In this paper, we introduce the concept of a triangular coefficient matrix ring and investigate the structure of its ideals.We then characterize the radicals of the ring R h [x]/x n for every positive integer n, where R h [x] denotes the Hurwitz polynomial ring and x n represents the ideal of this ring generated by x n .Furthermore, we explore several properties that are transferred between the base ring R and the matrix ring Hn(R), which is a proper subring of the triangular coefficient matrix ring.

This paper considers the Rao-Nakra sandwich beam damped by locally distributed feedback at the neighborhood of the boundary.The solution's exponential stability is established using the frequency domain method and the multiplier method.

A finite group G is called (l, m, n)-generated if it is generated by two elements x and y, such that the orders of x, y, and xy are l, m, and n, respectively.A triple (p, q, r) is called (p, q, r)-generation of a group G if G is (p, q, r)-generated.In [Nova J. Algebra Geom. 2 (1993) 277-285], Moori posed the question of finding all (p, q, r)-generations of non-abelian finite simple groups such that p, q, and r are prime numbers.In answering this question, we determine all (p, q, r)-generations of the Tits group 2 F4(2) , where p, q, and r are prime numbers dividing the order of this group.We primarily use the structure constant method, along with other results, to establish the generation and non-generation of 2 F4(2) by triples (p, q, r).We use the GAP (Groups, Algorithms and Programming) system and the Atlas of Finite Group Representations in our computations.

An (m, n)-near ring is an algebraic structure similar to an (m, n)-ring but satisfying fewer axioms.More precisely, the notion of (m, n)-near rings generalizes the concepts of rings, near rings, and (m, n)-rings.In this article, we define the notions of i-(m, n)-near ring, N -group, N -ideal, -primitive, constant (m, n)-near ring, modular j-ideal, and -modular, and investigate their properties.

A different and technical proof for a series representation of log s is provided.The mentioned series representation was used to reproduce some Bailey-Borwein-Plouffe (BBP) type formulas for a variety of numbers, including some classical BBP type formulas for π.A series representation, similar to that of log s, for log 2 (s) is also derived.

In this paper, the concept of the eccentrical graph of a graph is introduced.Let G be a connected graph with the vertex set V (G).The eccentrical graph of G is the graph (G) with the vertex set V ( (G)) = V (G) and two vertices vi, vj ∈ V ( (G)) are adjacent in (G) if and only if the distance between them is min{e(vi), e(vj)}, where e(vi) is the eccentricity of vi.A sufficient condition for the eccentrical graph of a connected graph to be connected is given.It is proved that the eccentrical graph of every tree is connected and its diameter does not exceed 3. The extremum values of the greatest eigenvalue of eccentrical graphs of trees and connected graphs of fixed order are also studied.Furthermore, spectra of eccentrical graphs of various classes of graphs are computed.