Some results on construction of orthogonal Latin squares by the method of sum composition

A method of sum composition for construction of orthogona Latin squares was introduced by A. Hedayat and E. Seiden [1]. In this paper we exhibit procedures for constructing a pair of orthogonal Latin squares of size p^α + 4 for primes of the form 4m + 1 or p ≡ 1, 2, 4 mod 7. We also show that for any p > 2n and n even one can construct and orthogonal pair of Latin squares of size p^α + n using the method of sum composition. We observe that the restriction xy = 1 used by Hedayat and Seiden is sometimes necessary.     

Efficient Computation of Roots in Finite Fields

We present an algorithm to compute rth roots in $\mathbb{F}_{q^m}We present an algorithm to compute rth roots in with complexity ?[(log m + r log q) m log q] if (m,q) = 1 and either (q(q−1),r) = 1 or r|(q−1) and ((q−1)/r,r) = 1. This compares well to previously known algorithms, which need O(r m³ log³ q) steps. Paulo S. L. M. Barreto: Supported by Scopus Tecnologia S. A. José Felipe Voloch: Supported by NSA grant MDA904-03-1-0117.     

Targeting large phosp(III)azane macrocyles [{P(mu-NR)}(2)(LL)](n) (n> or = 2)

The condensation reactions of the dimer [ClP(micro-NR)](2) with organic diacids [LL(H)(2)], possessing linear orientations of their organic groups, result in the formation of phospha(III)zane macrocyles of the type [{P(mu-NR)}(2)(LL)](n) of various sizes. The series of macrocycles [{P(mu-N(t)Bu)}(2){1,5-(NH)(2)C(10)H(6)}](3), [{P(mu-NCy)}(2)(1,5-O(2)C(10)H(6))](n) [n = 3; n = 4], [{P(mu-N(t)Bu)}(2){1,4-(NH)(2)C(6)H(4)}](4), [{P(mu-N(t)Bu)}(2)(1,4-O(2)C(6)H(4))], [{P(mu-NCy)}(2)(1,4-O(2)C(6)H(4))](3) and [{P(mu-N(t)Bu)}(2){(NH)C(6)H(4)OC(6)H(4)(NH)}](2) can be related to classical organic frameworks, like calixarenes.     

Nature of the chemical bond in protonated methane

Protonated methane, CH(5)(+), is a key reactive intermediate in hydrocarbon chemistry and a borderline case for chemical structure theory, being the simplest example of hypercoordinated carbon. Early quantum mechanical calculations predicted that the properties of this species could not be associated with only one structure, because it presents serious limitations of the Born-Oppenheimer approximation. However, ab initio molecular dynamics and diffusion Monte Carlo calculations showed that the most populated structure could be pictured as a CH(3) tripod linked to a H(2) moiety. Despite this controversy, a model for the chemical bonds involved in this ion still lacks. Here we present a modern valence bond model for the electronic structure of CH(5)(+). The chemical bond scheme derived directly from our calculations pictures this ion as H(3)C...H(2)(+). The fluxionality can be seen as the result of a proton transfer between C-H bonds. A new insight on the vibrational bands at approximately 2400 and approximately 2700 cm(-1) is suggested. Our results show that the chemical bond model can be profitably applied to such intriguing systems.     

Grid Methods in Computational Real Algebraic (and Semialgebraic) Geometry

In recent years, a family of numerical algorithms to solve problems in real algebraic and semialgebraic geometry has been slowly growing. Unlike their counterparts in symbolic computation they are numerically stable. But their complexity analysis, based on the condition of the data, is radically different from the usual complexity analysis in symbolic computation as these numerical algorithms may run forever on a thin set of ill-posed inputs.     

Graded polynomial identities for matrices with the transpose involution over an infinite field

Let F be an infinite field and let M_n(F) be the algebra of n×n matrices over F endowed with an elementary grading whose neutral component coincides with the main diagonal. In this paper, we find a basis for the graded polynomial identities of M_n(F) with the transpose involution. Our results generalize for infinite fields of arbitrary characteristic previous results in the literature, which were obtained for the field of complex numbers and for a particular class of elementary G-gradings.     

Description of the viscosity of honeys in the supercooled regime

For several honeys from different countries, we study the dependence of the Logarithmic Shift Factor (LSF$LSF$) with temperature that obeys the Williams–Landel–Ferry equation. We find that the LSF$LSF$ may be expressed in terms of a linear equation. On the other hand, the viscosities of different honeys present a corresponding state behavior through a master plot in terms of an adimensional temperature. This kind of behavior has been reported for other glass formers.     

Algorithmic Consistency in Computational Inelasticity – a Conceptual Completion

This paper communicates a new algorithmic concept, how higher-order Runge-Kutta (RK) methods for time integration of viscoelastic constitutive laws can be introduced into nonlinear finite element methods in order (i) to obtain the full nominal order p in time integration, (ii) to ensure that global equilibrium is only required at the end of time intervals Δt but not in the interior at RK-stages, and (iii) to obtain –based on (i) and (ii)– a considerable speed-up compared with Backward-Euler. The condition to realize (i)–(iii) is, that the approximation of total strain in time must be of the same order as the time-integration method, which is a completion of the concept of algorithmic consistency in computational inelasticity. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Colour diversification in octocorals based on conjugated polyenes: A Raman spectroscopic view

Polyenic pigments in octocorals have been investigated by Raman spectroscopy using laser excitation at 532, 785 and 1064 nm. The spectral features suggest the structural nature of carotenoids from Phyllogorgia dilatata, Leptogorgia punicea, Muricea atlantica, Carijoa riisei and conjugated polyenals from L. punicea, L. setacea, Muricea flamma and Renilla muelleri. The observed vibrational bands at ca. 1540–1520 ν₁(C=C), 1159 ν₂(C–C) and 1005 cm⁻¹ ρ₃(C–CH₃) were assigned to carotenoids, whereas the identification of non‐methylated conjugated polyenals have been proposed due to two major Raman bands at ca. 1500 and 1120 cm^‐1, assigned to ν(C=C) and ν(C–C), respectively. Copyright © 2012 John Wiley & Sons, Ltd.