Optical Bloch Equations Modified with Phonon-Induced Intensity-Dependent Dephasing

We extend the exciton population equations of a two-level quantum dot system with weak excitation to the ones with strong excitations, in which, the phonon-induced intensity-dependent dephasing time and decay rate are involved. The straightforward calculated populations from the modified population equations demonstrate the damping behavior of Rabi oscillation as the external field increasing. The effect of the intensity-dependent dephasing time and the intensity-dependent decay rate are also discussed.

Response of Slovene Informatics Teachers to the EUCIP On-line Course

In the paper, the authors present their experience and results related to the design and management of the on-line course ＂Development of e-learning resources based on the EUCIP （The European Certification of Informatics Professionals） certification scheme＂, which was organized under the auspices of the international Leonardo da Vinci project Sloop2desc （Sharing learning objects in an open perspective for development of European skills and competences）. The course was primarily aimed at teachers of informatics. Out of 64 participants that applied for the course, slightly less than 50% managed to reach the last course module. In line with other research, the authors＇ experience showed that in order to minimize participants＇ drop-out rate, a sustained communication flow between tutors and participants was necessary and specific assignments had to be provided by the tutors, along with guidance. The authors expect the participants who successfully finished the on-line course to become a some kind of ambassadors for the introduction of the EUCIP scheme in Slovenia.

Recursion Operators of Two Supersymmetric Equations

From Lax representations,recursion operators for the supersymmetric KdV and the supersymmetric Kaup-Kupershimdt (SKK) equations are proposed explicitly.Under some special conditions,the recursion operator of the supersymmetric Sawada-Kotera equation can be recovered by the one of the SKK equation.

Variation of Two-photon Absorption Cross Sections and Optical Limiting of Compounds Induced by Static Electric Field

By numerically solving the Maxwell-Bloch equations using an iterative predictor-corrector finite-difference time-domain technique, we investigate propagating properties of a few-cycle laser pulse in a 4,4＇-bis（di-n-butylamino） stilbene （BDBAS） molecular medium when a static electric field exists. Dynamical two-photon absorption （TPA） cross sections are obtained and optical limiting （OL） behavior is displayed. The results show that when the static electric field intensity increases, the dynamical TPA cross section is enhanced and the OL behavior is improved. Moreover, both even- and odd-order harmonic spectral components are generated with existence of the static electric field because it breaks the inversion symmetry of the BDBAS molecule. This work provides a method to modulate the nonlinear optical properties of the BDBAS compounds.

Semi-batch Crystallization of 7-Amino-Desacetoxycephalos- poranic Acid

Semi-batch crystallization of 7-amino-desacetoxycephalosporanic acid (7-ADCA) is a complicated process, in which agglomeration occurs together with nucleation and crystal growth. To systematically study such a process, experiments were conducted to estimate the crystallization thermodynamics and kinetics, and then the process was simulated by a numerical method. The application of Monte Carlo concept in the algorithm to describe agglomeration event offers an alternative approach of solving the population balance, the intrinsic simplicity of which allows us to investigate several mechanisms and include several internal coordinates in the analysis. Furthermore, present study may be a valuable paradigm for other semi-batch crystallization processes.

A Static Solution of Yang-Mills Equation on Anti-de Sitter Space

Since product metric on AdS space has played a very important role in Lorentz version of AdS/CFT correspondence, the Yang Mills equation on AdS space with this metric is considered and a static solution is obtained in this paper, which helps to understand the AdS/CFT correspondence of Yang Mills fields.

A Test for the Local Intrinsic Lorentz Symmetry

Basing on a generalization of Wong＇s equations, the problem of motions for particles in the Lorentz gauge field configuration, which is Schwarzschild-like solution of Yang-Mills equations, is studied. The picture of interaction between particles with the Lorentz gauge field is described in an analogous manner to that between isotopic-spin-carrying particles and Yang-Mills field. By examining the effective potential and the equations of orbits for particles, it is found that the considered motions possess some qualitative features resembling to motions of particles in a centrally symmetric gravitational field.

