若干高维可积和不可积模型的严格解

可积和不可积模型可以描述自然科学中的诸多现象, 寻找高维非线性模型的严格解已成为可积系统的一个重要研究内容. 结合达布变换法和多线性分离变量法, 可以得到多个(2+1)维非线性模型包含任意函数的严格解, 通过选取不同的任意函数, 构造这些非线性模型新的相互激发模式. 进一步推广了形变映射理论, 建立了变系数 场和sine-Gordon以及双sine-Gordon场的形变映射关系, 从而得到高维不可积模型包含任意函数的新严格解. 对任意函数的不同选择, 构造了sine-Gordon和双sine-Gordon可积模型丰富的局域解和周期解, 如多solitoff解及其周期波推广、周期形变的蛇形孤波解以及变模的拟周期解等.     

A study on the phase transformation behaviour of Cu-20wt.Sn alloy produced using powder metallurgy method: Experimental and molecular dynamics modelling

In this study, Cu-20wt.Sn alloy was produced by powder metallurgy (PM) method by using high purity element powders. The phases in the microstructure of the produced alloy were determined by XRD study. The phase transformation behaviour of the alloy was investigated by DSC and modelling method. Moreover, the Cu-20wt.Sn alloy system was modelled with molecular dynamics (MD) simulation based on modified Embedded Atom Method (MEAM). The radial distribution function (RDF) was calculated to determine the structural properties of system during the phase transformations. The experimental results showed that the transformation ($\alpha +\delta$) → ($\alpha +\gamma$) occur at temperature above 500°C. The simulation results showed that the phase transformation $\alpha +\delta \to \alpha +\gamma$ occurs at 550°C temperature. Our simulation results are in reasonable agreement with the experimental data.     

A 1D Roe decomposition of a system of equations governing wave height transformation

A Roe‐type decomposition for a system of equations governing onshore/offshore wave transformation in coastal waters is derived. The equation set approximated pertains to coastal waters prior to wave breaking, and is based on depth‐averaging and time‐averaging of the Euler equations. The equations are those used in many commercial codes for simulation of wave height and wave‐averaged currents. This novel approach uses a combination of some standard Roe averages, together with physical reasoning and power series expansions to derive a Roe‐averaged Jacobian (with real, linearly independent eigenvectors) and ensures conservation, and thereby effects the decomposition. It is shown that the resulting derived Roe‐averaged quantities are accurate to a high degree, by comparing them with their analytical equivalents for a wide range of nondimensional water depths and slopes likely to be encountered in coastal problems. Numerical tests of time‐invariant wave height transformation and wave group propagation are undertaken; these indicate good performance of the scheme in practice. Copyright © 2011 John Wiley & Sons, Ltd.     

A New,Mild, and Rapid Transformation of Acylals to Bisulfites in One-Pot Synthesis by Bismuth (III) Nitrate Pentahydrate

Abstract

Direct conversion of acylals to the corresponding bisulfites can be easily performed in the presence of bismuth (III) nitrate pentahydrate in ethanol at room temperature in good yields.     

Established and emerging strategies for polymer chain-end modification

The development of “controlled” and “living” polymerization processes with high end-group fidelity has enabled an unprecedented range of polymeric materials with specific chain-end functionality to be prepared. This highlight provides an overview of available strategies and evaluation of recent approaches for the chain-end functionalization of polymers prepared through controlled chain-growth polymerizations. As a tribute to Professor Robert B. Grubbs on the occasion of his 75th birthday, we also take this opportunity to highlight methods for the chain-end modification of polymers prepared by ring-opening metathesis polymerization within the broader context of functional group tolerant, living polymerizations. Finally, we focus attention toward new directions in polymer chain-end modifications, describing existing gaps in current strategies, and detailing recently reported protocols that show significant improvements over traditional methods. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2017 , 55, 2903–2914     

The Effect of Some Physical Factors on the II → I Phase Transition of Isotactic Polybutene-1

Abstract

Isotactic polybutene-1 exhibits excellent physical, mechanical and chemical properties dependent on its most important polymorphic crystal forms, called forms I, II and III. The most stable form, form I, is generated via a slow, solid-state transformation of the tetragonal, kinetically favored form II. The slow transformation rate of form II to I, accompanied by sample shrinkage, attains its maximum at ca 25?°C and takes 7–10?days, which is a technical problem for iPB-1 practical applications. We describe here the results reported in the literature by the authors and others of the effect of various physical factors that affect the transformation rate, with the goal of determining means of accelerating it; it is noted explanations of the effects are limited and in many cases, not given.     

Transformation of the gas‐phase favored O‐protomer of p‐aminobenzoic acid to its unfavored N‐protomer by ion activation in the presence of water vapor: An ion‐mobility mass spectrometry study

An ion‐mobility mass spectrometry study showed that the preferred O‐protonated form of p‐aminobenzoic in the gas phase can be converted to the thermodynamically less favored N‐protomer by in‐source collision‐induced ion activation during the ion transfer process from the atmospheric region to the first vacuum region if the humidity is high in the ion source. Upon the addition of water vapor to the nitrogen gas used to promote the solid analyte to the gas phase under helium‐plasma ionization conditions, the intensity of the ion‐mobility arrival‐time peak for the N‐protomer increased dramatically. Evidently, the ion‐activation process in the first vacuum region is able to provide the energy required to surmount the barrier to isomerize the O‐protomer to the more energetic N‐protomer. The transfer of the proton attached to the carbonyl oxygen atom of the O‐protomer to the amino group takes place by a water‐bridge mechanism. Apparently, the postionization transformations that take place during the transmission of ions from the atmospheric‐pressure ion source to the detector, via different physical compartments of low to high vacuum, play an eminent role in determining the population ratios eventually manifested at the detector.     

关于全国大学生数学竞赛决赛试题的解析与思考

本文对二道全国大学生数学竞赛决赛试题(数学类)给予了诠释与解析.