Iranian Mathematical SocietyJournal of the Iranian Mathematical Society2717-16127120260201Geometry of variable-exponent Bochner-Lebesgue spaces: Dentability, Radon-Nikodym property, and uniform convexity11223808510.30504/jims.2026.567288.1310ENM.YaremenkoNational Technical University of Ukraine, “Igor Sikorsky Kyiv Polytechnic Institute”, Kyiv, Ukraine.0000-0002-9209-6059Journal Article20251219This paper provides a comprehensive study of geometric properties of variable-exponent Lebesgue-Bochner spaces $L^{p(\cdot)}(E<span lang="AR-SA" style="font-family: 'Arial',sans-serif; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi;"></span>, <span lang="AR-SA" style="font-family: 'Arial',sans-serif; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi;"></span>X)$<span lang="AR-SA" style="font-family: 'Arial',sans-serif; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi;"></span>. <span lang="AR-SA" style="font-family: 'Arial',sans-serif; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi;"></span>We establish that $L^{p(\cdot)}(E, X)$ has the Radon-Nikodym property (RNP) if and only if $X$ does, <span lang="AR-SA" style="font-family: 'Arial',sans-serif; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi;"></span>under the condition $p_m > 1$<span lang="AR-SA" style="font-family: 'Arial',sans-serif; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi;"></span>. <span lang="AR-SA" style="font-family: 'Arial',sans-serif; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi;"></span>We investigate dentability of specific subsets<span lang="AR-SA" style="font-family: 'Arial',sans-serif; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi;"></span>, <span lang="AR-SA" style="font-family: 'Arial',sans-serif; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi;"></span>showing that while the unit ball inherits dentability from $X$<span lang="AR-SA" style="font-family: 'Arial',sans-serif; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi;"></span>, <span lang="AR-SA" style="font-family: 'Arial',sans-serif; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi;"></span>the set of simple functions may remain nondentable even when the space possesses RNP<span lang="AR-SA" style="font-family: 'Arial',sans-serif; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi;"></span>. <span lang="AR-SA" style="font-family: 'Arial',sans-serif; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi;"></span>The perseverance of uniform convexity and smoothness are shown when both $X$ and $L^{p(\cdot)}(E)$ have these properties<span lang="AR-SA" style="font-family: 'Arial',sans-serif; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi;"></span>. <span lang="AR-SA" style="font-family: 'Arial',sans-serif; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi;"></span>We introduce quantitative dentability moduli and relate the dentability modulus of $L^{p(\cdot)}(E,X)$ to that of $X$<span lang="AR-SA" style="font-family: 'Arial',sans-serif; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi;"></span>, <span lang="AR-SA" style="font-family: 'Arial',sans-serif; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi;"></span>showing the relevance to the measure of $E$<span lang="AR-SA" style="font-family: 'Arial',sans-serif; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi;"></span>, <span lang="AR-SA" style="font-family: 'Arial',sans-serif; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi;"></span>and the oscillation of $p(\cdot)$<span lang="AR-SA" style="font-family: 'Arial',sans-serif; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi;"></span>. <span lang="AR-SA" style="font-family: 'Arial',sans-serif; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi;"></span>The paper reveals how variable exponents create hybrid geometries mixing $L^1$ and $L^p$ behaviors<span lang="AR-SA" style="font-family: 'Arial',sans-serif; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi;"></span>, <span lang="AR-SA" style="font-family: 