Vali-e-Asr university of RafsanjanWavelet and Linear Algebra2383-193612220251201Redundancy and frame potential of finite frames11473322710.22072/wala.2024.2033719.1456ENMahdieh SadatAghaeiDepartment of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran.Mohammad AliHasankhani FardDepartment of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran.0000-0001-5734-1576Journal Article20240625This paper is concentrated on redundancy and frame potential of finite frames in $n$-dimensional Hilbert space $\mathcal{H}_n$. More precisely, all possible finite frame redundancies are characterized. Also, all possible frame potential of finite frames with prescribed norms is characterized. Finally, the results are presented for dimensions $n=2$ and $n=3$. ...https://wala.vru.ac.ir/article_733227_20d46f7bbe9725a08dea0160983c9eb5.pdfVali-e-Asr university of RafsanjanWavelet and Linear Algebra2383-193612220251201MAPS PRESERVING MIXED JORDAN TRIPLE PRODUCT OF OPERATORS ON PRIME ALGEBRAS152373322810.22072/wala.2025.2052271.1469ENSheidaAsghariDepartment of Mathematics, Faculty of Mathematical Sciences, University of MazandaranRojaHosseinzadehDepartment of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, P. O. Box 47416-1468, Babolsar, Iran.Journal Article20250203Let $\mathcal{A}$ and $\mathcal{B}$<br>be unital prime algebras and $\mathcal{A}$ contains a non-trivial idempotent $P_1$.<br>We consider a bijective map $\phi: \mathcal{A} \rightarrow \mathcal{B}$ which satisfies<br>\begin{equation*}<br>\phi (A.BoA)= \phi (A). \phi(B)o \phi(A)<br>\end{equation*}<br>for every element $A,B\in \mathcal{A}$, where '.' is a usual product and "$\circ$" is a Jordan product.https://wala.vru.ac.ir/article_733228_a7d523480af07bee7976731438e56274.pdfVali-e-Asr university of RafsanjanWavelet and Linear Algebra2383-193612220251201A Robust Optimization Approach244773357910.22072/wala.2025.2052894.1470ENAtefehMohebiSharif University of TechnologyHosseinMohebiShahid Bahonar University of KermanJournal Article20250208The theory of constrained best approximation in Hilbert spaces has been systematically developed well over a decade and effective characterizations of best approximations have been known under some qualifications on the constraints. Yet, the existing theory does not explain how to characterize a best approximation in the face of data uncertainty in the constraints, despite the reality that the data of the constraints are often uncertain (that is, they are not known exactly) due to estimation errors, prediction errors or lack of information. This paper explains when the best approximation over uncertain linear constraints in a real Hilbert space is immunized against bounded data uncertainty. This study is done by characterizing the best approximation of the robust counterpart of the uncertain constrained best approximation problem where the constraints are enforced for all possible uncertainties within the prescribed uncertainty sets. We show that under a new robust strong conical hull intersection property (robust strong CHIP) the same kind of effective characterizations of constrained best approximation hold for the robust best approximation that is immunized against bounded data uncertainty. We also establish a strong duality theorem for the robust constrained best approximation problem and its associated dual problem under the robust strong CHIP. Some examples are given to illustrate the obtained results.https://wala.vru.ac.ir/article_733579_e30b9dd56aefe51dda25a07ba73fab7c.pdfVali-e-Asr university of RafsanjanWavelet and Linear Algebra2383-193612220251201An Operator Bundle admitting no Frames485373358010.22072/wala.2025.2076825.1479ENMohammad BagherAsadiSchool of Mathematics, Statistics and Computer Science, College of Science, University of
Tehran, Tehran, IranZahraHassanpour-YakhdaniSchool of Mathematics, Statistics and Computer Science, College of Science, University of
Tehran, Tehran, IranJournal Article20251105In [4], we use equivariant functions on the space of irreducible representations<br>of a C∗-algebra A to develop a duality theory for Hilbert C∗-modules. Within this<br>framework, each Hilbert C∗-module corresponds to an operator bundle defined<br>over the set of all non-zero irreducible representations of A.<br>In this short note, we characterize the condition under which operator bundles,<br>regarded as Hilbert C∗-modules admit no frames.https://wala.vru.ac.ir/article_733580_ee6c6263545aad1ba78e4577572e4afc.pdfVali-e-Asr university of RafsanjanWavelet and Linear Algebra2383-193612220251201Mutual extraction of Bäcklund transformations and Lax representations for the Korteweg–de Vries equation73524810.22072/wala.2026.2082722.1487ENSayed MohammadHoseiniMathematics Dep. Vali-E-Asr University of RafsanjanAbedini MohajeriRezaVali-e-Asr Rafsanjan UniversityJournal Article20251231In this paper, we investigate the intrinsic relationship between Bäcklund transformations and Lax representations for the Korteweg–de Vries (KdV) equation. Viewing the KdV equation within the framework of integrable hierarchies, we analyze how its Bäcklund transformations encode the underlying spectral structure. We demonstrate that the Lax pair of the KdV equation can be systematically derived from its Bäcklund transformations, and conversely, that the Bäcklund transformations can be reconstructed directly from the associated Lax representation. This bidirectional correspondence clarifies the geometric and algebraic role of Bäcklund transformations as discrete symmetries of the KdV equation and highlights their interpretation as Darboux-type transformations acting on the spectral problem.