An Extension of Craig's Family of Lattices

Let p be a prime, and let zeta(p) be a primitive p-th root of unity. The lattices in Craig's family are (p - 1)-dimensional and are geometrical representations of the integral Z[zeta(p)]-ideals < 1 - zeta(p)>(i), where i is a positive integer. This lattice construction technique is a powerful one. Indeed, in dimensions p - 1 where 149 <= p <= 3001, Craig's lattices are the densest packings known. Motivated by this, we construct (p - 1)(q - 1)-dimensional lattices from the integral Z[zeta(pq)]-ideals < 1 - zeta(p)>(i) < 1 - zeta(q)>(j), where p and q are distinct primes and i and fare positive integers. In terms of sphere-packing density, the new lattices and those in Craig's family have the same asymptotic behavior. In conclusion, Craig's family is greatly extended while preserving its sphere-packing properties.

Simple derivation of general Fierz-type identities

General Fierz-type identities are examined and their well-known connection with completeness relations in matrix vector spaces is shown. In particular, I derive the chiral Fierz identities in a simple and systematic way by using a chiral basis for the complex 4 X 4 matrices. Other completeness relations for the fundamental representations of SU(N) algebras can be extracted using the same reasoning. (c) 2005 American Association of Physics Teachers.

Hq(4) symmetry: the linear q-harmonic oscillator based on generalized irreps of the q-deformed Heisenberg algebra

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

REDUCTION OF TODA LATTICE HIERARCHY TO GENERALIZED KDV HIERARCHIES AND THE 2-MATRIX MODEL

Toda lattice hierarchy and the associated matrix formulation of the 2M-boson KP hierarchies provide a framework for the Drinfeld-Sokolov reduction scheme realized through Hamiltonian action within the second KP Poisson bracket. By working with free currents, which Abelianize the second KP Hamiltonian structure, we are able to obtain a unified formalism for the reduced SL(M + 1, M - k) KdV hierarchies interpolating between the ordinary KP and KdV hierarchies. The corresponding Lax operators are given as superdeterminants of graded SL(M + 1, M - k) matrices in the diagonal gauge and we describe their bracket structure and field content. In particular, we provide explicit free field representations of the associated W(M, M - k) Poisson bracket algebras generalising the familiar nonlinear W-M+1 algebra. Discrete Backlund transformations for SL(M + 1, M - k) KdV are generated naturally from lattice translations in the underlying Toda-like hierarchy. As an application we demonstrate the equivalence of the two-matrix string model to the SL(M + 1, 1) KdV hierarchy.

Green functions of the Dirac equation with magnetic-solenoid field

Various Green functions of the Dirac equation with a magnetic-solenoid field (the superposition of the Aharonov-Bohm field and a collinear uniform magnetic field) are constructed and studied. The problem is considered in 2+1 and 3+1 dimensions for the natural extension of the Dirac operator (the extension obtained from the solenoid regularization). Representations of the Green functions as proper time integrals are derived. The nonrelativistic limit is considered. For the sake of completeness the Green functions of the Klein-Gordon particles are constructed as well. (C) 2004 American Institute of Physics.

A note on carcass characteristics of rabbits fed on a restricted system

Thirty four 65 days old New Zealand White female rabbits. weighting 1900 +/- 40 g, were separated in 3 groups and caged individually. One group was slaughtered when 70 days old (reference group, n=14). The second group was slaughtered 50 days later after ad libitum feeding (n = 6), and the third group was slaughtered also when 120 days old, but after restricted feeding since 70 days old i.e. 50% of the spontaneous feed intake of the 65-70 days period (restricted group n=14). Whole carcass weight and carcass cuts weights were measured after 24 hours storage at +4 degrees C. For each of the 3 groups in the previous order, slaughter live weight was 1992 - 2988 and 1887g; Chilled carcass percentage were 47.9 - 51.0 and 50.1. Feed restriction decreased the loin proportion of the carcass lower than that of the reference group (27.0 - 26.1 and 22.8% for the 3 groups in the same order) but increased the posterior limbs proportion (36.5 - 36.6 and 40.1).

A construção da verdade nos crimes de defloramento (1920-1940): práticas e representações do discurso jurídico na Comarca de Bauru (SP)

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Cerro Porã Batholith: post-orogenic A-type granite from the Amoguijá Magmatic Arc - Rio ApaTerrane - South of the Amazonian Craton

O Batólito Cerro Porã é um corpo de aproximadamente 30 por 4 km de extensão, localizado na região de Porto Murtinho, Mato Grosso do Sul. Situa-se nos domínios do Terreno Rio Apa, porção sul do Cráton Amazônico. Constitui-se pela Fácies sienogranítica rosa e Fácies monzogranítica cinza. A primeira é caracterizada por textura equi a, essencialmente, inequigranular xenomórfica e pela presença constante de intercrescimentos gráfico e granofíric; constitui-se por feldspatos alcalinos, quartzo e plagioclásio, tendo biotita como único máfico primário. A Fácies monzogranítica cinza apresenta textura porfirítica, com uma matriz de granulação fina gráfica a granofírica e consiste de quartzo, plagioclásio, feldspatos alcalinos e agregados máficos (biotita e anfibólio). Ambas foram metamorfizadas na fácies xisto verde e a Fácies sienogranítica rosa mostra-se milonitizada quando em zonas de cisalhamento. Foi identificado um evento deformacional dúctil-rúptil originado em regime compressivo, responsável pela geração de xistosidade e lineação de estiramento mineral. A Zona de Cisalhamento Esperança relaciona-se a esta fase e reflete a história cinemática convergente, reversa a de cavalgamento, com transporte de topo para NWW. Quimicamente, esses litotipos classificam-se como granitoides do tipo A2 da série alcalina potássica saturada em sílica. Determinação geocronológica obtida pelo método U-Pb (SHRIMP) em zircão, forneceu idade de 1749 ±45 Ma para sua cristalização. Do ponto vista geotectônico, admite-se que o Granito Cerro Porã corresponda a um magmatismo associado a um arco vulcânico desenvolvido no Estateriano e que sua colocação se deu no estágio tardi a pós-orogênico.

