New higher-order methods for the simultaneous inclusion of polynomial zeros

Higher-order methods for the simultaneous inclusion of complex zeros of algebraic polynomials are presented in parallel (total-step) and serial (single-step) versions. If the multiplicities of each zeros are given in advance, the proposed methods can be extended for multiple zeros using appropriate corrections. These methods are constructed on the basis of the zero-relation of Gargantini’s type, the inclusion isotonicity property and suitable corrections that appear in two-point methods of the fourth order for solving nonlinear equations. It is proved that the order of convergence of the proposed methods is at least six. The computational efficiency of the new methods is very high since the acceleration of convergence order from 3 (basic methods) to 6 (new methods) is attained using only n polynomial evaluations per iteration. Computational efficiency of the considered methods is studied in detail and two numerical examples are given to demonstrate the convergence behavior of the proposed methods.     

Primitive symmetric designs with up to 2500 points

By this article we conclude the construction of all primitive ( v, k,λ ) symmetric designs with v < 2500 , up to a few unsolved cases. Complementary to the designs with prime power number of points published previously, here we give 55 primitive symmetric designs with v ≠ p ^m , p prime and m positive integer, together with the analysis of their full automorphism groups. The research involves programming and wide‐range computations. We make use of the software package GAP and the library of primitive groups which it contains. © 2011 Wiley Periodicals, Inc. J Combin Designs 19:463‐474, 2011     

Turbulent Prandtl Number in Two Spatial Dimensions: Two-Loop Renormalization Group Analysis

Theoretical and Mathematical Physics - Using the field theory renormalization group technique in the framework of the so-called double-expansion scheme, which takes additional divergences that...     

Canonizing structural Ramsey theorems

At the beginning of 1950s Erd?s and Rado suggested the investigation of the Ramsey-type results where the number of colors is not finite. This marked the birth of the so-called canonizing Ramsey theory. In 1985 Prömel and Voigt made the first step towards the structural canonizing Ramsey theory when they proved the canonical Ramsey property for the class of finite linearly ordered hypergraphs, and the subclasses thereof defined by forbidden substructures. Building on their results in this paper we provide several new structural canonical Ramsey results. We prove the canonical Ramsey theorem for the class of all finite linearly ordered tournaments, the class of all finite posets with linear extensions and the class of all finite linearly ordered metric spaces. We conclude the paper with the canonical version of the celebrated Ne?et?il–Rödl Theorem. In contrast to the “classical” Ramsey-theoretic approach, in this paper we advocate the use of category theory to manage the complexity of otherwise technically overwhelming proofs typical in canonical Ramsey theory.     

Application of very weak formulation on homogenization of boundary value problems in porous media

Czechoslovak Mathematical Journal - The goal of this paper is to present a different approach to the homogenization of the Dirichlet boundary value problem in porous medium. Unlike the standard...     

CASPT2 and CCSD(T) calculations of dipole moments and polarizabilities of acetone in excited states

The acetone molecule is investigated in its ground state and valence ^1,3n-π*, ^1,3π-π*, and ^1,3σ-π* excited states and Rydberg ^1,3n-3s, ^1,3π-3?, ^1,3n-3p_y and ^1,3π-3p_y states using the CASSCF, CASPT2, and CCSD(T) methods. Equilibrium geometries of excited states are obtained and their changes with respect to the ground state are discussed. For most excited states the C_2v symmetry of the ground state is lowered to the C_s symmetry. A series of valence vertical and adiabatic excitation energies is presented along with excitation energies for Rydberg states. The main body of the paper contains Finite-Field Perturbation Theory (FFPT) calculations of electric properties of the vertically as well as geometry relaxed excited states. Dipole moments of valence excited states decrease significantly upon excitation, being about one half of the ground state dipole moment. Polarizabilities usually change upon excitation much less (increase by about 30%) but hyperpolarizabilities are enhanced up to one or two orders of magnitude. The orientation of the dipole moment is reversed in some vertically excited Rydberg states. Properties of the ground and excited states are discussed considering alterations of the electronic structure and shifts in the geometry.     

Emission Spectra of BeO in Near Ultraviolet Region

Abstract

The emission spectra of isotopic BeO molecules as excited in low-pressure arc have been photographed in the region 300–350 nm at medium dispersion. The bands have been assigned to the c³II ? a³II system. The vibrational numbering was obtained from a study of the vibrational isotope effect. Vibrational constants for involved states are derived from least-squares fits of the measured bandhead wavenumbers.     

Influence of the retardation of the multiplexing element in a dual channel Q-switched laser

We present an experimental and numerical analysis, how deviations of the multiplexer-retardation influence the output power of a time-multiplexed dual channel laser. The laser has two different channels, each one with its own gain medium. The channels are time-multiplexed by a single crystal photo-elastic modulator. It enables to double the repetition rate and output power of the laser. However, as multiplexing is based on polarization-switching, the retardation of the modulator should be kept within certain limits. By experimental measurement and theoretical analysis, we determine the operational window within which the retardation should be kept to avoid additional losses into the resonator. The analysis was done for two configurations of the laser setup, namely with and without a quarter-wave plate.     

Erbium photoluminescence excitation spectroscopy in Si: Er epitaxial structures

Excitation spectra of erbium photoluminescence in Si: Er epitaxial structures are studied within a broad pump wavelength range (λ_ex = 780–1500 nm). All the structures studied reveal a fairly strong erbium photoluminescence signal at photon energies substantially smaller than the silicon band-gap width (λ = 1060 nm) with no exciton generation. A possible mechanism of erbium ion excitation in silicon without exciton involvement is discussed.     

Magneto-optical effects in crystals at the normal incidence

We consider the interaction of a polarized electromagnetic wave in a magnetically ordered crystal plate surrounded by an isotropic ambient at the normal incidence. The crystalline medium of the plate is specified by the general non-symmetric permittivity tensor. The results are expressed in terms of the transmission and reflection matrices which relate the electric fields of the incident wave to those of transmitted and reflected waves. Their applications are illustrated by examples of an isotropic plate magnetized normal to the interface, a cubic crystal magnetized parallel to the interface and an orthorhombic crystal magnetized along the axis normal to the interface. The effect of the reflection from the interfaces and the interference effect are included. The paper treats the reflection at an interface between an isotropic ambient and an absorbing magnetic crystal at small non-zero angles of incidence. The general reflection matrix is applied to the determination of the magneto-optical effects quadratic in magnetization.