Results 21 to 30 of about 618,965 (192)
The integral part of a nonlinear form with a square, a cube and a biquadrate
Open Mathematics, 2020 In this paper, we show that if λ1,λ2,λ3{\lambda }_{1},{\lambda }_{2},{\lambda }_{3} are non-zero real numbers, and at least one of the numbers λ1,λ2,λ3{\lambda }_{1},{\lambda }_{2},{\lambda }_{3} is irrational, then the integer parts of λ1n12+λ2n23+λ3n34{
Ge Wenxu, Li Weiping, Zhao Feng
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Observation of vibrating systems at different time instants
Electronic Journal of Qualitative Theory of Differential Equations, 2014 In this paper, we obtain new observability inequalities for the vibrating string. This work was motivated by a recent paper of A. Szijártó and J.
Ambroise Vest
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Transference inequalities for multiplicative Diophantine exponents [PDF]
Proceedings of the Steklov Institute of Mathematics, 2010 In this paper we prove inequalities for multiplicative analogues of Diophantine exponents, similar to the ones known in the classical case. Particularly, we show that a matrix is badly approximable if and only if its transpose is badly approximable and establish some inequalities connecting multiplicative exponents with ordinary ones.
Oleg N. German
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Local Diophantine Nullstellen inequalities [PDF]
Journal of the American Mathematical Society, 1988 The main result of this paper is as follows. Let \(P_1,\ldots, P_n\) be polynomials of total degree at most \(D\) in \(x_1,\ldots,x_m\), with rational integer coefficients of absolute values at most \(H\).
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Diophantine transference inequalities: weighted, inhomogeneous, and intermediate exponents [PDF]
ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE, 2018 We extend the Khintchine transference inequalities, as well as a homogeneous-inhomogeneous transference inequality for lattices, due to Bugeaud and Laurent, to a weighted setting. We also provide applications to inhomogeneous Diophantine approximation on
Sam Chow +4 more
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An improved estimate for certain Diophantine inequalities [PDF]
Proceedings of the American Mathematical Society, 1980 Let λ 1 , … , λ 8 {\lambda _1}, \ldots ,{\lambda _8} be any nonzero real numbers such that not all λ j {\lambda _j} are of the same sign and not all ...
Ming Chit Liu +2 more
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Exponents of Diophantine Approximation and Sturmian Continued Fractions [PDF]
, 2004 Let x be a real number and let n be a positive integer. We define four exponents of Diophantine approximation, which complement the exponents w_n(x) and w_n^*(x) defined by Mahler and Koksma.
Bugeaud, Yann, Laurent, Michel
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Proportionally modular diophantine inequalities
Journal of Number Theory, 2003 The authors study the sets of nonnegative solutions of Diophantine inequalities of the form \(ax\) mod \(b \leq cx\) with \(a, b\) and \(c\) positive integers. These sets are numerical semigroups, which are investigated and characterized.
Rosales, J.C. +3 more
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Finiteness results for Diophantine triples with repdigit values [PDF]
, 2015 Let $g\ge 2$ be an integer and $\mathcal R_g\subset \mathbb N$ be the set of repdigits in base $g$. Let $\mathcal D_g$ be the set of Diophantine triples with values in $\mathcal R_g$; that is, $\mathcal D_g$ is the set of all triples $(a,b,c)\in \mathbb ...
Bérczes, Attila +3 more
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Quadratic Diophantine Inequalities
Journal of Number Theory, 2001 The theme of this paper is to investigate certain systems of Diophantine inequalities on real diagonal quadratic forms. First, let \(Q_1\) and \(Q_2\) be real diagonal quadratic forms in \(s\) variables, with \(s\geq 10\), and suppose that whenever \(\alpha\) and \(\beta\) are real numbers with \((\alpha,\beta)\neq(0,0)\), then the form \(\alpha Q_1 ...
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