Characteristics of sexual violence against adolescent girls and adult women

Background: Sexual violence is considered a serious violation of human rights which affects mainly young women and adolescents. There is little information about the conditions under which sexual offences occur. We evaluated characteristics of sexual violence against adolescent girls and adult women.Method: This is a quantitative, retrospective, descriptive study of sexual violence against adolescent girls and adult women. Analyses were carried out on data collected from 1118 women, 546 adolescents (10-19 years) and 572 adults (>= 20 years), with a complaint of rape treated at Hospital Perola Byington, Sao Paulo, between 1994 and 1999. The age limit of the adolescent sample met the World Health Organization's (WHO) criteria. We analyzed the type of sexual contact, degree of intimidation, perpetrator and activity of the victim during the approach.Results: Crimes without penetration were five times more frequent in adolescents and use of threats of death or intimidation was common in both groups. Mental illness was more prevalent in adult victims and the majority of adolescent victims were aged < 14 years. Uncle and stepfather perpetrators were more frequent among adolescents and partners or former intimate partners in adult women. In most cases the approach occurred in public places, although sex crimes at the perpetrator's residence were more frequent amongst adolescents.Conclusions: Although children and adolescents require the same intervention measures and legal protection, a considerable proportion of adolescent sex offenders can face conditions similar to those of adult women.

A method for calculating the compliance of bonded-interfaces under shrinkage: Validation for Class I cavities

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

Wavelet-galerkin method for computations of electromagnetic fields-computation of connection coefficients

One of the key issues which makes the waveletGalerkin method unsuitable for solving general electromagnetic problems is a lack of exact representations of the connection coefficients. This paper presents the mathematical formulae and computer procedures for computing some common connection coefficients. The characteristic of the present formulae and procedures is that the arbitrary point values of the connection coefficients, rather than the dyadic point values, can be determined. A numerical example is also given to demonstrate the feasibility of using the wavelet-Galerkin method to solve engineering field problems. © 2000 IEEE.

Television violence and young adults in Brazil: a content analysis of the popular telenovella, Malhação = Violência na televisão brasileira e jovens : uma análise de conteúdo da telenovela popular, Malahção

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

The Role of Manipulatives in the Eighth Grade Mathematics Classroom

In this action research study of my classroom of eighth grade mathematics, I investigated the use of manipulatives and its impact on student attitude and understanding. I discovered that overall, students enjoy using manipulatives, not necessarily for the benefit of learning, but because it actively engages them in each lesson. I also found that students did perform better on exams when students were asked to solve problems using manipulatives in place of formal written representations of situations. In the course of this investigation, I also uncovered that student attitude toward mathematics improved when greater manipulative use was infused into the lessons. Students felt more confident that they understood the material, which translated into a better attitude regarding math class. As a result of this research, I plan to find ways to implement manipulatives in my teaching on a more regular basis. I intend to create lessons with manipulatives that will engage both hands and minds for the learners.

Self-Organizing Maps of Molecular Descriptors for Sesquiterpene Lactones and Their Application to the Chemotaxonomy of the Asteraceae Family

The Asteraceae, one of the largest families among angiosperms, is chemically characterised by the production of sesquiterpene lactones (SLs). A total of 1,111 SLs, which were extracted from 658 species, 161 genera, 63 subtribes and 15 tribes of Asteraceae, were represented and registered in two dimensions in the SISTEMATX, an in-house software system, and were associated with their botanical sources. The respective 11 block of descriptors: Constitutional, Functional groups, BCUT, Atom-centred, 2D autocorrelations, Topological, Geometrical, RDF, 3D-MoRSE, GETAWAY and WHIM were used as input data to separate the botanical occurrences through self-organising maps. Maps that were generated with each descriptor divided the Asteraceae tribes, with total index values between 66.7% and 83.6%. The analysis of the results shows evident similarities among the Heliantheae, Helenieae and Eupatorieae tribes as well as between the Anthemideae and Inuleae tribes. Those observations are in agreement with systematic classifications that were proposed by Bremer, which use mainly morphological and molecular data, therefore chemical markers partially corroborate with these classifications. The results demonstrate that the atom-centred and RDF descriptors can be used as a tool for taxonomic classification in low hierarchical levels, such as tribes. Descriptors obtained through fragments or by the two-dimensional representation of the SL structures were sufficient to obtain significant results, and better results were not achieved by using descriptors derived from three-dimensional representations of SLs. Such models based on physico-chemical properties can project new design SLs, similar structures from literature or even unreported structures in two-dimensional chemical space. Therefore, the generated SOMs can predict the most probable tribe where a biologically active molecule can be found according Bremer classification.

Bourgin-Yang version of the Borsuk-Ulam theorem for Z(pk)-equivariant maps

Let G = Z(pk) be a cyclic group of prime power order and let V and W be orthogonal representations of G with V-G = W-G = W-G = {0}. Let S(V) be the sphere of V and suppose f: S(V) -> W is a G-equivariant mapping. We give an estimate for the dimension of the set f(-1){0} in terms of V and W. This extends the Bourgin-Yang version of the Borsuk-Ulam theorem to this class of groups. Using this estimate, we also estimate the size of the G-coincidences set of a continuous map from S(V) into a real vector space W'.