Related papers: Interval Semirings
The aim of this series of papers is to study $z$-ideals of semirings. In this article, we introduce some distinguished classes of $z$-ideals of semirings, which include $z$-prime, $z$-semiprime, $z$-irreducible, and $z$-strongly irreducible…
The main purpose of this article is to initiate a systematic study of Semihypergroups, first introduced by C. Dunkl [4], I. Jewett [13] and R. Spector [20] independently around 1972. We introduce and study several natural algebraic and…
In order to investigate the relationship between Shannon information measure of random variables, scholars such as Yeung utilized information diagrams to explore the structured representation of information measures, establishing…
Indexing intervals is a fundamental problem, finding a wide range of applications. Recent work on managing large collections of intervals in main memory focused on overlap joins and temporal aggregation problems. In this paper, we propose…
This paper illustrates the relationship between boolean propositional algebra and semirings, presenting some results of partial ordering on boolean propositional algebras, and the necessary conditions to represent a boolean propositional…
In this paper, we investigate zero-divisor, nilpotent, idempotent, unit, small, and irreducible elements in semiring extensions such as amount, content, and monoid semialgebras. We also introduce new concepts such as the prime avoidance…
Contribution: This secondary study examines the literature on immersive learning frameworks and reviews their state of the art. Frameworks have been categorized according to their purpose. In addition, the elements that compose them were…
We begin the investigation of the variety of semilattices of Mal'cev blocks, which we call SMB algebras.
This article presents an overview of the theory of integrable systems with symmetries, focusing on toric systems, semitoric systems, and their classifications via decorated polygons. We discuss certain one-parameter families of integrable…
In this article we analyze the structure of the semigroup of inner perturbations in noncommutative geometry. This perturbation semigroup is associated to a unital associative *-algebra and extends the group of unitary elements of this…
We say that a subring $R_0$ of a ring $R$ is semi-invariant if $R_0$ is the ring of invariants in $R$ under some set of ring endomorphisms of some ring containing $R$. We show that $R_0$ is semi-invariant if and only if there is a ring…
In this paper, a unified framework for representing uncertain information based on the notion of an interval structure is proposed. It is shown that the lower and upper approximations of the rough-set model, the lower and upper bounds of…
This paper is written as one chapter in a collection of essays on neutrino physics for beginning graduate students. The text presents important experimental methods and issues for those interested in searches for sterile neutrinos. Other…
This is Chapter 1 of the book {\it Approximation Theory and Harmonic Analysis on Spheres and Balls} by the authors. It provides a self-contained introduction to spherical harmonics. The book will be published as a title in {\it Springer…
We develop the theory of central ideals on commutative rings. We introduce and study the central seminormalization of a ring in another one. This seminormalization is related to the theory of regulous functions on real algebraic varieties.…
Over 300 sequences and many unsolved problems and conjectures related to them are presented herein. These notions, definitions, unsolved problems, questions, theorems corollaries, formulae, conjectures, examples, mathematical criteria, etc.…
This is an introduction to the theory of normal bases of finite fields. The first few chapters cover a wide range of topics on the theory of normal bases of finite fields. Most standard definitions and results, including proofs are given.…
To solve hard problems, AI relies on a variety of disciplines such as logic, probabilistic reasoning, machine learning and mathematical programming. Although it is widely accepted that solving real-world problems requires an integration…
This is the Habilitation Thesis manuscript presented at Besan\c{c}on on January 5, focusing on Matrix Analysis, Matrix Inequalities and Matrix Decompositions. There are also some topics in (Hilbert space) Operator Theory. The text should be…
Each family $\mathcal{M}$ of means has a natural, partial order (point-wise order), that is $M \le N$ iff $M(x) \le N(x)$ for all admissible $x$. In this setting we can introduce the notion of interval-type set (a subset $\mathcal{I}…