An investigation of finite-size scaling for systems with long-range interaction: The spherical model

A method is suggested for the derivation of finite-size corrections in the thermodynamic functions of systems with pair interaction potential decaying at large distancesr asr ^{–d –ntent/m76w1v3746m425nt/xxlarge963.gif" alt="sgr" align="BASELINE" BORDER="0">} , whered is the space dimensionality andntent/m76w1v3746m425nt/xxlarge963.gif" alt="sgr" align="BASELINE" BORDER="0">>0. It allows for a unified treatment of short-range (ntent/m76w1v3746m425nt/xxlarge963.gif" alt="sgr" align="BASELINE" BORDER="0">=2) and long-range (ntent/m76w1v3746m425nt/xxlarge963.gif" alt="sgr" align="BASELINE" BORDER="0"><2) interaction. The asymptotic analysis is illustrated by the mean spherical model of general geometryL ^{d–dntent/m76w1v3746m425nt/xxlarge8242.gif" alt="prime" align="BASELINE" BORDER="0">}×ntent/m76w1v3746m425nt/xxlarge8734.gif" alt="infin" align="MIDDLE" BORDER="0"> ^{dntent/m76w1v3746m425nt/xxlarge8242.gif" alt="prime" align="BASELINE" BORDER="0">} subject to periodic boundary conditions. The Fisher-Privman equation of state is generalized to arbitrary real values ofdntent/m76w1v3746m425nt/xxlarge10878.gif" alt="ges" align="MIDDLE" BORDER="0">ntent/m76w1v3746m425nt/xxlarge963.gif" alt="sgr" align="BASELINE" BORDER="0">, 0ntent/m76w1v3746m425nt/xxlarge10877.gif" alt="les" align="MIDDLE" BORDER="0">dntent/m76w1v3746m425nt/xxlarge8242.gif" alt="prime" align="BASELINE" BORDER="0">ntent/m76w1v3746m425nt/xxlarge10877.gif" alt="les" align="MIDDLE" BORDER="0">ntent/m76w1v3746m425nt/xxlarge963.gif" alt="sgr" align="BASELINE" BORDER="0">. It is shown that thentent/m76w1v3746m425nt/xxlarge949.gif" alt="epsi" align="BASELINE" BORDER="0">-expansion may be used to study the breakdown of standard finite-size scaling at the borderline dimensionalities.     

Polymorphism of sorbitol

The polymorphism of sorbitol was investigated, confirming the existence of four anhydrous crystalline phases plus the hydrate. The crystallised melt (CM), the alpha form, and the gamma form were obtained via a dry route. The CM was confirmed to be a crystalline state with a spherulite morphology. The alpha form was obtained via direct conversion from the CM, in contrast to more complicated routes previously reported, and was found to have a very high crystallinity. Gamma crystals were obtained by seeding the melt at high temperature; however, crystallinity was clearly less than for alpha crystals.     

多维GARCH模型的半参数有效估计

多元GARCH模型的估计一般采用拟极大似然法(quasi maximum likehood),对于这种方法估计的相合性及渐近正态性已经被很多学者证实,然而对于新息列的分布不是多元正态时,这种估计的有效性还没人研究,本文从拟极大似然估计得到的参数相合估计入手,提出用非参数方法估计多元新息列的分布.     

peri-Naphthylenediamines. 38. Naphthalene and acenaphthene “proton sponges” with +M substituents in ortho positions with respect to peri-dimethylamino groups

Previously unknown 4,5,6,7-tetrakis(dimethylamino)acenaphthene, which is the first acenaphthene derivative containing four vicinal dialkylamino groups, was synthesized based on 5,6-bis(dimethylamino)-4,7-dinitroacenaphthene. The total synthesis of 1,2,7,8-tetrakis(dimethylamino)naphthalene was carried out starting from 3,6-dinitronaphthalic anhydride. Other ntent/p20526877nt55561/xxlarge8220.gif" alt="ldquo" align="MIDDLE" BORDER="0">proton spongesntent/p20526877nt55561/xxlarge8221.gif" alt="rdquo" align="MIDDLE" BORDER="0"> of this type, viz., 1,7,8-tris(dimethylamino)-2-methoxy- and 1,8-bis(dimethylamino)-2,7-dipiperidinonaphthalenes, were prepared by the nucleophilic substitution in 2,7-dimethoxy-1,8-dinitronaphthalene. In solutions, 1,2,7,8-tetrakis(dimethylamino)naphthalene and its analogs can form di- and trications in the presence of acids. The basicity constants pK _a ¹ of the compounds measured in DMSO depend in a complex way on their structures but correlate with the basicity index B, which is determined by changes in the chemical shifts ntent/p20526877nt55561/xxlarge948.gif" alt="delta" align="BASELINE" BORDER="0">_H after the addition of the first proton. Due to low C-nucleophilicity of ortho-disubstituted ntent/p20526877nt55561/xxlarge8220.gif" alt="ldquo" align="MIDDLE" BORDER="0">proton spongesntent/p20526877nt55561/xxlarge8221.gif" alt="rdquo" align="MIDDLE" BORDER="0"> in combination with high basicity, these compounds hold considerable promise as reagents in organic synthesis.     

