Results 61 to 70 of about 24,531 (183)

Synchronization of unidirectional time delay chaotic networks and the greatest common divisor

, 2011
We present the interplay between synchronization of unidirectional coupled chaotic nodes with heterogeneous delays and the greatest common divisor (GCD) of loops composing the oriented graph.
Englert, A., Geissler, F., Kanter, I., Kinzel, W., Zigzag, M.   +4 more
core   +1 more source

An extension of the cogrowth formula to arbitrary subsets of the tree

Bulletin of the London Mathematical Society, Volume 58, Issue 1, January 2026.
Abstract What is the probability that a random walk in the free group ends in a proper power? Or in a primitive element? We present a formula that computes the exponential decay rate of the probability that a random walk on a regular tree ends in a given subset, in terms of the exponential decay rate of the analogous probability of the non‐backtracking
Doron Puder
wiley   +1 more source

The modular automorphisms of quotient modular curves

Mathematika, Volume 72, Issue 1, January 2026.
Abstract We obtain the modular automorphism group of any quotient modular curve of level N$N$, with 4,9∤N$4,9\nmid N$. In particular, we obtain some unexpected automorphisms of order 3 that appear for the quotient modular curves when the Atkin–Lehner involution w25$w_{25}$ belongs to the quotient modular group. We also prove that such automorphisms are
Francesc Bars, Tarun Dalal
wiley   +1 more source

Algebraic Structure Graphs over the Commutative Ring ${\mathbb{Z}}_m$: Exploring Topological Indices and Entropies Using $\mathbb{M}$-Polynomials

Mathematics, 2023
The field of mathematics that studies the relationship between algebraic structures and graphs is known as algebraic graph theory. It incorporates concepts from graph theory, which examines the characteristics and topology of graphs, with those from ...
Amal S. Alali, Shahbaz Ali, Noor Hassan, Ali M. Mahnashi, Yilun Shang, Abdullah Assiry   +5 more
doaj   +1 more source

Properties of Ideal-Based Zero-Divisor Graphs of Commutative Rings [PDF]

, 2014
Let R be a commutative ring with nonzero identity and I an ideal of R. The focus of this research is on a generalization of the zero-divisor graph called the ideal-based zero-divisor graph for commutative rings with nonzero identity.
Smith, Jesse Gerald, Jr.
core   +2 more sources

Zero-divisor graphs of idealizations

Journal of Pure and Applied Algebra, 2006
The authors of the reviewed paper (with \textit{J. Coykendall}) examined in [Commun. Algebra 33, No. 6, 2043--2050 (2005; Zbl 1088.13006)] the preservation, or lack thereof, of the diameter and girth of the graph of a commutative ring under extensions to polynomial and power series rings.
Axtell, Michael, Stickles, Joe
openaire   +2 more sources

Algebraic Connectivity Maximizing Regular Graphs: Special Case Analysis and Depth‐First Search

Concurrency and Computation: Practice and Experience, Volume 37, Issue 27-28, 25 December 2025.
ABSTRACT The algebraic connectivity is an indicator of how well connected a graph is. It also characterizes the convergence speed of some dynamic processes over networks. In this paper, taking into account that homogeneous networks are modeled as regular graphs, we tackle the following problem: given a pair (n,k)$$ \left(n,k\right) $$ of positive ...
Masashi Kurahashi, Najd Salaani, Tsuyoshi Migita, Norikazu Takahashi   +3 more
wiley   +1 more source

Left Zero Divisor Graphs of Totally Ordered Rings [PDF]

, 2016
In this paper we consider prime graph of R (denoted by ) of an associative ring R (introduced by Satyanarayana, Syam Prasad and Nagaraju [6]). This short paper is divided into two Sections. Section-1 is devoted for preliminary definitions.
Bhavanari, M. (Mallikarjun), Bhavanari, S. (Satyanarayana), Devanaboina, S. (Srinivasulu)   +2 more
core  

RevOrder: A novel equation format for arithmetic operations in language models

AI Magazine, Volume 46, Issue 4, Winter 2025.
Abstract This paper proposes to understand arithmetic operations in Language Models (LM) by framing them as digit‐based reasoning challenges. Our research focuses on arithmetic optimization challenges specific to LLMs, not on solving mathematical word problems.
Si Shen, Peijun Shen, Danhao Zhu
wiley   +1 more source

The Congruence-Based Zero-Divisor Graph [PDF]

, 2015
Let R be a commutative ring with nonzero identity and ~ a multiplicative congruence relation on R. Then, R/~ is a semigroup with multiplication [x][y] = [xy], where [x] is the congruence class of an element x of R.
Lewis, Elizabeth Fowler
core   +1 more source