S3上阿诺德弦猜想中的变分方法

本文使用变分方法证明了三维标准切触球的标准勒让德扭结，至少存在一个弦连结适应于标准切触结构的任何选定切触形式，这部分证明了著名的阿诺德弦猜想。     

Analytical study of a flattened Gaussian beam through multi-apertured optical imaging systems of B = 0

By using the methods of the matrix decomposition and expansion of the hard-edged aperture function into a finite sum of complex Gaussian functions, the recurrence propagation expressions for a flattened Gaussian beam (FGB) through multi-apertured optical imaging systems of B = 0 are derived and illustrated with numerical examples. Comparisons with the straightforward numerical integration of the Collins formula and with the previous work are made. It is shown that the main advantages of our methods and results are the more accuracy and great reduction of computer time.     

压缩偶相干态的制备及其非经典特性

通过保持非耗散介观LC电路的固有频率不变，而使电路参数作阶跃函数变化，就可将介观LC电路由初始的偶相干态制备到压缩偶相干态；在压缩偶相干态下，介观电路系统不仅有非经典的量子压缩效应，而且有非经典的反聚束效应. 关键词： 介观LC电路 单位阶跃函数 压缩算符 压缩偶相干态     

VALENCE AND EMISSION OF SAMARIUM IONS IN KMF(M:Mg、Ca)

The SmF_(2.01)was synthesized by reducing SmF_3 in H_2 stream.As it was doped inKM_gF_3 and KCaF_3.there was emission of Sm~(2+) in KMgF_3 but no emission of Sm~(2+) inKCaF_3 was observed.     

An alternative approach for non-linear optimal control problems based on the method of moments

We propose an alternative method for computing effectively the solution of non-linear, fixed-terminal-time, optimal control problems when they are given in Lagrange, Bolza or Mayer forms. This method works well when the nonlinearities in the control variable can be expressed as polynomials. The essential of this proposal is the transformation of a non-linear, non-convex optimal control problem into an equivalent optimal control problem with linear and convex structure. The method is based on global optimization of polynomials by the method of moments. With this method we can determine either the existence or lacking of minimizers. In addition, we can calculate generalized solutions when the original problem lacks of minimizers. We also present the numerical schemes to solve several examples arising in science and technology.     

A new generalized algebra method and its application in the (2 + 1) dimensional Boiti–Leon–Pempinelli equation

In the present paper, some types of general solutions of a first-order nonlinear ordinary differential equation with six degree are given and a new generalized algebra method is presented to find more exact solutions of nonlinear differential equations. As an application of the method and the solutions of this equation, we choose the (2 + 1) dimensional Boiti Leon Pempinelli equation to illustrate the validity and advantages of the method. As a consequence, more new types and general solutions are found which include rational solutions and irrational solutions and so on. The new method can also be applied to other nonlinear differential equations in mathematical physics.     

Crystallographic report: Bis(norfloxacin)dilead(II) tetranitrate, [Pb2(H‐Norf)2(ONO2)4]

The centrosymmetric binuclear structure of [Pb₂(H‐Norf)₂(ONO₂)₄]shows the geometry around each lead(II) atom to be distorted trigonal bipyramidal with Pb–O distances ranging from 2.357(3) to 2.769(4) Å. Copyright © 2003 John Wiley & Sons, Ltd.     

Synthesis of single crystalline layered lithium manganese oxide nanorods

Single-crystalline layered lithium manganese oxide nanorods were prepared via a low-temperature molten salt synthesis method. The material was investigated by a variety of techniques, including X-ray powder diffraction (XRD), transmission electron microscopy (TEM), and X-ray photoelectron spectrum (XPS).     

Structural effects of multiple-bonds on aggregating tendencies of long-chain esters

The kinetics of the hydrolysis of p-nitrophenyl esters of three types of single-chain carboxylic acids, namely, saturated, olefinic and acetylenic, was investigated in two aquiorgano binary solvent systems, DMSO-H₂O and dioxane (DX)-H₂O. The ester probes used are: octanoic (C8), dodecanoic (C12) , stearic (C18) , oleic (C18-ol) , elaidic (C18-el ) and stearolic (C18-st). The order of measured CAgC values is: C18-ol>C18-el>C18>C18-st, whereas the order of decreasing magnitude of the observed hydrolytic rate constants of the monomeric species (k_m) is: C18>C18-el>C18-ol> C18-st. These rather unanticipated results are discussed.     

Fully-angular polyhex chains with minimal total π-electron energy

By Hückel molecular orbital (HMO) theory, the calculation of the total energy of all π-electrons in conjugated hydrocarbons can be reduced to that of E(G)=|λ₁|+|λ₂|+?+|λn|, where λi are the eigenvalues of the corresponding graph G. Denote by Ψn the set of all fully-angular polyhex chains with n hexagons. In this paper, we show that Hn has the minimum total π-electron energy among chains in Ψn, where Hn is the helicene chain.