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”.     

Development of nanomaterial chemosensors for toxic metal ions sensing

Heavy metal ions are harmful to aquatic life and humans owing to their high toxicity and non‐biodegradability, so their removal from wastewater is an important task. Therefore, this work focuses on designing suitable, simple and economical nanosensors to detect and remove these metal ions with high selectivity and sensitivity. Based on this idea, different types of mesoporous materials such as hexagonal SBA‐15, cubic SBA‐16 and spherical MCM‐41, their chloro‐functionalized derivatives, as well as 4‐(4‐nitro‐phenylazo)‐naphthalen‐1‐ol (NPAN) azo dye have been synthesized, with the aim of designing some optical nanosensors for metal ions sensing applications. The mentioned azo dye has been anchored into the chloro‐functionalized mesoporous materials. The designed nanosensors were characterized using scanning and transmission electron microscopy as well as Fourier transform infrared and UV–visible spectral analysis, nitrogen adsorption–desorption isotherms, low‐angle X‐ray diffraction and thermogravimetric analyses. Their optical sensing to various toxic metal ions such as Cd (II), Hg (II), Mn (II), Fe (II), Zn (II) and Pb (II) at different values of pH (1.1, 4.9, 7 and 12) was investigated. The optimization of experimental conditions, including the effect of pH and metal ion concentration, was examined. The experimental results showed that the solution pH had a major impact on metal ion detection. The optical nanosensors respond well to the tested metal ions, as reflected by the enhancement in both absorption and emission spectra upon adding different concentrations of the metal salts and were fully reversible on adding ethylene diamine tetra acetic acid or citric acid to the formed complexes. High values of the binding constants for the designed nanosensors were observed at pHs 7 and 12, confirming the strong chelation of different metals to the nanosensor at these pHs. Also, high binding constants and sensitivity were observed for NPAN‐MCM‐41 as a nanosensor to detect the different metal ions. From the obtained results, we succeeded in transforming the harmful azo dye into an environmentally friendly form via designing of the optical nanosensors used to detect toxic metal ions in wastewater with high sensitivity.     

有耗介质层上多导体传输线的电磁耦合时域分析方法

目前,针对空间电磁场作用有耗介质层上传输线的电磁耦合,仍缺乏有效的数值分析方法.因此,本文提出一种高效的时域混合算法,很好地解决了有耗介质层上传输线电磁耦合建模难的问题.首先,对经典传输线方程进行改进,推导了适用于有耗介质层上多导体传输线电磁耦合分析的修正传输线方程.然后,结合时域有限差分方法和相应插值技术,求解修正传输线方程,获得多导线及其端接负载上的电压和电流响应,并实现空间电磁场辐射与多导线瞬态响应的同步计算.最后,通过相应计算实例的数值模拟,与CST软件的仿真结果进行对比,验证了时域混合算法的正确性和高效性.     

Thermoresponsive polymersome from a double hydrophilic block copolymer

The article describes synthesis and thermally triggered self‐assembly of a Poly (ethylene oxide)‐block‐poly (N‐insopropylacrylamide) (PEO‐b‐PNIPAm) in aqueous medium. At rt, the polymer remains as unimer, however, at lower critical solution temperature (LCST) of PNIPAm (32 °C), it forms a rather large undefined aggregate which at slightly elevated temperature (～40 °C) converges to well defined polymersome structure (Critical aggregation concentration = 0.45 mg/mL) with hydrodynamic diameter of 40–50 nm. By lowering the temperature, initial swelling of the compact vesicle followed by reversible disassembly to unimer was noticed. The polymersome exhibits encapsulation ability to a hydrophilic dye Calcein which can be spontaneously released by lowering the temperature below cloud point. Likewise a hydrophobic dye namely 8‐Anilino‐1‐naphthalenesulfonic acid (ANS) can also be encapsulated and released by thermal trigger. Detail photoluminescence studies reveal ANS dye can be used as a generalized probe molecule for detecting LCST of a thermoresponsive polymer by “fluorescence on” above LCST even by cursory observation. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2015 , 53, 2444–2451     