Comparison of Beer Quality Produced Using Malt from Kosovo and Other Countries

Aiming to optimize the beer production process by improving the properties of beer and reducing production costs at the J.S.C. ＂Birra Peja＂ brewery, Peja, Kosovo, this study did an evaluation of beer produced using six different malts. Four of the six studied malts were produced in four European countries： Ukraine, Croatia, Serbia and Kosovo; and, the other two malts were obtained from two （2） 30：70 proportion mixtures： one from Kosovo and Ukraine and another one from Kosovo and Croatia. Chemical, microbiological, sensory and tasting analyses were carried on beers produced by these malts. The study included three working groups from： ＂Birra Peja＂; the Agricultural University of Tirana, Albania and ＂Union Brewery＂, Ljubljana, Slovenia. Chemical and microbiological tests were based on methods under the EBC （European Beer Convention） and MEBAK （Mitteleurop^iische Brautechnische Analysenkommision e.V.） guidelines. The analyses and assessments made for the quality of beer have come to the conclusion that beer produced by Croatian origin malt corresponds to a better quality beer.

明李翔墓志铭述考

明代《赠刑科给事中李公合葬之墓》志铭2011年12月出土于马鞍山市。墓志铭虽有部分风化,但基本可识。志铭历史信息丰富,不仅是一部墓主家族简史,对补充《明史.刘珝传》中对其宦迹记载的阙如,佐证《刘珝年谱》的正确性,研究姜立纲、程洛书法艺术风格的形成,考证明代书法史和明代楷书字体演变也具有重要意义。

Magnetic-structure coupling dynamic model of a ferromagnetic plate parallel moving in air-gap magnetic field

Aiming at the air-gap magnetic field excited by wall armatures,Laplace’s partial differential equation of air-gap magnetic potential is achieved by means of the electromagnetic field theory.According to the magnetic boundary conditions and the method of separation of variables,the magnetic potential of the air-gap magnetic field is obtained.Based on the magnetization force model and Lorentz force of ferromagnetic thin-walled structures,and introducing the electromagnetic constitutive relations and boundary conditions,the calculation model of electromagnetic force of the soft ferromagnetic thin plate moving in air-gap magnetic field is established.Considering geometric nonlinearity,expressions of strain energy and kinetic energy of the elastic thin plate and the work of forces are given,respectively.The magnetic-structure coupling nonlinear vibration equations of ferromagnetic thin plate parallel moving in the air-gap magnetic field excited by armatures are obtained by using the Hamilton principle,which can be of the characterization of the system dynamics model with electro-magneto-velocity-mechanical interaction.Through numerical examples,primary resonance characteristics of the strip thin plate under the action of air-gap magnetic force are obtained.The results show that the two stable amplitude values will increase as amplitude of magnetic potential increases and thickness of air-gap decreases,and the amplitude’s multi-valued region will change due to the varieties of magnetic potential,air-gap and velocity.The model established in this paper is a theoretical reference for investigation on the multi-field coupling dynamic behaviors of structures moving in complex electromagnetic fields.

A PICARD TYPE THEOREM AND BLOCH LAW

A picard type theorem is proved, and a counterexample is given to show that the Bolch Lawis not true generally.

Model-free conditional independence feature screening for ultrahigh dimensional data

Feature screening plays an important role in ultrahigh dimensional data analysis.This paper is concerned with conditional feature screening when one is interested in detecting the association between the response and ultrahigh dimensional predictors(e.g.,genetic makers)given a low-dimensional exposure variable(such as clinical variables or environmental variables).To this end,we first propose a new index to measure conditional independence,and further develop a conditional screening procedure based on the newly proposed index.We systematically study the theoretical property of the proposed procedure and establish the sure screening and ranking consistency properties under some very mild conditions.The newly proposed screening procedure enjoys some appealing properties.(a)It is model-free in that its implementation does not require a specification on the model structure;(b)it is robust to heavy-tailed distributions or outliers in both directions of response and predictors;and(c)it can deal with both feature screening and the conditional screening in a unified way.We study the finite sample performance of the proposed procedure by Monte Carlo simulations and further illustrate the proposed method through two real data examples.

