Algebraic Integers
Mostrando 1-10 de 10 artigos, teses e dissertações.
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1. Construction of Complex Lattice Codes via Cyclotomic Fields
ABSTRACT Through algebraic number theory and Construction A we extend an algebraic procedure which generates nested complex lattice codes from the polynomial ring F 2 x / x n - 1, where F 2 = 0 , 1, by using ideals from the generalized polynomial ring F 2 x , 1 2 ℤ 0 x 1 2 2 n - 1 through the ring of integers ���� of t
Trends in Computational and Applied Mathematics. Publicado em: 2022
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2. Constructions of algebraic lattices
In this work we present constructions of algebraic lattices in Euclidean space with optimal center density in dimensions 2, 3, 4, 6, 8 and 12, which are rotated versions of the lattices Λn, for n = 2,3,4,6,8 and K12. These algebraic lattices are constructed through twisted canonical homomorphism via ideals of a ring of algebraic integers. Mathematical subje
Computational & Applied Mathematics. Publicado em: 2010
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3. Re-significando a disciplina teoria dos números na formação do professor de matemática na licenciatura
This study is part of the issue that questions which algebra should be taught in the different levels of schooling, especially in the development of mathematics teachers for basic education. In this context, this study was guided by the question: Which Number Theory is or should be understood as a piece of knowledge to be taught in mathematics teacher develo
Publicado em: 2007
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4. On a classification of the integral rings, finite semigroups and RA-loops with the hyperbolic property / Sobre uma classificação dos anéis de inteiros, dos semigrupos finitos e dos RA-loops com a propriedade hiperbólica
For a given division algebra of a quaternion algebra, we construct and define two types of units of its $\Z$-orders: Pell units and Gauss units. Also, for the quadratic imaginary extensions over the racionals and some fixed group $G$, we classify the algebraic integral rings for which the unit group ring is a hyperbolic group. We also classify the finite sem
Publicado em: 2006
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5. Construction of optical orthogonal codes for use in cdma fiber-optics systems / Propostas de codigos ortogonais para sistemas OCDMA
This thesis presents a study of optical orthogonal codes (OOe) for application in communication systems using the technique of fiber-optics code division multiple access (OCDMA). The Prime Sequence codes and Quadratic codes are, for the first time in literature, characterized as Slepian group codes (spherical codes) and Quadratic Residues codes, respectively
Publicado em: 2005
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6. (Pré-) álgebra: introduzindo os números inteiros negativos
This research is mainly concerned with the convenience and viability of introducing nine-year-old students to the study of the integers and of (pre-)Algebra. We begin with the integers and use their additive structure to model and solve additive problems, with special attention to the problems proposed by Vergnaud in 1976. The point here is to show that stud
Publicado em: 2002
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7. The cyclotomic trace and the K-theoretic analogue of Novikov's conjecture
A trace construction, the cyclotomic trace, is given. It associates to algebraic K-theory of a group ring, or better to Waldhausen's A-theory, equivariant stable homotopy classes of the free-loop space of its classifying space. The cyclotomic trace detects the Borel classes in algebraic K-theory of the integers. It is used to prove, for a wide class of group
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8. Algebraic aspects of the computably enumerable degrees.
A set A of nonnegative integers is computably enumerable (c.e.), also called recursively enumerable (r.e.), if there is a computable method to list its elements. The class of sets B which contain the same information as A under Turing computability (
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9. Post's program and incomplete recursively enumerable sets.
A set A of nonnegative integers is recursively enumerable (r.e.) if A can be computably listed. It is shown that there is a first-order property, Q(X), definable in E, the lattice of r.e. sets under inclusion, such that (i) if A is any r.e. set satisfying Q(A) then A is nonrecursive and Turing incomplete and (ii) there exists an r.e. set A satisfying Q(A). T
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10. On some applications of diophantine approximations
Siegel's results [Siegel, C. L. (1929) Abh. Preuss. Akad. Wiss. Phys.-Math. Kl. 1] on the transcendence and algebraic independence of values of E-functions are refined to obtain the best possible bound for the measures of irrationality and linear independence of values of arbitrary E-functions at rational points. Our results show that values of E-functions a