Damghan University PressAnalytical and Numerical Solutions for Nonlinear Equations3060-785X8220240822An Extension of Order Bounded Operators11011843610.22128/gadm.2024.783.1105ENKazem Haghnejad AzarDepartment of Mathematics and Application, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil, IranSajjad Ghanizadeh ZareDepartment of Mathematics and Application, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil, IranSomayeh HazratiDepartment of Mathematics and Application, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil, IranJournal Article20240123Let $E$ be a normed lattice and an g-order dense majorizing sublattice of a vector lattice $E^t$. We extend the norm of $E$ to $E^t$, denoted by $\Vert.\Vert_t$. The pair $(E^t,\Vert.\Vert_t)$ forms a normed lattice and preserves certain lattices and topological properties whenever these properties hold in $E$. As a consequence, every positive linear operator defined on a normed lattice $E$ has a linear extension to $E^t$. This manuscript provides an explicit formula for these extensions. The extended operator $T^t$ is a lattice homomorphism from $E^t$ into $F$, and it belongs to $\mathcal{L}_n(E^t,F)$ whenever $0\leq T\in \mathcal{L}_n(E,F)$ and $T(x\wedge y)=Tx \wedge Ty$ for all $0\leq x,y\in E$. Furthermore, if $T\in \mathcal{L}_b(E,F)$ and certain lattice and topological properties hold for $T$, then $T^t\in \mathcal{L}_b(E^t,F)$ will also preserve these properties.https://ansne.du.ac.ir/article_436_15e4ed6be36d7bac4c00561156a2cd20.pdfDamghan University PressAnalytical and Numerical Solutions for Nonlinear Equations3060-785X8220240822On NeutroEngelGroups11912543210.22128/gadm.2024.781.1104ENElahe MohammadzadehDepartment of Mathematics, Payame Noor University, P.O. Box 19395–3697, Tehran, IranFahime MohammadzadehDepartment of Mathematics, Payame Noor University, P.O. Box 19395–3697, Tehran, IranJournal Article20240120In this paper We introduce the notion of NeutroEngelGroups and we show some of it's results. Also, we show that the intersection of two NeutroEngelGroups and the quotient of a NeutroEngelGroups are NeutroEngelGroups too. Moreover, we prove that NeutroEngel is closed with respect to homomorphic image. Also, by several examples we show the diferences between Engel groups and NeutroEngelGroups.https://ansne.du.ac.ir/article_432_906d3721558936ef6d87fbe2d37b9b58.pdfDamghan University PressAnalytical and Numerical Solutions for Nonlinear Equations3060-785X8220240822Formulas for the Drazin Inverse of Anti-Triangular Matrices12613743310.22128/gadm.2024.823.1109ENAli GhaffariDepartment of Mathematics, Semnan University, P.O.Box 35195-363, Semnan, IranTahere HaddadiDepartment of Mathematics, Semnan Branch, Islamic Azad University, Semnan, IranJournal Article20240506Let $\mathcal{A}$ be a Banach algebra. In this paper, for two Drazin invertible elements $a, b \in \mathcal{A}$, explicit formulas for the Drazin inverse $(a+b)$ are given in the cases of $a^2ba=0$, $(ba)^2=0$ and $ab^2=0$. By using these formulas, the representations for the Drazin inverse of the anti-triangular operator matrices over Banach algebras are obtained, which also extend some existing results.https://ansne.du.ac.ir/article_433_38e6c8e40a66f05c35f7ecaafeb6075f.pdfDamghan University PressAnalytical and Numerical Solutions for Nonlinear Equations3060-785X8220240925Upwind Implicit Scheme for the Numerical Solution of Stochastic Advection-Diffusion Partial Differential Equations13816243410.22128/gadm.2024.859.1118ENMehran NamjooDepartment of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran0000-0001-5949-6766Mehran AminianDepartment of Mathematics,
Vali-e-Asr University of Rafsanjan,
Rafsanjan, IranAli MohebbianDepartment of Mathematics,
Vali-e-Asr University of Rafsanjan,
Rafsanjan, IranMehdi KaramiDepartment of Mathematics,
Vali-e-Asr University of Rafsanjan,
Rafsanjan, IranHossein SalmeiDepartment of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, IranJournal Article20240810Stochastic partial differential equations (SPDEs) are significant in various fields such as epidemiology, mechanics, microelectronics, chemistry, and finance. Obtaining analytical solutions for SPDEs is either difficult or impossible; therefore, researchers are very interested in effective numerical methods for studying the behavior of these equations. In this paper, we introduce a stochastic finite difference (SFD) scheme for the numerical solution of the It\^{o} stochastic advection--diffusion equation. We discuss the consistency, stability, and convergence of the scheme, and we also determine its order of convergence. Finally, to validate the effectiveness and accuracy of the SFD scheme, we analyze the numerical results and compare them with those from existing SFD schemes.https://ansne.du.ac.ir/article_434_db2592f41b970d7c3f1ff0afd0dd4bf2.pdfDamghan University PressAnalytical and Numerical Solutions for Nonlinear Equations3060-785X8220240826Analysis of Stability for