Minimum Distance Between the Faces of Two Convex Polyhedra: A Sufficient Condition

The problem of finding the Euclidean distance between two convex polyhedra can be reduced to the combinatorial optimization problem of finding the minimum distance between their faces. This paper presents a global optimality criterion for this problem. An algorithm (QLDPA) for the fast computation of the distance between convex and bounded polyhedra is proposed as an application of it. Computer experiments show its fast performance, especially when the total number of vertices is large.     

Subgroup separability of graphs of abelian groups

In the present paper we give necessary and sufficient conditions for the subgroup separability of the fundamental group of a finite graph of groups with finitely generated abelian vertex groups.

     

社会经济管理系统和谐性模型的构建与分析

本文从非线性自然观的视野。引用与分析了社会经济系统功能模型与效应模型。构建了系统和谐状态模型与和谐状态可信度模型，形象地说明了企业系统的和谐既是一个随机不确定状态。又是企业和谐力量与不和谐力量相互抗争干涉的过程。依据协同学原理提出了企业系统和谐演进的机制，表明企业系统的和谐发展是子系统和谐协同的过程。即子系统竞争合作的过程。文中所构建的模型，从理论上清晰地说明了企业系统和谐有序运行的机理，为如何构建和谐企业。提供了建设性的思考。     

Cauchy problems for linear thermoelastic systems of type III in one space variable

The goal of the paper is to analyse properties of solutions for linear thermoelastic systems of type III in one space variable. Our approach does not use energy methods, it bases on a special diagonalization procedure which is different in different parts of the phase space. This procedure allows to derive explicit representations of solutions. These representations help to prove results for well‐posedness of the Cauchy problem, L^P–L^q decay estimates on the conjugate line and results for propagation of singularities. Copyright © 2005 John Wiley & Sons, Ltd.     

Selective synthesis of dehydroamino acids from threonines

Dehydropeptides containing dehydroamino acid (ΔAA) are frequently found in natural resources with important biological activity. Herein, we report the selective synthesis of Z- and E-ΔAbu from l- and l-allo-threonine as starting materials through selenation and oxidative elimination. The detailed reaction mechanism of phosphine-assisted selenoether formation is also discussed.     

Mesoscopic details of crack tip deformation field by application of differential interference contrast method

An experimental method is developed to examine the near tip deformation at the mesoscopic scale level. The differential interference contrast (DIC) method is used by application of the Nomarski prism in polarized microscope for measuring the out of surface deformation. The method is very sensitive to small height changes detected by different interference color. Discussed are results for the crack tip deformation field.     

Measurements of Time-Varying Characteristics of Optical Signals and Inhomogeneities of Tested Substances with Additional Phase Modulation

The problem of investigation of the amplitude and phase structure of a time-varying probing optical signal and the structure of time-varying inhomogeneities of a substance tested by this signal is considered. The analysis is concerned, in particular, with determination of the structure of signals and processes with resolution in the pico- and femtosecond range. The scheme used for the analysis is based on registration of four spatially separated spectra of the studied radiation. The spectra are formed in a four-channel scheme with a twin-wave Michelson interferometer and a spectral device. Modulators based on electrooptical crystals (perovskites) are placed in the channels. The sum spectra are formed: without modulators, with the effect of either of the modulators, and with both of them affecting the radiation. The effect of the studied substance implies either modulating the radiation (in this case it is described by multiplication) or redistributing the radiation (then it is described by convolution).     

A Semiconductor Laser of the Visible Range as an Exciting Source of Raman Scattering

A possibility of application of semiconductor lasers of the visible range as exciting sources for Raman spectroscopy is studied. An experimental set-up for measuring Raman spectra of polycrystalline dielectrics and broad-gap semiconductors excited by a semiconductor laser with a wavelength of 640 nm was created. The conditions under which the spectral width of the lasing line of a semiconductor laser was within 10^-3 cm^-1 in the continuous mode with a power of 10 mW are realized. The characteristics of various types of exciting sources used in Raman spectroscopy are compared. The results of studies of the characteristic Raman spectra excited with a semiconductor laser in polycrystalline sulfur are presented.     

Sulfonated poly(aryl ether ketone)s containing naphthalene moieties obtained by direct copolymerization as novel polymers for proton exchange membranes

A series of sulfonated poly(aryl ether ketone)s (SPAEKs) were prepared by aromatic nucleophilic polycondensation of 2,6‐dihydroxynaphthalene with 5,5′‐carbonyl‐bis(2‐fluorobenzenesulfonate) and 4,4′‐difluorobenzophenone. The structure and degree of sulfonation (DS) of the SPAEKs were characterized using ¹H NMR spectroscopy. The experimentally observed DS values were close to the expected values derived from the starting material ratios. The thermal stabilities of the SPAEKs were characterized by thermogravimetric analysis, which showed that in acid and sodium salt forms they were thermally stable in air up to about 240 and 380 °C, respectively. Transparent membranes cast from the directly polymerized SPAEKs exhibited good mechanical properties in both dry and hydrated states. The dependence of water uptake and of membrane swelling on the DS at different temperatures was studied. SPAEK membranes with a DS from 0.72 to 1.60 maintained adequate mechanical properties after immersion in water at 80 °C for 24 h. The proton conductivity of SPAEK membranes with different degrees of sulfonation was measured as a function of temperature. The proton conductivity of the SPAEK films increased with increased DS, and the highest room temperature conductivity (4.2 × 10^?2 S/cm) was recorded for a SPAEK membrane with a DS of 1.60, which further increased to 1.1 × 10^?1 S/cm at 80 °C. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 2866–2876, 2004     

UV‐ignited frontal polymerization of an epoxy resin

By combining frontal polymerization and radical‐induced cationic polymerization, it was possible to cure thick samples of an epoxy monomer bleached by UV light. The effect of the relative amounts of cationic photoinitiator and radical initiator was thoroughly investigated and was related to the front's velocity and its maximum temperature. The materials obtained were characterized by quantitative conversion also in the deeper layers, not reached by UV light. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 2066–2072, 2004