6元素集合上T0拓扑总数的计算

文中证明了有限预序集与有限偏序集的一些性质,并基于有限集上的拓扑和其上预序的一一对应关系,利用这些性质通过对极小元和极大元个数进行分类讨论,以一种有别于计算机算法而又容易理解的计算方法得出6元素集合上的T₀拓扑总数为130023.     

Partial regularity for certain classes of polyconvex functionals related to nonlinear elasticity

Consider the variational integral where Ω⊂ℝ ⁿ andp≥n≥2. H: (0, ∞)→[0, ∞) is a smooth convex function such that . We approximateJ by a sequence of regularized functionalsJ _δ whose minimizers converge strongly to anJ-minimizing function and prove partial regularity results forJ _δ-minimizers.     

Molar heat capacities and volumes of transfer of cytosine,thymine, caffeine and 1,3-diethylthymine to aqueous solutions of glycyl-glycine and L-α-alanyl-L-α-alanine at 25°C

Densities and specific heat capacities of ternary aqueous systems containing dipeptides (glycyl-glycine or L--alanyl-L--alanine) and nucleic acid bases (cytosine or thymine) or their alkyl derivatives (1,3-diethylthymine or caffeine) were determined at 25°C by flow calorimetry and flow densimetry. The partial molar volumes and heat capacities of transfer at infinite dilution of the different nucleic acid bases from water to water+dipeptide solutions were obtained therefrom. Except for the case of the transfer of cytosine to aqueous glycyl-glycine solutions where a small positive dependence of the transfer quantities was observed with the dipeptide concentration, the values of the heat capacities of transfer were in general low, positive or negative, depending on the compensation of hydrophobic-hydrophilic interactions between the dipeptide and the base. The volumes of transfer of most of the bases are very small, within the limit of the experimental error.     

Parameter choice by discrepancy principles for ill-posed problems leading to optimal convergence rates

Schock (Ref. 1) considered a general a posteriori parameter choice strategy for the Tikhonov regularization of the ill-posed operator equationTx=y which provides nearly the optimal rate of convergence if the minimal-norm least-squares solution belongs to the range of the operator (T ^* T) ^v , o<v1. Recently, Nair (Ref. 2) improved the result of Schock and also provided the optimal rate ifv=1. In this note, we further improve the result and show in particular that the optimal rate can be achieved for 1/2v1.The final version of this work was written while M. T. Nair was a Visiting Fellow at the Centre for Mathematics and Its Applications, Australian National University, Canberra, Australia. The work of S. George was supported by a Senior Research Fellowship from CSIR, India.     

X-ray emission spectroscopy with EPMA applied to high Tc Superconductors using new spectrometer crystals

The High Temperature Superconductors are characterized by a very anisotropical structure and by typical arrangements of Cu- and O-atoms within CuO₂-planes. In studying the electronic structure of these compounds there is a strong demand for high resolution valence band spectroscopy. Using an electron probe microanalyzer we study the X-ray emission of O-K_ga and Cu-L emerging from polycrystalline YBa₂Cu₃O₇ and Tl₂Ba₂Ca₂Cu₃O₁₀. The O-K emission band is analyzed using a chlinochlore crystal in (001) orientation (2d = 28.4 Å). For the Cu-L emission band we use a beryl crystal in (10¯10) orientation (2d = 15.9 Å). Furthermore, orientation dependent X-ray emission spectroscopy of single-crystalline YBa₂Cu₃O₇ and Tl₂Ba₂Ca₁Cu₂O₈ specimens was performed. We present the partial O-K spectra which represent the O-2p ( = x, y, z) electronic densities of states of the valence band and compare them with calculated data.     

Generalized solutions of a stochastic partial differential equation

We discuss the Cauchy problem of a certain stochastic parabolic partial differential equation arising in the nonlinear filtering theory, where the initial data and the nonhomogeneous noise term of the equation are given by Schwartz distributions. The generalized (distributional) solution is represented by a partial (conditional) generalized expectation ofT(t)° _0,t ^–1 , whereT(t) is a stochastic process with values in distributions and _s,t is a stochastic flow generated by a certain stochastic differential equation. The representation is used for getting estimates of the solution with respect to Sobolev norms.Further, by applying the partial Malliavin calculus of Kusuoka-Stroock, we show that any generalized solution is aC -function under a condition similar to Hörmander's hypoellipticity condition.     

Determination of thermodynamic functions of sorption for cyclohexyl-, piperidyl-, morpholyl-, and thiomorpholyl-n-alkanes by capillary gas-liquid chromatography

The values of partial molar free energy (G), enthalpy (H), and entropy (S) of sorption in the homologous series ofN-alkylpiperidines,N-alkylmorpholines,N-alkyl thiomorpholines, and alkylcyclohexanes were determined. It was found that the free energy of sorption is determined to a greater extent by the enthalpy term than by the entropy one. The free energy of sorption of the first homolog decreases when then-alkyl chain is attached directly to the carbon atom of the cycle and increases in the case ofN-alkylsubstituted heterocycles. The influence of the heteroatom nature on intermolecular interactions of homologs with the nonpolar stationary phase was quantitatively estimated on the basis of thermodynamic data.Dead time necessary for calculation of the retention factor was determined by the retention of methane injected into the column simultaneously with the sample.Translated from Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 8, pp. 2030–2032, August, 1996.     

校正峰电位漂移偏最小二乘极谱催化波同时测定轻稀土

应用Ｍ２７３．Ａ电化学系统中的线性扫描技术，确定了８．０×１０－５ｍｏｌ／Ｌ二甲酚橙及ｐＨ４．０ＨＡｃ－ＮａＡｃ缓冲体系为偏最小二乘极谱法同时测定Ｌａ、Ｃｅ、Ｐｒ、Ｎｄ、Ｓｍ、Ｅｕ的最佳极谱体系。６种稀土元素的线性范围均在１．０× １０－７～１．２ × １０－５ｍｏｌ／Ｌ。并对极谱峰电位随浓度漂移进行了校正，提高了方法的准确度。     

偏最小二乘-速差动力学分光光度法同时测定杀虫剂残杀威和异丙威两组分

采用速差动力学分光光度法对氨基甲酸脂类杀虫剂残杀威和异丙威进行同时测定，这两种化 的能在碱性条件下水解生成酚盐，进而与对氨基苯酚及高碘酸钾的反应产物醌亚胺发生偶联反应，生成蓝色化合物。反应的速率适中，可用于动力学分析。实验采集了多个时间点下538－700nm间的动力学－吸光度数据，构成量测矩阵，并采用偏最小二乘（PLS）法对量测数据进行解析。本文还对合成样品和环境水样中的残杀威和异丙威含量进行测定，获较好的结果。     

Calculation of vertical ionization potentials of difluoramine by perturbation corrections to koopmans' theorem

The vertical ionization potentials of difluoramine are calculated by perturbation corrections to Koopmans' theorem. The calculation shows that difluoraimine has three overlapping bands between 15 and 16 eV. The calculated results compare well with the experimental values. The photoelectron spectrum of difluoramine is compared with that of OF₂ and CH₂F₂.