一类带阻尼项的拟线性双曲型方程

本文讨论了从细杆的振动中提出的一类带阻尼项的拟线性双曲型方程的初边值问题的解在唯一性，利用已有的线性结果及动点定理结合能量估计建立了解的存在唯一性。     

双层桥梁耦合系统的强迫振动

本文研究作为双层桥模型的梁方程耦合系统，利用Ｌｅｒａｙ－Ｓｃｈａｕｄｅｒ不动点定理，得到了一个关于这种系统的解的存在性定理，它类似于ＭｃＫｅｎｎａ和Ｗａｌｔｅｒ文２中关于吊桥方程的一个定理。     

非齐次Toda晶格的对称,精确解和可积性

研究非齐次Toda晶格，即一类非齐次非线性微分差分方程的对称与可积性。给出了这一类方程的Lie点对称，条件对称和精确解。给出这类方程与Toda晶格之间的可逆点变换，从而表明这一类方程是可积的。     

Growth,optical, mechanical and electrical studies of nonlinear optical crystal: l-Valinium oxalate

l-Valinium oxalate (LVO) single crystal has been grown by solution growth technique at room temperature. The crystal structure and lattice parameters were determined for the grown crystal by single crystal X-ray diffraction studies. Optical constants like band gap, refractive index, reflectance, extinction coefficient and electric susceptibility were determined from UV–vis–NIR spectrum. The microhardness studies reveal the mechanical strength of the grown crystal. The dielectric constant, dielectric loss and AC conductivity of the compound were calculated at different temperatures and frequencies to analyze the electrical properties. Nonlinear optical property was discussed to confirm the SHG efficiency of the grown crystal.     

几类非线性差分方程的对称和精确解

本文将微分方程的Lie变换群方法推广到差分方程,给出了三类非线性差分方程的不变变换,利用这种变换由差分方程的平凡解得到非平凡的单参数解族。     

Combining approximate solutions for linear discrete ill-posed problems

Linear discrete ill-posed problems of small to medium size are commonly solved by first computing the singular value decomposition of the matrix and then determining an approximate solution by one of several available numerical methods, such as the truncated singular value decomposition or Tikhonov regularization. The determination of an approximate solution is relatively inexpensive once the singular value decomposition is available. This paper proposes to compute several approximate solutions by standard methods and then extract a new candidate solution from the linear subspace spanned by the available approximate solutions. We also describe how the method may be used for large-scale problems.     

溶液pH对羟基苯硫酚同分异构体脱羟基反应影响的SERS研究

金属纳米结构因表面等离激元(SPR)而产生光学增强和催化效应已成为表面科学研究热点之一。SPR和电化学联用可以诱导催化一些非常规反应,并且不同pH值电解质溶液可改变表面吸附分子的存在形式,影响SPR光催化反应。以羟基苯硫酚的同分异构体为探针,采用电化学表面增强拉曼光谱(SERS)研究了取代基羟基位置、溶液pH值等对其在银电极表面吸附和SPR催化反应行为。结果表明,不同羟基取代基位置的羟基苯硫酚SPR催化脱羟基反应对溶液pH值的敏感程度不同,邻羟基苯硫酚(OHTP)的C—O键谱峰强度的变化与溶液pH值相关,其O端更易与金属作用而吸附在表面,且随pH增大而增强。对羟基苯硫酚(PHTP)在碱性条件下被完全抑制的脱羟基反应在间羟基苯硫酚(MHTP)和OHTP中均可发生。MHTP在中性(pH 7)溶液中SPR催化脱羟基反应效率最高,约为酸性(pH 2)的1.36倍,碱性(pH 12)的2.70倍。OHTP在碱性(pH 12)溶液中SPR催化脱羟基反应效率最高,约为酸性(pH 2)的13.71倍,中性(pH 7)的4.95倍。SPR催化脱羟基主要源于非去质子化条件以及形成Ag—O键这两种途径。酸性条件下MHTP及OHTP的脱羟基反应主要是未去质子化的羟基反应,碱性条件主要因去质子化后形成Ag—O键所致。中性条件下,两种贡献同时发生。对MHTP而言,由于位阻效应仅部分分子去质子化后形成Ag—O键而促进SPR催化脱羟基,因此pH 7溶液中两种效应的同时作用导致催化效率最高。对于OHTP分子,去质子化状态的O端更易与电极表面发生作用,且pH升高羟基呈现的去质子化程度更加彻底,更有利于发生脱羟基反应,在pH 12溶液中脱羟基反应主要由于形成Ag—O键,其效率亦最高。同分异构体结构以及介质酸碱度对SPR催化脱羟基反应的研究对于拓宽SPR催化反应类型及从分子水平解析其机理具有重要意义。     

Yet another way of calculating moments of the Kesten's distribution and its consequences for Catalan numbers and Catalan triangles

We calculate moments of the so-called Kesten distribution by means of the expansion of the denominator of the density of this distribution and then integrate all summands with respect to the semicircle distribution. By comparing this expression with the formulae for the moments of Kesten's distribution obtained by other means, we find identities involving polynomials whose power coefficients are closely related to Catalan numbers, Catalan triangles, binomial coefficients. Finally, as applications of these identities we obtain various interesting relations between the aforementioned numbers, also concerning Lucas, Fibonacci and Fine numbers.     

Existence and Uniqueness of Solutions for a Class of Reaction-diffusion Systems

61.Intr0ducti0nInthispaper,wediscussareactionnetinacombusti0nmodel:V={R,,R2},whereR,andR2aredistinctreacti0nprocesses:Rl:A1+A,-A,,R2:A2+A3-P,A,(j=1,2,3)denotesthereactant,andPdenotestheinertproduct.Thesereactionsareexothermicreactions-LetQ,,Q2standforheatenergiesandU=(U,,U,,U,,U,)forstatevariablesdescribingreactions,whereUoisreactiontemporature,andU,(j=1,2,3)isthemolarityofthej-threactant.AssumethatV,(i=1,2)isthereactantvariablefortheithreactionpr0cess:V,=(Q,,1,-l,l)",V2=(Q,,O,-l,-…     

A parallel multi-neighborhood cooperative tabu search for capacitated vehicle routing problems

This paper presents a parallel tabu search algorithm that utilizes several different neighborhood structures for solving the capacitated vehicle routing problem. Single neighborhood or neighborhood combinations are encapsulated in tabu search threads and they cooperate through a solution pool for the purpose of exploiting their joint power. The computational experiments on 32 large scale benchmark instances show that the proposed method is highly effective and competitive, providing new best solutions to four instances while the average deviation of all best solutions found from the collective best results reported in the literature is about 0.22%. We are also able to associate the beneficial use of special neighborhoods with some test instance characteristics and uncover some sources of the collective power of multi-neighborhood cooperation.