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”.     

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.     

Study of Endogen Substrates,Drug Substrates and Inhibitors Binding Conformations on MRP4 and Its Variants by Molecular Docking and Molecular Dynamics

Multidrug resistance protein-4 (MRP4) belongs to the ABC transporter superfamily and promotes the transport of xenobiotics including drugs. A non-synonymous single nucleotide polymorphisms (nsSNPs) in the ABCC4 gene can promote changes in the structure and function of MRP4. In this work, the interaction of certain endogen substrates, drug substrates, and inhibitors with wild type-MRP4 (WT-MRP4) and its variants G187W and Y556C were studied to determine differences in the intermolecular interactions and affinity related to SNPs using protein threading modeling, molecular docking, all-atom, coarse grained, and umbrella sampling molecular dynamics simulations (AA-MDS and CG-MDS, respectively). The results showed that the three MRP4 structures had significantly different conformations at given sites, leading to differences in the docking scores (DS) and binding sites of three different groups of molecules. Folic acid (FA) had the highest variation in DS on G187W concerning WT-MRP4. WT-MRP4, G187W, Y556C, and FA had different conformations through 25 ns AA-MD. Umbrella sampling simulations indicated that the Y556C-FA complex was the most stable one with or without ATP. In Y556C, the cyclic adenosine monophosphate (cAMP) and ceefourin-1 binding sites are located out of the entrance of the inner cavity, which suggests that both cAMP and ceefourin-1 may not be transported. The binding site for cAMP and ceefourin-1 is quite similar and the affinity (binding energy) of ceefourin-1 to WT-MRP4, G187W, and Y556C is greater than the affinity of cAMP, which may suggest that ceefourin-1 works as a competitive inhibitor. In conclusion, the nsSNPs G187W and Y556C lead to changes in protein conformation, which modifies the ligand binding site, DS, and binding energy.     

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.     

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。     

Clifford分析中无界域上正则函数的边值问题

在引入修正Cauchy核的基础上,讨论了无界域上正则函数的带共轭值的边值问题：a(t)Φ (t) b(t)Φ (t) c(t)Φ-(t) d(t)Φ=g(t)．首先给出了无界域上正则函数的Plemelj公式,然后利用积分方程方法和压缩不动点原理证明了问题解的存在唯一性．     

Harmonic mappings of the Sierpinski gasket to the circle

Harmonic mappings from the Sierpinski gasket to the circle are described explicitly in terms of boundary values and topological data. In particular, all such mappings minimize energy within a given homotopy class. Explicit formulas are also given for the energy of the mapping and its normal derivatives at boundary points.

     

A FUNDAMENTAL SOLUTION FOR THE LAPLACE OPERATOR ON THE QUATERNIONIC HEISENBERG GROUP

In this paper, the author studies the Laplace operator on the quaternionic Heisenberg group, construct a fundamental solution for it and use this solution to prove the Lp-boundedness and the weak (1-1) boundedness of certain singular convolution operators on the quaternionic Heisenberg group.