Related papers: Four quotient set gems
The main purpose of this note is to pose a couple of problems which are easily formulated thought some seem to be not yet solved. These problems are of general interest for discrete mathematics including a new twig of a bough of theory of…
We analyze and partially solve system of recurrences that can be derived from the properties of martingale orthogonal polynomials that characterize quadratic harnesses (QH). We also specify conditions for the existence of moments of one…
We give a survey of some known and some new results about factors of different sorts of $q-$Fibonacci numbers.
This article offers a gentle introduction to the axiom of choice. We introduce the axiom, discuss some common objections to it, and present three kinds of reasons to accept it. Although the exposition is aimed at non-experts in set theory,…
The fundamental quandle is a powerful invariant of knots and links, but it is difficult to describe in detail. It is often useful to look at quotients of the quandle, especially finite quotients. One natural quotient introduced by Joyce is…
The simple continued fractions for the Golden & Silver means are well-known. It is astonishing that, as far as we know, no one has published half-iterates (let alone quarter-iterates) for the corresponding algorithms. We also examine the…
We introduce and study monomial ideals with regular quotients, which can be seen as an extension of monomial ideals with linear quotients. Based on these investigations, we are able to calculate the Betti numbers of toric ideals belonging…
In this paper, we present some applications of quaternions and octonions. We present the real matrix representations for complex octonions and some of their properties which can be used in computations where these elements are involved.…
The history of complementary observables and mutual unbiased bases is reviewed. A characterization is given in terms of conditional entropy of subalgebras. The concept of complementarity is extended to non-commutative subalgebras.…
Several authors have introduced various type of coherent-like rings and proved analogous results on these rings. It appears that all these relative coherent rings and all the used techniques can be unified. In [2], several coherent-like…
The satisfactory development of Quaternionic Analysis has indicated new solutions for physical and mathematical problems. It is worth mentioning the fact that quaternions possess four dimensions, and in this way they may be considered as…
These are notes on some entanglement properties of quantum field theory, aiming to make accessible a variety of ideas that are known in the literature. The main goal is to explain how to deal with entanglement when -- as in quantum field…
Some of the currently most popular conjectures for the structure of the recently discovered heavy mesons that do not find a place in the quark model quarkonium spectrum are sketched. Furthermore, some observables are identified that should…
Starting with a novel definition of divided differences, this essay derives and discusses the basic properties of, and facts about, (univariate) divided differences.
Let $A$ be a subset of $\mathbb{Z} / N\mathbb{Z}$ and let $\mathcal{R}$ be the set of large Fourier coefficients of $A$. Properties of $\mathcal{R}$ have been studied in works of M.-- C. Chang, B. Green and the author. In the paper we…
In recent literature there are an increasing number of papers where the forbidden sets of difference equations are computed. We review and complete different attempts to describe the forbidden set and propose new perspectives for further…
At present many of the endeavours in physics are made to recognize in quantum substance classical reality, time, subjectivity, consciousness and many other physical and nonphysical features. The purpose of these remarks is to draw attention…
It is presented a critical consideration of all unusual properties of the scalar $a_0(980)$ and $f_0(980)$-mesons in the four-quark, two-quark and molecular models. The arguments are adduced that the four-quark model is more preferable. It…
In the article "The Tale of Two Queens and Two Towering Figures" published in CNJ in 2012 (CNJ vol. 57 No. 5, pp. 304-315), we discussed the contributions of Copernicus and Newton to coin minting and monetary reforms, as well as the…
This paper has a double goal, the first one is to make a slight survey of some theoretical results about the existence of positively invariant curves that allow to describe important properties of the set of bounded orbits and its boundary…