Results 21 to 30 of about 3,571 (122)
Simultaneous diophantine approximation with square-free numbers [PDF]
Acta Arithmetica, 1993 A set \(\alpha_ 1,\dots,\alpha_ s\) of real numbers is said to be weakly compatible if \(\sum_{j=1}^ s \ell_ j \alpha_ j=u/v\) with \((u,v)=1\) implies that \(v\) is square-free. This condition is necessary and sufficient for \[ \liminf_{\mu^ 2(n)=1} \max_ j\|\alpha_ j n\|=0, \] where \(\|\cdot\|\) denotes the fractional part, as usual.
Baker, Roger C. +2 more
openaire +3 more sources
Successful cryptanalysis on RSA type modulus N=p2q
e-Prime: Advances in Electrical Engineering, Electronics and EnergyAs internet technology advances and our interactions increasingly take place online, cryptography emerges as a valuable tool to address security concerns. Cryptography serves as a means to guarantee the protection of privacy and confidential information,
Normahirah Nek Abd Rahman
doaj +1 more source
Zero-one laws in simultaneous and multiplicative Diophantine approximation
, 2012 Answering two questions of Beresnevich and Velani, we develop zero-one laws in both simultaneous and multiplicative Diophantine approximation. Our proofs rely on a Cassels-Gallagher type theorem as well as a higher-dimensional analogue of the cross ...
Beresnevich +5 more
core +1 more source
Energy Science &Engineering, EarlyView.This study introduces bipolar q‐fractional fuzzy sets and new aggregation operators to support renewable energy selection under uncertainty. The proposed decision‐making framework effectively integrates positive and negative evaluations, ensuring consistent ranking and robust performance, as demonstrated through practical analysis and comparative ...
Sagvan Y. Musa +3 more
wiley +1 more source
Simultaneous diophantine approximation of rational numbers [PDF]
Acta Arithmetica, 1972 For any real number \(x\), let \(\Vert x\Vert\) denote the distance from \(x\) to the nearest integer. Let \(n\) be any positive integer and let \(\sigma = (s_1, \ldots, s_n)\) denote an arbitrary point in the set \(S^n\) of \(n\)-dimensional points all of whose coordinates are rational noninteger numbers.
openaire +2 more sources
GCD inequalities arising from codimension‐2 blowups
Bulletin of the London Mathematical Society, Volume 58, Issue 4, April 2026.Abstract Assuming a deep Diophantine geometry conjecture by Vojta, Silverman proved an inequality giving an upper bound for the greatest common divisor (GCD). In this paper, we unconditionally prove a weaker version of this inequality. The main ingredient is the Ru–Vojta theory, which provides an efficient method of using Schmidt subspace theorem.
Yu Yasufuku
wiley +1 more source
Vertical shift and simultaneous Diophantine approximation on polynomial curves
, 2013 The Hausdorff dimension of the set of simultaneously tau well approximable points lying on a curve defined by a polynomial P(X)+alpha, where P(X) is a polynomial with integer coefficients and alpha is in R, is studied when tau is larger than the degree ...
Adiceam, Faustin
core +2 more sources
Some bounds related to the 2‐adic Littlewood conjecture
Mathematika, Volume 72, Issue 2, April 2026.Abstract For every irrational real α$\alpha$, let M(α)=supn⩾1an(α)$M(\alpha) = \sup _{n\geqslant 1} a_n(\alpha)$ denote the largest partial quotient in its continued fraction expansion (or ∞$\infty$, if unbounded). The 2‐adic Littlewood conjecture (2LC) can be stated as follows: There exists no irrational α$\alpha$ such that M(2kα)$M(2^k \alpha)$ is ...
Dinis Vitorino, Ingrid Vukusic
wiley +1 more source
Low-discrepancy sequences for piecewise smooth functions on the two-dimensional torus
, 2015 We produce explicit low-discrepancy infinite sequences which can be used to approximate the integral of a smooth periodic function restricted to a convex domain with positive curvature in R^2.
Brandolini, Luca +3 more
core +1 more source
Mathematika, Volume 72, Issue 2, April 2026.Abstract In 2019 Kleinbock and Wadleigh proved a “zero‐one law” for uniform inhomogeneous Diophantine approximations. We generalize this statement to arbitrary weight functions and establish a new and simple proof of this statement, based on the transference principle. We also give a complete description of the sets of g$g$‐Dirichlet pairs with a fixed
Vasiliy Neckrasov
wiley +1 more source