Results 41 to 50 of about 52,649 (219)
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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On the algebraic numbers computable by some generalized Ehrenfest urns [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 This article deals with some stochastic population protocols, motivated by theoretical aspects of distributed computing. We modelize the problem by a large urn of black and white balls from which at every time unit a fixed number of balls are drawn and ...
Marie Albenque, Lucas Gerin
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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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On the approximation to algebraic numbers by algebraic numbers
Glasnik matematički, 2009 Let n be a positive integer. Let ξ be an algebraic real number of degree greater than n. It follows from a deep result of W. M. Schmidt that, for every positive real number ε, there are infinitely many algebraic numbers α of degree at most n such that |ξ - α| < H(α)-n - 1 + ε, where H(α) denotes the naive height of α.
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On algebraic approximations of certain algebraic numbers
Journal of Number Theory, 2003 The main result of the present paper consists of an effective improvement on Liouville's bound for the approximations by rational numbers to algebraic numbers of a special type. Namely, the author considers \(n\)-th roots of imaginary quadratic irrationals.
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Counting rational points on algebraic varieties [PDF]
, 2006 For any N ≥ 2, let Z ⊂ ℙN be a geometrically integral algebraic variety of degree d. This article is concerned with the number Nz(B) of ℚ-rational points on Z which have height at most B. For any ε > 0, we establish the estimate NZ(B) = O d,ε,N(Bdim Z+ε),
Heath-Brown, D. R. +9 more
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An Upper Bound of the Bezout Number for Piecewise Algebraic Curves over a Rectangular Partition
International Journal of Mathematics and Mathematical Sciences, 2012 A piecewise algebraic curve is a curve defined by the zero set of a bivariate spline function. Given two bivariate spline spaces (Δ) over a domain D with a partition Δ, the Bezout number BN(m,r;n,t;Δ) is defined as the maximum finite number of the ...
Feng-Gong Lang, Xiao-Ping Xu
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Algebraic Properties of Chromatic Polynomials and Their Roots [PDF]
, 2015 In this thesis we examine chromatic polynomials from the viewpoint of algebraic number theory. We relate algebraic properties of chromatic polynomials of graphs to structural properties of those graphs for some simple families of graphs.
Gilmore, Hamish Julian
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Lower bounds for the normalized height and non-dense subsets of varieties in an abelian variety [PDF]
, 2010 This work is the third part of a series of papers. In the first two we considered curves and varieties in a power of an elliptic curve. Here we deal with subvarieties of an abelian variety in general.
Viada, Evelina
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