Results 1 to 10 of about 74 (72)
Unconventional height functions in simultaneous Diophantine approximation. [PDF]
Mon Hefte Math, 2017 Simultaneous Diophantine approximation is concerned with the approximation of a point $\mathbf x\in\mathbb R^d$ by points $\mathbf r\in\mathbb Q^d$, with a view towards jointly minimizing the quantities $\|\mathbf x - \mathbf r\|$ and $H(\mathbf r)$. Here $H(\mathbf r)$ is the so-called "standard height" of the rational point $\mathbf r$. In this paper
Fishman L, Simmons D.
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Simultaneous p-adic Diophantine approximation [PDF]
Mathematical Proceedings of the Cambridge Philosophical Society, 2023 AbstractThe aim of this paper is to develop the theory of weighted Diophantine approximation of rational numbers to p-adic numbers. Firstly, we establish complete analogues of Khintchine’s theorem, the Duffin–Schaeffer theorem and the Jarník–Besicovitch theorem for ‘weighted’ simultaneous Diophantine approximation in the p-adic case.
Beresnevich, Victor +2 more
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Mathematics, 2021 The Lattice String Approximation algorithm (or LSA algorithm) of M. L. Lapidus and M. van Frankenhuijsen is a procedure that approximates the complex dimensions of a nonlattice self-similar fractal string by the complex dimensions of a lattice self ...
Michel L. Lapidus +2 more
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Mathematics, 2021 The modulus of type N=p2q is often used in many variants of factoring-based cryptosystems due to its ability to fasten the decryption process. Faster decryption is suitable for securing small devices in the Internet of Things (IoT) environment or ...
Muhammad Asyraf Asbullah +3 more
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IET Information Security, 2021 A simultaneous Diophantine approximation (SDA) algorithm takes instances of the partial approximate common divisor (PACD) problem as input and outputs a solution.
Wonhee Cho, Jiseung Kim, Changmin Lee
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RESTRICTED SIMULTANEOUS DIOPHANTINE APPROXIMATION [PDF]
Mathematika, 2016 We study the problem of Diophantine approximation on lines in $\mathbb{R}^d$ under certain primality restrictions.
Baier, Stephan, Ghosh, Anish
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Witnessing a Poincaré recurrence with Mathematica
Results in Physics, 2017 The often elusive Poincaré recurrence can be witnessed in a completely integrable system. For such systems, the problem of recurrence reduces to the classic mathematical problem of simultaneous Diophantine approximation of multiple numbers.
J.M. Zhang, Y. Liu
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Simultaneous Diophantine approximation
Duke Mathematical Journal, 1946 The simplest problems of Diophantine approximation relate to the approximation of a single irrational number 0 by rational numbers pjq, and the principal question is how small we can make the error 0 — pjq in relation to q for infinitely many approximations. It is well known that this question can be answered almost completely in terms of the continued
Davenport, H., Mahler, K.
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SIMULTANEOUS DIOPHANTINE APPROXIMATION ON POLYNOMIAL CURVES [PDF]
Mathematika, 2009 Let \(\psi: {\mathbb N} \rightarrow {\mathbb R}_+\) be a decreasing function tending to zero. A vector \(x \in {\mathbb R}^n\) is said to be simultaneously \(\psi\)-approximable if the inequality \[ | q x -p | < \psi(| q |) \] has infinitely many solutions \(q \in {\mathbb Z}\), \(p \in {\mathbb Z}^n\).
Budarina, Natalia +2 more
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PKCHD: Towards a Probabilistic Knapsack Public-Key Cryptosystem with High Density
Information, 2019 By introducing an easy knapsack-type problem, a probabilistic knapsack-type public key cryptosystem (PKCHD) is proposed. It uses a Chinese remainder theorem to disguise the easy knapsack sequence. Thence, to recover the trapdoor information, the implicit
Yuan Ping +4 more
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