Observability Inequality for the Kirchhoff-Rayleigh Plate Like Equation in a Short Time

In this paper, for any given observation time and suitable moving observation domains, the author establishes a sharp observability inequality for the Kirchhoff-Rayleigh plate like equation with a suitable potential in any space dimension. The approach is based on a delicate energy estimate. Moreover, the observability constant is estimated by means of an explicit function of the norm of the coefficient involved in the equation.     

Rapid analysis of tetracaine for a tape stripping pharmacokinetic study using short‐end capillary electrophoresis

A rapid and simple short‐end (reverse) capillary zone electrophoresis method was developed and validated for the separation and quantification of tetracaine in skin using tape samples. The separation was performed in a 485 mm (400 mm to window) × 50 µm internal diameter fused silica capillary using a background electrolyte of phosphoric acid–Tris pH2.5 at –25 kV. The extraction of tetracaine from tape samples was achieved using methanol diluted to 50% with water before injection. Procaine was the internal standard. The migration times for procaine and tetracaine were 1.25 and 1.36 min, respectively. The limit of quantification for tetracaine was 50 µg, with a signal‐to‐noise ratio greater than 10. The calibration curve was linear from 50 to 1200 µg with r² greater than 0.99. The CV for both within‐ and between‐assay imprecision and the percentage inaccuracy for the quality control samples including lower and upper limits of quantitation were <12.1% and <11%, respectively. The absolute mean recovery of tetracaine was >97%. The accuracy and selectivity of this method allowed the rapid measurement of tetracaine in tape samples obtained from a skin tape stripping study of local anaesthetics in healthy subjects. Copyright © 2008 John Wiley & Sons, Ltd.     

A Novel Method of Spectral Analysis of Oscillatory Belousov–Zhabotinsky Reaction

This paper is a preliminary study of time–frequency behavior of homogenous Belousov–Zhabotinsky reaction in a batch reactor. A series of measurements performed for a variable concentration of the reaction substrates led to the conclusion that there exists time-dependency of an instantaneous frequency of fundamental frequency and harmonics and of electrode potential fluctuations generated during the process discussed. The Short Time Fourier Transformation (STFT) was proposed for analyzing electrode potential registers. On the basis of STFT analysis a decrease in frequency of oscillations of exponential character has been postulated.     

Ethylene/1‐octene copolymerization studies with in situ supported metallocene catalysts: Effect of polymerization parameters on the catalyst activity and polymer microstructure

Ethylene and 1‐octene copolymerizations were carried out with an in situ supported rac‐[dimethylsilylbis(methylbenzoindenyl)] zirconium dichloride catalyst. In a previous study, it was found that some in situ supported metallocenes produced polyethylene/α‐olefin copolymers with broad and bimodal short chain branching distributions and narrow molecular weight distributions. The ability to produce polyolefins with multimodal microstructural distributions in a single metallocene and a single reactor is attractive for producing polymers with balanced properties with simpler reactor technology. In this study, a factorial experimental design was carried out to examine the effects of the polymerization temperature and ethylene pressure, the presence of hydrogen and an alkylaluminum activator, and the level of the comonomer in the feed on the catalyst activity, short chain branching distribution, and molecular weight distribution of the polymer. The temperature had the most remarkable effect on the polymer microstructure. At high 1‐octene levels, the short chain branching distribution of the copolymer broadened significantly with decreasing temperature. Several factor interactions, including the hydrogen and alkylaluminum concentrations, were also observed, demonstrating the sensitivity of the catalyst to the polymerization conditions. For this catalyst system, the responses to the polymerization conditions are not easily predicted from typical polymerization mechanisms, and several two‐factor interactions seem to play an important role. Given the multiple‐site nature of the catalyst, it has been shown that predicting the polymerization activity and the resulting microstructure of the polymer is a challenging task. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 40: 4426–4451, 2002     

