A threshold for the size of random caps to cover a sphere

Consider a unit sphere on which are placed N random spherical caps of area 4p(N). We prove that if % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGGipm0dc9vqaqpepu0xbbG8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa0aaaeaaca% qGSbGaaeyAaiaab2gaaaWaaeWaaeaacaWGWbWaaeWaaeaacaWGobaa% caGLOaGaayzkaaGaai4Taiaad6eacaGGVaGaaeiBaiaab+gacaqGNb% Gaaeiiaiaad6eaaiaawIcacaGLPaaacqGH8aapcaaIXaaaaa!454E!\[\overline {{\rm{lim}}} \left( {p\left( N \right)\cdotN/{\rm{log }}N} \right) < 1\], then the probability that the sphere is completely covered by N caps tends to 0 as N , and if % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGGipm0dc9vqaqpepu0xbbG8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaWaaaeaaca% qGSbGaaeyAaiaab2gaaaWaaeWaaeaacaWGWbWaaeWaaeaacaWGobaa% caGLOaGaayzkaaGaai4Taiaad6eacaGGVaGaaeiBaiaab+gacaqGNb% Gaaeiiaiaad6eaaiaawIcacaGLPaaacqGH+aGpcaaIXaaaaa!4551!\[\underline {{\rm{lim}}} \left( {p\left( N \right)\cdotN/{\rm{log }}N} \right) > 1\], then for any integer n>0 the probability that each point of the sphere is covered more than n times tends to 1 as N .     

A remark on the KAM theorem applied to a four-vortex system

We consider a planar four-vortex system with unit intensities and apply the KAM theorem for two-dimensional tori with fixed frequency. We obtain a rigorous lower bound for the stochasticity threshold of the torus with rotation number=(5—1)/2 and compare our result with numerical experiments.     

电位滴定法测定模拟高放废液中的游离酸

本文研究了用电位滴定法测定模拟高放废液中游离酸的方法。用草酸钾做络合剂以消除Ｆｅ＾３＋、Ａｌ＾３＋、Ｎｄ＾３＋等多种水解离子的影响，用标准碱直接进行电位滴定，即可快速准确地测定模拟高放废液中游离酸的含量。方法的相对标准偏差为１．８％，标准加入回收率为１００－１０１％，能为放射性废物固化试验提供可靠的分析数据。     

WOx/TiO2光催化剂的可见光催化活性机理探讨

采用磁控溅射技术在用浸渍提拉法制得的TiO2薄膜上，溅射氧化钨层,通过气相反应中光催化降解二甲苯的实验表明，WOx/TiO2薄膜具有可见光活性.通过UV-Vis吸收光谱、X射线光电子能谱（XPS）等方法对其可见光活性的机理进行探索.UV-Vis吸收光谱表明WOx,TiO2对可见光响应的范围有一定的扩展,吸收强度增加.XPS表明WOx/TiO2薄膜表面形成了明显的W杂质能级和Ti缺陷能级,这是WOx/TiO2在可见光范围有一吸收的主要原因,也是光催化剂具有可见光活性的必要条件之一，同时杂质能级的存在使半导体费米能级上移,载流子增加,光催化效率提高.     

Chemical thermodynamics

The curing of composition containing epoxy bond is complicated chemical and technological process where under temperature and pressure conditions a change of its structure occurs. The structure changes are possible to know by thermal methods as DSC, DTA, etc. and also by measurement of dielectrical response under the low frequency electrical field.     

白菜DNA甲基化水平的反相离子对高效液相色谱法研究

建立了反相离子对液相色谱测定白菜的DNA甲基化水平的方法。采用的色谱柱为HypersilBDSC18柱(200mm×4.0mm,5μm),以pH4.0的甲醇-5mmol·L-1庚烷磺酸钠-三乙胺(10:90:0.2,体积比)的混合液为流动相,UV检测器波长为273nm。通过测定DNA水样所产生的胞嘧啶和甲基胞嘧啶的含量,即可得知DNA甲基化程度。胞嘧啶和甲基胞嘧啶回收率分别为99.6%及103.3%,RSD为3.7%(日内)及5.2%(日间)。     

WO3/(TiO2-SiO2)催化剂的表面分散状态及催化性能的研究

用气相流动吸附法制备复合载体,用浸渍法制备WO3/(TiO2-S iO2)催化剂.应用LRS和TPR技术研究WO3在复合载体TIO2-S iO2表面的分散状态,发现TiO2在S iO2表面的分散可增强WO3与载体之间的相互作用,提高WO3在载体表面的分散阈值.另外TPR实验证明,TiO2的存在不仅大大改善WO3的分散状态,而且使WO3在TiO2-S iO2的还原温度升高,WO3与载体之间的作用增强.负载于经TiO2调变的S iO2上的催化剂其HDS、HYD、BHD活性高于负载于单纯S iO2上的催化剂的活性.     

Synthesis and Stereochemistry of New Bis(1,3-Oxathian-2-yl) Derivatives: Epimerisation and Chair–Twist Equilibria

The synthesis and stereochemistry of some new bis(1,3-oxathian-2-yl) derivatives are reported. The conformational behavior of these compounds and the orientation of their substituents are deduced from the NMR spectra, from the X-ray crystal structures of two compounds and from the ab-initio level calculations. The epimerization of diastereoisomers and the chair ⇌ 22,5-twist equilibria were studied by variable temperature NMR.     

Theoretical study of reaction channels for the weakly bound complex systems created with HF,CO2, and various amines

This investigation conducted reaction channels of weakly bound complexes CO₂…HF, CO₂…HF…NH₃, CO₂…HF…NH₂CH₃, CO₂…HF…NH(CH₃)₂, and CO₂…HF…N(CH₃)₃ systems, using the Gaussian 98 package at the B3LYP/6‐311++G(3df,2pd) level. The syn‐fluoroformic acid or syn‐fluoroformic acid plus NH₃ or amine conformers are more stable than the related anti‐fluoroformic acid or anti‐fluoroformic acid plus NH₃ or amine conformers. However, the above‐mentioned weakly bound complexes are more stable than both the related syn‐ and anti‐type fluoroformic acid or acid plus NH₃ or amine conformers and their related decomposed into CO₂ + HF or CO₂ + NHR₃F (R?H, CH₃) combined molecular systems. Five reaction channels of the weakly bound complexes exist. Each channel includes weakly bound complexes and their related above‐mentioned systems. Moreover, each reaction channel contains two transition states. The transition state between the weakly bound complex and anti‐fluoroformic acid type structure (T₁₃) is significantly higher than that of internal rotation (T₂₃) between syn‐ and anti‐FCO₂H (or FCO₂H…NR₃) structures. However, the above‐mentioned T₁₃ can significantly decrease its energy by adding the third molecule NH₃ or NR₃ (R?H or CH₃). The more CH₃ that is substituted in NR₃ of the reaction channel, the lower the activation energy of the transition state in the system is affected. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

MoO3、NiO、ZnO在小表面金红石上的分散行为

Dispersion of MoO3, NiO, ZnO on rutile TiO2 with low specific surface area was studied with Mercury Porosimeter, SEM, XPS and Ammonia Extraction method. The dispersion thresholds of MoO3, NiO, ZnO on three rutile TiO2 carriers were obtained with XPS, and com-pared with those on anatase TiO2 with high specific surf are area. Ammonia Extraction method was used to identify the surface oxide species interarting with support surface in different strength and it was found that the proportions of oxides that can not be extracted by ammonia extraction are different for MoO3, NiO and ZnO which are supported on rutile TiO2.