'Arial',sans-serif; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi;"></span>with implications for PDE theory<span lang="AR-SA" style="font-family: 'Arial',sans-serif; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi;"></span>, <span lang="AR-SA" style="font-family: 'Arial',sans-serif; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi;"></span>optimization<span lang="AR-SA" style="font-family: 'Arial',sans-serif; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi;"></span>, <span lang="AR-SA" style="font-family: 'Arial',sans-serif; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi;"></span>and geometric analysis<span lang="AR-SA" style="font-family: 'Arial',sans-serif; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-bidi-theme-font: minor-bidi;"></span>.https://jims.ims.ir/article_238085_74858c10672f1866351aa1776e771dfb.pdfIranian Mathematical SocietyJournal of the Iranian Mathematical Society2717-16127120260201Analysis of balance in the products of conjugate Skew Gain graphs132323901310.30504/jims.2026.547899.1285ENK.BijuDepartment of Mathematics, PRNSS College, Mattanur, Kannur University, Kerala, India.0000-0002-8809-8019K.Shahul HameedResearch Supervisor
Hermann Gundert Central Library, Kannur University, Kerala, India0000-0003-0905-3865Journal Article20250918A conjugate skew gain graph is a graph whose edges are oriented and assigned labels—termed edge skew gains—from the multiplicative group $\mathbb{C}^\times$ of nonzero complex numbers, such that reversing the orientation of an edge replaces its label with its complex conjugate. In this article, we define various products of conjugate skew gain graphs such as the cartesian product, the lexicographic product, the strong product, and the tensor product. We characterize the balance in these product graphs in terms of the balance of the constituent conjugate skew gain graphs.https://jims.ims.ir/article_239013_fa9b6fd7c8a6f8e4f16a40fd1b58b4aa.pdfIranian Mathematical SocietyJournal of the Iranian Mathematical Society2717-16127120260201Identifying code number of some of the middle graphs253424012410.30504/jims.2026.538124.1271ENH.Nadimi DafraziDepartment of Mathematics, Faculty of Science, Imam Khomeini International University, P.O. Box 34148-96818, Qazvin, Iran.E.VatandoostDepartment of Mathematics, Faculty of Science, Imam Khomeini International University, P.O. Box 3414896818, Qazvin, Iran.Journal Article20250730Let $G=(V, E)$ be a simple graph. A subset $C$ of vertices of $G$ is an identifying code of $G$ if for every two vertices $x$ and $y$ the sets $N_{G}[x] \cap C$ and $N_{G}[y] \cap C$ are distinct and non-empty. Given a graph $G,$ the smallest size of an identifying code of $G$ is called the identifying code number of $G$ and is denoted by $\gamma^{ID}(G).$ In this paper, we show that for every graph $G,$ the middle graph of $G$ is an identifiable graph. We prove that the identifying code number of the middle graph of $G$ is at most $|V(G)|$. Also, we determine the identifying code number of the middle graph of some graphs. In particular, we determine the identifying code number of the middle graph of a bipartite graph.https://jims.ims.ir/article_240124_d45b88cf3ca438bbd0cb9446059a3483.pdfIranian Mathematical SocietyJournal of the Iranian Mathematical Society2717-16127120260201Cesàro hypercyclicity and transitivity for $C_0$-semigroups354223959610.30504/jims.2026.559943.1298ENM.MoosapoorDepartment of Mathematics Education, Farhangian
