Mixed finite-element methods for Hamilton-Jacobi-Bellman-type equations

The numerical solution of Dirichlet's problem for a second-orderelliptic operator in divergence form with arbitrary nonlinearitiesin the first- and zero-order terms is considered. The mixedfinite-element method is used. Existence and uniqueness of theapproximation are proved and optimal error estimates in L² aredemonstrated for the relevant functions. Error estimates arealso derived in L^q, 2q+     

一类新型环金属配体——(口恶)二唑衍生物的化学结构及其性能

合成了5个2,5-二芳基-1,3,4-(口恶)二唑衍生物环金属配合物配体,其化学结构经1H NMR、IR和元素分析得到确证. 利用紫外光谱、荧光光谱、差热分析(DSC)和循环伏安法测试技术分别研究了它们的光谱性能、热性能和电化学性能. 结果表明,该类衍生物在二氯甲烷溶液中的最大紫外吸收波长在268～327 nm范围,在二氯甲烷溶液和固体膜中的最大荧光发射波长分别在332～390 nm和359～439 nm范围;DSC分析结果表明,5个(口恶)二唑衍生物的起始吸热峰位于120～328 ℃之间,其中对称结构的(口恶)二唑衍生物显示了较高的熔融温度;由循环伏安图和相关计算结果表明,5个(口恶)二唑衍生物的还原电位位于-1.03～-0.98 V,其相应的最低非占有分子轨道能级(LUMO)在-3.71～-3.76 eV之间.     

SUPERPOROUS HYDROGELS: FAST RESPONSIVE HYDROGEL SYSTEMS

ABSTRACT

Superporous hydrogels, hydrogels with pore sizes in the range of 100 μm and larger, were synthesized using N-isopropyl-acrylamide (NIPAM) and acrylamide (AM). The superporous hydrogels were synthesized by crosslinking polymerization of monomers in the presence of gas bubbles. The pores of superporous hydrogels were connected to each other to form open capillary channels, which provided fast response to the changes in the environmental temperature. Upon increase in temperature from 10°C to 65°C, the superporous hydrogel made from a monomer solution of NIPAM:AM = 9:1 shrank from the fully swollen state (volume of 36 cm³) to the fully collapsed state (volume of 6.5 cm³) in 72±14 sec. When the temperature was changed back to 10°C, the superporous hydrogel swelled to 36 cm³ in 78±15 sec. This deswelling-swelling cycle was repeated many times without changes in the thermo-reversible property of the superporous hydrogel. The response time of the superporous hydrogels was thousand times faster than that of conventional hydrogels. The fast response of the superporous hydrogels is due to the rapid uptake or exclusion of water molecules through the extensive capillary channels. Because superporous hydrogels still maintain the open capillary structure even after drying, the dried superporous hydrogels can also swell to the equilibrium swelling state within minutes. These fast responsive hydrogels can find many pharmaceutical and medical applications.     

Preparation and evaluation of PANI/PTT electromagnetic shielding fabric by in-situ chemical polymerization

To prepare the flexible and stretchable electromagnetic shielding (EMS) fabric with environmental stability, this paper uses polytrimethylene terephthalate (PTT) fabric as substrate, the aniline monomer as raw material, hydrochloric acid (HCl) as the doping agent, ammonium persulfate (APS) as the oxidant to produce polyaniline (PANI)/PTT electromagnetic shielding fabric by in-situ chemical polymerization. It studies the influence of APS and HCl concentration on the surface electrical resistance and the absorption loss of electromagnetic shielding fabric. It can be observed that an increasing APS and HCl facilitate the absorption and spread of PANI into PTT fabric to form a conductive network, and improve the absorption loss efficiency, while the excess APS and HCl will hinder the PANI polymerization. The high electrical conductivity and absorption loss of the PANI/PTT fabric are obtained at the concentration of An 0.4 M, APS 0.4 M, HCl 1.25 M, and polymerization reaction time 120 min. Meanwhile, in-situ polymerization of PANI does not introduce new impurities and destroy the molecular structure of PTT.     

