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The summatory function of the number of binomial coefficients not divisible by a prime is known to exhibit regular periodic oscillations, yet identifying the less regularly behaved minimum of the underlying periodic functions has been open for almost
Externí odkaz:
http://arxiv.org/abs/2408.06817
Autor:
Kozhan, Rostyslav, Vaktnäs, Marcus
We identify a connection between the Christoffel transform of orthogonal polynomials and multiple orthogonality systems containing a finitely supported measure. In consequence, the compatibility relations for the nearest neighbour recurrence coeffici
Externí odkaz:
http://arxiv.org/abs/2407.13946
In this article, we show new effective approximation measures for the shifted logarithm of algebraic numbers which belong to a number field of arbitrary degree. Our measures refine previous ones including those for usual logarithms. We adapt Pade app
Externí odkaz:
http://arxiv.org/abs/2406.10820
The \textit{order of appearance} $ z(n) $ of a positive integer $ n $ in the Fibonacci sequence is defined as the smallest positive integer $ j $ such that $ n $ divides the $ j $-th Fibonacci number. A \textit{fixed point} arises when, for a positiv
Externí odkaz:
http://arxiv.org/abs/2309.14501
Autor:
Batterman, Zoë X., Jambhale, Aditya, Miller, Steven J., Narayanan, Akash L., Sharma, Kishan, Yang, Andrew K., Yao, Chris
Zeckendorf proved that every natural number $n$ can be expressed uniquely as a sum of non-consecutive Fibonacci numbers, called its Zeckendorf decomposition. Baird-Smith, Epstein, Flint, and Miller created the Zeckendorf game, a two-player game playe
Externí odkaz:
http://arxiv.org/abs/2309.12748
Autor:
Efrem, Christos N.
In this paper, the joint distribution of the sum and maximum of independent, not necessarily identically distributed, nonnegative random variables is studied for two cases: i) continuous and ii) discrete random variables. First, a recursive formula o
Externí odkaz:
http://arxiv.org/abs/2309.10548
In this paper, we provide a comprehensive solution to the open problem regarding the existence of a recurrence formula for computing fixed points of the Josephus function precisely when the reduction constant is three. Incorporating this formula into
Externí odkaz:
http://arxiv.org/abs/2310.12984
Autor:
Rogava, Jemal, Vashakidze, Zurab
Publikováno v:
Z Angew Math Mech. 104, No. 4, e202300608 (2024)
This paper considers the Cauchy problem for the nonlinear dynamic string equation of Kirchhoff-type with time-varying coefficients. The objective of this work is to develop a time domain discretization algorithm capable of approximating a solution to
Externí odkaz:
http://arxiv.org/abs/2303.10350
A new approach to analyzing intrinsic properties of the Josephus function, $J_{_k}$, is presented in this paper. The linear structure between extreme points of $J_{_k}$ is fully revealed, leading to the design of an efficient algorithm for evaluating
Externí odkaz:
http://arxiv.org/abs/2303.15457
Often, polynomials or rational functions, orthogonal for a particular inner product are desired. In practical numerical algorithms these polynomials are not constructed, but instead the associated recurrence relations are computed. Moreover, also typ
Externí odkaz:
http://arxiv.org/abs/2302.00355