Time-Invariant Linear Systems with Interval Coefficients16317143510.22128/gadm.2024.840.1113ENHadi Shokouhi AmiriDepartment of Mathematics, Payame Noor University, Tehran, IranAkbar Hashemi BorzabadiDepartment of Applied Mathematics, University of Science and Technology of Mazandaran, Behshahr, IranAghileh HeydariDepartment of Mathematics, Payame Noor University, Tehran, IranJournal Article20240610In this paper, the stability of time-invariant (continuous-time) free linear system with interval coefficients is researched. After the introduction of parametric representation for intervals and<br />subsequently the extension of this representation to interval matrices, stability with the concept of Lyapunov is discussed and<br />investigated. The most important result of this idea, is the ability of checking stability without considering some constraints on the<br />system. By presenting several examples, the stability of these systems, is researched by using the expressed approach.https://ansne.du.ac.ir/article_435_1687c527301bb831ca087fceec5806e7.pdfDamghan University PressAnalytical and Numerical Solutions for Nonlinear Equations3060-785X8220241022Quadrature Rules for Solving Two-Dimensional Fredholm Integral Equations of Second Kind17218143710.22128/gadm.2024.855.1116ENManochehr KazemiDepartment of Mathematics, Ashtian Branch, Islamic Azad University, Ashtian, Iran;
Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran0000-0001-8392-6690Hamid RezaSahebiDepartment of Mathematics, Ashtian Branch, Islamic Azad University, Ashtian, Iran0000-0001-8258-6719Journal Article20240727In this paper, an iterative method of successive approximations based on the trapezoidal quadrature rule to solve two-dimensional Fredholm integral equations of second kind (2DFIE) is proposed. The error estimation of the proposed method is presented. The benefit of the method is that we do not have to solve a system of algebraic equations. Finally, a numerical example verify the theoretical results and show the accuracy of the method.https://ansne.du.ac.ir/article_437_8435d297360901a6efb81253375004fc.pdfDamghan University PressAnalytical and Numerical Solutions for Nonlinear Equations3060-785X8220241022The Maximum Edge Eccentricity Energy of a Graph18219043810.22128/gadm.2024.863.1119ENAkram Sadat Banihashemi DehkordiFaculty of Mathematics, Statistics and Computer Science, Semnan University, P.O. Box: 35195--363, Semnan, IranSaeed Mohammadian SemnaniFaculty of Mathematics, Statistics and Computer Science, Semnan University, P.O. Box: 35195--363, Semnan, Iran0000-0001-6755-4911Journal Article20240819This paper presents a new concept in graph theory, focusing on a connected graph's edge eccentricity. We define a new matrix, the maximum edge eccentricity matrix $M_{e_{e}}(\Upsilon)$, which represents the maximum edge distance between all pairs of edges in the graph. This matrix is derived from the graph's structure and the eccentricity values of its edges. Our work explores the characteristics of this matrix, including the determination of specific coefficients within its characteristic polynomial, denoted as $P(\Upsilon,\nu)$. Furthermore, we introduce the concept of maximum edge eccentricity energy $M_{e_{e}}(\Upsilon)$ for connected graphs and provide calculations for well-known graphs. We establish upper and lower bounds for $E_{M_{e_{e}}}(\Upsilon)$ and prove that if the maximum edge eccentricity energy of a graph is rational, it must be an even number.https://ansne.du.ac.ir/article_438_993af8aea015cb7aa068139e9f259e5e.pdfDamghan University PressAnalytical and Numerical Solutions for Nonlinear Equations3060-785X8220241101Numerical Solutions of the Mechanical Vibrations via the Haar Wavelet Segmentation Method19120143910.22128/gadm.2024.875.1120ENAbdolreza MomeniDepartment of Mathematics, Faculty of Mathematics, Statistics and Computer Sciences, Semnan University, P.O. Box 35195-363, Semnan, IranKazem NouriDepartment of Mathematics, Faculty of Mathematics, Statistics and Computer Sciences, Semnan University, P.O. Box 35195-363, Semnan, Iran0000-0002-7922-5848Journal Article20240917Due to the importance of fluctuating nonlinear differential equations in various branches of engineering, basic and applied sciences, various analytical and numerical methods have been used by researchers to solve such equations. Therefore, in this research, we have analyzed and investigated such equations and presented a useful method to find the approximate solutions of these equations, and we have compared the numerical results obtained from this method with their analytical or Runge-Kutta solutions.https://ansne.du.ac.ir/article_439_ae3027670c3465c54e1f3a81c17cdc57.pdfDamghan University PressAnalytical and Numerical Solutions for Nonlinear Equations3060-785X8220241118An Extension of the Min-Max Method for Approximate Solutions of Multiobjective Optimization Problems20221144110.22128/gadm.2024.858.1117ENHossein SalmeiDepartment