RIEMANN ZETA ZEROS AND PRIME NUMBER SPECTRA IN QUANTUM FIELD THEORY

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Solutions for a class of integro-differential equations with time periodic coefficients

In this work, a series solution is found for the integro-differential equation y″ (t) = -(ω2 c + ω2 f sin2 ωpt)y(t) + ωf (sin ωpt) z′ (0) + ω2 fωp sin ωpt ∫t 0 (cos ωps) y(s)ds, which describes the charged particle motion for certain configurations of oscillating magnetic fields. As an interesting feature, the terms of the solution are related to distinct sequences of prime numbers.

Criptografia de chave pública, criptografia RSA

Pós-graduação em Matemática Universitária - IGCE

Números primos e divisibilidade: estudo de propriedades

Pós-graduação em Matemática em Rede Nacional - IBILCE

Números transcedentes e de Liouville

Pós-graduação em Matemática em Rede Nacional - IBILCE

Números primos: propriedades, aplicações e avanços

Pós-graduação em Matemática em Rede Nacional - IBILCE

Explorando o universo dos números primos

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Aritmética por apps

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Comparison of microbial numbers in soils by using various culture media and temperatures

The influence of different media and incubation temperatures on the quantification of microbial populations in sorghum, eucalyptus and forest soils was evaluated. Microbial growth was compared by using complex (tryptone soybean agar, TSA, casein-starch, CS, and Martin) and saline (Thorton, M3, Czapeck) media and incubation temperatures of 25 and 30° C. Higher numbers of total bacterial. and fungal colony-forming units (CFU) were observed in sorghum soils, and of spore-forming and Gram-negative bacteria in forest soils than other soils. Actinomycetes counts were highest in forest soil when using CS medium at 30° C and in sorghum soil at 25° C in M3 medium. Microorganism counts were dependent on the media and incubation temperatures. The counts at temperatures of 30° C were significantly higher than at 25° C. Microbial quantification was best when using TSA medium for total. and spore-forming bacteria, Thorton for Gram-negative bacteria, M3 for actinomycetes, and Martin for fungi. © 2005 Elsevier GmbH. All rights reserved.

Computations of the flow past a still sphere at moderate reynolds numbers using an immersed boundary method

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

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.

Exact static soliton solutions of (3+1)-dimensional integrable theory with nonzero Hopf numbers

In this paper, we explicitly construct an infinite number of Hopfions (static, soliton solutions with nonzero Hopf topological charges) within the recently proposed (3 + 1)-dimensional, integrable, and relativistically invariant field theory. Two integers label the family of Hopfions we have found. Their product is equal to the Hopf charge which provides a lower bound to the soliton's finite energy. The Hopfions are explicitly constructed in terms of the toroidal coordinates and shown to have a form of linked closed vortices.

Free actions of abelian p-groups on the n-torus

In this work we make some contributions to the theory of actions of abelian p-groups on the n-Torus T-n. Set congruent to Z(pk1)(h1) x Z(pk2)(h2) x...x Z(pkr)(hr), r >= 1, k(1) >= k(2) >=...>= k(r) >= 1, p prime. Suppose that the group H acts freely on T-n and the induced representation on pi(1)(T-n) congruent to Z(n) is faithful and has first Betti number b. We show that the numbers n, p, b, k(i) and h(i) (i = 1,..,r) satisfy some relation. In particular, when H congruent to Z(p)(h), the minimum value of n is phi(p) + b when b >= 1. Also when H congruent to Z(pk1) x Z(p) the minimum value of n is phi(p(k1)) + p - 1 + b for b >= 1. Here phi denotes the Euler function.

Distribution and insertion numbers of transposable elements in species of the Drosophila saltans group

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