Majorana Transformation for Differential Equations

We present a method for reducing the order of ordinary differential equations satisfying a given scaling relation (Majorana scale-invariant equations). We also develop a variant of this method, aimed to reduce the degree of nonlinearity of the lower order equation. Some applications of these methods are carried out and, in particular, we show that second-order Emden–Fowler equations can be transformed into first-order Abel equations. The work presented here is a generalization of a method used by Majorana in order to solve the Thomas–Fermi equation.     

On Analogs of the Tits Alternative for Groups of Homeomorphisms of the Circle and of the Line

In [1] G. Margulis proved Ghys's conjecture stating the validity of the following analog of the Tits alternative: either the group of homeomorphisms of the circle possesses a free subgroup with two generators or there is an invariant probabilistic measure on S ¹ . In the present paper, we prove the following strengthening of Margulis's statement: an invariant probabilistic measure for a group exists if and only if the quotient group does not contain a free subgroup with two generators (here is some specific subgroup of G defined in a canonical way). We also formulate and prove analogs of the Tits alternative for groups of homeomorphisms of the line.     

Exact Values of Widths of Classes of Analytic Functions on the Disk and Best Linear Approximation Methods

In the Hardy space H _p, (p1, 0< 1, H _p,1 H _p) we develop best linear approximation methods (previously studied by Taikov and Ainulloev) for the classes W(r,,) of analytic functions on the unit disk and calculate the exact values of linear, Gelfand, and informational n-widths of these classes.     

On Generating Discrete Orthogonal Bivariate Polynomials

In this paper we present an algorithm for recursively generating orthogonal bivariate polynomials on a discrete set S ². For this purpose we employ commuting pairs of real symmetric matrices H, K ^n×n to obtain, in a certain sense, a two dimensional Hermitian Lanczos method. The resulting algorithm relies on a recurrence having a slowly growing length. Practical implementation issues an applications are considered. The method can be generalized to compute orthogonal polynomials depending on an arbitrary number of variables.     

Sigma-Boundary Statistics by Length and Number

This paper presents a rationale for comparative use of length fraction and number fraction statistics in grain boundary analysis from orientation maps generated by electron back-scatter diffraction (EBSD). The length and number fraction statistics for 3 ⁿ coincidence site lattice (CSL) boundaries were measured and compared. The length fraction of 3 boundaries was 0.48 whereas the number fraction was significantly less, 0.36. A simple model was generated to estimate both the length fraction and number fraction of annealing twins (a subset of 3). The model showed that the number fraction of twins is 0.68, 0.75, 0.79 and 0.82 of the length fraction for 1, 2, 3 and 4 twins-per-grain respectively. For the experimental data the number fraction was 0.76 of the length fraction, implying that there were on average two twins-per-grain. In contrast to the 3 case, the length fraction for 9 and 27 boundaries was less than the number fraction. There are more inaccuracies involved in obtaining the number fraction than in obtaining the length fraction from EBSD maps, therefore the length fraction should be recommended as the standard reporting method. However a knowledge of the distribution in the microstructure of 3 ⁿ segments is often crucial to the inquiry in addition to the length fraction.     

The Surface Energy of MgO: Multiscale Reconstruction from Thermal Groove Geometry

The surface energy of MgO is determined using experimental data collected from equilibrated thermal grooves circumscribing island grains. Local equilibrium assumptions at each groove require that the Herring equations be satisfied at each data site, thereby yielding a large and overdetermined system of equations involving the surface energy . This inverse problem is then solved using a new technique that is statistical in nature and multiscale in implementation. The resulting discrete solution represents a statistically significant representation of the surface energy of MgO as a function of surface orientation. Comparisons to results derived from a more traditional approach, along with suggested further applications, are discussed.     

Entanglement of Resonantly Coupled Field Modes in Cavities with Vibrating Boundaries

We study time dependence of various measures of entanglement (covariance entanglement coefficient, purity entanglement coefficient, normalized distance coefficient, entropy coefficients) between resonantly coupled modes of the electromagnetic field in ideal cavities with oscillating boundaries. Two types of cavities are considered — a three-dimensional cavity possessing eigenfrequencies ₃ = 3₁, whose wall oscillates at the frequency _w = 2₁, and a one-dimensional (Fabry–Perot) cavity with an equidistant spectrum _n = n₁ where the distance between perfect mirrors oscillates at the frequencies ₁ and 2₁. The behavior of entanglement measures in these cases turns out to be completely different, although all three coefficients demonstrate qualitatively similar time dependences in each case (except some specific situations where the covariance entanglement coefficient based on traces of covariance submatrices seems to be essentially more sensitive to entanglement than other measures, which are based on determinants of covariance submatrices). Different initial states of the field, namely, vacuum, squeezed vacuum, thermal, Fock, and even/odd coherent states, are considered.     

Continuous variables quantum switch teleportation using two-mode squeezed light

We propose a novel quantum switch teleportation with a continuous variable, which can teleport a quantum state to two different receivers alternatively, using a pair of two-mode squeezed lights as the quantum switching to manipulate the transmission route. In this scheme, the EPR entangled beams shared by sender and receivers are produced by mixing a pair of two-mode squeezed lights on one beamsplitter and separating them by using a polarizing beam splitter. The teleportation capability of this system is examined by the criteria proposed by Ralph and Lam [#!ralph!#] from a small signal quantum optical point of view. Received 20 May 2002 / Received in final form 29 July 2002 Published online 24 September 2002 RID="a" ID="a"e-mail: zhangyun@crl.go.jp     

高平均功率固体激光及其大气传输

固体激光器是一种具有重要应用背景的高功率激光器,对包括激光波长、光束发射口径、发射功率、光束质量等在内的激光器参数的选择进行了分析,研究了大气介质的光学性质、激光大气传输效应以及激光辐射与靶目标的耦合机制与耦合效率等因素的影响.相关结果表明100 kW的固体激光器的综合效能可与2～3倍平均输出功率的DF化学激光器相当,这说明高平均功率固体激光器是一种具有潜在优势和良好发展前景的高功率激光器.