Results 91 to 100 of about 22,960 (196)
Exact local distribution of the absolutely continuous spectral measure
Proceedings of the London Mathematical Society, Volume 132, Issue 4, April 2026.Abstract It is well‐established that the spectral measure for one‐frequency Schrödinger operators with Diophantine frequencies exhibits optimal 1/2$1/2$‐Hölder continuity within the absolutely continuous spectrum (Avila and Jitomirskaya, Commun. Math. Phys. 301 (2011), 563–581).
Xianzhe Li, Jiangong You, Qi Zhou
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A note on Erdös-Diophantine graphs and Diophantine carpets [PDF]
, 2005 A Diophantine figure is a set of points on the integer grid $\mathbb{Z}^{2}$ where all mutual Euclidean distances are integers. We also speak of Diophantine graphs. In this language a Diophantine figure is a complete Diophantine graph.
Kohnert, Axel, Kurz, Sascha
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Journal of Geophysical Research: Space Physics, Volume 131, Issue 3, March 2026.Abstract The wave telescope is an analysis technique for multi‐point spacecraft data that estimates power spectra in reciprocal position space (k $k$‐space). It has been used to reveal the spatial properties of waves and fluctuations in space plasmas. Originally designed as an analysis tool for 4 spacecraft constellations, new multi‐scale missions such
L. Schulz +7 more
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Diophantine sets over algebraic integer rings. II [PDF]
Transactions of the American Mathematical Society, 1980 We prove that Z is diophantine over the ring of algebraic integers in any totally real number field or quadratic extension of a totally real number field.
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Applications of AG-Groupoids in Decision-Making via Linear Diophantine Fuzzy Sets
Discrete Dynamics in Nature and Society, 2023 In this paper, we investigated the notion of a linear Diophantine fuzzy set (LDFS) by using the concept of a score function to build the LDF-score left (right) ideals and LDF-score (0,2)-ideals in an AG-groupoid.
Faisal Yousafzai +4 more
doaj +1 more source
, 2009 A Diophantine $m$-tuple is a set $A$ of $m$ positive integers such that $ab+1$ is a perfect square for every pair $a,b$ of distinct elements of $A$. We derive an asymptotic formula for the number of Diophantine quadruples whose elements are bounded by $x$
Martin, Greg, Sitar, Scott
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Linear Diophantine equations and conjugator length in 2‐step nilpotent groups
Bulletin of the London Mathematical Society, Volume 58, Issue 3, March 2026.Abstract We establish upper bounds on the lengths of minimal conjugators in 2‐step nilpotent groups. These bounds exploit the existence of small integral solutions to systems of linear Diophantine equations. We prove that in some cases these bounds are sharp.
M. R. Bridson, T. R. Riley
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Arithmetic progressions at the Journal of the LMS
Journal of the London Mathematical Society, Volume 113, Issue 3, March 2026.Abstract We discuss the papers P. Erdős and P. Turán, On some sequences of integers, J. London Math. Soc. (1) 11 (1936), 261–264 and K. F. Roth, On certain sets of integers, J. London Math. Soc. (1) 28 (1953), 104–109, both foundational papers in the study of arithmetic progressions in sets of integers, and their subsequent influence.
Ben Green
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Diophantine sets in general are Cantor sets
, 2020 Let $ \in(0;\frac{1}{2}), \geq 1$ and define the "$ , $ Diophantine set" as: $$D_{ , }:=\{ \in (0;1): ||q ||\geq\frac {q^ }\quad\forall q\in\Bbb{N}\},\qquad||x||:=\inf_{p\in\Bbb{Z}}|x-p|. $$ In this paper we study the topology of these sets and we show that, for large $ $ and for almost all $ >0$, $D_{ , }$ is a Cantor set.
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Diophantine Approximation Properties of Certain Infinite Sets [PDF]
Transactions of the American Mathematical Society, 1983 We exhibit various infinite sets of reals whose finite subsets do not have good simultaneous rational approximations. In particular there is an infinite set such that each finite subset is "badly approximable" in the sense that Dirichlet’s theorem is best possible up to a multiplicative constant.
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