Algebra Research Papers

An Algebraic Characterization of Prefix-Strict Languages

Let Σ+ be the set of all finite words over a finite alphabet Σ. A word u is called a strict prefix of a word v, if u is a prefix of v and there is no other way to show that u is a subword of v. A language L⊆Σ+ is said to be prefix-strict, i...

Influence of Non - Condensable Gases on the Processes of Heat and Mass Transfer during Film Condensation of Steam in Heat Exchangers

The aim of the article is a quantitative assessment of the influence of non-condensable gases on the intensity of heat and mass transfer processes during film condensation of steam in the specific conditions for heat exchanger. The task is ...

ON CLASSIFICATION OF YANGIAN IRREDUCIBLE REPRESENTATIONS OF LIE SUPERALGEBRA SL (1, 2)

The classification of Yangian irreducible finite-dimensional representations of Lie superalgebra sl(1,2) – Hopf superalgebra is obtained. The classification is of great use in modern theoretical and mathematical physics. Some feasible appli...

Mathematical logic

Mathematics: Frontiers and Perspectives

Mathematical structures of language

This book attempts to show how one can arrive at an abstract system which characterizes precisely natural language. This is done by taking the data of language and finding within the data such relations as can be organized into a suitable m...

Conceptual Mathematics

In the last 60 years, the use of the notion of category has led to a remarkable unification and simplification of mathematics. Conceptual Mathematics introduces this tool for the learning, development, and use of mathematics, to beginning s...

Mathematical Logic

Undergraduate students with no prior instruction in mathematical logic will benefit from this multi-part text. Part I offers an elementary but thorough overview of mathematical logic of 1st order. Part II introduces some of the newer ideas ...

Quantum logic as motivated by quantum computing

§1. Introduction. Our understanding of Nature comes in layers, so should the development of logic. Classic logic is an indispensable part of our knowledge, and its interactions with computer science have recently dramatically changed our li...

Topological preparation of non-stabilizer states and Clifford evolution in SU(2)1 Chern-Simons theory

Abstract We develop a topological framework for preparing families of non-stabilizer states, and computing their entanglement entropies, in SU(2)1 Chern-Simons theory. Using the Kac-Moody algebra, we construct Pauli and Clifford operators a...

The Role and Application of Matrices in Artificial Intelligence: Foundations, Methods, and Advancements

Matrices are foundational to artificial intelligence (AI), serving as critical tools for data representation, manipulation, and transformation across various applications. From machine learning algorithms to neural network architectures, ma...

Quantum computing and the Jones polynomial

This paper is an exploration of relationships between the Jones polynomial and quantum computing. We discuss the structure of the Jones polynomial in relation to representations of the Temperley Lieb algebra, and give an example of a unitar...

Fuzzy logic, neural networks, and soft computing

article Free Access Share on Fuzzy logic, neural networks, and soft computing Author: Lotfi A. Zadeh Univ. of California, Berkeley Univ. of California, BerkeleyView Profile Authors Info & Claims Communications of the ACMVolume 37Issue 3Marc...

Logics of Statements in Context-Category Independent Basics

Based on a formalization of open formulas as statements in context, the paper presents a freshly new and abstract view of logics and specification formalisms. Generalizing concepts like sets of generators in Group Theory, underlying graph o...

The Mode of Constructing Safe Trajectories of Motion of the Unmanned Aerial Vehicle while Monitoring Power Lines Considering the Influence of their Electromagnetic Fields

The aim of this paper is to increase the flight safety of an unmanned aerial vehicle that monitors power lines under the negative influence of electromagnetic fields on the on-board equipment. This problem was solved with algorithms for pho...

Quaternions in Computer Vision and Robotics

Computer vision and robotics suffer from not having good tools for manipulating three-dimensional objects. Vectors, coordinate geometry, and trigonometry all have deficiencies. Quaternions can be used to solve many of these problems. Many p...

Topological Data Analysis: Foundations, Algorithms, and Emerging Applications

Topological data analysis (TDA) has evolved into a flexible and robust paradigm for obtaining qualitative, geometry-inspired insights from high-dimensional, noisy, and complex data. Grounded in algebraic topology, geometry, statistics, and ...

Guarding against artificial intelligence – hallucinated citations: The case for full-text reference deposit.

The tendency of generative artificial intelligence (AI) to ‘hallucinate’ false information is well known; AI-generated citations to non-existent sources have penetrated the bibliographies of peer-reviewed publications. D...