Results 71 to 80 of about 2,483 (259)
Metrical Diophantine approximation for quaternions [PDF]
, 2014 Analogues of the classical theorems of Khintchine, Jarnik and Jarnik-Besicovitch in the metrical theory of Diophantine approximation are established for quaternions by applying results on the measure of general `lim sup ...
Everitt, Brent, Dodson, Maurice
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Witnessing a Poincaré recurrence with Mathematica
Results in Physics, 2017 The often elusive Poincaré recurrence can be witnessed in a completely integrable system. For such systems, the problem of recurrence reduces to the classic mathematical problem of simultaneous Diophantine approximation of multiple numbers.
J.M. Zhang, Y. Liu
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One Diophantine inequality with unlike powers of prime variables
Journal of Inequalities and Applications, 2016 In this paper, we show that if λ 1 $\lambda_{1}$ , λ 2 $\lambda_{2}$ , λ 3 $\lambda_{3}$ , λ 4 $\lambda _{4}$ , λ 5 $\lambda_{5}$ are nonzero real numbers not all of the same sign, η is real, 0 < σ < 1 720 ...
Wenxu Ge, Weiping Li
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Diophantine approximation and automorphic spectrum
, 2012 This paper establishes quantitative estimates on the rate of diophantine approximation in homogeneous varieties of semisimple algebraic groups. The estimates established generalize and improve previous ones, and in a number of important cases are shown ...
Nevo, Amos +5 more
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Diophantine approximation with one prime, two squares of primes and one kth power of a prime
Open Mathematics, 2021 Let ...
Gambini Alessandro
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Introduction to Diophantine Approximation
Formalized Mathematics, 2015 Abstract In this article we formalize some results of Diophantine approximation, i.e. the approximation of an irrational number by rationals. A typical example is finding an integer solution (x, y) of the inequality |xθ − y| ≤ 1/x, where 0 is a real number. First, we formalize some lemmas about continued fractions. Then we prove that the
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Simultaneous Diophantine approximation
Duke Mathematical Journal, 1946 The simplest problems of Diophantine approximation relate to the approximation of a single irrational number 0 by rational numbers pjq, and the principal question is how small we can make the error 0 — pjq in relation to q for infinitely many approximations. It is well known that this question can be answered almost completely in terms of the continued
Davenport, H., Mahler, K.
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Simultaneous Diophantine approximation on the circle and Hausdorff dimension [PDF]
, 2001 The functional relations between the coordinates of points on a manifold make the study of Diophantine approximation on manifolds much harder than the classical theory in which the variables are independent.
Dickinson, H. +3 more
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Energy Science &Engineering, EarlyView.This study introduces bipolar q‐fractional fuzzy sets and new aggregation operators to support renewable energy selection under uncertainty. The proposed decision‐making framework effectively integrates positive and negative evaluations, ensuring consistent ranking and robust performance, as demonstrated through practical analysis and comparative ...
Sagvan Y. Musa +3 more
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An extension of the mixed integer part of a nonlinear form
Journal of Inequalities and Applications, 2017 Our aim in this paper is to consider the integer part of a nonlinear form representing primes. We establish that if λ 1 , λ 2 , … , λ 8 $\lambda_{1},\lambda _{2},\ldots,\lambda_{8}$ are positive real numbers, at least one of the ratios λ i / λ j ...
Yunhan Wang, Jiani Mu
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