Results 51 to 60 of about 1,187,035 (128)
GEOMETRIC THEOREMS, DIOPHANTINE EQUATIONS, AND ARITHMETIC FUNCTIONS [PDF]
, 2002 This book contains short notes or articles, as well as studies on several topics of Geometry and Number theory. The material is divided into ve chapters: Geometric theorems; Diophantine equations; Arithmetic functions; Divisibility properties of numbers ...
Sándor, József
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Combinatorics on number walls and the P(t)$P(t)$‐adic Littlewood conjecture
Mathematika, Volume 72, Issue 1, January 2026.Abstract In 2004, de Mathan and Teulié stated the p$p$‐adic Littlewood conjecture (p$p$‐LC) in analogy with the classical Littlewood conjecture. Let Fq$\mathbb {F}_q$ be a finite field P(t)$P(t)$ be an irreducible polynomial with coefficients in Fq$\mathbb {F}_q$. This paper deals with the analogue of p$p$‐LC over the ring of formal Laurent series over
Steven Robertson
wiley +1 more source
A Linear Diophantine Fuzzy Graph‐Theoretic Approach for Planar Dynamic Traffic Optimization
Applied Computational Intelligence and Soft Computing, Volume 2026, Issue 1, 2026.Dynamic urban traffic signal control systems face uncertainties such as fluctuating vehicle densities, unpredictable incidents, and varying driver behaviors, making precise decision‐making highly challenging. To address these complexities, fuzzy planar graphs have been employed for uncertainty modeling.
Waheed Ahmad Khan +5 more
wiley +1 more source
International Journal of Mathematics and Mathematical Sciences, Volume 2026, Issue 1, 2026.A linear Diophantine Z‐number Aczel–Alsina t‐norm operator is implemented for solving a linear Diophantine Z‐number problem, along with explaining its reliability, along with the solution derived. Some basic mathematical characteristics of the introduced operator, such as monotonicity, boundedness, and homogeneity, are rigorously deduced mathematically
Muhammad Umar Mirza +4 more
wiley +1 more source
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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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
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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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Simultaneous Diophantine Approximation and Asymptotic Formulae on Manifolds
Journal of Number Theory, 1996 Let \(\psi(q) \in \mathbb{N}\) for \(q=1, 2, 3, \dots\) be decreasing such that for some \(k \in \mathbb{N}\) the series \(\sum\psi(q)^k\) is divergent. As a slight variation of Khintchine's theorem on simultaneous diophantine approximation, it is known that, for almost all \((x_1, \dots, x_k) \in\mathbb{R}^k\) there are infinitely many solutions of ...
Dodson, M.M. +2 more
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Topological triple phase transition in non-Hermitian Floquet quasicrystals. [PDF]
Nature, 2022 Weidemann S +3 more
europepmc +1 more source
Diophantine approximation and special Liouville numbers [PDF]
, 2013 summary:This paper introduces some methods to determine the simultaneous approximation constants of a class of well approximable numbers $\zeta_{1},\zeta_{2},\ldots ,\zeta_{k}$.
Schleischitz, Johannes
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