Amirkabir University of TechnologyAUT Journal of Mathematics and Computing2783-24495320240701An iterative scheme for a class of generalized Sylvester matrix equations195215535810.22060/ajmc.2024.22444.1159ENMehdiDehghanDepartment of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), Iran0000-0002-2573-9755GholamrezaKaramaliFaculty of Basic Sciences, Shahid Sattari Aeronautical University of Sciences and Technology, South Mehrabad, Tehran, IranAkbarShirilordDepartment of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), IranJournal Article20230604In this study based on the accelerated over relaxation (AOR) method we make an iterative scheme for solving generalized Lyapunov matrix equation<br />$$ {A}{X}+{X}{B}+\sum_{j=1}^{m}{N}_j{X}{M}_j={C},$$<br />over complex or real matrices. Then we analyze the convergence of the new iterative method in detail. There have been discussions for the calculation of optimal parameters. Finally a numerical example is given to demonstrate the capability of the new method.https://ajmc.aut.ac.ir/article_5358_3a246af2678dfad0d536e0a62cf49179.pdfAmirkabir University of TechnologyAUT Journal of Mathematics and Computing2783-24495320240701Strong domination number of a modified graph217223520710.22060/ajmc.2023.22327.1152ENSaeidAlikhaniDepartment of Mathematical Science, Yazd University, 89195-741, Yazd, IranNimaGhanbariDepartment of Informatics, University of Bergen, P.O. Box 7803, 5020 Bergen, NorwayJournal Article20230410Let $G=(V,E)$ be a simple graph. A set $D\subseteq V$ is a strong dominating set of $G$, if for every vertex $x\in V\setminus D$ there is a vertex $y\in D$ with $xy\in E(G)$ and $\deg(x)\leq \deg(y)$. The strong domination number $\gamma_{\rm st}(G)$ is defined as the minimum cardinality of a strong dominating set. In this paper, we study the effects on $\gamma_{\rm st}(G)$ when $G$ is modified by operations on vertices and edges of $G$.https://ajmc.aut.ac.ir/article_5207_246a3c5544feb054f3ea718f61adfa16.pdfAmirkabir University of TechnologyAUT Journal of Mathematics and Computing2783-24495320240701On biprojectivity and Connes biprojectivity of a dual Banach algebra with respect to a $w^*$ -closed ideal225231516410.22060/ajmc.2023.22285.1149ENAmirSahamiDepartment of Mathematics, Faculty of Basic Sciences, Ilam University, P.O. Box 69315-516, Ilam, Iran0000-0003-0041-509XS. FatemehShariatiFaculty of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), IranMehdiRostamiFaculty of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), Iran0000-0002-8989-0286MonaAjDepartment of Mathematics, Farhangian University of Kermanshah, Kermanshah, IranJournal Article20230322In this paper, we introduce a notion of Connes biprojectivity for a dual Banach algebra $A$ with respect to its $w^{*}$-closed ideal $I$, say $I$-Connes biprojectivity. Some Lipschitz algebras $Lip_{\alpha}(X)$ and some matrix algebras are studied under this new notion. Also, with some mild assumptions, the relation between $I$-Connes biprojectivity and left $\phi$-contractibility is given, where $\phi$ is a $w^{*}$-continuous multiplicative linear functional on $A$. As an application, we characterize Connes biprojectivity of some Lipschitz algebras.https://ajmc.aut.ac.ir/article_5164_eb30fa42eeb3bf429cb7e3a3d7061b3b.pdfAmirkabir University of TechnologyAUT Journal of Mathematics and Computing2783-24495320240701Text steganography by changing the black color233244517710.22060/ajmc.2023.21801.1111ENBahmanKhosraviDepartment of Mathematics, Qom University of Technology, Qom, Iran0000-0001-6254-209XJournal Article20220923Recently, a serious problem in communications is security. Hiding data is one of the most important security techniques. Steganography is the art and science of hiding information in a cover media. Texts are the most usual method of communication and so they are very suitable for cover objects. In this paper, we give a new technique for text steganography. There exist different models, such as RGB, HSL, HSV to determine a color. The main goal of the proposed algorithm is the fact that some different but very similar colors in RGB have the same code in HSL. We use this fact to hide data. For this purpose, first we find a color <em>B</em><sup>′ </sup>in RGB, which is very similar to black in such a way that they have