an example is studied, and the existence of 3 limit cycles on the center manifold is proved. In terms of high- order singularities in high-dimensional systems, our results are new. 相似文献
53.
《Communications in Nonlinear Science & Numerical Simulation》2014,19(7):2294-2308
This paper presents an explicit, computationally efficient, recursive formula for computing the normal forms, center manifolds and nonlinear transformations for general n-dimensional systems, associated with semisimple singularities. Based on the formula, we develop a Maple program, which is very convenient for an end-user who only needs to prepare an input file and then execute the program to “automatically” generate the result. Several examples are presented to demonstrate the computational efficiency of the algorithm. 相似文献
54.
对解析函数f(z)=p(z)/q(z),当z=a分别是p(z)和q(z)的m级零点和n级零点,且0≤m<n时,特别地n=m+2时,讨论了求f(z)在极点z=a处留数的方法并举例说明其应用. 相似文献
55.
Hua‐Huai Chern María‐Inés Fernández‐Camacho Hsien‐Kuei Hwang Conrado Martínez 《Random Structures and Algorithms》2014,44(1):67-108
An unusual and surprising expansion of the form as , is derived for the probability pn that two randomly chosen binary search trees are identical (in shape, hence in labels of all corresponding nodes). A quantity arising in the analysis of phylogenetic trees is also proved to have a similar asymptotic expansion. Our method of proof is new in the literature of discrete probability and the analysis of algorithms, and it is based on the logarithmic psi‐series expansions for nonlinear differential equations. Such an approach is very general and applicable to many other problems involving nonlinear differential equations; many examples are discussed in this article and several attractive phenomena are discovered.Copyright © 2012 Wiley Periodicals, Inc. Random Struct. Alg., 44, 67–108, 2014 相似文献
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J. Kim A. Maciel E. D. O'Sullivan J. F. Ryan A. Schwarz A. Kaluza H. Hardtdegen Th. Schpers H. Lüth D. Meertens Ch. Dieker 《Physica E: Low-dimensional Systems and Nanostructures》2000,7(3-4)
We report the observation of strong Fermi-edge singularities in the photoluminescence spectrum of strongly-confined, modulation-doped GaAs v-groove quantum wires. The behaviour of the singularity has been investigated at high excitation intensity, and both lattice and electrical heating. The latter produces a strong reduction of the singularity due to Fermi surface smearing, whereas, increased photoexcitation produces complex electron–hole correlation effects. 相似文献
59.
HUANG Xiaojun 《中国科学A辑(英文版)》2006,49(11):1441-1450
In this paper, we discuss some recent studies on the complex structure of an isolated normal singularity by using the information
from its link. We also give some open problems to be further pursued.
Dedicated to Professor Sheng GONG on the occasion of his 75th birthday 相似文献
60.
YAU Stephen S T 《中国科学A辑(英文版)》2006,(11)
Let V be a hypersurface with an isolated singularity at the origin in Cn 1. It is a natural question to ask when V is defined by weighted homogeneous polynomial or homogeneous polynomial up to biholomorphic change of coordinates. In 1971, a beautiful theorem of Saito gives a necessary and sufficient condition for V to be defined by a weighted homogeneous polynomial. For a two-dimensional isolated hypersurface singularity V, Xu and Yau found a coordinate free characterization for V to be defined by a homogeneous polynomial. Recently Lin and Yau gave necessary and sufficient conditions for a 3-dimensional isolated hypersurface singularity with geometric genus bigger than zero to be defined by a homogeneous polynomial. The purpose of this paper is to prove that Lin-Yau's theorem remains true for singularities with geometric genus equal to zero. 相似文献