Exponential stability in thermoviscoelastic mixtures of solids

In this paper we investigate the asymptotic behavior of solutions to the initial boundary value problem for a one-dimensional mixture of thermoviscoelastic solids. Our main result is to establish the exponential stability of the corresponding semigroup and the lack of exponential stability of the corresponding semigroup.     

Geometric Approach to Pontryagin’s Maximum Principle

Since the second half of the 20th century, Pontryagin’s Maximum Principle has been widely discussed and used as a method to solve optimal control problems in medicine, robotics, finance, engineering, astronomy. Here, we focus on the proof and on the understanding of this Principle, using as much geometric ideas and geometric tools as possible. This approach provides a better and clearer understanding of the Principle and, in particular, of the role of the abnormal extremals. These extremals are interesting because they do not depend on the cost function, but only on the control system. Moreover, they were discarded as solutions until the nineties, when examples of strict abnormal optimal curves were found. In order to give a detailed exposition of the proof, the paper is mostly self-contained, which forces us to consider different areas in mathematics such as algebra, analysis, geometry.     

Polymerization of Styrene by Neutral Ni (II) Acetylide Complex

Over the past few years, the utilization of late transition metal-based soluble complexes as styrene polymerization catalysts has received considerable attention1. Various systems have been explored. For example, cationic h3-allylnickel complexes alone2 or modified by P (III) ligands3 as well as a few other systems (e. g., cationic h3-benzylic nickel complexes4) are active homogeneous catalysts for the low molecular weight polymerization of styrene by simple cationic mechanism2,3,4. Neut…     

CuI晶体缺陷态电子结构及其施主-受主对发光机理的研究

运用相对论密度泛函理论和嵌入分子团簇方法，模拟计算了具有γ相CuI晶体的本征缺陷态电子结构.结果表明，四面体间隙Cu和Cu空位最有可能在禁带中引入浅施主和受主能级，从而形成施主-受主对(DAP)，产生420—430 nm的DAP复合发光. 关键词： γ-CuI晶体 密度泛函理论 电子结构 发光机理     

PARTITION PROPERLY OF DOMAIN DECOMPOSITION WITHOUT ELLIPTICITY

1. IntroductionDomain decomposition methods have undergone great development in the past decade andthere has been rich mathematical theory for model problems. It is worthy to examine how theSemethods can be effectively applied to predical problems where the model problem analysis doesnot trivially apply. It is far from of~ng that there remains not much new for domain decomposition theoretically and Practically. In terms of domain partition, domain decompositionmethods are claSsiced as twO ir…     

Photorefractive properties and self-pumped phase conjugation in a series of BaTiO3 crystals

This paper presents the experimental results of two-wave mixing and self-pumped phase conjugation (SPPC) in barium titanate (BaTiO₃) crystals doped with Rh or Ce. It has been shown that the main parameters of SPPC depend very strongly on the concentrations of dopants, the incident angles and the crystal cut used. High gain in two-wave mixing corresponds to low phase-conjugate reflectivity in all samples. It is impossible to maintain the highest reflectivity and gain simultaneously, because the gain will definitely be limited when we try to get the highest reflectivity, and vice versa. Some qualitative explanation of the experimental results is also given. Received: 5 January 2001 / Final version: 25 May 2001 / Published online: 19 September 2001     

Gain and Noise Figure of a Double-Pass Waveguide Amplifier Based on Er/Yb-Doped Phosphate Glass

A waveguide amplifier is fabricated by Ag^＋-Na^＋ two-step ion exchange on Er/Yb-doped phosphate glass. The spectroscopic performance of glass and the properties of channel waveguide are characterized. A double-pass configuration is adopted to measure the gain and noise figure （NF） of the waveguide amplifier, and the comparison of gain and NF for the single and double-pass configuration of the waveguide amplifier is presented. The results show that the double-pass configuration can make the gain increase from 8.8dB （net gain 2.2dB/cm） of the single-pass one to 14.6dB （net gain 3.65dB/cm） for small input power at 1534nm, and the NF are all lower than 5.5dB for both the configurations.     

Asymptotic expression near the ellipse of convergence of Jacobi series in complex plane

In this paper, we shall give in Abel type theorem of Jacobi series and then based on it discuss asymptotic expressions near the ellipse of convergence of Jacobi series in complex plane.     

Poly(ethylene‐co‐1,4‐cyclohexylenedimethylene terephthalate) copolyesters obtained by ring opening polymerization

Cyclic oligomer fractions of ethylene terephthalate c(ET)_n and 1,4‐cyclohexylenedimethylene terephthalate c(CT)_n were obtained by cyclodepolymerization of their respective polyesters, the former containing around 80 mol % of trimer and the latter with around 70 mol % of trimer to pentamer. Mixtures of these fractions at selected compositions were subjected to ring opening copolymerization to give a series of poly(ethylene‐co‐cyclohexylenedimethylene terephthalate) copolyesters with ET/CT comonomer ratios ranging from 90/10 to 10/90. The copolyesters were characterized by GPC and NMR, and their thermal properties were evaluated by DSC and TGA. They had essentially the same composition as the feed from which they were produced and had an average‐weight molecular weights between 30,000 and 40,000 g/mol with polydispersities between 2 and 2.7. The distribution of the monomeric units in these copolyesters was essentially at random although it evolved to be a blocky microstructure as the contents in the two comonomers became more dissimilar. Their thermal behavior was the expected one for these types of copolyesters with crystallinity and heating stability decreasing with the content in CT units. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 5954–5966, 2009