Historical perspectives on living anionic polymerization

A brief overview of the role that Dr. Michael Szwarc has played in unraveling the mechanism of living anionic polymerization is presented. Emphasis is placed on the different ionic species that control the propagation reaction in ether-type solvents. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 40: 2101–2107, 2002     

Multiarm star block copolymers via Diels‐Alder click reaction

Two types of multiarm star block copolymers: (polystyrene)_m‐poly(divinylbenzene)‐poly(methyl methacrylate)_n, (PS)_m‐polyDVB‐(PMMA)_n and (polystyrene)_m‐poly(divinylbenzene)‐poly(tert‐butyl acrylate)_k, (PS)_m‐polyDVB‐(PtBA)_k were successfully prepared via a combination of cross‐linking and Diels–Alder click reactions based on “arm‐first” methodology. For this purpose, multiarm star polymer with anthracene functionality as reactive periphery groups was prepared by a cross‐linking reaction of divinyl benzene using α‐anthracene end functionalized polystyrene (PS‐Anth) as a macroinitiator. Thus, obtained multiarm star polymer was then reacted with furan protected maleimide‐end functionalized polymers: PMMA‐MI or PtBA‐MI at reflux temperature of toluene for 48 h resulting in the corresponding multiarm star block copolymers via Diels–Alder click reaction. The multiarm star and multiarm star block copolymers were characterized by using ¹H NMR, SEC, Viscotek triple detection SEC (TD‐SEC) and UV. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 178–187, 2009     

三类有向三元系之间关系的一种猜想

一个Mendelsohn (Directed, 或Hybrid)三元系 MTS$(v, \lambda)$~(DTS$(v, \lambda)$,或HTS$(v,\lambda))$, 是由$v$元集$X$ 上的一些循环（可迁，或循环和可迁）三元组(简称区组)构成的集合${\cal B}$, 使得$X$上每个由不同元素组成的有序对都恰在 ${\cal B}$的$\lambda$个区组中出现.本文主要讨论了这三类有向三元系之间的一种关联关系，给出猜想：任意MTS$(v,\lambda)$的区组关联图$G(\     

企业三重绩效评价模型—空间几何模型

按照可持续发展战略的要求,从经济、生态、社会三个方面构建了企业的三重绩效评价指标体系.运用空间几何方法建立了一套企业三重绩效评价模型,该模型包括静态绩效评价、静态平衡度评价、动态协调度评价以及综合评价.最后,对评价模型进行了初步应用.     

Von Neumann Regularity and Quadratic Conorms in JB^＊-triples and C^＊-algebras

We revise the notion of von Neumann regularity in JB^＊-triples by finding a new characterisation in terms of the range of the quadratic operator Q（a）. We introduce the quadratic conorm of an element a in a JB^＊-triple as the minimum reduced modulus of the mapping Q（a）. It is shown that the quadratic conorm of a coincides with the infimum of the squares of the points in the triple spectrum of a. It is established that a contractive bijection between JBW^＊-triples is a triple isomorphism if, and only if, it preserves quadratic conorms. The continuity of the quadratic conorm and the generalized inverse are discussed. Some applications to C^＊-algebras and von Neumann algebras are also studied.     

Nonlinear resonances and self-excited oscillations of a rotor caused by radial clearance and collision

This paper investigates oscillations in a flexible rotor system with radial clearance between an outer ring of the bearing and a casing by experiments and numerical simulations. The mathematical model considers the collisions of the bearing with the casing. The following phenomena are found: (1) Nonlinear resonances of subharmonic, super-subharmonic and combination oscillation occur. (2) Self-excited oscillation of a forward whirling mode occurs in a wide range above the major critical speed. (3) Entrainment phenomena from self-excited oscillation to nonlinear forced oscillation occur at these nonlinear resonance ranges. Moreover, this study analyzes periodic solutions of the mathematical model by the Harmonic Balance Method (HBM). As the results, the nonlinear resonances of subharmonic oscillation and its entrainment phenomenon can be explained theoretically by investigating the stability of the periodic solutions. The influence of the static force and the bearing damping on these oscillation are also clarified.     

Fractional Lévy processes on Gel’fand triple and stochastic integration

In this paper, we investigate the long-range dependence of fractional Lévy processes on Gel’fand triple and construct stochastic integral with respect to fractional Lévy processes for a class of deterministic integrands.      

Melting of microinclusions close packed in an elastic matrix

A novel representation is proposed of the liquid state in a microcavity, the collective nature of that state being taken into account. In this case a microinclusion undergoing melting is described as a single two-level system. The phase transition of melting in a close-packed system of such inclusions embedded in an elastic medium is described rigorously within the framework of the self-consistent approach. When an additional intermediate premelting state is taken into account, the curve of the steady-state phase transition with a critical point that happens on the phase diagram can be transformed in different ways, depending on the values of the specific parameters. In the simplest case shortening of the straight line takes place; bending is also possible. There is a region of the parameters where the critical line is split. In the latter case the existence of the triple point is also possible. The results obtained are in agreement with the experimental data.     

Special and extreme triple shock-wave configurations

Triple shock-wave configurations in steady supersonic flows of an inviscid perfect gas are considered. Triple configurations with special intensities of shock waves and extreme ratios of various flow parameters behind these configurations are determined. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 4, pp. 39–53, July–August, 2006.     

Fundamental and subharmonic resonances in a system with a ‘1-1’ internal resonance

The fundamental and subharmonic resonances of a two degree-of-freedom oscillator with cubic stiffness nonlinearities and linear viscous damping are examined using a multiple-seales averaging analysis. The system is in a 1–1 internal resonance, i.e., it has two equal linearized eigenfrequencies, and it possesses nonlinear normal modes. For weak coupling stiffnesses the internal resonance gives rise to a Hamiltonian Pitchfork bifurcation of normal modes which in turn affects the topology of the fundamental and subharmonic resonance curves. It is shown that the number of resonance branches differs before and after the mode bifurcation, and that jump phenomena are possible between forced modes. Some of the steady state solutions were found to be very sensitive to damping: a whole branch of fundamental resonances was eliminated even for small amounts of viscous damping, and subharmonic steady state solutions were shifted by damping to higher frequencies. The analytical results are verified by a numerical integration of the equations of motion, and a discussion of the effects of the mode bifurcation on the dynamics of the system is given.