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”.     

基于单体的Q和e值绘制二元共聚双曲线*

采用Matlab中的Plot函数,首次以单体的Q、e值为中间变量,绘制出二元共聚双曲线。将二元共聚物组成曲线F1-f1和F2-f2同时呈现在一个图上,使隐含的第二单体的共聚行为可视化,有助于加深学习者对二元共聚的理解。     

Enzyme-regulated the changes of pH values for assembling a colorimetric and multistage interconnection logic network with multiple readouts

Based on enzymatic reactions-triggered changes of pH values and biocomputing, a novel and multistage interconnection biological network with multiple easy-detectable signal outputs has been developed. Compared with traditional chemical computing, the enzyme-based biological system could overcome the interference between reactions or the incompatibility of individual computing gates and offer a unique opportunity to assemble multicomponent/multifunctional logic circuitries. Our system included four enzyme inputs: β-galactosidase (β-gal), glucose oxidase (GOx), esterase (Est) and urease (Ur). With the assistance of two signal transducers (gold nanoparticles and acid–base indicators) or pH meter, the outputs of the biological network could be conveniently read by the naked eyes. In contrast to current methods, the approach present here could realize cost-effective, label-free and colorimetric logic operations without complicated instrument. By designing a series of Boolean logic operations, we could logically make judgment of the compositions of the samples on the basis of visual output signals. Our work offered a promising paradigm for future biological computing technology and might be highly useful in future intelligent diagnostics, prodrug activation, smart drug delivery, process control, and electronic applications.     

Missing value imputation strategies for metabolomics data

The origin of missing values can be caused by different reasons and depending on these origins missing values should be considered differently and dealt with in different ways. In this research, four methods of imputation have been compared with respect to revealing their effects on the normality and variance of data, on statistical significance and on the approximation of a suitable threshold to accept missing data as truly missing. Additionally, the effects of different strategies for controlling familywise error rate or false discovery and how they work with the different strategies for missing value imputation have been evaluated. Missing values were found to affect normality and variance of data and k‐means nearest neighbour imputation was the best method tested for restoring this. Bonferroni correction was the best method for maximizing true positives and minimizing false positives and it was observed that as low as 40% missing data could be truly missing. The range between 40 and 70% missing values was defined as a “gray area” and therefore a strategy has been proposed that provides a balance between the optimal imputation strategy that was k‐means nearest neighbor and the best approximation of positioning real zeros.     

对“四舍六入五留双”修约规则的商榷*

数值修约是分析化学教学的重要内容。目前,主流分析化学教材均采用 “四舍六入五留双”数值修约规则。详细剖析了该规则中尾数与进舍条件的关系,指出“四舍六入五留双”修约规则中应采用“尾数的首位”而不是“尾数”设置进舍条件,否则存在逻辑错误。对比分析表明,“四舍六入五留双”以数字4、5和6为比较值设置的修约规则等价于GBT8170—2008国家标准中以数字5为比较值设置的进舍规则,但GBT8170—2008国家标准的进舍规则的逻辑、表述等优于“四舍六入五留双”规则。因此,建议分析化学教材采用GBT8170—2008国家标准规定的数值修约相关内容。     

Entire functions sharing one small function CM with their shifts and difference operators

In this article, we mainly devote to proving uniqueness results for entire functions sharing one small function CM with their shift and difference operator simultaneously. Let f(z) be a nonconstant entire function of finite order, c be a nonzero finite complex constant,and n be a positive integer. If f(z), f(z + c), and ?_c~n f(z) share 0 CM, then f(z + c) ≡ Af(z),where A(= 0) is a complex constant. Moreover, let a(z), b(z)( ≡ 0) ∈ S(f) be periodic entire functions with period c and if f(z)-a(z), f(z + c)-a(z), ?_c~n f(z)-b(z) share 0 CM, then f(z + c) ≡ f(z).     

Liposomal structure: A comparative study on light scattering and chromatography techniques

Liposomes play an important role in medical and pharmaceutical science as, nanoscale drug carriers. One of the most important features is their size and size distribution, influencing both their bio-distribution and their targeting efficiency to tumors and also therapeutic activity of liposomal antitumor drugs. In this study, the effect of preparation method and molecular interaction on size and shape of liposome was studied. The size and shape characterization of liposomes was performed by asymmetrical flow field-flow fractionation coupled online with multi-angle light scattering (AF4-MALS). The size distributions obtained by AF4-MALS were compared to mean particle sizes and size distribution measured with other standard method such as Photon Correlation Spectroscopy (PCS). Furthermore, the effect of molecular interaction (hydrophilic and hydrophobic model drugs) on liposomal structure was assessed.     

早期视网膜分支静脉阻塞患者倍频固体激光治疗对临床疗效及CMT值变化的影响

本文探讨了早期视网膜分支静脉阻塞患者倍频固体激光治疗对临床疗效及黄斑中心视网膜厚度(CMT)值变化的影响。将因视网膜分支静脉阻塞行激光治疗的30例患者纳入激光组,同期行常规治疗的30例患者纳入对照组,对比两组临床疗效、视力、CMT值变化、眼底荧光血管造影(FFA)检查渗透率及并发症。结果显示,治疗后激光组患者临床治疗总有效率、各个时间点视力变化、CMT值及FFA检查渗透发生率均优于对照组(P<0.05),两组患者均随访6个月,并发症比较差异无统计学意义(P>0.05)。说明早期视网膜分支静脉阻塞患者使用倍频固体激光治疗临床效果显著,可有效提高其视力水平,降低CMT值。