von Neumann’s trace inequality for Hilbert–Schmidt operators

von Neumann’s inequality in matrix theory refers to the fact that the Frobenius scalar product of two matrices is less than or equal to the scalar product of the respective singular values. Moreover, equality can only happen if the two matrices share a joint set of singular vectors, and this latter part is hard to find in the literature. We extend these facts to the separable Hilbert space setting, and provide a self-contained proof of the “latter part”.     

Identifying aspirin polymorphs from combined DFT-based crystal structure prediction and solid-state NMR

A combined experimental and computational approach was used to distinguish between different polymorphs of the pharmaceutical drug aspirin. This method involves the use of ab initio random structure searching (AIRSS), a density functional theory (DFT)-based crystal structure prediction method for the high-accuracy prediction of polymorphic structures, with DFT calculations of nuclear magnetic resonance (NMR) parameters and solid-state NMR experiments at natural abundance. AIRSS was used to predict the crystal structures of form-I and form-II of aspirin. The root-mean-square deviation between experimental and calculated ¹H chemical shifts was used to identify form-I as the polymorph present in the experimental sample, the selection being successful despite the large similarities between the molecular environments in the crystals of the two polymorphs.     

Design and development of a two‐dimensional system based on hydrophilic and reversed‐phase liquid chromatography with on‐line sample treatment for the simultaneous separation of excreted xenobiotics and endogenous metabolites in urine

In the present work we describe a two‐dimensional liquid chromatographic system (2D‐LC) with detection by mass spectrometry (MS) for the simultaneous separation of endogenous metabolites of clinical interest and excreted xenobiotics deriving from exposure to toxic compounds. The 2D‐LC system involves two orthogonal chromatographic modes, hydrophilic interaction liquid chromatography (HILIC) to separate polar endogenous metabolites and reversed‐phase (RP) chromatography to separate excreted xenobiotics of low and intermediate polarity. Additionally, the present proposal has the novelty of incorporating an on‐line sample treatment based on the use of restricted access materials (RAMs), which permits the direct injection of urine samples into the system. The work is focused on the instrumental coupling, studying all possible options and attempting to circumvent the problems of solvent incompatibility between the RAM device and the two chromatographic columns, HILIC and RP. The instrumental configuration developed, RAM‐HILIC‐RPLC‐MS/MS, allows the simultaneous assessment of urinary metabolites of clinical interest and excreted compounds derived from exposure to toxic agents with minimal sample manipulation. Thus, it may be of interest in areas such as occupational and environmental toxicology in order to explore the possible relationship between the two types of compounds. Copyright © 2015 John Wiley & Sons, Ltd.     

Second-order random wave solutions for interfacial internal waves in N-layer density-stratified fluid

This paper studies the random internal wave equations describing the density interface displacements and the velocity potentials of N-layer stratified fluid contained between two rigid walls at the top and bottom. The density interface displacements and the velocity potentials were solved to the second-order by an expansion approach used by Longuet-Higgins （1963） and Dean （1979） in the study of random surface waves and by Song （2004） in the study of second- order random wave solutions for internal waves in a two-layer fluid. The obtained results indicate that the first-order solutions are a linear superposition of many wave components with different amplitudes, wave numbers and frequencies, and that the amplitudes of first-order wave components with the same wave numbers and frequencies between the adjacent density interfaces are modulated by each other. They also show that the second-order solutions consist of two parts： the first one is the first-order solutions, and the second one is the solutions of the second-order asymptotic equations, which describe the second-order nonlinear modification and the second-order wave-wave interactions not only among the wave components on same density interfaces but also among the wave components between the adjacent density interfaces. Both the first-order and second-order solutions depend on the density and depth of each layer. It is also deduced that the results of the present work include those derived by Song （2004） for second-order random wave solutions for internal waves in a two-layer fluid as a particular case.     

A rational approximation and its applications to nonlinear partial differential equations on the whole line

An orthogonal system of rational functions is discussed. Some inverse inequalities, imbedding inequalities and approximation results are obtained. Two model problems are considered. The stabilities and convergences of proposed rational spectral schemes and rational pseudospectral schemes are proved. The techniques used in this paper are also applicable to other problems on the whole line. Numerical results show the efficiency of this approach.     

On a stochastic nonlinear equation in one-dimensional viscoelasticity

In this paper we discuss an initial-boundary value problem for a stochastic nonlinear equation arising in one-dimensional viscoelasticity. We propose to use a new direct method to obtain a solution. This method is expected to be applicable to a broad class of nonlinear stochastic partial differential equations.

     

用Java实现网上结构图实验仿真

基于线性系统仿真的连接矩阵方法，用Java语言开发面向结构图的实验仿真程序，以Applet小应用程序的形式插入网页中运行，实现了信号与系统网上实验教学中的结构图实验仿真。经试用，程序在浏览器中运行正常，可以完成一般线性系统仿真，与以MATLAB，LABView等程序开发的实验仿真程序相比，该程序运行环境简单，几乎所有常用的Web浏览器都支持Java运行，不需另行安装相应组件。对于线性系统结构图，实现了所见即所得的图形化编程环境，具有较好的人机交互性。