Results 21 to 30 of about 13,363 (161)

Simultaneous diophantine approximation [PDF]

Bulletin of the Australian Mathematical Society, 1972
AbstractUsing a method suggested by E. S. Barnes, it is shown that the simultaneous inequalities r(p — αr)2 < c, r(q — βr)2 < c have an infinity of integral solutions p, q, r (with r > 0), for arbitrary irrationals α and β, provided that c > 1/2.6394.
openaire   +3 more sources

Fibonacci Numbers with a Prescribed Block of Digits

Mathematics, 2020
In this paper, we prove that F 22 = 17711 is the largest Fibonacci number whose decimal expansion is of the form a b … b c … c . The proof uses lower bounds for linear forms in three logarithms of algebraic numbers and some tools from ...
Pavel Trojovský
doaj   +1 more source

Failure of strong approximation on an affine cone [PDF]

, 2018
We use the Brauer-Manin obstruction to strong approximation on a punctured affine cone to explain a curious property of coprime integer solutions to a homogeneous Diophantine equation.Comment: Changes following referee's ...
Bright, Martin, Kok, Ivo
core   +3 more sources

Quasiperiodic Patterns of the Complex Dimensions of Nonlattice Self-Similar Strings, via the LLL Algorithm

Mathematics, 2021
The Lattice String Approximation algorithm (or LSA algorithm) of M. L. Lapidus and M. van Frankenhuijsen is a procedure that approximates the complex dimensions of a nonlattice self-similar fractal string by the complex dimensions of a lattice self ...
Michel L. Lapidus, Machiel van Frankenhuijsen, Edward K. Voskanian   +2 more
doaj   +1 more source

How smooth is quantum complexity?

Journal of High Energy Physics, 2021
The “quantum complexity” of a unitary operator measures the difficulty of its construction from a set of elementary quantum gates. While the notion of quantum complexity was first introduced as a quantum generalization of the classical computational ...
Vir B. Bulchandani, S. L. Sondhi
doaj   +1 more source

Location of approximations of a Markoff theorem

International Journal of Mathematics and Mathematical Sciences, 1990
Relative to the first two theorems of the well known Markoff Chain (J.W.S. Cassels, “An introduction to diophantine approximation” approximations are well located.
K. C. Prasad, M. Lari, P. Singh
doaj   +1 more source

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
doaj   +1 more source

A new proof of Nishioka’s theorem in Mahler’s method

Comptes Rendus. Mathématique, 2023
In a recent work [3], the authors established new results about general linear Mahler systems in several variables from the perspective of transcendental number theory, such as a multivariate extension of Nishioka’s theorem.
Adamczewski, Boris, Faverjon, Colin
doaj   +1 more source

Factoring the Modulus of Type N = p²q by Finding Small Solutions of the Equation er − (Ns + t) = αp² + βq²

Mathematics, 2021
The modulus of type N=p2q is often used in many variants of factoring-based cryptosystems due to its ability to fasten the decryption process. Faster decryption is suitable for securing small devices in the Internet of Things (IoT) environment or ...
Muhammad Asyraf Asbullah, Normahirah Nek Abd Rahman, Muhammad Rezal Kamel Ariffin, Nur Raidah Salim   +3 more
doaj   +1 more source

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
doaj   +1 more source