双孔干涉产生偏振奇点分析

在近轴近似的条件下,采用标量衍射积分的方法,对电磁场的双孔干涉进行了研究,并对千涉场中产生偏振奇点的情况进行了推广。在研究中通过双孔的光电场为线偏振状态,具有不同的偏振方向。数值计算结果表明,即使通过双孔的光电场的相位相同,只要双孔的尺寸存在一定的差异,干涉场中除了能够产生普通的的线偏振外,圆偏振奇点也会出现。     

Vortex structures with complex points singularities in two-dimensional Euler equations. New exact solutions

In this work we present a new class of exact stationary solutions for two-dimensional (2D) Euler equations. Unlike already known solutions, the new ones contain complex singularities. We consider point singularities which have a vector field index greater than 1 as complex. For example, the dipole singularity is complex because its index is equal to 2. We present in explicit form a large class of exact localized stationary solutions for 2D Euler equations with a singularity whose index is equal to 3. The solutions obtained are expressed in terms of elementary functions. These solutions represent a complex singularity point surrounded by a vortex satellite structure. We also discuss the motion equation of singularities and conditions for singularity point stationarity which provide the stationarity of the complex vortex configuration.     

Lightcone dualities for hypersurfaces in the sphere

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.     

LIMIT CYCLES BIFURCATION FOR A CLASS OF DEGENERATE SINGULARITY

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.     

An explicit recursive formula for computing the normal forms associated with semisimple cases

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.     

一个求留数方法的注记

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.     

Psi‐series method for equality of random trees and quadratic convolution recurrences

An unusual and surprising expansion of the form as , is derived for the probability p_n 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     

Fermi-edge singularities in the photoluminescence spectrum of modulation-doped GaAs v-groove quantum wires

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.