Results 41 to 50 of about 10,492,721 (271)
Constructions of Dense Lattices over Number Fields
Trends in Computational and Applied Mathematics, 2020 In this work, we present constructions of algebraic lattices in Euclidean space with optimal center density in dimensions 2,3,4,5,6,8 and 12, which are rotated versions of the lattices Lambda_n, for n =2,3,4,5,6,8 and K_12.
Antonio A. Andrade +3 more
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Visual and Symbolic Representations as Components of Algebraic Reasoning
Journal of Numerical Cognition, 2023 Sixty (35 girls) ninth graders were assessed on measures of algebraic reasoning and usage of visual and symbolic representations (with a prompt for visual use) to solve equations and inequalities.
Zehra E. Ünal +4 more
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Kummer theory for number fields and the reductions of algebraic numbers
International Journal of Number Theory, 2019 For all number fields the failure of maximality for the Kummer extensions is bounded in a very strong sense. We give a direct proof (without relying on the Bashmakov–Ribet method) of the fact that if [Formula: see text] is a finitely generated and ...
Antonella Perucca, Pietro Sgobba
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Polynomials Generating Maximal Real Subfields of Circular Fields [PDF]
Учёные записки Казанского университета: Серия Физико-математические науки, 2016 We have constructed recurrence formulas for polynomials qn(x) ɕ Q[x], any root of which generates the maximal real subfield of circular field K2n. It has been shown that all real subfields of fixed field K2n can be described by using polynomial qn(x) and
I.G. Galyautdinov, E.E. Lavrentyeva
doaj
The dual fuzzy matrix equations: Extended solution, algebraic solution and solution
AIMS Mathematics, 2023 In this paper, we propose a direct method to solve the dual fuzzy matrix equation of the form $ \mathbf{A}\widetilde{\mathbf{X}}+\widetilde{\mathbf{B}} = \mathbf{C}\widetilde{\mathbf{X}}+\widetilde{\mathbf{D}} $ with $ \mathbf{A} $, $ \mathbf{C ...
Zengtai Gong , Jun Wu, Kun Liu
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On the approximation of algebraic numbers by algebraic integers [PDF]
Journal of the Australian Mathematical Society, 1963 In his Topics in Number Theory, vol. 2, chapter 2 (Reading, Mass., 1956) W. J. LeVeque proved an important generalisation of Roth's theorem (K. F. Roth, Mathematika 2,1955, 1—20).Let ξ be a fixed algebraic number, σ a positive constant, and K an algebraic number field of degree n.
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Distribution of algebraic numbers [PDF]
Journal für die reine und angewandte Mathematik (Crelles Journal), 2011 Schur studied limits of the arithmetic means $A_n$ of zeros for polynomials of degree $n$ with integer coefficients and simple zeros in the closed unit disk. If the leading coefficients are bounded, Schur proved that $\limsup_{n\to\infty} |A_n| \le 1-\sqrt{e}/2.$ We show that $A_n \to 0$, and estimate the rate of convergence by generalizing the Erd s ...
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The number of connected components of certain real algebraic curves
International Journal of Mathematics and Mathematical Sciences, 2001 For an integer n≥2, let p(z)=∏k=1n(z−αk) and q(z)=∏k=1n(z−βk), where αk,βk are real. We find the number of connected components of the real algebraic curve {(x,y)∈ℝ2:|p(x+iy)|−|q(x+iy)|=0} for some αk and βk.
Seon-Hong Kim
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An Example of Two-Fold Fuzzy Algebras Based On Neutrosophic Real Numbers [PDF]
Neutrosophic Sets and SystemsThis paper is dedicated to defining and studying for the first time a two-fold algebra over the neutrosophic real number ring by merging the fuzzy set mapping with the algebraic operations of the neutrosophic real number ring.
Abdallah Shihadeh +5 more
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Gr\"obner Bases over Algebraic Number Fields
, 2015 Although Buchberger's algorithm, in theory, allows us to compute Gr\"obner bases over any field, in practice, however, the computational efficiency depends on the arithmetic of the ground field.
Boku, Dereje Kifle +3 more
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