Thermal processes in the systems with Li-battery cathode materials and LiPF6 -based organic solutions

Thermodynamic instability of positive electrodes (cathodes) in Li-ion batteries in humid air and battery solutions results in capacity fading and batteries degradation, especially at elevated temperatures. In this work, we studied thermal interactions between cathode materials Li₂MnO₃, xLi₂MnO₃ ^.(1???x)Li(MnNiCo)O₂,LiNi_0.33Mn_0.33Co_0.33O₂, LiNi_0.4Mn_0.4Co_0.2O₂, LiNi_0.8Co_0.15Al_0.05O₂ LiMn_1.5Ni_0.5O₄, LiMn(or Fe)PO₄, and battery solutions containing ethylene carbonate (EC) or propylene carbonate (PC), dimethyl carbonate (DMC) or ethylmethyl carbonate (EMC) and LiPF₆ salt in the temperature range of 40–400 °C. It was found that these materials are stable chemically and well performing in LiPF₆-based solutions up to 60 °C. The thermal decomposition of the electrolyte solutions starts >180 °C. The macro-structural transformations of cathode materials upon exothermic reactions were studied by transmission electron microscopy (TEM), X-ray difraction (XRD) and Raman spectroscopy. Differential scanning calorimetry (DSC) studies have shown that the exothermic reactions in the temperature range of 60–140 °C lead to partial decomposition of both the cathode material and electrolyte solution. The systems thus formed consisted of partially decomposed solutions and partially chemically delithiated cathode materials covered by reactions products. Thermal reactions terminate and this system reaches equilibrium at about 120 °C. It remains stable up to the beginning of the solution decomposition at about 180 °C. The increased content of surface Li₂CO₃ is found to significantly affect the thermal processes at high temperature range due to extensive exothermic decomposition at low temperatures.     

Examples of entropy generating sequence

We introduce the notion of entropy generating sequence for infinite words and define its dimension when it exists. We construct an entropy generating sequence for each symbolic example constructed by Cassaigne such that the dimension of the sequence is the same as its topological entropy dimension. Hence the complexity can be measured via the dimension of an entropy generating sequence. Moreover, we construct a weakly mixing example with subexponential growth rate.     

THE FUNDAMENTAL GROUP OFTHE AUTOMORPHISM GROUP OFA NONCOMMUTATIVE TORUSTHE FUNDAMENTAL GROUP OFTHE AUTOMORPHISM GROUP OFA NONCOMMUTATIVE TORU

1. IntroductionGiven a locally compact abelian group G and a multiplier p on G, one can associate tothem the twisted group C*-algebra C*(G, p), which is the universal object for unitary prepresentations of G. C* (Zm, p) is said to be a noncommutative torns of rank m and denotedby A.. The multiplier p determines a subgroup S. of G, called its symmetry group, andthe multiplier p is called totally skew if the symmetry group S. is trivial. And A. is calledcompletely irrational if p is totally…     

链间耦合对聚合物中双激子态反向极化的影响

从紧束缚模型出发，研究了链间相互作用对双激子态反向极化的影响.结果发现：加链间耦合后，双激子态仍主要局域在一条链中.当简并破缺较小时，反向极化程度随耦合强度的增加大幅提高；当简并破缺较大时，反向极化程度随耦合强度的增加基本不变. 关键词： 反向极化 双激子态 链间耦合     

Wedge Operations and Doubling Operations of Real Toric Manifolds

This paper deals with two things.First,the cohomology of canonical extensions of real topological toric manifolds is computed when coefficient ring G is a commutative ring in which 2 is unit in G.Second,the author focuses on a specific canonical extensions called doublings and presents their various properties.They include existence of infinitely many real topological toric manifolds admitting complex structures,and a way to construct infinitely many real toric manifolds which have an odd torsion in their cohomology groups.Moreover,some questions about real topological toric manifolds related to Halperin's toral rank conjecture are presented.