Results 51 to 60 of about 102 (92)

Approximating good simultaneous Diophantine approximations is almost NP-hard [PDF]

, 1996
Given a real vector α=(α1,..., α d ) and a real number e>0 a good Diophantine approximation to α is a number Q such that ∥Qα mod ℤ∥∞ ≤e, where ∥ · ∥∞ denotes the l∞-norm ∥x∥t8 ≔ max1 ≤i≤d ¦ xi¦ for x=(x1,..., xd).
Rössner, Carsten, Seifert, Jean-Pierre
openaire   +1 more source

Strong characterizing sequences in simultaneous diophantine approximation

Journal of Number Theory, 2003
In this paper, it is proved that: if \(1,\alpha_1,\dots, \alpha_t\in\mathbb{R}\) are linearly independent over the rationals, there is a subset \(A\subset\mathbb{N}\), \(| A|=\infty\), such that \(\sum_{n\in A}\| n\beta\|\) is finite if and only if \(\beta\in G\), the group generated by \(1,\alpha_1,\dots, \alpha_t\).
Biró, András, T. Sós, Vera
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Unification of the Nature's Complexities via a Matrix Permanent-Critical Phenomena, Fractals, Quantum Computing, ♯P-Complexity. [PDF]

Entropy (Basel), 2020
Kocharovsky V, Kocharovsky V, Tarasov S.
europepmc   +1 more source

Robust and efficient coding with grid cells. [PDF]

PLoS Comput Biol, 2018
Vágó L, Ujfalussy BB.
europepmc   +1 more source

Lévy-Khintchin Theorem for best simultaneous Diophantine approximations

Annales Scientifiques de l'École Normale Supérieure
We extend two results about the ordinary continued fraction expansion to best simultaneous Diophantine approximations of vectors or matrices. The first is Levy-Khintchin Theorem about the almost sure growth rate of the denominators of the convergents. The second is a Theorem of Bosma, Hendrik and Wiedijk about the almost sure limit distribution of the ...
Cheung, Yitwah, Chevallier, Nicolas
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On applications of diophantine approximations. [PDF]

Proc Natl Acad Sci U S A, 1984
Chudnovsky GV.
europepmc   +1 more source

The computation of classical constants. [PDF]

Proc Natl Acad Sci U S A, 1989
Chudnovsky DV, Chudnovsky GV.
europepmc   +1 more source

Rational approximations to solutions of linear differential equations. [PDF]

Proc Natl Acad Sci U S A, 1983
Chudnovsky DV, Chudnovsky GV.
europepmc   +1 more source

Asymptotic diophantine approximations. [PDF]

Proc Natl Acad Sci U S A, 1966
Lang S.
europepmc   +1 more source

On estimating the constant of simultaneous Diophantine approximation

, 2018
The paper is devoted to the problem of estimating the constant of the best Diophantine approximations. The estimates of lower bound $ C_n $ for $ n = 5 $ and $ n = 6 $ was improved. The first chapter gives an overview of the history of estimates of the constant of the best Diophantine approximations.
openaire   +2 more sources