Volumes of restricted Minkowski sums and the free analogue of the entropy power inequality

In noncommutative probability theory independence can be based on free products instead of tensor products. This yields a highly noncommutative theory: free probability theory (for an introduction see [9]). The analogue of entropy in the free context was introduced by the second named author in [8]. Here we show that Shannon's entropy power inequality ([6, 1]) has an analogue for the free entropy (X) (Theorem 2.1).The free entropy, consistent with Boltzmann's formulaS=klogW, was defined via volumes of matricial microstates. Proving the free entropy power inequality naturally becomes a geometric question.Restricting the Minkowski sum of two sets means to specify the set of pairs of points which will be added. The relevant inequality, which holds when the set of addable points is sufficiently large, differs from the Brunn-Minkowski inequality by having the exponent 1/n replaced by 2/n. Its proof uses the rearrangement inequality of Brascamp-Lieb-Lüttinger ([2]). Besides the free entropy power inequality, note that the inequality for restricted Minkowski sums may also underlie the classical Shannon entropy power inequality (see 3.2 below).Research supported in part by grants from the National Science Foundation.     

简易型离子选择电极-流动注射分析仪的研制及卤水中氯、溴和碘的连续测定

本文设计研制了简单实用的流通池,组装了简易型离子选择电极—流动注射分析仪,对体系的分析特点和影响因素进行了考察。此装置性能可靠,能满足简单流注分析的需要,并建立了卤水中Cl~-、Br~-和I~-的连续测定方法。     

Precipitation and recrystallization of uniform CuCl particles formed by aggregation of nanosize precursors

Uniform, spherical CuCl particles were obtained by mixing aqueous solutions of CuCl ₂ and ascorbic acid in the presence of polyvinylpyrrolidone (PVP) as dispersing agent. The size and the uniformity of the resulting particles depended on the volume ratio of the reactant solutions, their concentrations, the distribution of the stabilizers, and the mixing method. The single jet precipitation yielded large spheres of broad size distributions, while the particles obtained by the double jet technique were rather uniform in size. The final colloidal CuCl particles were formed by the aggregation of nanocrystals, initially generated in the system. Depending on the pH of the reaction mixture, these particles slowly change to large CuCl crystals on aging in the mother liquor.     

五配位Cu(Ⅰ)配合物[Cu(4′-Phtpy)(PPh_3)_2](BF_4)的合成、结构及光谱性质研究

由[Cu(MeCN)2 (PPh3)2 ](BF4 )和 4′ 苯基 2,2′:6′,2″ 三联吡啶(4′ Phtpy)在室温下反应,合成了一个新颖的具有光致发光性能的五配位配合物[Cu(4′ Phtpy)(PPh3)2 ](BF4 ).对配合物进行了X射线衍射结构表征,并进行了红外光谱、紫外可见光谱、荧光光谱等光谱学分析.晶体属单斜晶系,空间群Pn,晶胞参数:a =1 0 80 7(6)nm,b =1 0 943 (6)nm,c=2 1610(12 )nm,α =90°,β =10 2 785(10 )°,γ =90°,V =2 492(2 )nm3,Z =2,Dc=1 3 5 4g·cm-3.配合物中,Cu(Ⅰ)与 4′ Phtpy的 3个N,2个PPh3的P配位呈变形三角双锥型结构,其轴向由Cu键合联吡啶的末端 2个N所组成,赤道平面由联吡啶的中心N原子和 2个PPh3的P原子所组成     

Structural Characterization of Anhydroicaritin Glycosides Using ESI—FT—ICR Mass Spectrometry

Fourier transform ion cyclotron resonance mass spectrometry (FT-ICR-MS) was used to determine the structures of anhydroicaritin glycosides by the MS/MS experiments of anhydroicaritin glycosides and their methylated derivatives,With high accuracy FT-ICR-MS provides much information about the structures of compounds ,FT-ICR-MS shows the great potential application in the structural characterization of unknown compounds.     

Synthesis of 5-cyclopropyluracil and 5-cyclopropylcytosine by the Pd(0)-catalyzed coupling reaction

5-Cyclopropyluracil and cyclopropylcytosine were prepared by the Pd(0)-catalyzed coupling reaction of 5-bromo-2,4-di(trimethylsilyloxy)pyrimidine and 5-bromo-2,4-O,N-bis-trimethylsilylcytosine with tributylstan-nylcyclopropane. The reactions also gave dehalogenated pyrimidine bases as by-products. Attempts to use 2,4-O,N-bis-trimethylsilyl-5-iodocytosine as the halide gave complete dehalogenation.     

(2E,4E)-3-苯基-2-[2-(N-乙氧羰基甲基氨基)-苯硫基]-2,4-己二烯酸乙酯——一个新的分子内重排反应产物

２，３－二氢－２－甲基－４－苯基－１，５－苯并硫氮杂卓与重氮乙酸乙酯反应，得到非预期的分子内重排的开环产物。通过元素分析、ＩＲ，１ＨＮＭＲ，ＭＳ及Ｘ－晶体衍射分析确定了它的结构，并根据产物的结构，对这一新反应的反应机理进行了探讨和研究。     

三元配合物钯（Ⅱ）-2,2''-联吡啶-L-天冬氨酸与DNA作用研究

The ternary complex Pd(Ⅱ)-2,2‘-bipyridine-L-asparagic acid was synthesized and characterized by elemental analysis, IR-spectra and molar conductance. The formula of the complex is Pd(bipy)(L-asp). The interaction of the complex with DNA has been studied by UV-spectra, fluorescence spectra, CD-spectra and gel electrophoresis. The results showed that the interaction of the complex with DNA performed mainly in intercalative mode and the extent of interaction was dependent on the concentration of the complex.