The Unit Group of Small Group Algebras and the Minimum Counterexample to the Isomorphism Problem

Solvable Lie algebras with $N(R_n,m,r)$ nilradical

In this paper, we classify the indecomposable non-nilpotent solvable Lie algebras with $N(R_n,m,r)$ nilradical,by using the derivation algebra and the automorphism group of $N(R_n,m,r)$.We also prove that these solvable Lie algebras are complete and unique, up to isomorphism.

Unit commitment by a fast and new analytical non-iterative method using IPPD table and “λ-logic” algorithm

Many different methods have been presented to solve unit commitment (UC) problem in literature with different advantages and disadvantages. The need for multiple runs, huge computational burden and time, and poor convergence are some of the disadvantages, where are especially considerable in large scale systems. In this paper, a new analytical and non-iterative method is presented to solve UC p...

On Isomorphism of Simplicial Complexes and Their Related Algebras

Radical and It’s Applications in BCH-Algebras

Let $X$ be a $BCH$-algebra and $I$ be an ideal of $X$. In this paper, we introduce the concept of $sqrt{I}$. We show that it is an ideal of $X$, when $I$ is closed ideal of $X$. Then we verify some useful properties of it. We prove that it is the ::::union:::: of all $k-$nil ideals of $I$. Moreover, if $I$ is a closed ideal of $X$, then $sqrt{I}$ is a closed translation ideal and so we can cons...

A brief introduction to quaternion matrices and linear algebra and on bounded groups of quaternion matrices

The division algebra of real quaternions, as the only noncommutative normed division real algebra up to isomorphism of normed algebras, is of great importance. In this note, first we present a brief introduction to quaternion matrices and quaternion linear algebra. This, among other things, will help us present the counterpart of a theorem of Herman Auerbach in the setting of quaternions. More ...