First-passage failure of MDOF nonlinear oscillator

First-passage failure of multiple-degree-of-freedom nonlinear oscillators with lightly nonlinear dampings and strongly nonlinear stiffness subject to additive and/or parametric Gaussian white noise excitations is studied. First, by using the stochastic averaging method based on the generalized harmonic functions, the averaged It stochastic differential equation for the amplitudes of the nonlinear oscillators can be derived. Then the associated backward Kolmogorov equation of the conditional reliability function is established, and the conditional reliability is approximately expressed as a series expansion in terms of Kummer functions with time-dependent coefficients. By using the Galerkin method, the time dependent coefficients of the associated conditional reliability function can be solved by a set of differential equations. Finally, the proposed procedure is applied to Duffing-Van der Pol systems under external and/or parametric excitations of Gaussian white noises. The results are also verified by those obtained from Monte Carlo simulation of the original system. The effects of system parameters on first-passage failure are discussed briefly.

Propagation of Lorentz–Gaussian Beams in Strongly Nonlocal Nonlinear Media

In this paper the propagation of Lorentz–Gaussian beams in strongly nonlinear nonlocal media is investigated by the ABCD matrix method. For this purpose, an expression for field distribution during propagation is derived and based on it, the propagation of Lorentz–Gaussian beams is simulated in this media. Then, the evolutions of beam width and curvature radius during propagation are discussed.

Zero-Absorption Isolines in a 2-Photon 2-Level Atom Model

The c-number atomic Bloch equations modelling the coupling of a 2-photon 2-1evel single atom with a non-resonant （A # O） squeezed vacuum （SV） radiation reservoir show that： （i） The quantum interference （QI） process, of parameter f O, between the 2-photon transition channels causes coupling of the atomic variables （inversion and polarisation）, and, （ii） The SV reservoir parameters （N, M） induce periodic coefficients and hence inhibited oscillatory behaviour in the atomic variables. Perturbative analytical solutions of these non-autonomous B1och equations are derived and used to calculate the absorption spectrum of a weak field probing the system. Of particular, the zero-absorption isolines in the relevant （N, f）- and （A, f ）-planes of the the largest set of points, where absorption is zero, in parameter （M） of the SV reservoir. system parameters are identified computationally. It is found that, the （A, f）-plane depends on the choice of the degree of squeezing

On the existence of traveling wave solutions and upper and lower bounds for some Fisher-iolmogorov type equations

In this paper, we use a dynamical systems approach to prove the existence of traveling waves solutions for the Fisher-Kolmogorov density-dependent equation. Moreover, we prove the existence of upper and lower bounds for these traveling wave solutions found previously. Finally, we present a particular example which has several applications in the mathematical biology field.

A CRACK PROBLEM WITH A BROKEN LINE INTERFACE

The equilibrium problem for the infinite elastic plane consisting of two different media is considered, in which the interface is a broken line, there is a straight crack touching the vertex of the broken line with some symmetry and the same uniform pressures are applied to both of its sides. The problem is reduced to a uniquely solvable singular integral equation on the interface and the crack. The order of singularity at the vertex is considered, which may be determined by a transcendental equation.

Applications of the representative points in statistical simulations

The paper gives a new approach to statistical simulation and resampling by the use of numbertheoretic methods and representative points. Resempling techniques take samples from an approximate population. The bootstrap suggests to use a random sample to form an approximate population. We propose to construct some approximate population distribution by the use of two kinds of representative points, and samples are taken from these approximate distributions. The statistical inference is based on those samples. The statistical inference in this paper involves estimation of mean, variance, skewness, kurtosis, quantile and density of the population distribution. Our results show that the new method can significantly improve the results by the use of Monte Carlo methods.

Approximate Solutions of Nonlinear Fractional Kolmogorov-Petrovskii-Piskunov Equations Using an Enhanced Algorithm of the Generalized Two-Dimensional Differential Transform Method

By constructing the iterative formula with a so-called convergence-control parameter, the generalized two-dimensional differential transform method is improved. With the enhanced technique, the nonlinear fractional Kolmogorov-Petrovskii-Piskunov equations are dealt analytically and approximate solutions are derived. The results show that the employed approach is a promising tool for solving many nonlinear fractional partial differential equations. The algorithm described in this work is expected to be employed to solve more problems in fractional calculus.