of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, IranMehran NamjooDepartment of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran0000-0001-5949-6766Journal Article20240806It is a common characteristic of many multiobjective optimization problems that the efficient solution set can only be identified approximately. This study addresses scalarization techniques for solving multiobjective optimization problems. The min-max scalarization technique is considered, and efforts are made to overcome its weaknesses in studying approximate efficient solutions. To this end, two modifications of the min-max scalarization technique are proposed. First, an alternative form of the min-max method is introduced. Additionally, by using slack and surplus variables in the constraints and penalizing violations in the objective function, we obtain easy-to-check conditions for approximate efficiency. The established theorems clarify the relationship between $\varepsilon$-(weakly and properly) efficient solutions of the multiobjective optimization problem and $\epsilon$-optimal solutions of the proposed scalarized problems, without requiring any assumptions of convexity.https://ansne.du.ac.ir/article_441_3ac0fda3f57295d46d8e30eeb59c4d29.pdfDamghan University PressAnalytical and Numerical Solutions for Nonlinear Equations3060-785X8220250120Metric Dimension of $C_n(1, 2, 3)$ for $ n \equiv 0 \pmod{6}$21221746010.22128/ansne.2025.898.1121ENMostafa Mohagheghi NejhadAdib Mazandaran Institute of Higher Education, Sari, Iran.0000-0001-8529-0673Journal Article20241029The <em>metric dimension</em> of a connected graph $G$ is the minimum number of vertices in a subset $B$ of $G$ such that all other vertices are uniquely determined by their distances to the vertices in $B$. In this case, $B$ is called a \textit{metric basis} for $G$ and written $dim(G)=\Vert B\Vert$. We have solved an open problem which shows dimension of circulant graph, $dim(C_n(1,2,3))=4, n \equiv 0 \pmod{6}$. To prove this result, we employ a combination of combinatorial techniques, including distance-based analysis and structural properties of circulant graphs, to carefully analyze the relationship between the graphs structure and its metric dimension. The solution not only answers a previously unresolved question in graph theory but also provides valuable insights into the metric dimensions of more general classes of graphs, particularly in network theory, where understanding the metric dimension is essential for applications in sensor networks, graph-based data storage, and network routing. This work lays the groundwork for future research on the metric dimensions of other families of graphs and has potential applications in optimizing communication and sensor placement in large-scale networks.https://ansne.du.ac.ir/article_460_f3003618255d98c2e428aa9a80dfa0c8.pdfDamghan University PressAnalytical and Numerical Solutions for Nonlinear Equations3060-785X8220250122Some Remarks on $\phi$-Graded Semi-$n$-Absorbing Submodules21822646110.22128/ansne.2025.841.1114ENMohammad Hosein Moslemi KoopaeiDepartment of Mathematics, Roudehen Branch, Islamic
Azad University, Roudehen, IranMasoud ZolfaghariDepartment of Mathematics, Faculty of Mathematics, Statistics and Computer Sciences Semnan University, Semnan, IranJournal Article20240610Let $R$ be a $G$-graded commutative ring with identity and $M$ be a unitary $G$-graded $R$-module. Let $S(M)$ be the set of all graded submodules of $M$ and $\phi:S(M)\rightarrow S(M)\cup \lbrace\emptyset\rbrace$ be a function. A proper graded submodule $N$ of $M$ is called {\em $\phi$-graded semi-$n$-absorbing }submodule if whenever $r \in h(R)$ and $m\in h(M)$ with $r^{n}m\in N\backslash\phi(N)$, then $r^{n}\in (N:M)$ or $r^{n-1}m\in N$ ($n\geq2$). In this work, firstly, we state with deeper results on the structure of generalizations of prime submodules as $\phi $-graded prime submodules. Moreover $\phi$-graded semi-$n$-absorbing submodules are studied and some results are obtained.https://ansne.du.ac.ir/article_461_fc22a4040e1208ab1faf46a679dc5f9f.pdfDamghan University PressAnalytical and Numerical Solutions for Nonlinear Equations3060-785X8220250220On the Index Set of Complete Multipartite Graphs22723246610.22128/ansne.2025.941.1125ENSamaneh BahramianSemnan Branch, Islamic Azad University, Semnan, Iran0000-0002-1710-0126Journal Article20250114For an undirected graph G, and an abelian group A, an A-magic labelling is an assignment of non-zero element of A, to the edges of G, such that the sum of the values of all edges incident with each vertex is constant. A constant on magic sum is called an index set of G. Shiu and Low proved that, zero is in the index set of complete multipartite graph. In this paper, for $t\geq2$ we determine the index set of the complete multipartite graph $K_{n_{1},\ldots,n_{t}}$, where $n_{i}\geq2$ (for $i=1,\ldots,t$).https://ansne.du.ac.ir/article_466_65d920abe2faa047e9811f01ce35e865.pdf