Gas-chromatographic method of evaluation ofn-alkanol ability for self-association in pure liquid

The values of the gas-chromatographic indicator reflecting the capacity of analytes for self-association in pure liquids, δT _b.p., were estimated for C₁–C₉ and C₁₁ n-alkanols by capillary gas chromatography on a nonpolar stationary phase under isothermal conditions. The δT _b.p. values ofn-alkanols, found as the difference between the boiling points measured directly and those calculated from GC data, are correlated with thermodynamic characteristics of the formation ofn-alkanol associates in pure liquids. Usingn-alkanols as analytes with insignificant temperature increments of the retention indices, it was shown that the δT _b.p. values can be determined under conditions used in gas chromatography with temperature programming. In this way a single chromatographic run can be used to compare the capacities for self-association of analytes boiling over a wide temperature range. The C₂–C₉ n-alkanethiols, which are not associated in neat liquids, have negative δT _b.p. values. An interpretation of this finding is proposed. Translated fromIzvestiya Akademii Nauk, Seriya Khimicheskaya, No. 2, pp. 315–318 February, 2000.     

Weak surface energy in nematic dispersions: Saturn ring defects and quadrupolar interactions

The role of surface energy in the behavior of colloidal particles in liquid crystalline phases is investigated. When the surface energy dominates, a hedgehog defect is formed and, according to an electrostatic analogy, the distortions around the particles exhibit a dipolar character. By contrast, for weaker anchoring, the configuration becomes quadrupolar as evidenced by the structure of latex clusters in lyotropic systems and the observation of defects reminiscent of Saturn rings in thermotropic systems. Received 21 June 1999     

中国城市竞争力评价量化模型研究

本文建立一种将主、客观指标赋权方法优点相结合的城市竞争力综合评价分层构权主成分分析模型,在构建中国城市竞争力综合评价指标体系的基础上,基于该模型方法给出31个中国主要城市的城市竞争力的评价实例。并以并以判别分析方法对相关评价结果进行校验,实证分析的结果表明:这是一种适合于城市竞争力定量评价、稳定性较好且切实有效的方法模型。     

On critical values of numerical parameters characterizing intersections of embedded sets

To study intersections of embedded bounded closed sets in Banach space, a numerical parameter was introduced earlier; in a certain sense, this parameter describes the deviation of the shape of a set from that of a sphere. Critical values of this parameter for some classes of Banach spaces are determined, a new numerical parameter serving the same purpose is introduced, and the relation between the two parameters is examined. Translated fromMatematicheskie Zametki, Vol. 68, No. 2, pp. 303–310, August, 2000.     

流产后宫内胎物组织残留的超声诊断

回顾性分析了４６例临床被证实为宫内胎物组织残留的病例。结果表明，流产后较长时间有不规则阴道流血，而作Ｂ超检查能发现特征性改变。声像图显示，子宫增大，宫内有异常光团和不规则液性暗区或宫腔局部膨隆，周边见很亮光条。认为诊断宫内残留组织，可以结合病只与声像技术较易诊断出来。本组超声诊断符合率达９８％。对减少因宫内残留造成的子宫收缩不良、不规则阴道流血等现象，避免并发感染及导致绒癌发生等不良后果，有重要的     

The near-field effect in a system of two-level dipole particles

We have solved a self-consistent problem on interaction of two dipole atoms located at an arbitrary distance from each other with the field of a quasiresonance light wave, whose intensity is sufficient for the system to manifest nonlinear properties. The atoms are considered as two-level systems described by means of Bloch optical equations, while the field inside of the system includes both Coulomb and retarded parts. We consider a situation where atoms are identical and the distance between them is much smaller than the length of an outer light wave. The distribution of an electric field both inside of a small object and outside of it is found numerically. It is shown that the amplitude of the electric field in a wave zone depends substantially on the frequency of the external field and interatomic distance, while the field distribution differs from the field pattern of an electric dipole. At definite values of the external field intensity an optical multistability is a feature of the system under investigation. We have elucidated the conditions under which the multistability is manifested in the present system. The results obtained are considered as the near-field effect in the optics of small objects, which makes it possible to investigate the structure of small objects by means of optical radiation. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 67, No. 3, pp. 375–378, May–June, 2000. The present work was supported by the Russian Foundation for Fundamental Research (grant 98-02-16035) and by a grant from the Federal Purpose-Oriented Program “Integration.”     

FPTAS for optimizing polynomials over the mixed-integer points of polytopes in fixed dimension

We show the existence of a fully polynomial-time approximation scheme (FPTAS) for the problem of maximizing a non-negative polynomial over mixed-integer sets in convex polytopes, when the number of variables is fixed. Moreover, using a weaker notion of approximation, we show the existence of a fully polynomial-time approximation scheme for the problem of maximizing or minimizing an arbitrary polynomial over mixed-integer sets in convex polytopes, when the number of variables is fixed. A conference version of this article, containing a part of the results presented here, appeared in Proceedings of the 17th Annual ACM-SIAM Symposium on Discrete Algorithms, Miami, FL, January 22–24, 2006, pp. 743–748. The first author gratefully acknowledges support from NSF grant DMS-0608785, a 2003 UC-Davis Chancellor’s fellow award, the Alexander von Humboldt foundation, and IMO Magdeburg. The remaining authors were supported by the European TMR network ADONET 504438.     

Comparison of Lagrangian bounds for one class of generalized assignment problems

Classical and modified Lagrangian bounds for the optimal value of optimization problems with a double decomposable structure are examined. For the class of generalized assignment problems, this property of constraints is used to design a Benders algorithm for solving the modified dual problem. Numerical results are presented that compare the quality of classical and modified bounds.     

Hermite四点插指公式

文章利用Hermite插值基函数,将求解Hermite四点插指问题转换为求解8个派生出来的多项式插值问题,证明了Hermite四点插指公式的存在唯一性,并用两种方法构造出Hermite四点插指公式,最后给出了一个算例.