arXiv subjects
Publications and source records attributed to Veselin Jungić.
In this article we provide a motivation for studying integrals $\displaystyle \int_0^{\fracπ{2}}x\cos^mx~dx$, $m\in \mathbb{N}$. We demonstrate several properties of this class of integrals and show that it is closely related to the class of Wallis integrals, $\displaystyle \int_0^{\fracπ{2}}\cos^mx~dx$, $m\in \mathbb{N}$.
In this note we are interested in the problem of whether or not every increasing sequence of positive integers $x_1x_2x_3...$ with bounded gaps must contain a double 3-term arithmetic progression, i.e., three terms $x_i$, $x_j$, and $x_k$ such that $i + k = 2j$ and $x_i + x_k = 2x_j$. We consider a few variations of the problem, discuss some related properties of double arithmetic progressions, and present several results obtained by using RamseyScript, a high-level scripting language.
The study of the structure of infinite words having bounded abelian complexity was initiated by G. Richomme, K. Saari, and L. Q. Zamboni. In this note we define bounded additive complexity for infinite words over a finite subset of Z^m. We provide an alternative proof of one of the results of Richomme, Saari, and Zamboni.