the same code in HSL. Then, by changing the color of each character of the text to black or <em>B</em><sup>′</sup>, we conceal the information. We will show that the capacity of this method is better than some other methods of text steganography, and then we show that the invisibility of this algorithm is very high, which is the most prominent feature of the proposed technique.https://ajmc.aut.ac.ir/article_5177_54391c872fe1c8b4f98095c5d6ec7ec7.pdfAmirkabir University of TechnologyAUT Journal of Mathematics and Computing2783-24495320240701Almost Ricci soliton in $Q^{m^{\ast}}$245256519010.22060/ajmc.2023.22115.1134ENHamedFarajiDepartment of Pure Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, IranShahroudAzamiDepartment of Pure Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, Iran0000-0002-8976-2014Journal Article20230120In this paper, we will focus our attention on the structure of $h$-almost Ricci solitons on complex hyperbolic quadric. We will prove non-existence a contact real hypersurface in the complex hyperbolic quadric $Q^{m^*}, m\geq 3$, admitting the gradient almost Ricci soliton. Moreover, the gradient almost Ricci soliton function $f$ is trivial.https://ajmc.aut.ac.ir/article_5190_47698c15fb83a1e5bb1400accbb17f82.pdfAmirkabir University of TechnologyAUT Journal of Mathematics and Computing2783-24495320240701Variational problem, Lagrangian and $\mu$-conservation law of the generalized Rosenau-type equation257265519710.22060/ajmc.2023.22352.1154ENKhodayarGoodarziDepartment of Mathematics, Broujerd Branch, Islamic Azad University, Broujerd, IranJournal Article20230421The goal of this article is to compute conservation law, Lagrangian and $\mu$-conservation law of the generalized Rosenau-type equation using the homotopy operator, the $\mu$-symmetry method and the variational problem method. The generalized Rosenau-type equation includes the generalized Rosenau equation, the generalized Rosenau-RLW equation and the generalized Rosenau-KdV equation, which admits the third-order Lagrangian. The article also compares the conservation law and the $\mu$-conservation law of these three equation. https://ajmc.aut.ac.ir/article_5197_ea06ed6e977637a81ea9d22b3090e28a.pdfAmirkabir University of TechnologyAUT Journal of Mathematics and Computing2783-24495320240701Existence and convergence of fixed points for noncyclic $\varphi$-contractions267274517110.22060/ajmc.2023.21992.1127ENAkramSafari-HafshejaniDepartment of Pure Mathematics, Payame Noor University (PNU), P. O. Box: 19395-3697, Tehran, Iran0000-0002-5955-2470Journal Article20221205In the paper, we introduce a new class of noncyclic $\varphi$-contractions as a generalization of the class of noncyclic contractions which was first introduced in the paper [R. Esp´ınola, M. Gabeleh, On the structure of minimal sets of relatively nonexpansive mappings, Numerical Functional Analysis and Optimization 34 (8), 845-860, 2013] and study the existence, uniqueness and convergence of a fixed point for such class of noncyclic mapping in the framework of uniformly convex Banach spaces. We obtain existence results of the best proximity points for cyclic $\varphi$-contractions as a consequence of our main theorems.https://ajmc.aut.ac.ir/article_5171_9161ab7a1b61012c4c303f10b4c16b2c.pdfAmirkabir University of TechnologyAUT Journal of Mathematics and Computing2783-24495320240701Interpolatory four-parametric adaptive method with memory for solving nonlinear equations275287524810.22060/ajmc.2023.22090.1132ENValiTorkashvandDepartment of Mathematics Education, Farhangian University, P.O. Box 14665-889, Tehran, IranJournal Article20230110The adaptive technique enables us to achieve the highest efficiency index theoretically and practically. The idea of introducing an adaptive self-accelerator (via all the old information for Steffensen-type methods) is new and efficient to obtain the highest efficiency index. In this work, we have used four self-accelerating parameters and have increased the order of convergence from 8 to 16, i. e. any new function evaluations improve the convergence order up to 100%. The numerical results are compared without and with memory methods. It confirms that the proposed methods have more efficiency index.https://ajmc.aut.ac.ir/article_5248_81bc798a42a7ce40810bf523f24deee1.pdf