A kinematic formula for integral invariant of degree 4 in real space form

In this paper,kinematic formulae in a real space form are investigated.A kinematic formula for homogeneous polynomial of degree 4 on the second fundamental forms in a real space form is obtained.The formula obtained is a concrete form of the result of Howard and the analogue of the known formula of Chen and Zhou.     

Synthesis,Characterization, DNA‐binding Properties,and ­Antioxidant Activity of a Copper(II) Complex with 1, 3‐Bis­(1‐allaylbenzimidazol‐2‐yl)‐2‐oxopropane

A new complex of copper(II) picrate (pic) with 1, 3‐bis(1‐allaylbenzimidazol‐2‐yl)‐2‐oxopropane (aobb), with the composition [Cu(aobb)₂](pic)₂, was synthesized and characterized. The crystal structure of the copper(II) complex revealed that the coordination environment around the central copper(II) atom is a distorted octahedral arrangement. Electronic absorption spectroscopy, ethidium bromide displacement experiments and viscosity measurements indicate that the ligand and the Cu^II complex can strongly bind to calf thymus DNA, presumably by an intercalation mechanism. Furthermore, the antioxidant activity of the Cu^II complex was determined by superoxide and hydroxyl radical scavenging method in vitro, which indicate that the Cu^II complex has the activity to suppress OH ^· and O₂ ^{· –}.     

Hypervalent Iodine Reagents Enable Chemoselective Deboronative/Decarboxylative Alkenylation by Photoredox Catalysis

Chemoselective C(sp³)? C(sp²) coupling reactions under mild reaction conditions are useful for synthesizing alkyl‐substituted alkenes having sensitive functional groups. Reported here is a visible‐light‐induced chemoselective alkenylation through a deboronation/decarboxylation sequence under neutral aqueous reaction conditions at room temperature. This reaction represents the first hypervalent‐iodine‐enabled radical decarboxylative alkenylation reaction, and a novel benziodoxole‐vinyl carboxylic acid reaction intermediate was isolated. This C(sp³)? C(sp²) coupling reaction leads to aryl‐and acyl‐substituted alkenes containing various sensitive functional groups. The excellent chemoselectivity, stable reactants, and neutral aqueous reaction conditions of the reaction suggest future biomolecule applications.     

ANTI-PERIODIC BOUNDARY VALUE PROBLEM FOR FUNCTIONAL DIFFENERTIAL EQUATION

By using upper and lower solutions coupled with monotone iterative technique, we discuss the anti-periodic boundary value problem for first order functional diffenertial equation. A sufficient condition for the existence of the solution is obtained.     

具非线性边界条件的奇异扩散方程

本文讨论具非线性第二边界条件的一端无界的奇异扩散方程的初边值间题,利用先验估计方法得到的主要结果是:存在唯一的整体光滑解,且解连续依赖于初值．     

A facile method to fabricate ZnO hollow spheres and their photocatalytic property

This paper presents a novel and facile method for the fabrication of ZnO hollow spheres. In this approach, zinc ions were first adsorbed onto the surfaces of sulfonated polystyrene core-shell template spheres, and then reacted with NaOH to form a ZnO crystal nucleus, which was followed by a growth step to form ZnO nanoshells. During the formation of ZnO nanoshells or later on, the template spheres were "dissolved" in the same media to obtain ZnO hollow spheres directly. Neither additional dissolution nor calcination process was needed in this method to remove the templates, and the reaction conditions were very mild: neither high temperature nor long time was needed. Transmission electron microscopy, scanning electron microscopy, X-ray photoelectron spectroscopy, X-ray diffraction, and Brunauer-Emmett-Teller analysis were used to investigate the morphology, surface composition, crystalline structure, specific surface area, and porosity of the ZnO hollow spheres, respectively. UV-visible spectra show that these ZnO hollow spheres had very good photocatalytic activity.     

Notes on piecewise-Koszul algebras

The relationships between piecewise-Koszul algebras and other “Koszul-type” algebras are discussed. The Yoneda-Ext algebra and the dual algebra of a piecewise-Koszul algebra are studied, and a sufficient condition for the dual algebra A ^! to be piecewise-Koszul is given. Finally, by studying the trivial extension algebras of the path algebras of Dynkin quivers in bipartite orientation, we give explicit constructions for piecewise-Koszul algebras with arbitrary “period” and piecewise-Koszul algebras with arbitrary “jump-degree”.     

室温离子液体EMIES的标准生成焓

在(298.15 ±0.01) K下用转动弹热量计测定了离子液体硫酸乙酯-1-甲基-3-乙基咪唑(EMIES)及合成它的原料1-甲基咪唑的恒容燃烧热,通过计算得到它们的标准燃烧焓 分别为(－2671±2) 和(－286.3±0.5) kJ·mol－1;标准生成焓 分别为(－3060±3) kJ·mol－1和(－2145±4) kJ·mol－1.结合文献上硫酸二乙酯的标准生成焓数据,得到了合成离子液体EMIES的反应热(－102.3±1.0) kJ·mol－1,与合成实验中观察到的强烈放热现象是一致的.根据离子液体EMIES的热容数据,计算了不同温度下EMIES的标准生成焓.     

Diastereo‐ and Enantioselective Palladium‐Catalyzed Dearomative [3+2] Cycloaddition of 3‐Nitroindoles

Diastereo‐ and enantioselective cycloaddition of 3‐nitroindoles with vinyl aziridine was realized under Pd‐catalysis using commercially available Walphos as the ligand, affording pyrroloindolines in high yields with high diastereo‐ and enantioselectivities. The reaction can be scaled up to a gram scale and the reaction products are easily converted to amino pyrroloindoline and other pyrroloindoline derivatives.     

Concise Synthesis and Antimicrobial Activities of New Substituted 5‐Isoxazolpenicillins

The synthesis of a series of new 5‐isoxazolpenicillins is described, which were obtained by coupling substituted isoxazoles with 6‐APA. Concise large‐scale synthesis of 3,5‐disubstituted isoxazoles by 1,3‐dipolar cycloaddition using copper(I) as catalyst was also investigated. Representative compounds were assayed for antimicrobial activities, showing satisfactory antimicrobial activities against Gram‐negative bacteria.