Vali-e-Asr university of RafsanjanWavelet and Linear Algebra2383-193613120260701Solving Tensor Equation Systems under the Semi-Tensor Product: A t-Product Approach14673785710.22072/wala.2026.2079726.1481ENJavadFathiDepartment of Mathematics, University of hormozgan, Bandarabbas, IranJournal Article20251202This paper addresses the solvability of the tensor system A⋉X = B, X ⋉C = D using the<br>semi-tensor product framework. Initially, we examine the associated tensor-vector system<br>under the semi-tensor product operation, deriving necessary and sufficient conditions for<br>the existence of solutions and propose explicit solution methods. Furthermore, we introduce suitable tensor partitioning techniques that enable the reduction of the tensor-vector<br>system to a linear system formulated via the t-product. This approach facilitates a comprehensive study of the solvability of the tensor system when the unknown tensor X is a<br>vector, matrix or a higher-order tensor under the semi-tensor product. We apply the STP<br>framework to model and control Boolean gene regulatory networks with pinning control<br>inputs. Several illustrative examples are provided to demonstrate the applicability and effectiveness of the proposed approaches. Our study includes the tensor equation A⋉X = B<br>and the matrix system A ⋉ X = B, X ⋉ C = D as special cases.https://wala.vru.ac.ir/article_737857_877a760a46fbfe56915115e961d95c45.pdfVali-e-Asr university of RafsanjanWavelet and Linear Algebra2383-193613120260701Results on operator relationships and their ranges equality in \( C^* \)-modules475673785810.22072/wala.2026.2080618.1483ENMahdiAli-AkbariDepartment of Computer Engineering, University of Torbat Heydarieh, Torbat
Heydarieh, IranMehdiMohammadzadeh KarizakiDepartment of Computer Engineering, University of Torbat Heydarieh, Torbat
Heydarieh, Iran0000-0001-7645-1076Journal Article20251212In this paper, by employing the concept of operator ranges and their equality, and utilizing the invertibility of certain operators, we establish the equality of ranges of related operators in Hilbert <br>\(C^{*}\)-modules. The concept of operator ranges, combined with the invertibility of these operators, provides a tool for identifying and proving range equalities of related operators.https://wala.vru.ac.ir/article_737858_245493d4e9352cf3954b15233decaca6.pdfVali-e-Asr university of RafsanjanWavelet and Linear Algebra2383-193613120260701Automatic continuity of linear mappings and homomorphisms on topological algebras576573785910.22072/wala.2026.2081221.1484ENAliNaziri-KordkandiDepartment of Mathematics, Payame Noor University, IranJournal Article20251218In this paper, we investigate the automatic continuity of linear mappings and homomorphisms on certain class of fundamental F-algebras and more generally on topological algebras. Some examples illustrating these results are presented as well.In this paper, we investigate the automatic continuity of linear mappings and homomorphisms on certain class of fundamental F-algebras and more generally on topological algebras. Some examples illustrating these results are presented as welhttps://wala.vru.ac.ir/article_737859_71b5f47c04dbed94941256f2cea6db3e.pdfVali-e-Asr university of RafsanjanWavelet and Linear Algebra2383-193613120260701Generalized Equation Characterizations of Normal Matrices and Applications to Lyapunov, Quadratic, and Matrix Square Root Problems73785610.22072/wala.2026.2075707.1476ENAlimohammadNazariArak university of Iran0000-0002-3231-0340Journal Article20251025This paper explores the Lyapunov, quadratic matrix, and matrix square root equations under normality assumptions on the system matrix, utilizing the Moore-Penrose inverse ($A^\dagger$) for solvability in singular cases. We provide a detailed historical overview and extend our spectral decomposition method to achieve unique solutions for these equations, building on prior work for invertible matrices. The proposed approach handles singular normal matrices via orthogonality conditions on the kernel, and numerical examples confirm its accuracy and efficiency compared to conventional methods.