Results 51 to 60 of about 618,965 (192)
On pairs of cubic Diophantine inequalities
Mathematika, 1991 \textit{H. Davenport} and \textit{H. Heilbronn} [J. Lond. Math. Soc. 21, 185--193 (1946; Zbl 0060.11914)] proved that if \(Q({\mathbf x})=\sum^5_{j=1}\lambda_jx^2_j\) is an indefinite quadratic form with real coefficients \(\lambda_j\), such that at least one of the ratios \(\lambda_i/\lambda_j\) is irrational, then for any \(\varepsilon>0\) there ...
Brüdern, Jörg, Cook, R. J.
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On an Erdős similarity problem in the large
Bulletin of the London Mathematical Society, Volume 57, Issue 6, Page 1801-1818, June 2025.Abstract In a recent paper, Kolountzakis and Papageorgiou ask if for every ε∈(0,1]$\epsilon \in (0,1]$, there exists a set S⊆R$S \subseteq \mathbb {R}$ such that |S∩I|⩾1−ε$\vert S \cap I\vert \geqslant 1 - \epsilon$ for every interval I⊂R$I \subset \mathbb {R}$ with unit length, but that does not contain any affine copy of a given increasing sequence ...
Xiang Gao +2 more
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Local spectral estimates and quantitative weak mixing for substitution Z${\mathbb {Z}}$‐actions
Journal of the London Mathematical Society, Volume 111, Issue 4, April 2025.Abstract The paper investigates Hölder and log‐Hölder regularity of spectral measures for weakly mixing substitutions and the related question of quantitative weak mixing. It is assumed that the substitution is primitive, aperiodic, and its substitution matrix is irreducible over the rationals.
Alexander I. Bufetov +2 more
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Lattices in function fields and applications
Mathematika, Volume 71, Issue 2, April 2025.Abstract In recent decades, the use of ideas from Minkowski's Geometry of Numbers has gained recognition as a helpful tool in bounding the number of solutions to modular congruences with variables from short intervals. In 1941, Mahler introduced an analogue to the Geometry of Numbers in function fields over finite fields.
Christian Bagshaw, Bryce Kerr
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A classification of infinite staircases for Hirzebruch surfaces
Journal of Topology, Volume 18, Issue 1, March 2025.Abstract The ellipsoid embedding function of a symplectic manifold gives the smallest amount by which the symplectic form must be scaled in order for a standard ellipsoid of the given eccentricity to embed symplectically into the manifold. It was first computed for the standard four‐ball (or equivalently, the complex projective plane) by McDuff and ...
Nicki Magill +2 more
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On the Number of Nonnegative Solutions to the Inequality a1 +....ar < n [PDF]
, 2010 In this paper, we present a simple and fast method for counting the number of nonnegative integer solutions to the equality a1x1+a2x2+: : :+arxr = n where a1; a2; :::; ar and n are positive integers.
Farzaneh , A. +3 more
core
On Sequences With Exponentially Distributed Gaps
Random Structures &Algorithms, Volume 66, Issue 1, January 2025.ABSTRACT It is well known that a sequence (xn)n∈ℕ⊆[0,1]$$ {\left({x}_n\right)}_{n\in \mathbb{N}}\subseteq \left[0,1\right] $$ which has Poissonian correlations of all orders necessarily has exponentially distributed nearest‐neighbor gaps. It is natural to ask whether this implication also holds in the other direction, that is, whether a sequence with ...
Christoph Aistleitner +2 more
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Diophantine Inequalities for Polynomial Rings
Journal of Number Theory, 1999 The author studies the Hardy-Littlewood method for the Laurent series field \(\mathbb F_q ((1/T))\) over the finite field \(\mathbb F_q\) with \(q\) elements. He shows that if \(\lambda_1\), \(\lambda_2\), \(\lambda_3\) are nonzero elements in \(\mathbb F_q ((1/T))\) satisfying \(\lambda_1/\lambda_2\not\in \mathbb F_q(T)\) and \(\text{sgn} (\lambda_1)+
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The Journal of Engineering, Volume 2025, Issue 1, January/December 2025.The article shows how novel general two‐degree‐of‐freedom feedback loop factorisation for single‐input single‐output systems is applied to oscillating plants with time delay, periodic changes of controlled plant parameters and astatism using the D‐K iteration and algebraic approach.
Marek Dlapa
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Optimality of two inequalities for exponents of Diophantine approximation [PDF]
Journal of Number Theory, 2021 J. Schleischitz
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