The Exterior Tricomi Problem for Generalized Mixed Equations with Parabolic Degeneracy

This paper deals with the exterior Tricomi problem for generalized mixed equations with parabolic degeneracy. Firstly the representation of solutions of the problem for the equations is given, and then the uniqueness and existence of solutions are proved by a new method.     

Finite and impulsive motion of constrained mechanical systems via Jourdain's principle: discrete and hybrid parameter models

The main purpose of this paper is to present a unified analytical dynamics framework for the analysis of finite and impulsive motion of mechanical systems using Jourdain's principle. Emphasis is given to the general case when a mechanical system is described by a hybrid (discrete-distributed) parameter model. A large group of finite and impulsive, generally non-holonomic, constraints are analysed in detail and a so-called extended Appellian classification is presented for these constrained motion problems. The fundamental dynamic equation of constrained systems is developed in terms of velocity variations (Jourdain's principle). Based on this equation and the constraints, the methods of quasivelocities and Lagrangian multipliers are adopted and interpreted for the finite motion of hybrid parameter models of mechanical systems; and the methods of independent quasivelocity variations and Lagrangian multipliers are introduced for the analysis of impulsive motion of such models. To illustrate the proposed material, an example of a one-link flexible arm intercepting and capturing a moving target is considered.     

结构可靠度的当量正态PFSORM算法

对结构功能函数为相关非正态随机变量构成情况 ,使用PFSORM算法确定结构二次可靠指标须使用随机变量的条件分布函数及其反函数。工程实践中随机变量的条件分布函数及其反函数常不易确定。基于此 ,本文提出当量正态PFSORM算法 ,仅需要随机变量的分布函数、分布密度函数及其相关系数即可     

Structural Quantum Effects In Hydrogeneous Liquids And Glasses: Part I Review Of Early Methods And Experiments

The atomic or molecular structure of simple liquids may be studied experimentally through radiation scattering experiments. Normally, these experiments involve either beams of E-M radiation or of thermal neutrons, and frequently the samples included both hydrogenated and deuterated liquids. In order to interpret such data it has been assumed (frequently) that the liquid structure was unchanged when the H/D composition was changed. Similar comments apply to hydrogeneous glasses. As the quality of the data and of model calculations improved with passing years, limits to these assumptions were discovered. Part I of this review will cover both the background material and the research which led to an understanding of this field, and also determined the magnitude and shape of the observable effects. Subsequent research from the 90s onwards will be reviewed in Part II.     

Phase Transitions of Colloidal Suspensions Under External Potential

We review phase transitions in a system of charge-stabilized colloids subject to laser beams with wavevectors tuned to the ordering wavevector of the liquid. Density-functional theory shows that the first-order freezing transition becomes continuous for large strengths of the modulation potential, if the wavevectors satisfy certain symmetry requirements. Computer simulations indicate that, apart from laser induced freezing (LIF), there is laser induced melting (LIM) as well. Recent experiments have shown the existence of both transitions. Theoretical arguments, based on the dislocation-mediated melting scenario in two dimensions; confirm the LIM phenomenon.     

From the bulk to clusters: Solid-liquid phase transitions and precursor effects

A review is given of the experiments done in order to understand the initial stages of melting and solidification of a material. We emphasize on new results obtained for ultrafine metal particles by using high sensitivity reflectance and electron microscopy measurements. These experiments show that melting certainly begins through a continuous and reversible transition and proceeds through the usual first-order transition. For ultrafine particles, these two processes have a relative importance which depend on the size, the first process having the major importance for the smallest particles. Undercooled state and subsequent solidification depend also on the size of the particle. For the smallest particles, the maximum supercooling temperature is found to coincide with the final temperature of the continuous transition leading to disappearance of the hysteretic behaviour usually found in solid-liquid transitions for ultrafine particles.     

On Linear Implicit Non-autonomous Systems of Difference Equations

This paper deals with the solvability of initial-value problems (IVPs) and multipoint boundary-value problems (MPBVPs) for linear implicit non-autonomous systems of difference equations.     

Neue Thiosubstituierte Butadien- Und Butenin Verbindungen Aus Hexachlorbutenen Und Thiolen

2,3-Di-H-butene compound 1 gave compounds 3a-f , 4a , 4e , and 5a-d in the presence of thiols 2a-f and Et 3 N (or NaOH). Compound 7e was obtained from the reaction of 1,3-Di-H-butene 6 with naphthylthiol in DMF. In the presence of NaOH, compound 6 and 2 mmol of thiol 2g in EtOH gave compounds 8 , 9 , 10 , and 11 .     

An Approach to Providing Mathematical Annotation in Plots

Abstract

A simple method for providing mathematical annotation of plots produced with the R environment is described. Although the implementation is specific to R, a similar method could be used in any environment which uses an expression-based command interface and provides a basic quoting mechanism.