Results 21 to 30 of about 1,187,035 (128)
ON THE LITTLEWOOD CONJECTURE IN SIMULTANEOUS DIOPHANTINE APPROXIMATION [PDF]
Journal of the London Mathematical Society, 2006 For any given real number $α$ with bounded partial quotients, we construct explicitly continuum many real numbers $β$ with bounded partial quotients for which the pair $(α, β)$ satisfies a strong form of the Littlewood conjecture. Our proof is elementary and rests on the basic theory of continued fractions.
Adamczewski, Boris, Bugeaud, Yann
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New Cryptanalytic Attack on RSA Modulus N = pq Using Small Prime Difference Method
Cryptography, 2018 This paper presents new short decryption exponent attacks on RSA, which successfully leads to the factorization of RSA modulus N = p q in polynomial time. The paper has two parts.
Muhammad Rezal Kamel Ariffin +3 more
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An equivalence principle between polynomial and simultaneous Diophantine approximation
, 2020 Mahler partitioned the real numbers into S, T and U-numbers subject to the growth of the sequence of Diophantine exponents (w(n)(zeta))(n >= 1) associated to a real number zeta. Koksma introduced a similar classification that turned out to be equivalent.
Schleischitz, Johannes
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A note on weighted simultaneous Diophantine approximation on manifolds [PDF]
, 2022 This is the final version. Available on open access from the Université de Bordeaux via the DOI in this recordIn this note we present an improvement to a recent result due to Beresnevich, Levesley, and Ward (2021) pertaining to weighted simultaneous ...
Allen, Demi +5 more
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Diophantine approximation in Banach spaces [PDF]
, 2014 In this paper, we extend the theory of simultaneous Diophantine approximation to infinite dimensions. Moreover, we discuss Dirichlet-type theorems in a very general framework and define what it means for such a theorem to be optimal.
Urbański, Mariusz +2 more
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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
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On simultaneous inhomogeneous Diophantine approximation [PDF]
Acta Arithmetica, 2006 In this paper, the authors study inhomogeneous problems in metrical Diophantine approximation. For a tuple \(\underline{\alpha} = (\alpha_1, \dots, \alpha_k) \in {\mathbb R}^k\) and real numbers \(v,w>0\), let \({\mathcal V}_v(\underline{\alpha})\) denote the set of \(\xi \in {\mathbb R}\) for which there is a \(c > 0\) such that the inequality ...
Bugeaud, Yann, Chevallier, Nicolas
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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.
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Fourier Expansion‐Based Approach to the Parameter Space of Classical Systems
Annalen der Physik, Volume 538, Issue 7, July 2026.ABSTRACT We propose a new approach to compute the classical metric tensor (CMT) and the Hannay curvature using Fourier series expansions in action‐angle variables. This approach circumvents the need for complex time‐domain integrals or the construction of generating functions, replacing them with algebraic combinations of Fourier coefficients. We prove
Marcos J. Hernández +3 more
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Energy Science &Engineering, Volume 14, Issue 7, Page 3250-3271, July 2026.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