Results 111 to 120 of about 157,707 (146)
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Mathematics of the USSR-Izvestiya, 1977
A new estimate of the solutions of the generalized Thue-Mahler equation is derived, which explicitly exhibits the influence of all fundamental parameters of the equation on the magnitude of the solutions. Also, an effective power sharpening is given of "Liouville's inequality" relating to the approximation of algebraic numbers by algebraic numbers of a
Kotov, S. V., Sprindzuk, V. G.
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A new estimate of the solutions of the generalized Thue-Mahler equation is derived, which explicitly exhibits the influence of all fundamental parameters of the equation on the magnitude of the solutions. Also, an effective power sharpening is given of "Liouville's inequality" relating to the approximation of algebraic numbers by algebraic numbers of a
Kotov, S. V., Sprindzuk, V. G.
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The Best Approximation of Algebraic Numbers by Multidimensional Continued Fractions
Journal of Mathematical Sciences, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Approximation by Algebraic Numbers
2004Algebraic numbers can approximate and classify any real number. Here, the author gathers together results about such approximations and classifications. Written for a broad audience, the book is accessible and self-contained, with complete and detailed proofs.
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Exact polynomial factorization by approximate high degree algebraic numbers
Proceedings of the 2009 conference on Symbolic numeric computation, 2009For factoring polynomials in two variables with rational coefficients, an algorithm using transcendental evaluation was presented by Hulst and Lenstra. In their algorithm, transcendence measure was computed. However, a constant c is necessary to compute the transcendence measure.
Jing-wei Chen +3 more
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Approximation of a fuzzy number by a fuzzy element of fuzzy algebra
2020 IEEE 6th International Conference on Optimization and Applications (ICOA), 2020In the present work, the fuzzy algebra is defined, a condition of approximation is presented and we finished by an application to solve a fuzzy differential equation.
I. Bakhadach +4 more
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Diophantine approximation by conjugate algebraic numbers
2013In 1969, Davenport and Schmidt provided upper bounds for the approximation of a real number by algebraic integers. Their novel approach was based on the geometry of numbers and involved the duality for convex bodies. In the present thesis we study the approximation of a real number by conjugate algebraic numbers.
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On the measure of approximation of the number π by algebraic numbers
Mathematical Notes, 1999By means of the method of the Laurent interpolation determinant, it is proved that, if ζ is an algebraic number, the real numbersd andL satisfy the inequalitiesd≥degζ,L≥L(ζ), andL≥3, and the numberd is sufficiently large, then the inequality $$|\pi - \varsigma | \geqslant \exp (
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Rational approximation to algebraic numbers of small height: the Diophantine equation |axn - byn|= 1
Journal für die reine und angewandte Mathematik (Crelles Journal), 2001The main tool of this long and important work is the \textit{multidimensional hypergeometric method} for rational and algebraic approximation of certain algebraic numbers, which was considered first by K.~Mahler and sharpened by G.~Chudnovsky. Here the author obtains explicit results. His most spectacular result is the following definitive Theorem. Let
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Integrative oncology: Addressing the global challenges of cancer prevention and treatment
Ca-A Cancer Journal for Clinicians, 2022Jun J Mao,, Msce +2 more
exaly
Approximations of Algebraic Numbers by Rationals: A Theorem of Thue
2003We begin with some preliminaries on algebraic numbers. Let α be an algebraic number. Then we observe that α satisfies the polynomial of minimal degree such that it has relatively prime integer coefficients and the leading coefficient positive. This is the minimal polynomial of α. The degree of this polynomial is called the degree of α.
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