Stability and Nonlinear Deformation of Cylindrical Grids

The general stability of single-layer cylindrical grids is studied in linear and nonlinear formulations. Dependence of the general buckling load on the geometry and stiffness parameters of a grid is established in an analytical form. Such grids are numerically analyzed for stability. It is established that the general buckling load is much less than the local buckling load. Typical general buckling modes are found. It is shown that such grids are weakly sensitive to imperfections     

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.     

Effective stability for generalized Hamiltonian systems

An effective stability result for generalized Hamiltonian systems is obtained by applying the simultaneous approximation technique due to Lochak. Among these systems, dimensions of action variables and angle variables might be distinct.     

非线性Schrdinger方程的高精度守恒差分格式

本文首先分析线性Schrodinger方程一种高阶差分格式的构造方法,得到方程的耗散项.在此基础上对三次非线性Schrodinger方程,提出了一种精度为O(r2 h2)的差分格式,证明了该格式保持了连续方程的两个守恒量,且是收敛的与稳定的.并通过数值例子与已有隐格式进行了比较,结果表明,本文格式在计算量类似的情况下,提高了数值精度.     

Oracle Inequalities for Efromovich–Pinsker Blockwise Estimates

Oracle inequality is a relatively new statistical tool for the analysis of nonparametric adaptive estimates. Oracle is a good pseudo-estimate that is based on both data and an underlying estimated curve. An oracle inequality shows how well an adaptive estimator mimics the oracle for a particular underlying curve. The most advanced oracle inequalities have been recently obtained by Cavalier and Tsybakov (2001) for Stein type blockwise estimates used in filtering a signal from a stationary white Gaussian process. The authors also conjecture that a similar result can be obtained for Efromovich–Pinsker (EP) type blockwise estimators where their approach, based on Stein's formula for risk calculation, does not work. This article proves the conjecture and extends it upon more general models which include not stationary and dependent processes. Other possible extensions, a discussion of practical implications and a numerical study are also presented.     

Probability Inequalities and Limit Theorems for Generalized L-Statistics

We obtain exponential upper bounds for tails of distributions of generalized L-statistics based on a sample from an exponential distribution. We prove the asymptotic normality of generalized L-statistics based on a sample from the uniform distribution on [0,1] and of L-statistics with decomposed kernels (without any restrictions on the sample distribution type).     

三苯甲基自由基及其二聚体稳定性的理论研究

采用量子化学AM1 MO方法优化了三苯甲基自由基及其两种二聚体的构型，并计算了反应物和二聚物的生成焓、活化能以及它们的电荷布居，计算结果表明，三苯甲基自由基是一种较稳定的自由基，在这个自由基中存在明显的共轭效应，分子中电子云呈平均化分布．它的二聚体1，4—环己二烯衍生物分子中的5个苯基排布在环己二烯环平面的两端，明显降低了苯基之间的空间排斥力，使二聚物—环己二烯衍生物分子的稳定性大大高于六苯乙烷．因此，三苯甲基自由基的二聚体是1，4—环己二烯衍生物而不是六苯基乙烷，得到了与实验事实一致的结果。     

Detecting instabilities in flows of viscoelastic fluids

There is a growing interest in developing numerical tools to investigate the onset of physical instabilities observed in experiments involving viscoelastic flows, which is a difficult and challenging task as the simulations are very sensitive to numerical instabilities. Following a recent linear stability analysis carried out in order to better understand qualitatively the origin of numerical instabilities occurring in the simulation of flows viscoelastic fluids, the present paper considers a possible extension for more complex flows. This promising method could be applied to track instabilities in complex (i.e. essentially non‐parallel) flows. In addition, results related to transient growth mechanism indicate that it might be responsible for the development of numerical instabilities in the simulation of viscoelastic fluids. Copyright © 2003 John Wiley & Sons, Ltd.     

The Development of the Asymptotic Viscous Dissipation Profile in a Vertical Free Convective Boundary Layer Flow in a Porous Medium

The effect of viscous dissipation on the development of the boundary layer flow from a cold vertical surface embedded in a Darcian porous medium is investigated. It is found that the flow evolves gradually from the classical Cheng–Minkowycz form to the recently discovered asymptotic dissipation profile which is a parallel flow.     

Polyelectrolyte complexes. VI. Polycation structure,polyanion molar mass,and polyion concentration effects on complex nanoparticles based on poly(sodium 2‐acrylamido‐2‐methylpropanesulfonate)

The formation and characterization of some interpolyelectrolyte complex (IPEC) nanoparticles based on poly(sodium 2‐acrylamido‐2‐methylpropanesulfonate) (NaPAMPS), as a function of the polycation structure, polyanion molar mass, and polyion concentration, were followed in this work. Poly(diallyldimethylammonium chloride) and two polycations (PCs) containing (N,N‐dimethyl‐2‐hydroxypropyleneammonium chloride) units in the backbone (PCA₅ and PCA₅D₁) were used as starting polyions. The complex stoichiometry, (n^?/n⁺)_iso, was pointed out by optical density at 500 nm (OD₅₀₀), polyelectrolyte titration, and dynamic light scattering. IPEC nanoparticle sizes were influenced by the polycation structure and polyanion molar mass only before the complex stoichiometry, which was higher for the more hydrophilic polycations (PCA₅ and PCA₅D₁) and for a higher NaPAMPS molar mass, and were almost independent of these factors after that, at a flow rate of the added polyion of about 0.28 mL × (mL PC)^?1 × h^?1. The IPEC nanoparticle sizes remained almost constant for more than 2 weeks, both before and after the complex stoichiometry, at low concentrations of polyions. NIPECs as stable colloidal dispersions with positive charges in excess were prepared at a ratio between charges (n^?/n⁺) of 0.7, and their storage colloidal stability, as a function of the polycation structure and polyion concentration (from 0.8 to ca. 7.8 mmol/L), was demonstrated. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 2495–2505, 2004