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”.     

李雅普诺夫：逐梦唯美天空的俄罗斯数学家

 李雅普诺夫是圣彼得堡数学学派的中流砥柱，创立了运动稳定性理论、旋转液团平衡形状理论和微分方程定性理论，探索了概率论中心极限定理和一系列其他深刻数学力学问题，为俄罗斯跻身世界科技强国做出了卓越贡献。通过采撷李雅普诺夫的动人爱情诗篇和唯美科学奋斗目标，展示了其美丽的爱情观和追求卓越的科学精神、人生观和宇宙观。     

Validated Stability-Indicating GC-MS Method for Characterization of Forced Degradation Products of Trans-Caffeic Acid and Trans-Ferulic Acid

When dealing with simple phenols such as caffeic acid (CA) and ferulic acid (FA), found in a variety of plants, it is very important to have control over the most important factors that accelerate their degradation reactions. This is the first report in which the stabilities of these two compounds have been systematically tested by exposure to various different factors. Forced degradation studies were performed on pure standards (trans-CA and trans-FA), dissolved in different solvents and exposed to different oxidative, photolytic and thermal stress conditions. Additionally, a rapid, sensitive, and selective stability-indicating gas chromatographic-mass spectrometric method was developed and validated for determination of trans-CA and trans-FA in the presence of their degradation products. Cis-CA and cis-FA were confirmed as the only degradation products in all the experiments performed. All the compounds were perfectly separated by gas chromatography (GC) and identified using mass spectrometry (MS), a method that additionally elucidated their structures. In general, more protic solvents, higher temperatures, UV radiation and longer storage times led to more significant degradation (isomerization) of both trans-isomers. The most progressive isomerization of both compounds (up to 43%) was observed when the polar solutions were exposed to daylight at room temperature for 1 month. The method was validated for linearity, precision as repeatability, limit of detection (LOD) and limit of quantitation (LOQ). The method was confirmed as linear over tested concentration ranges from 1−100 mg L⁻¹ (r²s were above 0.999). The LOD and LOQ for trans-FA were 0.15 mg L⁻¹ and 0.50 mg L⁻¹, respectively. The LOD and LOQ for trans-CA were 0.23 mg L⁻¹ and 0.77 mg L⁻¹, respectively.     

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.     

共产主义实现过程的数学刻画

指出了极限蕴含着理想与现实的统一,以此刻画了共产主义的实现过程——人类社会可以无限地趋近共产主义.把人类社会视为一个系统,提出了它的两条基本公理.借助于公理法,利用逻辑推理论证了劳动将逐渐成为人们的第一需要、劳动创造财富、人类的思想觉悟可以逐渐达到共产主义人生观等重要结论.     

New organoruthenium metallates containing ferrocenecarboxalidine thiosemicarbazones and their nucleic acid/albumin binding and in vitro cytotoxicity

A string of four new hetero binuclear Ru(III) complexes of ferrocenecarboxaldehyde-4(N)-substituted thiosemicarbazones were synthesized and characterized by various spectral (infrared, ultraviolet–visible, Electron Paramagnetic Resonance (EPR) and High Resolution Mass Spectrometry (HR-MS) techniques. The binding abilities of the ligands/complexes with nucleic acid (calf thymus DNA, CT-DNA) and bovine serum albumin (BSA) were analyzed by absorption and emission titration methods. The complexes exhibited better DNA binding affinity than their parent ligands. The interaction with CT-DNA was found to be intercalative and with BSA static quenching mechanism was observed. All the synthesized Ru(III) complexes were subjected to study their in vitro cytotoxicity against MCF-7 (human breast cancer) and HT-29 (human colon cancer) cell lines. Among the four complexes, complex 3 [RuCp (FF-etsc)PPh₃]Cl exhibited the highest cytotoxicity in MCF-7 cells and complex 4 [RuCp (FF-ptsc)PPh₃]Cl was the most active on HT-29 cells.     

基于WEB的在线答疑系统的设计与实现

根据登录者的身份，基于WWW技术的在线答疑系统设计为三大模块：学生模块、教师模块和系统管理员模块，它们可分别完成提问、回答和版务管理等功能．还探讨了系统主要的实现技术。     

统计学的产生与发展

论述了统计学发展的四个阶段，并给出了现代统计学的三个特点。     

高职教育改革四议

高等职业教育以能力为本位，培养面向生产、建设、管理及服务一线的高级技术型应用人才。其培养目标、培养模式应始终坚持为经济发展建设服务，依托于经济，服务于经济，服务于社会。