Involutions and free pairs of bicyclic units in integral group rings

If * : G -> G is an involution on the finite group G, then * extends to an involution on the integral group ring Z[G] . In this paper, we consider whether bicyclic units u is an element of Z[G] exist with the property that the group < u, u*> generated by u and u* is free on the two generators. If this occurs, we say that (u, u*)is a free bicyclic pair. It turns out that the existence of u depends strongly upon the structure of G and on the nature of the involution. One positive result here is that if G is a nonabelian group with all Sylow subgroups abelian, then for any involution *, Z[G] contains a free bicyclic pair.

Timelike Christoffel pairs in the split-quaternions

We characterize the Christoffel pairs of timelike isothermic surfaces in the four-dimensional split-quaternions. When restricting the receiving space to the three-dimensional imaginary split-quaternions, we establish an equivalent condition for a timelike surface in R(2)(3) to be real or complex isothermic in terms of the existence of integrating factors.

Solvation in Pure Liquids: What Can Be Learned from the Use of Pairs of Indicators?

The solvation of six solvatochromic probes in a large number of solvents (33-68) was examined at 25 degrees C. The probes employed were the following: 2,6-diphenyl-4-(2,4,6-triphenylpyridinium-1-yl) phenolate (RB); 4-[(E)2-(1-methylpyridinium-4-yl)ethenyl] phenolate, MePM; 1-methylquinolinium-8-olate, QB; 2-bromo-4-[(E)-2-(1-methylpyridinium-4-yl)ethenyl] phenolate, MePMBr, 2,6-dichloro-4-(2,4,6-triphenyl pyridinium-1-yl) phenolate (WB); and 2,6-dibromo-4-[(E)-2-(1-methylpyridinium-4-yl)ethenyl] phenolate, MePMBr(2), respectively. Of these, MePMBr is a novel compound. They can be grouped in three pairs, each with similar pK(a) in water but with different molecular properties, for example, lipophilicity and dipole moment. These pairs are formed by RB and MePM; QB and MePMBr; WB and MePMBr(2), respectively. Theoretical calculations were carried out in order to calculate their physicochemical properties including bond lengths, dihedral angles, dipole moments, and wavelength of absorption of the intramolecular charge-transfer band in four solvents, water, methanol, acetone, and DMSO, respectively. The data calculated were in excellent agreement with available experimental data, for example, bond length and dihedral angles. This gives credence to the use of the calculated properties in explaining the solvatochromic behaviors observed. The dependence of an empirical solvent polarity scale E(T)(probe) in kcal/mol on the physicochemical properties of the solvent (acidity, basicity, and dipolarity/polarizability) and those of the probes (pK(a), and dipole moment) was analyzed by using known multiparameter solvation equations. For each pair of probes, values of E(T)(probe) (for example, E(T)(MePM) versus E(T)(RB)) were found to be linearly correlated with correlation coefficients, r, between 0.9548 and 0.9860. For the mercyanine series, the values of E(T)(probe) also correlated linearly, with (r) of 0.9772 (MePMBr versus MePM) and 0.9919 (MePMBr(2) versus MePM). The response of each pair of probes (of similar pK(a)) to solvent acidity is the same, provided that solute-solvent hydrogen-bonding is not seriously affected by steric crowding (as in case of RB). We show, for the first time, that the response to solvent dipolarity/polarizability is linearly correlated to the dipole moment of the probes. The successive introduction of bromine atoms in MePM (to give MePMBr, then MePMBr(2)) leads to the following linear decrease: pK(a) in water, length of the phenolate oxygen-carbon bond, length of the central ethylenic bond, susceptibility to solvent acidity, and susceptibility to solvent dipolarity/polarizability. Thus studying the solvation of probes whose molecular structures are varied systematically produces a wealth of information on the effect of solute structure on its solvation. The results of solvation of the present probes were employed in order to test the goodness of fit of two independent sets of solvent solvatochromic parameters.

All maximal-pairs in step-leap representation of melodic sequence

This paper proposes an efficient pattern extraction algorithm that can be applied on melodic sequences that are represented as strings of abstract intervallic symbols; the melodic representation introduces special “binary don’t care” symbols for intervals that may belong to two partially overlapping intervallic categories. As a special case the well established “step–leap” representation is examined. In the step–leap representation, each melodic diatonic interval is classified as a step (±s), a leap (±l) or a unison (u). Binary don’t care symbols are used to represent the possible overlapping between the various abstract categories e.g. *=s, *=l and #=-s, #=-l. We propose an O(n+d(n-d)+z)-time algorithm for computing all maximal-pairs in a given sequence x=x[1..n], where x contains d occurrences of binary don’t cares and z is the number of reported maximal-pairs.

All maximal-pairs in step-leap representation of melodic sequence

This paper proposes an efficient pattern extraction algorithm that can be applied on melodic sequences that are represented as strings of abstract intervallic symbols; the melodic representation introduces special “binary don’t care” symbols for intervals that may belong to two partially overlapping intervallic categories. As a special case the well established “step–leap” representation is examined. In the step–leap representation, each melodic diatonic interval is classified as a step (±s), a leap (±l) or a unison (u). Binary don’t care symbols are used to represent the possible overlapping between the various abstract categories e.g. *=s, *=l and #=-s, #=-l. We propose an O(n+d(n-d)+z)-time algorithm for computing all maximal-pairs in a given sequence x=x[1..n], where x contains d occurrences of binary don’t cares and z is the number of reported maximal-pairs.

