Dual Characterizations of Set Containments with Strict Convex Inequalities

Characterizations of the containment of a convex set either in an arbitrary convex set or in the complement of a finite union of convex sets (i.e., the set, described by reverse-convex inequalities) are given. These characterizations provide ways of verifying the containments either by comparing their corresponding dual cones or by checking the consistency of suitable associated systems. The convex sets considered in this paper are the solution sets of an arbitrary number of convex inequalities, which can be either weak or strict inequalities. Particular cases of dual characterizations of set containments have played key roles in solving large scale knowledge-based data classification problems where they are used to describe the containments as inequality constraints in optimization problems. The idea of evenly convex set (intersection of open half spaces), which was introduced by W. Fenchel in 1952, is used to derive the dual conditions, characterizing the set containments.     

相位差与q变形广义相干叠加态的压缩特性

对于q变形的非简谐振子广义相干态的叠加态β〉+eiφβeiδ〉,其量子涨落的可能高阶压缩阶数可以表示为k≠2πn/δ,这里n是整数.当δ=π时,压缩阶数不能是偶数即只能是奇数,这正是q变形非简谐振子广义奇偶相干态的结果.由此表明参数相位差δ对决定q变形的非简谐振子广义相干态叠加态的高阶压缩阶数起决定性作用.     

Dispersion and distribution of organically modified montmorillonite in nylon‐66 matrix

Nylon‐66 nanocomposites were prepared by melt‐compounding nylon‐66 with an alkyl ammonium surfactant pretreated montmorillonite (MMT). The thermal stability of the organic MMT powders was measured by thermogravimetric analysis. The decomposition of the surfactant on the MMT occurred from 200 to 500 °C. The low onset decomposition temperature of the organic MMT is one shortcoming when it is used to prepare polymer nanocomposites at high melt‐compounding temperatures. To provide greater property enhancement and better thermal stability of the polymer/MMT nanocomposites, it is necessary to develop MMT modified with more thermally stable surfactants. The dispersion and spatial distribution of the organic MMT layers in the nylon‐66 matrix were characterized by X‐ray diffraction. The organic MMT layers were exfoliated but not randomly dispersed in the nylon‐66 matrix. A model was proposed to describe the spatial distribution of the organic MMT layers in an injection‐molded rectangular bar of nylon‐66/organic MMT nanocomposites. Most organic MMT layers were oriented in the injection‐molding direction. Layers near the four surfaces of the bar were parallel to their corresponding surfaces; whereas those in the bulk differed from the near‐surface layers and rotated themselves about the injection‐molding direction. The influence of the spatial distribution of the organic MMT on crystallization of nylon‐66 was also investigated. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 1234–1243, 2003     

Fixed-point theorems for families of weakly non-expansive maps

In this paper, we present some fixed-point theorems for families of weakly non-expansive maps under some relatively weaker and more general conditions. Our results generalize and improve several results due to Jungck [G. Jungck, Fixed points via a generalized local commutativity, Int. J. Math. Math. Sci. 25 (8) (2001) 497-507], Jachymski [J. Jachymski, A generalization of the theorem by Rhoades and Watson for contractive type mappings, Math. Japon. 38 (6) (1993) 1095-1102], Guo [C. Guo, An extension of fixed point theorem of Krasnoselski, Chinese J. Math. (P.O.C.) 21 (1) (1993) 13-20], Rhoades [B.E. Rhoades, A comparison of various definitions of contractive mappings, Trans. Amer. Math. Soc. 226 (1977) 257-290], and others.     

FREE DEFORMATION RETRACTION IN INJECTIVE METRIC SPACES

In this paper the authors establish the concept of generalized ball-intersection (GBI) and prove that an injective metric space is freely contractible to its each GBI, which generalizes a result of Isbell from a point to a GBI.     

Analysis of plane and axisymmetric flows of incompressible fluids with the stream tube method: Numerical simulation by trust-region optimization algorithm

New concepts for the study of incompressible plane or axisymmetric flows are analysed by the stream tube method. Flows without eddies and pure vortex flows are considered in a transformed domain where the mapped streamlines are rectilinear or circular. The transformation between the physical domain and the computational domain is an unknown of the problem. In order to solve the non-linear set of relevant equations, we present a new algorithm based on a trust region technique which is effective for non-convex optimization problems. Experimental results show that the new algorithm is more robust compared to the Newton-Raphson method.     

Dielectric relaxation and aging effect in interpenetrating network polymers of poly(urethane)-poly(methyl methacrylate)

The permittivity and loss of poly(methyl methacrylate) (PMMA) network crosslinked with trimethylol-1,1,1 propane and its interpenetrating network polymers with 10, 34, and 50% (by weight) poly(urethane) have been measured from 100 to 400 K over a frequency range of 12 to 1 × 10⁵ Hz. Two relaxation processes, γ and β, are observed in the PMMA network, and a third process, α_pu, in the 10% poly(urethane) IPN. At higher concentrations of poly(urethane), the γ process is removed from the temperature-frequency range of our study. Crosslinking in pure PMMA slows the segmental motions involved in the β process and raises its activation energy. Physical aging of the 10 wt% poly(urethane)-PMMA causes its γ process to become indiscernible and the α_pu process to become better resolved. A discussion of these results in terms of local regions of segmental motion is provided.     

Fluorescence from the second excited singlet state of [18] annulenes

The emission spectra of the second excited singlet state of [18] annulene and of monofluoro [18] annulene (in a 3-methylpentane glass at 4 K) are reported. The large energy gap between the first and second excited singlet states inhibits fast internal conversion and favours the appearance of S₂ → S₀ emission. In addition, fluorescence from the S₁ state can be observed in monofluoro [13] annulene by exciting into the S₂ or directly into the S₁ absorption.     

Anionic polymerization of 1,2-butylene oxide

Anionic polymerizations of 1,2-butylene oxide were carried out in vacuum-sealed dilatometers in the range of 30–60°C. Potassium terbutoxide and dimsyl sodium were used as initiators; dimethyl sulfoxide (DMSO) and mixtures of DMSO with tetrahydrofuran were solvents. The polymer products were analyzed by gel permeation chromatography and infrared spectroscopy. The object of the investigation was to obtain information on the mechanism of the reaction and to elucidate some of its kinetic aspects. It has been shown that the polymerizations occur by two different processes, depending on the choice of experimental conditions. One of the processes involves free ions and ion-pairs, the other, ion-pairs alone. In the first case, where dimethyl sulfoxide is used as solvent, the order of the reaction with respect to the initiator concentration far exceeds unity (～1.8), while in the second case, involving mixed solvents, the order of the reaction, for all practical purposes, is one.