Related papers: Interval Linear Algebra
Let A be a set of integers dense in a finite interval. We establish upper and lower bounds for the longest regularly-spaced and convex subsets of A and of A-A.
We give a self-contained exposition of some mathematical aspects of the Mueller-Stokes formalism. In the first part we review some basic notions of linear algebra and establish a proper notation. In the second part we introduce the…
This primer is an attempt to provide a detailed summary of the different facets of lifelong learning. We start with Chapter 2 which provides a high-level overview of lifelong learning systems. In this chapter, we discuss prominent scenarios…
We study some examples when there is actually an equality in the linear algebra bound. When the vectors considered span in fact the entire space. We would like to point out that in some cases this provides some interesting extra information…
In past few decades, tensor algebra also known as multi-linear algebra has been developed and customized as a tool to be used for various engineering applications. In particular, with the help of a special form of tensor contracted product,…
A quantitative model of concurrent interaction is introduced. The basic objects are linear combinations of partial order relations, acted upon by a group of permutations that represents potential non-determinism in synchronisation. This…
In this book, there are five chapters: The Laplace Transform, Systems of Homogeneous Linear Differential Equations (HLDE), Methods of First and Higher Orders Differential Equations, Extended Methods of First and Higher Orders Differential…
These are lecture notes on the algebraic approach to regular languages. The classical algebraic approach is for finite words; it uses semigroups instead of automata. However, the algebraic approach can be extended to structures beyond…
In our previous paper entitled "Axiomatic differential geometry -towards model categories of differential geometry-, we have given a category-theoretic framework of differential geometry. As the first part of our series of papers concerned…
This paper establishes a new combinatorial framework for the study of coarse median spaces, bridging the worlds of asymptotic geometry, algebra and combinatorics. We introduce a simple and entirely algebraic notion of coarse median algebra…
This study introduces an evaluation benchmark for middle school algebra to be used in artificial intelligence(AI) based educational platforms. The goal is to support the design of AI systems that can enhance learner conceptual understanding…
In this paper, we show how a resource allocation problem can be solved through Integer Linear Programming (ILP). A detailed illustrative example is presented, together with an exhaustive overview of the mathematical model. The size of the…
The work is devoted to the construction of a new interval arithmetic which would combine algorithmic efficiency and high quality estimation of the ranges of expressions.
This is a survey on the finite basis problem for varieties of algebraic systems. Our exposition is in two directions: (i) We give numerous examples of varieties which are not finitely based. (ii) We give examples of important varieties with…
We introduce the classes of descendingly flexible and descendingly alternative algebras over an arbitrary field $\mathbb{F}$. We suggest a new method based on the sequence of differences between the dimensions of the linear spans of words,…
This book is mainly an exposition of the author's works and his joint works with his former students on explicit representations of finite-dimensional simple Lie algebras, related partial differential equations, linear orthogonal algebraic…
We study maximal subalgebras of an arbitrary finite dimensional algebra over a field, and obtain full classification/description results of such algebras. This is done by first obtaining a complete classification in the semisimple case, and…
This work develops problem statements related to encoders and autoencoders with the goal of elucidating variational formulations and establishing clear connections to information-theoretic concepts. Specifically, four problems with varying…
This is a survey article on real algebra and geometry, and in particular on its recent applications in optimization and convexity. We first introduce basic notions and results from the classical theory. We then explain how these relate to…
In \cite{BigAlg-3gen}, an explicit description of bi-quadratic algebras on three generators with PBW basis was obtained. There are four classes: I-IV. The aim of the paper is to study algebras that belong to one of the classes: class II.1.…