Carleson measure characterization of Bloch functions

We give several equivalences of Bloch functions and little Bloch functions. Using these results we obtain the generalized Carleson measure characterization of Bloch functions and the generalized vanishing Carleson measure characterization of little Bloch functions, that is,f B if and only if |D f(z)| ^p (1-|z|²)^p-1 dm(z) is a generalized Carleson measure;f B ₀ if and only if |D f(z)| ^p (1-|z|²)^p-1 dm(z) is a generalized vanishing Carleson measure, whereD f( > 0) is the fractional derivative of analytic functionf of order, m denotes the normalised Lebesgue measure.Supported partly by the Young Teacher Natural Science Foundation of Shandong Province.     

Repeat Space Theory Applied to Carbon Nanotubes and Related Molecular Networks. I

The present article is the first part of a series devoted to extending the Repeat Space Theory (RST) to apply to carbon nanotubes and related molecular networks. Four key problems are formulated whose affirmative solutions imply the formation of the initial investigative bridge between the research field of nanotubes and that of the additivity and other network problems studied and solved by using the RST. All of these four problems are solved affirmatively by using tools from the RST. The Piecewise Monotone Lemmas (PMLs) are cornerstones of the proof of the Fukui conjecture concerning the additivity problems of hydrocarbons. The solution of the fourth problem gives a generalized analytical formula of the pi-electron energy band curves of nanotube (a, b), with two new complex parameters c and d. These two parameters bring forth a broad class of analytic curves to which the PMLs and associated theoretical devices apply. Based on the above affirmative solutions of the problems, a central theorem in the RST, called the asymptotic linearity theorem (ALT) has been applied to nanotubes and monocyclic polyenes. Analytical formulae derived in this application of the ALT illuminate in a new global context (i) the conductivity of nanotubes and (ii) the aromaticity of monocyclic polyenes; moreover an analytical formula obtained by using the ALT provides a fresh insight into Hückel’s (4n+2) rule. The present article forms a foundation of the forthcoming articles in this series. The present series of articles is closely associated with the series of articles entitled ‘Proof of the Fukui conjecture via resolution of singularities and related methods’ published in the JOMC.     

Radiation grafting from binary monomer mixtures. I. Vinyl ether of monoethanolamine and vinyl ether of ethyleneglycol

Gamma-radiation grafting of vinyl ether of monoethanolamine and vinyl ether of ethyleneglycol (VEEG) on polyethylene films has been studied from binary monomer mixtures. The effect of co-monomer composition and total exposure radiation dose on the grafting process is investigated. A combination of potentiometric and gravimetric techniques is applied to determine the grafting degree of each monomer in the final graft copolymer. The presence of more active monomer VEEG in the mixture was found to enhance the grafting of both monomers because the increasing of copolymerization rate which in turn increases the total grafting degree. The modification of the hydrophilic properties of the graft copolymer is studied by examining the grafted films for water- and copper (II) ions uptake.     

双柱气相色谱法测定有机物的正辛醇/水分配系数

通过对烷烃，醇类等有机物在五种不同极性固定相上的气相色谱保留值的测定，提出了从有机物气相色谱保留值测定其正辛醇/分配系数的公式，研究了从不同极性固定相上测得的保留值来测定其分配系数的准确性，得出烷烃类在所有柱上测得的保留值与其分配系数间均具有很好的关联，烷烃醇类在极性相异柱上的保留值之比值与其分配系数间也有很好的相关性，从而为烷烃及醇类等有机物分配系数的测定提供了一种简单、可靠，易行的新方法。     

Thermodynamics for Coulomb systems: A problem at vanishing particle densities

In this paper I combine techniques recently developed by Charles Fefferman with the well-known methods of Joel Lebowitz and Elliott Lieb to resolve some technical problems left unsettled by Lebowitz and Lieb's fundamental 1972 paper The constitution of matter: Existence of thermodynamics for systems composed of electrons and nuclei.     

On Deciding between Space Groups Pnam and Pna21 for the Crystal Structure of Zr3N4

The crystal structure of Zr₃N₄ is shown to crystallize in the centrosymmetric space group Pnam rather than in the noncentrosymmetric space group Pna2₁.     

Molar excess heat capacities and volumes for mixtures of alkanoates with cyclohexane at 25°C

Molar excess volumes V ^E at 25°C have been determined by vibrating-tube densimetry, as a function of mole fraction x for different series of an alkanoate (H _2m+1 C _m COOC _n H _2n+1 )+cyclohexane. Three types of alkanoates were investigated, i.e., methanoates (m=0, with n=3 and 4), ethanoates (m=1, with n=2, 3, and 4) and propanoates (m=2, with n=1, 2, and 3). In addition, a Picker flow calorimeter was used to obtain molar excess heat capacities C _p ^E at constant pressure at the same temperature. V ^E is positive for all systems and rather symmetric, with V ^E (x=0.5) amounting to almost identical values in a series of mixtures containing an alkanoate isomer of same formula (say C₄H₈O₂, C₅H₁₀O₂, or C₆H₁₂O₂). The composition dependence of C _p ^E is rather unusual in that two more or less marked minima are observed for most of the mixtures, especially when the alkanoate is a methanoate or an ethanoate. These results are discussed in terms of possible changes in conformation of both the ester and cyclohexane.     

LiCl—HOAc和LiCl—HOAc—H2O体系（25℃）相图

测定了LiCl-HOAc和LiCl-HOAc-H_2O体系25℃时的溶度,绘制了溶度图.在LiCl-HOAc体系的相图中有LiCl及LiCl·1/2HOAc2种固相,后者是固液异成分化合物,体系中未发现LiCl·5HOAc或LiCL·HOAc的生成.LiCl-HOAc-H_2O体系25℃时的相图中有3种固相,即LiCl·H_2O、LiCl和LiCl·(1/2)HOAc.相变LiCl·H_2O→LiCl→LiCl·(1/2)HOAc表明HOAc在该三元体系中具有盐溶、脱水和溶剂合3种作用.此结果提供了一种制备无水LiCl的新方法.     

Volumetric properties of the boldine + alcohol mixtures at atmospheric pressure from 283.15 to 333.15 K: A new method for the determination of the density of pure boldine

Densities of boldine + alcohol binary mixtures were measured over the whole accessible range of boldine compositions at temperatures from 283.15 to 333.15 K using an Anton-Paar digital vibrating glass tube densimeter. The binary systems studied include, as a solvent, seven normal alcohols from n-C₁ to n-C₆, n-C₈, and isopropanol. The density of these systems has been found an increasing function of the boldine composition. A new methodology based on density data of solutions of solid solutes with normal alcohols is described in order to determine solid molar volume of pure solutes. This methodology was validated with pure solid naphthalene molar volumes data at 298.15 K, with an average uncertainty of 6%.