β-环糊精与两性表面活性剂相互作用β

用表面张力法研究了β-环糊精与十一烷基酰胺甲酸钠(C11H23CONHCOONa,SF)两性表面活性剂在不同温度下的包结作用。结果表明:SF的表面张力值(β)及表观临界胶束浓度(cmc)加入β-CD后增加,β-CD浓度越大,γ和cmc增加越多,且SF的cmc与β-CD浓度存在线性关系,随温度的升高,两性表面活性剂的表面张力值降低,意味着它们的表面活性随温度升高而增强。利用表面张力测定了β-CD-SF体系在不同温度下的包结形成常数Ka,进而求得了包结过程的焓变和熵变,结果表明,该过程是焓和熵均有利的过程,进一步说明疏水作用是形成包结物最重要的的作用力之一。     

Adsorption of adamantanol isomers on graphitized thermal carbon black

The thermodynamic characteristics of adsorption of some adamantanol isomers on graphitized thermal carbon black were calculated and determined experimentally. The parameters of the potential function for the intermolecular interaction between hydroxyl oxygen and carbon of the graphite basis plane were determined for the first time. The adsorption properties of adamantanols are largely determined by electron density distribution in the adamantane cage, which are related to the ntent/gl7h2nt5331g3228/xxlarge8220.gif" alt="ldquo" align="MIDDLE" BORDER="0">cagentent/gl7h2nt5331g3228/xxlarge8221.gif" alt="rdquo" align="MIDDLE" BORDER="0"> effect.     

Crystallization of D2O thin films on Ru(0 0 1) surfaces

The phase conversion of amorphous solid water (ASW) to crystalline ice (CI) has been investigated in the very thin (∼10 monolayers) film regime on a Ru(0 0 1) surface. We analyze the converted CI fraction with the Avrami model, and recognize that one-dimensional CI growth occurs, which can be contrasted to the three-dimensional CI growth generally established in the thick (≥50 monolayers) film regime. We evaluate activation energy for the ASW crystallization to be about 1.0 eV. We suggest that the ASW crystallization is not influenced by the substrate even near the substrate-ice interface.     

Determination of metastable zone width for combined anti-solvent/cooling crystallization

The metastable zone width (MSZW), induction time and primary nucleation kinetics have been measured and estimated for simultaneous anti-solvent and cooling crystallization of paracetamol in iso-propanol/water solution. ATR-FTIR spectroscopy and laser back-scattering are used to measure the solute concentration and primary nucleation event, respectively. Response surface analysis was applied to find the contribution of the crystallization mechanism on the MSZW and obtain a statistical model for quick estimation of the MSZW. Two theoretical approaches for the estimation of nucleation rate kinetic parameters from experimental data are presented. The methods are obtained by modifying the classical Nyvlt's correlation for simultaneous cooling/anti-solvent crystallizations. The nucleation order n for primary nucleation was deduced from the slope of a linear plot of log(MSZW) vs. log(cooling and anti-solvent rates). The induction time was also estimated by changing the classical methods for combined cooling and anti-solvent crystallization.     

关于SL(2,R)上主级数表示、离散级数表示的矩阵系数的平方可积性

人们知道SU（２）的不可约酉表示的矩阵元是相互正交且平方可积的（Ｐｅｔｅｒ Ｗｅｙｌ定理）． 对于SU（２，R）的主级数表示和离散级数表示的矩阵系数是否有类似的结果？在该文中，作者部分给出了这个问题的肯定回答，即关于主级数表示的矩阵系数是准平方可积的，关于离散级数表示 的矩阵系数是平方可积的． 此外，他们还得到了离散级数表示（除狀＝±１外）在子空间′狀上的矩阵系数是绝对可积的．     

A uniform molecular model of δ opioid agonist and antagonist pharmacophore conformations

On the basis of a model of the pharmacophore conformations of agonist of the ntent/p70215nt72238335/xxlarge948.gif" alt="delta" align="BASELINE" BORDER="0">-opioid receptor the corresponding ntent/p70215nt72238335/xxlarge948.gif" alt="delta" align="BASELINE" BORDER="0">-antagonist conformations were determined by means of force field calculations. The results explain the unusual behavior of several cyclic ntent/p70215nt72238335/xxlarge946.gif" alt="beta" align="MIDDLE" BORDER="0">-casomorphin analogues on the molecular level. Thus, for instance, the model helps to understand why Tyr-c[D-Orn-2-Nal-D-Pro-Gly] is a mixed ntent/p70215nt72238335/xxlarge956.gif" alt="mgr" align="MIDDLE" BORDER="0">-agonist and ntent/p70215nt72238335/xxlarge948.gif" alt="delta" align="BASELINE" BORDER="0">-antagonist. Furthermore, the model is consistent with low energy conformations of other ntent/p70215nt72238335/xxlarge948.gif" alt="delta" align="BASELINE" BORDER="0">-antagonists such as Tyr-Tic-Phe, Tyr-Tic-Phe-Phe, naltrindole and BNTX. The occupation of a special spatial area by bulky groups close to the protonated N-terminus of opioid peptides is assumed to be highly critical for the switch from agonist to antagonist behavior.