A Dynamical Systems Approach to Geodesics in Bianchi Cosmologies

To understand the observational properties of cosmological models, in particular, the temperature of the cosmic microwave background radiation, it is necessary to study their null geodesics. Dynamical systems theory, in conjunction with the orthonormal frame approach, has proved to be an invaluable tool for analyzing spatially homogeneous cosmologies. It is thus natural to use such techniques to study the geodesics of these models. We therefore augment the Einstein field equations with the geodesic equations, all written in dimensionless form, obtaining an extended system of first-order ordinary differential equations that simultaneously describes the evolution of the gravitational field and the behavior of the associated geodesics. It is shown that the extended system is a powerful tool for investigating the effect of space-time anisotropies on the temperature of the cosmic microwave background radiation, and that it can also be used for studying geodesic chaos.     

Polynomial interpolation in several variables

This is a survey of the main results on multivariate polynomial interpolation in the last twenty-five years, a period of time when the subject experienced its most rapid development. The problem is considered from two different points of view: the construction of data points which allow unique interpolation for given interpolation spaces as well as the converse. In addition, one section is devoted to error formulas and another to connections with computer algebra. An extensive list of references is also included. This revised version was published online in June 2006 with corrections to the Cover Date.     

Diffraction effects in guided photonic band gap structure

The concept of the photonic band gap (PBG) structures stems from ideas of Yablonovitch. The idea is to design components so that they affect the properties of photons, in much the same way that ordinary semiconductor crystals affect the properties of electrons. In fact, the PBG structures forbid propagation of photons for a particular range of energy. They can be used to realise optical filters with large stop band and sharp transmission resonance. In the guided PBG structures, the existence of diffractive effects in the vertical dimension could limit the quality factor of such filters. In this paper, we have investigated the origin of diffraction losses in one-dimensional guided PGB structures using 2D and 3D numerical tools. We propose an analytical approach based on Bragg diffraction relation to explain these losses phenomenon. From this approach, the influence of some design parameters on the electromagnetic behaviour and the spectral response of PBG resonators will be explained.     

Generalized Local Time of the Indefinite Wiener Integral:White Noise Approach

In this paper,the generalized local time of the indefinite Wiener integral Xt is discussed through white noise approach,which means to regard the local time as a Hida distribution.Moreover,similar resu...     

Preparation of optical active single-handed helical barium titanate nanotubes and characterization of dielectric properties

Left and right-handed helical barium titanate nanotubes are prepared with the impregnation of Ba(OH)_2 into single-handed helical titania nanotubes.Wide angle X-ray diffraction pattern and transmission electron microscopy image indicate that they are constructed by nanoparticles with a partially crystalline structure.The diffuse reflertance circular dichroism spectra indicate that they exhibit optical activity which was proposed to originate from chiral defects on the inner surfaces of the nanotubes.Both the dielectric constant and tanδ decrease with increasing the frequency.At 10 and 100 Hz,one dielectric constant peak at 9.6℃ and one tanδ peak at 5.0℃ are observed at -120℃ to 180℃.     

Hybrid approach for two dimensional damage localization using piezoelectric smart aggregates

In the paper, a novel approach for damage localization in reinforced concrete plates, based on the computational analysis of piezoelectric smart aggregates, has been presented. The hybrid approach for damage localization is based on two criteria: wave propagation energy and time of flight. The comprehensive numerical analysis using standard and explicit finite element method has been conducted. In addition, the proposed algorithm of the hybrid method has been coded in MATLAB. The approach has been verified numerically using different square reinforced concrete plate models, considering different number, position and size of damage, as well as different number and position of the piezoelectric smart aggregates. Obtained results confirm the successful application of the novel approach to the damage localization.     

HOF分子非谐性力场、光谱常数和振动能级的迭代三激发耦合簇计算

采用包含迭代三激发的耦合簇理论(CC3和CCSDT-3), 在aug-cc-pVTZ基组水平上对HOF分子几何构型进行优化. 通过解析二阶导数结合有限差分技术获得HOF二阶、完全三阶和半对角四阶力场. 通过非谐性分析, 得到其基频、旋振相互作用常数、非谐性常数和离心畸变光谱常数. 应用二阶振动微扰理论(VPT2)得到HOF多个泛频峰位置. 目前计算值与实验及其它文献结果符合良好.     

Kinetic theory of monochromatic waves bunching in a low-voltage beam discharge in rare gases

The kinetic theory of phase focusing, that is bunching in a low-voltage beam discharge in rare gases (LVBD) during the propagation of longitudinal electrostatic oscillations at the Knudsen numbers of the order of unity have developed. The anomalous relaxation of the almost monoenergetic electron beam in momentum and energy is described for the case when this process cannot be explained by electron–atom collisions. The paper has shown the important role of electrons that have the beam energy and isotropic directional distribution, which is formed as a result of elastic collisions between the beam electrons and atoms. The dependence of the anomalous relaxation length on parameters of the LVBD in rare gases is studied.The developed theory makes it possible to quantitatively interpret experimental data on the LVBD under conditions when the electron mean free path is of the order of the interelectrode gap. According to these data, regardless of the density of the charged particles in the LVBD plasma in rare gases, five Langmuir plasma wavelengths fit along the length of the anomalous relaxation of the electron beam. The study of the electron beam dynamics laws in a plasma is important for the development of plasma-electrical devices, where the beam discharge is applied, namely: widely used all-movable stabilizers, sources of intense electromagnetic radiation, controlled elements of electronic circuits, plasma chemical reactors, etc.     

Book review of advances in gabor analysis,applied and numerical harmonic analysis,Hans G. Feichtinger and Thomas Strohmer (Eds.), Birkhäuser,Boston-Basel-Berlin, 2002, 356 pages. ISBN 0-8176-4239-0

In some recent publications it was shown that certain stationary stochastic dynamic programming problems with general state and action spaces can be solved by generalized linear programming. It Is the main aim of the present paper to demonstrate that a similar linear programming approach is feasible even in the non-stationary case. For this end, we formulate a programming problem (D^?) and show that (D^?) is equivalent to the problem of finding a p=optimal policy for the stochastic dynamic program, whereas a modification of (D^?) turns out to be the dual program of a pair of general linear programs.