Novel halogenated cyclopentasilylene-2,4-dienes via DFT

In view of immense importance of silylenes and the fact that their properties undergo significant changes on substitution with halogens, here, we have used B3LYP/6-311++G** level of theory to access the effects of 1–4 halogens (X = F, Cl, Br, and I) on four unprecedented sets of cyclopentasilylene-2,4-dienes; with the following formulas: SiC₄H₃X ( 1 _X ), SiC₄H₂X₂ ( 2 _X ), SiC₄HX₃ ( 3 _X ), and SiC₄X₄ ( 4 _X ). In going down from F to I, the singlet (s)-triplet (t) energy gap (ΔE_s-t, a possible indication of stability), and band gap (ΔE_H-L) decrease while nucleophilicity (N), chemical potential (μ), and proton affinity (PA) increase. The overall order of N, μ, and PA for each X is 2 _X > 1 _X > 3 _X > 4 _X . Precedence of 2 _X over 1 _X is attributed to the symmetric cross conjugation in the former. The highest and lowest N are shown by 2 _I and 4 _F . The trend of divalent angle () for each X is 4 _X > 1 _X > 3 _X > 2 _X . The results show that in going from electron withdrawing groups (EWGs) to electron donating groups (EDGs), the ΔE_s-t and ΔE_H-L decrease while N, μ, and PA increase. Also, rather high N of our scrutinized silylenes may suggest new promising ligands in organometallic chemistry.     

Influence of the sulfonate countercation on the thermal stability of nafion perfluorosulfonate membranes

We report a strong dependence of the thermal stability of Nafion® perfluorosulfonate ionomer on the nature of the counterion associated with the fixed sulfonate site. These results were obtained using thermal gravimetric analysis on a series of alkali metal and alkyl ammonium cation-exchanged Nafion films. We have found that the temperature of decomposition of Nafion is inversely dependent on the size of the exchanged cation; i.e., Nafion films show improved thermal stability as the size of the counter cation decreases. We attribute this inverse relationship of thermal stability with counterion size to an initial decomposition reaction which is strongly influenced by the strength of the sulfonate-coun-terion interaction. © 1993 John Wiley & Sons, Inc.     

The destabilizing effect of boundary slip on Bénard convection

We investigate the influence of slip boundary conditions on the onset of Bénard convection in an infinite fluid layer. It is shown that the critical Rayleigh number is a decreasing function of the slip length, and therefore boundary slip is seen to have a destabilizing effect. Chebyshev‐tau and compound matrix formulations for solving the eigenvalue problem are presented. Copyright © 2005 John Wiley & Sons, Ltd.     

THE QUALITATIVE CONTENT OF RENEWABLE RESOURCE MODELS

This paper analyzes the extent to which standard dynamic renewable resource models possess refutable implications. Both the steady state comparative static and local comparative dynamic properties of the standard model are studied. A unified framework is developed which enables one to analyze the qualitative properties of any standard renewable resource model. This is achieved by explicitly linking the local stability, steady state comparative static, and local comparative dynamic properties of the model.     

A primer on perfect simulation for spatial point processes

This primer provides a self-contained exposition of the case where spatial birth-and-death processes are used for perfect simulation of locally stable point processes. Particularly, a simple dominating coupling from the past (CFTP) algorithm and the CFTP algorithms introduced in [13], [14], and [5] are studied. Some empirical results for the algorithms are discussed. Received: 30 June 2002     

Highly accurate calculation of radial spheroidal functions

A new method for calculating the radial spheroidal functions of the first kind is proposed for the arguments that are greater than unity in modulus. A well-known representation of these functions is refined and used for this purpose. The constructs and the software implementation proposed in the paper provide an efficient tool for the calculation of the functions with a desired accuracy in a wide range of parameters.     

有限时滞微分系统依照双测度的实际稳定性

本文对具有有限时滞的泛函微分方程建立了关于依照两种测度的实际稳定性的Razumikhin型判定定理，其中未采用通常的辅助函数，且可运用多个含有状态变量x的部分变元的Lyapunov函数，得出部分变远实际稳定性的判定定理，从而改进了已有的结果。     

Stability of steady nonisothermal flow in a vertical layer with permeable boundaries in the microconvection model

The problem of the stability of steady convective viscous incompressible fluid flow in a vertical layer with boundaries at different temperatures is considered in the presence of transverse blowing through the layer. The complete spectral problem is solved for a silicon melt. The neutral curve is constructed and the critical Grashof number is found. The numerical calculations show that the presence of transverse blowing significantly affects the flow stability. As compared with the Oberbeck-Boussinesq model, in the microconvection model the instability develops at lower wavenumbers.     

Variational Derivative for Buckling Loads of Beams and Frames

The finite-difference method is a numerical technique for obtaining approximate solutions to differential equations. The main objective of the present study is to give a new aspect to the finite-difference method by using a variational derivative. By applying this formulation, accurate values of the buckling loads of beams and frames with various end supports are obtained. The performance of this formulation is verified by comparison with numerical examples in the literature __________ Published in Prikladnaya Mekhanika, Vol. 41, No. 7, pp. 139–144, July 2005.     

Sensitivity analysis of an optimized bar-spring model with hill-top branching

Summary Characteristics of optimal solutions under nonlinear buckling constraints are investigated by using a bar-spring model. It is demonstrated that optimization under buckling constraints of a symmetric system often leads to a structure with hill-top branching, where a limit point and bifurcation points coincide. A general formulation is derived for imperfection sensitivity of the critical load factor corresponding to a hill-top branching point. It is shown that the critical load is not imperfection-sensitive even for the case where an asymmetric bifurcation point exists at the limit point.