University, P.O. Box 14665-889, Tehran, Iran.0000-0003-4194-6495M.Shams YousefiFaculty of Mathematical Sciences, University of Guilan, Rasht, Iran.Journal Article20251115In this paper<span lang="AR-SA"></span>, <span lang="AR-SA"></span>we introduce the concepts of Ces<span>à</span>ro hypercyclicity and Cesàro transitivity for $C_0$-semigroups<span lang="AR-SA"></span>. <span lang="AR-SA"></span>We prove that a $C_0$-semigroup is Cesàro transitive if and only if it possesses a dense set of Cesàro hypercyclic vectors<span lang="AR-SA"></span>. <span lang="AR-SA"></span>Subsequently<span lang="AR-SA"></span>, <span lang="AR-SA"></span>we demonstrate that Cesàro transitive $C_0$-semigroups are hypercyclic<span lang="AR-SA"></span>. <span lang="AR-SA"></span>Also<span lang="AR-SA"></span>, <span lang="AR-SA"></span>we provide an example of a Cesàro hypercyclic $C_0$-semigroup that is not hypercyclic<span lang="AR-SA"></span>. <span lang="AR-SA"></span>We establish that if a $C_0$-semigroup contains a Cesàro hypercyclic operator<span lang="AR-SA"></span>, <span lang="AR-SA"></span>then the entire semigroup is Cesàro hypercyclic<span lang="AR-SA"></span>. <span lang="AR-SA"></span>Furthermore<span lang="AR-SA"></span>, <span lang="AR-SA"></span>we characterize the structure of Cesàro hypercyclic vectors<span lang="AR-SA"></span>. <span lang="AR-SA"></span>Additionally<span lang="AR-SA"></span>, <span lang="AR-SA"></span>we define sequentially Cesàro mixing $C_0$-semigroups that is a subset of Cesàro hypercyclic $C_0$-semigroups<span lang="AR-SA"></span>. <span lang="AR-SA"></span>We provide certain criteria for sequential Cesàro mixing<span lang="AR-SA"></span>, <span lang="AR-SA"></span>and use them to make an example of a Cesàro mixing $C_0$-semigroup<span lang="AR-SA"></span>.https://jims.ims.ir/article_239596_6020c1a9aef046d4e6d23349748f0303.pdfIranian Mathematical SocietyJournal of the Iranian Mathematical Society2717-16127120260201On the domination roots of friendship graphs and book graphs435124030310.30504/jims.2026.572620.1318ENAZeydi AbdianDepartment of Computer Science, Shahid Bahonar University of Kerman, Kerman, Iran.S.AlikhaniDepartment of Mathematical Sciences, Yazd University, 89195-741, Yazd, Iran.0000-0002-1801-203XJournal Article20260128The domination polynomial of a graph $G$ of order $n$ is $D(G,x)=\sum_{i=1}^{n} d(G,i) x^i$, where $d(G,i)$ is the number of dominating sets of $G$ of size $i$. For the friendship graph $F_n$, which is the join of $K_1$ with $nK_2$, the domination polynomial is known to be $D(F_n,x)=(2x+x^2)^n+x(1+x)^{2n}$. Motivated by proposed open problems in [S. Alikhani, J.I. Brown, S. Jahari, On the domination polynomials of friendship graphs, Filomat 30:1 (2016), 169-178], we prove that for every even positive integer $n$, $D(F_n,x)$ has exactly three real roots: $x=0$, one root in $(-2,-1)$, and one root in $(-1,0)$. Second, we establish an asymptotic upper bound on the modulus of the complex domination roots of $F_n$: for any root $x$ of $D(F_n,x)$ and for sufficiently large $n$, we have $|x| \leq \sqrt{2n/\ln n} + 1$, so that $|x| = O\left(\sqrt{n/\ln n}\right)$. Furthermore, we address the domination roots of the book graph $B_n$, obtained by gluing $n$ copies of $C_4$ along a common edge. We describe the limiting curve of the roots of $D(B_n,x)$ as $n\to\infty$ and provide an asymptotic bound on their moduli. These results provide a deeper understanding of the nature of domination roots for these important families of graphs.https://jims.ims.ir/article_240303_1b9da19779da2e72e4215e77f0e7e441.pdfIranian Mathematical SocietyJournal of the Iranian Mathematical Society2717-16127120260201On I2-convergence of complex uncertain double sequences536624220410.30504/jims.2026.573153.1320ENA.HalderDepartment of Mathematics, Tripura University (A Central University), Suryamaninagar, 799022, Agartala, India.0000-0002-3059-7202S.DebnathDepartment of Mathematics, Tripura University (A Central University), Suryamaninagar, 799022, Agartala, India.0000-0003-2804-6564Journal Article20260131In the context of the uncertainty theory of Liu, we extend the notion of I-convergence of complex uncertain sequences for a single sequence to that of I<sub>2</sub>-convergence for double sequences. We compare (uniformly) almost surely I<sub>2</sub>-convergence with convergence in measure, in mean, and in distribution. In each case, we either show a deductive relation or provide a counterexample. https://jims.ims.ir/article_242204_132294e63eb0391842db55f36a44573e.pdf