Related papers: A Class of Continued Radicals
We introduce and study the concept of cyclicity degree of a finite group $G$. This quantity measures the probability of a random subgroup of $G$ to be cyclic. Explicit formulas are obtained for some particular classes of finite groups. An…
We give an explicit formula for the Jones polynomial of any rational link in terms of the denominators of the canonical continued fraction of the slope of the given rational link.
We give a lower bound for the degree of an irreducible factor of a given polynomial. This improves and generalizes the results obtained in [4, On the irreducible factors of a polynomial, Proc. Amer. Math. Soc., 148 (2020] 1429 -- 1437].
The real type of a finite family of univariate polynomials characterizes the combined sign behavior of the polynomials over the real line. We derive an explicit formula for the number of real types subject to given degree bounds. For the…
In this note, given a regular Courant algebroid, we compute its group of automorphisms relative to a dissection. We also propose an infinitesimal version and recover examples of the literature.
We present new classes of permutation polynomials over finite fields.
These are notes for a graduate-level introductory course on singularity categories.
We propose investigating a summation analog of the paradigm for parallel integration. We make some first steps towards an indefinite summation method applicable to summands that rationally depend on the summation index and a P-recursive…
We prove a uniqueness result for limit cycles of a class of second order ODE's. As a special case, we prove limit cycle's uniqueness for an ODE studied in \cite{ETBA}.
We give combinatorial descriptions of the terms occurring in continuants of general continued fractions that diverge to three limits. Equating these with the usual combinatorial descriptions due to Euler, Sylvester, and Minding induces…
We introduced a new continued fraction expansions in our previous paper. For these expansions, we show formulae of probability about incomplete quotients. Furthermore, we prove the existence of invariant measures with respect to the…
We present a sharp upper bound for the number of generators of a finite group in terms of the ratio between the order and the exponent.
Separations among the first order logic ${\cal R}ing(0,+,*)$ of finite residue class rings, its extensions with generalized quantifiers, and in the presence of a built-in order are shown, using algebraic methods from class field theory.…
This work describes the number of restricted finite words in the alphabet A={a,b} required to identify an infinite word with some period n in the set of all infinite words in this alphabet given up to a shift. Also reviewed the case of…
In this paper, we represent a continued fraction expression of Mathieu series by a continued fraction formula of Ramanujan. As application, we obtain some new bounds for Mathieu series.
Classes of algebraic structures that are defined by equational laws are called varieties or equational classes. A variety is finitely generated if it is defined by the laws that hold in some fixed finite algebra. We show that every…
The numerical radius of the general $2\times2$ complex matrix is calculated.
We show that for each positive integer $a$ there exist only finitely many prime numbers $p$ such that $a$ appears an odd number of times in the period of continued fraction of $\sqrt{p}$ or $\sqrt{2p}$. We also prove that if $p$ is a prime…
For each positive integer n greater than or equal to 2, a new approach to expressing real numbers as sequences of nonnegative integers is given. The n=2 case is equivalent to the standard continued fraction algorithm. For n=3, it reduces to…
We extend a result of Han\v{c}l, Kolouch and Nair on the irrationality and transcendence of continued fractions. We show that for a sequence $\{\alpha_n\}$ of algebraic integers of bounded degree, each attaining the maximum absolute value…