Short H· · ·H distances in norbornene derivatives

A short H···H intramolecular interaction was reported previously for an anhydride of syn-sesquinorbornene. The synthesis and structure of a such an anhydride with an additional five-membered dithiole ring has been investigated. While hydrogen atom positions are not accurately located, the 1.62 Å separation indicates this molecule is a candidate for the shortest H···H interaction. Two cycloadducts of norbornadiene, which literature suggests might exhibit additional short interactions, are reported also; however, the isomers with minimal intramolecular interactions are the isolated products. C₂₂H₂₀O₃S₂, 3, crystallizes in P with a = 10.881(4), b = 13.712(8), C = 6.548(8) Å, = 101.32(6), = 107.49(5), = 90.49(4)°, D _calc = 1.445 g cm^–3, and Z = 2, C₂₁H₂₀O₄Cl₈, 5, in P2₁/n with a = 8.168(2), b = 13.488(4), c = 23.500(6) Å, = 94.72(2)°, D _calc = 1.597 g cm^–3, and Z = 4, C₂₁H₂₈O₄, 6, in P> with a = 12.667(2), b = 12.792(2), c = 12.540(2) Å, = 113.51(1), = 98.18(1), = 74.39(1)°, D _calc = 1.276 g cm^–3, and Z = 4.     

短视频慈善主体的“双重变现”隐忧和规制研究

使用一个包含自媒体平台、慈善行动主体和网民用户的三方演化博弈模型研究了自媒体视域下的慈善行为监管问题,并进一步研究慈善行动主体有限总数情境下的演化情况。研究发现:当参与慈善的追随网民初始比例比较小时,在网民资金支持概率比例较小的情况下系统也可以很快到达均衡,当参与慈善的网民人数比较多时,可以呼吁网民在一定范围内以金钱支持;网民遭受慈善主体不诚实的情感伤害越大,系统朝理想状态演化的时间越长。在有限总数的情境下单独考察慈善行动主体发现:诚实的慈善行动主体“侵入”炒作主体需要满足三分之一的成本条件。     

Scaling relations,virial theorem,and energy densities for long‐range and short‐range density functionals

Decomposition of the Coulomb electron–electron interaction into a long‐range and a short‐range part is described within the framework of density functional theory, deriving some scaling relations and the corresponding virial theorem. We study the behavior of the local density approximation in the high‐density limit for the long‐range and the short‐range functionals by carrying out a detailed analysis of the correlation energy of a uniform electron gas interacting via a long‐range‐only electron–electron repulsion. Possible definitions of exchange and correlation energy densities are discussed and clarified with some examples. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

短密度梯度尺度等离子体中的软X射线激光

通过数值求解等离子体流体力学方程组，研究了短脉冲激光打靶结束后形成的短密度梯度尺度等离子体的冷降温过程，讨论了热传导，膨胀作功，辐射损失三种冷却机制对降温过程的贡献，并用解流体力学方程组得到的等离子参数计算ＭｇＸＩ等离子体中波长小于２０ｎｍ的所有可能跃迁的自发辐射放大增益系数，分析了它们与环境条件的关系，指出了在ＭｇＸＩ等离子体中获取水窗附近乃至水窗波段软Ｘ射线激光的可能性。     

A statistical investigation of the behavior of short fatigue crack in medium carbon steels

Rotary bending fatigue tests were carried out by using smooth specimens of medium carbon steel with two ferrite grain sizes. In order to clarity the physical background of the scatter in fatigue behaviour, the statistical characteristics of the initiation and growth of short fatigue crack were investigated. Results show that the short crack initiation and growth life distribution can be express by two-or three-parameter Weibull distribution. The Weibull distribution of the mixed type is well fitted to the crack length distribution for both steels. The knee values of Weibull plots are related to the grain size. The crack length distribution before the knee point can be expressed by a two-parameter Weibull distribution, and that after the knee point can be represented by two-or three-parameter Weibull distribution. It was found that the initiation Life, growth life and crack length distribution were affected by the grain size.