Results 51 to 60 of about 565 (158)
Kripke on Gödel Incompleteness
Theoria, EarlyView.ABSTRACT This paper surveys six of Saul Kripke's highly creative ideas and results on Gödel incompleteness, from when he was an undergraduate to last publications. These include his extension of incompleteness from sentences to predicates, his model‐theoretic proof of incompleteness of arithmetic, his compelling analysis of incompleteness in terms of ...
Daniel Isaacson
wiley +1 more source
Real-world applications of number theory [PDF]
ریاضی و جامعهThe above abstract has been extracted by the translator from the original article (J. Klaška, Real-world applications of number theory, South Bohemia Mathematical Letters, 25 no.
Rahim Rahmati-Asghar
doaj +1 more source
Linear Recurrence Sequences in Diophantine Analysis [PDF]
, 2022 Diophantine analysis is an area of number theory concerned with finding integral solutions to polynomial equations defined over the rationals, or more generally over a number field.
Bellah, Elisa
core
Random Diophantine equations in the primes
Mathematika, Volume 72, Issue 3, July 2026.Abstract We consider equations of the form a1x1k+⋯+asxsk=0$a_{1}x_{1}^{k}+\cdots +a_{s}x_{s}^{k}=0$ where the variables xi$x_{i}$ are all taken to be primes. We define an analogue of the Hasse principle for solubility in the primes (which we call the prime Hasse principle), and prove that, whenever k⩾2$k\geqslant 2$, s⩾3k+2$s\geqslant 3k+2$, this holds
Philippa Holdridge
wiley +1 more source
Moderate Deviation Principles for Lacunary Trigonometric Sums
Mathematische Nachrichten, Volume 299, Issue 5, Page 1028-1044, May 2026.ABSTRACT Classical works of Kac, Salem, and Zygmund, and Erdős and Gál have shown that lacunary trigonometric sums despite their dependency structure behave in various ways like sums of independent and identically distributed random variables. For instance, they satisfy a central limit theorem (CLT) and a law of the iterated logarithm.
Joscha Prochno, Marta Strzelecka
wiley +1 more source
Solving a linear diophantine equation with lower and upper bounds on the variables
, 1998 We develop an algorithm for solving a linear diophantine equation with lower and upper bounds on the variables. The algorithm is based on lattice basis reduction, and first finds short vectors satisfying the diophantine equation.
Lenstra, A.K. +8 more
core +2 more sources
On the exceptional set in Littlewood's discrete conjecture
Bulletin of the London Mathematical Society, Volume 58, Issue 5, May 2026.Abstract We consider a discrete analogue of the well‐known Littlewood conjecture on Diophantine approximations and obtain a strong upper bound for the number of exceptional vectors in this conjecture.
I. D. Shkredov
wiley +1 more source
Unified linear time-invariant model predictive control for strong nonlinear chaotic systems
Nonlinear Analysis, 2016 It is well known that an alone linear controller is difficult to control a chaotic system, because intensive nonlinearities exist in such system. Meanwhile, depending closely on a precise mathematical modeling of the system and high computational ...
Yuan Zhang, Mingwei Sun, Zengqiang Chen
doaj +1 more source
, 2010 In the first chapter we have given some definations, theorems, lemmas on Elementary Number Theory. This brief discussion is useful for next discussion on the main topic.
Strnadová, Pavlína, Panda, Sagar
core
Double‐jump phase transition for the reverse Littlewood–Offord problem
Journal of the London Mathematical Society, Volume 113, Issue 5, May 2026.Abstract Erdős conjectured in 1945 that for any unit vectors v1,…,vn$v_1, \ldots, v_n$ in R2$\mathbb {R}^2$ and signs ε1,…,εn$\varepsilon _1, \ldots, \varepsilon _n$ taken independently and uniformly in {−1,1}$\lbrace -1,1\rbrace$, the random Rademacher sum σ=ε1v1+⋯+εnvn$\sigma = \varepsilon _1 v_1 + \cdots + \varepsilon _n v_n$ satisfies ∥σ∥2⩽1$\Vert \
Lawrence Hollom +2 more
wiley +1 more source