Related papers: Four quotient set gems
The review of modern study of algebraic, geometric and differential properties of quaternionic (Q) numbers with their applications. Traditional and "tensor" formulation of Q-units with their possible representations are discussed and groups…
The point-line geometry known as a \textit{partial quadrangle} (introduced by Cameron in 1975) has the property that for every point/line non-incident pair $(P,\ell)$, there is at most one line through $P$ concurrent with $\ell$. So in…
Furstenberg, Glasscock, Bergelson, Beiglboeck have been studied abundance in arithmatic progression on various large sets like piecewise syndetic, central, thick, etc. but also there are so many sets in which abundance in progression is…
The evidence for the existence of mesons with exotic quantum numbers and of hybrid candidates with non-exotic quantum numbers is critically reviewed, including candidates with hidden charm. Aims and methods of future searches for hybrid…
We give some very interesting matrices which are orthogonal over groups and, as far as we know, referenced, but in fact undocumented. This note is not intended to be published but available for archival reasons.
In this paper we present some interesting results involving summation of series in particular trigonometric ones. We failed to locate these results in existing literature or in the web like MathWorld (http://mathworld.wolfram.com/) nor…
We present some estimations on geometry of the exceptional value sets of non-zero constant Jacobian polynomial maps of $\C^2$ and it's components.
This is a pedagogical article cited in the foregoing research note, quant-ph/9911050
A critical review is presented on the most recent attempt to generally explain the notion of "statistical symmetry". This particular explanation, however, is incomplete and misses one important and essential aspect. The aim of this short…
We show that the following are consistent with ZFC: 1. Strongly meager sets form an ideal with the same additivity as the ideal of meager sets. 2. There exists a strong measure zero set of size > d (dominating number).
We prove the existence of quadratic polynomials having a Julia set with positive Lebesgue measure in three cases: the presence of a Cremer fixed point, the presence of a Siegel disk, the presence of infinitely many (satellite)…
The goal of this note is to give a characterization of generalized quaternion $2$-groups by using their posets of cyclic subgroups.
This work delves into the {\it quotient of an affine semigroup by a positive integer}, exploring its intricate properties and broader implications. We unveil an {\it associated tree} that serves as a valuable tool for further analysis.…
These notes present an approach to obtaining the basic operations of addition and multiplication on the natural numbers in terms of elementary results about commutative monoids.
In this short note, we are interested in discussing characteristics of finite generating sets for $\mathcal{F}$, the set of all semiflows with non negative coefficients of a Petri Net. By systematically positioning these results over semi…
The goal of this paper is to introduce some rings that play the role of the jet spaces of the quantum plane and unlike the quantum plane itself possess interesting nontrivial prime ideals. We will prove some results (theorems 1-4) about the…
The theory of quaternionic modular forms has been studied for decades as an example of the modular forms of many variables. The purpose of this study is to provide some congruence relations satisfied by such quaternionic modular forms.
The concepts of localizable set, localization of a ring and a module at a localizable set are introduced and studied. Localizable sets are generalization of Ore sets and denominator sets, and the localization of a ring/module at a…
The aim of this note is to point out some inaccuracies in our paper \cite{HD} and to fix them. Some new notions are introduced and properties of them are investigated.
Light scalar mesons are found to fit rather well a diquark-antidiquark description. The resulting nonet obeys mass formulae which respect, to a good extent, the OZI rule. OZI allowed strong decays are reasonably reproduced by a single…