Pairs trading : aplicação no mercado acionário brasileiro

Esta dissertação estuda a aplicação da estratégia Pairs Trading no mercado acionário brasileiro. Envolve basicamente a identificação de pares de ações que tenham movimentos de preço semelhantes e posteriormente a operação do diferencial entre seus preços. É possível observar no mercado a existência de um valor de equilíbrio de longo prazo para alguns pares de ações e quando o diferencial divergir de certa quantidade pré-definida opera-se o diferencial no intuito de que o mesmo retorne ao seu valor de equilíbrio de longo prazo, ou seja, espera-se que ocorra uma reversão à média do diferencial. A metodologia para a identificação desses pares de ações que descrevem movimentos semelhantes vem do conceito de cointegração. Essa metodologia é aplicada sobre as ações do índice Bovespa de 04-Jan-1993 a 30-Jun-2005. Inicialmente é feita uma pré-seleção dos pares de ações via correlação, ou medida de distância. Para a seleção final é feito o teste de cointegração, onde é utilizado o método de Dickey-Fuller aumentado (Augmented Dickey-Fuller test – ADF) para verificar a existência de raiz unitária da série de resíduo da combinação linear do logaritmo dos preços. Após a seleção, os pares são simulados historicamente (backtesting) para se analisar a performance dos retornos dos pares de ações, incluindo também os custos operacionais.

Pairs trading: uma aplicação ao mercado acionário brasileiro

Neste trabalho, verificamos viabilidade de aplicação da estratégia de pairs trading no mercado acionário brasileiro. Diferentemente de outros estudos do mesmo tema, construímos ativos sintéticos a partir de uma combinação linear de preços de ações. Conforme Burgeois e Minko (2005), utilizamos a metodologia de Johansen para a formação dos pares a serem testados. Após a identificação de pares cointegrados, para assegurar a estacionaridade do ativo sintético contruído a partir da relação linear de preços das ações, utilizamos os testes DF-GLS e KPSS e filtramos àqueles que apresentavam raiz unitária em sua série de tempo. A seguir, simulamos a estratégia (backtesting) com os pares selecionados e para encontrar os melhores parâmetros, testamos diferentes períodos de formação dos pares, de operação e de parâmetros de entrada, saída e stop-loss. A fim de realizarmos os testes de forma mais realista possível, incluímos os custos de corretagem, de emolumentos e de aluguel, além de adicionar um lag de um dia para a realização das operações

X-chromosome inactivation patterns in monozygotic twins and sib pairs discordant for nonsyndromic cleft lip and/or palate

Nonsyndromic clefts of the lip and/or palate are common birth defects with a strong genetic component. Based on unequal gender ratios for clefting phenotypes, evidence for linkage to the X chromosome and the occurrence of several X-linked clefting syndromes, we investigated the role of skewed X chromosome inactivation (XCI) in orofacial clefts. Our samples consisted of female monozygotic (MZ) twins (n = 8) and sister pairs (n = 152) discordant for nonsyndromic clefting. We measured the XCI pattern in peripheral blood lymphocyte DNA using a methylation based androgen receptor gene assay. Skewing of XCI was defined as the deviation in inactivation pattern from a 50:50 ratio. Our analysis revealed no significant difference in the degree of skewing between twin pairs (P = 0.3). However, borderline significant differences were observed in the sister pairs (P = 0.02), with the cleft lip with cleft palate group showing the most significant result (P=0.01). We did not find evidence for involvement of skewed XCI in the discordance for clefting in our sample of female MZ twins. However, results from the paired sister study suggest the potential contribution of skewed XCI to orofacial clefting, particularly cleft lip and palate. (C) 2007 Wiley-Liss, Inc.

Heterologous microsatellite primer pairs informative for the whole genus Arachis

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Asymptotics for Gegenbauer-Sobolev orthogonal polynomials associated with non-coherent pairs of measures

Inner products of the type < f, g >(S) = < f, g >psi(0) + < f', g'>psi(1), where one of the measures psi(0) or psi(1) is the measure associated with the Gegenbauer polynomials, are usually referred to as Gegenbauer-Sobolev inner products. This paper deals with some asymptotic relations for the orthogonal polynomials with respect to a class of Gegenbauer-Sobolev inner products. The inner products are such that the associated pairs of symmetric measures (psi(0), psi(1)) are not within the concept of symmetrically coherent pairs of measures.

Zeros of Gegenbauer-Sobolev Orthogonal Polynomials: Beyond Coherent Pairs

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Asymptotics for Jacobi-Sobolev orthogonal polynomials associated with non-coherent pairs of measures

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

On pairs of regular foliations in R(3) and singularities of map-germs

We study germs of pairs of codimension one regular foliations in R(3) . We show that the discriminant of the pair determines the topological type of the pair. We also consider various classifications of the singularities of the discriminant.