Results 41 to 50 of about 92,931 (194)

A number theoretical method for calculating high order correlation functions of the Tchebyscheff maps

四川大学学报. 自然科学版, 2022
Correlation functions play a key role in the statistical description of chaotic maps. The main concern of this paper is the calculation of correlation functions of the Tchebyscheff maps, which is traditionally handled by using the graph theoretical ...
ZHOU Xing-Wang
doaj  

On the Exponential Diophantine Equation 5x - 2.3y = z2

Annals of Pure and Applied Mathematics, 2022
In this article, we study and establish one theorem of the exponential Diophantine equation 2 5 2 3 x y − ⋅ = z where x y, and z are non-negative integers. The study reveals that the equation is solvable.
S. Thongnak, W. Chuayjan, T. Kaewong
semanticscholar   +1 more source

Small two-variable exponential Diophantine equations [PDF]

Mathematics of Computation, 1993
We examine exponential Diophantine equations of the form a b x = c d y + e a{b^x} = c{d^y} + e . Consider a ≤ 50 a \leq 50 , c ≤
openaire   +1 more source

Nonlinear-Adaptive Mathematical System Identification

Computation, 2017
By reversing paradigms that normally utilize mathematical models as the basis for nonlinear adaptive controllers, this article describes using the controller to serve as a novel computational approach for mathematical system identification.
Timothy Sands
doaj   +1 more source

On the exponential Diophantine equation $ (a(a-l)m^{2}+1)^{x}+(alm^{2}-1)^{y} = (am)^{z} $

AIMS Mathematics, 2022
Suppose that $ a $, $ l $, $ m $ are positive integers with $ a\equiv1\pmod2 $ and $ a^{2}m^{2}\equiv-2\pmod p $, where $ p $ is a prime factor of $ l $.
Jinyan He, Jiagui Luo, Shuanglin Fei
semanticscholar   +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

On the Diophantine Equation $(8r^2+1)^x+(r^2-1)^y=(3r)^z$ Regarding Terai's Conjecture

Communications in Advanced Mathematical Sciences
This study establishes that the sole positive integer solution to the exponential Diophantine equation $(8r^2+1)^x+(r^2-1)^y=(3r)^z$ is $(x,y,z)=(1,1,2)$ for all $r>1$.
Murat Alan, Tuba Çokoksen
doaj   +1 more source

Solutions of a family exponential Diophantine equation and the solutions of Goormaghtigh's conjecture for m=3(一类指数丢番图方程的解及m=3的Goormaghtigh猜想)

Zhejiang Daxue xuebao. Lixue ban, 2007
用渐近连分数的性质和Pell方程的解类特点，得到了指数丢番图方程的解（x，y，n）的性质及其较为精确的上界 ...
YANGShi-chun(杨仕椿), HEBo(何波)
doaj   +1 more source

On the exponential Diophantine equation $ \left(\frac{q^{2l}-p^{2k}}{2}n\right)^x+(p^kq^ln)^y = \left(\frac{q^{2l}+p^{2k}}{2}n\right)^z $

AIMS Mathematics, 2022
Let $ k, l, m_1, m_2 $ be positive integers and let both $ p $ and $ q $ be odd primes such that $ p^k = 2^{m_1}-a^{m_2} $ and $ q^l = 2^{m_1}+a^{m_2} $ where $ a $ is odd prime with $ a\equiv 5\pmod 8 $ and $ a\not\equiv 1\pmod 5 $. In this paper, using
C. Feng, Jiagui Luo
semanticscholar   +1 more source

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, Julien Portier, Victor Souza   +2 more
wiley   +1 more source