超音速等离子体炬的磁流体动力学数值研究

针对设计的喉径2mm、工作电流为100A的拉瓦尔喷嘴,在二维轴对称模型的基础上,对超音速等离子体炬中的流动及其外部射流进行了数值模拟。通过在阳极喷嘴内部采用基于磁矢量势的磁流体动力学模型,避免了对磁感应强度的复杂积分计算,得到了喷嘴内部多场耦合的结果及外部射流的流动状态,分析了喷嘴内部电磁场对等离子体的加速作用及射流发展过程。结果显示,等离子体经历了亚音速→跨音速→超音速的发展过程,最终获得2.3 Ma的超音速射流。研究结果为超音速等离子体炬的工业应用提供了理论基础。     

Prediction of branch on branch and topological characteristics of low‐density polyethylene polymerization by a novel stochastic approach

A novel approach using Monte Carlo method applied to simulation of low‐density polyethylene (LDPE) polymerization in tubular reactor showing topological characteristics, and the comprehensive kinetic mechanism has been taken into consideration. The results show the precise details of the structure of a chain in the three levels of the backbone, the main branches, and branches on branch. The chain types include dead polymer, dead polymer with unsaturated end, and live polymer with primary radical, secondary radical, and tertiary radical. In this work, the branches on branch were identified in terms of number, length, and position of the branch. Sixty percent of branches on branch are 1 to 5 carbons long, and the longest branch on branch is about 50 carbons. Thus, this study provides a tool for more accurately mapping the polymer chains architecture, superior to determine the number, and position of long‐ and short‐chain branches in past researches. Finally, this approach will advance the prediction of microstructure‐related properties of polymer one step further.     

Quantitative characterization of holographic displays based on liquid-crystal-on-silicon spatial light modulator

This report discusses the effect of speckle size on the quality of holographic images based on a liquid-crystal-on-silicon (LCoS) spatial light modulator (SLM). Further, it proposes methods of quantifying the average speckle size and holographic image resolution. These methods enable both characteristics to be compared using the same unit (the number of pixels in the holographic image), providing an intuitive and effective comparative analysis method. In particular, by varying the LCoS resolution ratio, the change in the resolvable minimum pixels of the holographic image is interpreted in conjunction with the average speckle size; moreover, an analysis of the correlation between the latter two is presented. This approach, based on LCoS resolution division, could provide useful insights into single-SLM-based, full-color holographic displays using space division. Furthermore, it could be extended to other components, including more advanced LCoS SLMs, and used to identify the relative effects on image quality with speckles.     

Information percolation and cutoff for the random‐cluster model

We consider the random‐cluster model (RCM) on with parameters p∈(0,1) and q ≥ 1. This is a generalization of the standard bond percolation (with edges open independently with probability p) which is biased by a factor q raised to the number of connected components. We study the well‐known Fortuin‐Kasteleyn (FK)‐dynamics on this model where the update at an edge depends on the global geometry of the system unlike the Glauber heat‐bath dynamics for spin systems, and prove that for all small enough p (depending on the dimension) and any q>1, the FK‐dynamics exhibits the cutoff phenomenon at with a window size , where λ_∞ is the large n limit of the spectral gap of the process. Our proof extends the information percolation framework of Lubetzky and Sly to the RCM and also relies on the arguments of Blanca and Sinclair who proved a sharp mixing time bound for the planar version. A key aspect of our proof is the analysis of the effect of a sequence of dependent (across time) Bernoulli percolations extracted from the graphical construction of the dynamics, on how information propagates.     

Minimizing Side Product Formation in Alkyne Functionalization of Ruthenium Complexes by Introduction of Protecting Groups

The synthesis of alkyne functionalized bipyridine ruthenium complexes are reported. The improved synthetic approach through application of stable protecting groups prevents formation of possible side products while facilitating purification. By applying copper-catalysed azide-alkyne cycloaddition reactions (CuAAC) pyrene units with flexible alkyl linkers are introduced at the periphery of the complex, opening up various applications including surface immobilization and DNA intercalation. All complexes are characterized structurally as well as photophysically, especially regarding the influence of the introduced alkyne and triazolyl substituents on their photophysical behavior.