Holomorphic Factorization of Determinants of Laplacians using Quasi-Fuchsian Uniformization

For a quasi-Fuchsian group Γ with ordinary set Ω, and Δ _n the Laplacian on n-differentials on Γ\Ω, we define a notion of a Bers dual basis for ker Δ _n . We prove that det , is, up to an anomaly computed by Takhtajan and the second author in (Commun. Math Phys 239(1-2):183–240, 2003), the modulus squared of a holomorphic function F(n), where F(n) is a quasi-Fuchsian analogue of the Selberg zeta function Z(n). This generalizes the D’Hoker–Phong formula det , and is a quasi-Fuchsian counterpart of the result for Schottky groups proved by Takhtajan and the first author in Analysis 16, 1291–1323, 2006.      

Periodic defect modes of one-dimensional crystals containing single-negative materials

The transmission properties of a one-dimensional (1D) photonic crystal containing two kinds of single-negative (permittivity or permeability negative) material with an inserted array of defects (RHM and LHM) were presented by the transfer matrix method (TMM). The dependence of the defect modes on the structure parameters was discussed by using the TMM. In contrast to the Bragg gaps, the properties (the central frequency and width of the gap) of zero effective phase (zero−φ_eff) and gap are invariant with a change in scale length and insensitive to the incident angles. The property of the periodic defect modes in the SNG host periodic structure was studied. It illustrates that the defect modes properties changed more by insert periodic defect than by single-media defect. The defect modes are sensitive to the parameters of the defect layers and the incident angle.     

Properties of period integrals of complex algebraic curves

The period integrals of non-singular complex algebraic curves in are shown to satisfy a set of polynomial relations that can be used to formulate the corresponding the Picard-Fuchs equations. Their derivation employs elementary mathematical techniques that have also application in the context of Seiberg-Witten theories.     

非尖锐界面多层膜对软X光衍射研究

本文研究超薄膜情况下,提出一个新物理模型,研究膜系内密度呈周期性连续变化时X射线正入射衍射强度理论计算,并由此得到水窗波段超薄膜设计参数,与用光学常数得到的参数非常一致。理论上推出一个质量密度呈余弦变化的多层膜仍然有高的软X光反射率。     

Heuristic algorithms for the 2-period balanced Travelling Salesman Problem in Euclidean graphs

In the 2-period Travelling Salesman Problem some nodes, called double nodes, are visited in both of two periods while the remaining ones, called single nodes, are visited in either one of the periods. In this paper we study the case in which a balance constraint is also introduced. We require that the difference between the number of visited nodes in the two periods must be below a fixed threshold. Moreover, we suppose that distances between nodes are Euclidean. The problem is NP-hard, and exact methods, now available, appear inadequate. Here, we propose three heuristics. Computational experiences and a comparison between the algorithms are also given.     

A delayed modified Ricker map and its cicada-type oscillations

Without trying to develop a model for a biological system, we introduce a delay map that shows a large spike followed by 16 iterations of much smaller values. Upon variation of one of the parameters, we can get a 13 cycles stable oscillation. The analyses of the bifurcation diagrams for the delayed extended Ricker's map yield a straightforward approach to find parameter values for any periodicity. In particular, we determine the values for the 13 and 17 periodic oscillations. We also notice that the bifurcation diagrams show no chaotic regions, and their structures show self-similarity properties. In general, the bifurcation diagrams have self-similarity structures, where n-periodic oscillations change into (n-1)-periodic oscillations.     

线宽增强因子对外光注入半导体激光器非线性单周期振荡特性的影响

线宽增强因子是影响半导体激光器输出特性的一个重要参量,不同材料不同结构类型的半导体激光器的线宽增强因子有较大的差异.利用光注入半导体激光器的单模速率方程模型,数值研究了线宽增强因子对外光注入半导体激光器的非线性单周期振荡特性的影响.结果表明:外光注入半导体激光器的动态特性对线宽增强因子的变化极为敏感,随着线宽增强因子的增加,在负失谐注入范围内单周期振荡区域显著增大,同时注入锁定的稳态输出被大大抑制.分析了线宽增强因子对非线性单周期振荡光谱特性和振荡频率的影响,结果表明:随着半导体激光器线宽增强因子的增大,单周期振荡的频率越大|当线宽增强因子不变时,单周期振荡的频率随注入光强度和频率失谐的增加而增加.     

Concomitance in single bubble sonoluminescence of period doubling in emission and shape distortion

We report the first direct observation for a single stable sonoluminescing bubble of a shape instability. Furthermore we show that stable saturation of the shape distortion caused by the instability for a certain range of parameters is experimentally possible and furthermore is directly linked to the curious phenomenon of flash by flash period doubling of the sonoluminescent emission as the afterbounce instability causing the shape distortion is always period doubled whenever the emission is & vice versa.     

Maximal periods of (Ehrhart) quasi-polynomials

A quasi-polynomial is a function defined of the form q(k)=cd(k)kd+cd−1(k)kd−1+?+c₀(k), where c₀,c₁,…,cd are periodic functions in k∈Z. Prominent examples of quasi-polynomials appear in Ehrhart's theory as integer-point counting functions for rational polytopes, and McMullen gives upper bounds for the periods of the cj(k) for Ehrhart quasi-polynomials. For generic polytopes, McMullen's bounds seem to be sharp, but sometimes smaller periods exist. We prove that the second leading coefficient of an Ehrhart quasi-polynomial always has maximal expected period and present a general theorem that yields maximal periods for the coefficients of certain quasi-polynomials. We present a construction for (Ehrhart) quasi-polynomials that exhibit maximal period behavior and use it to answer a question of Zaslavsky on convolutions of quasi-polynomials.