https://jims.ims.ir/ Journal of the Iranian Mathematical Society en daily 1 Sun, 01 Feb 2026 00:00:00 +0330 Sun, 01 Feb 2026 00:00:00 +0330 https://jims.ims.ir/article_238085.html This paper provides a comprehensive study of geometric properties of variable-exponent Lebesgue-Bochner spaces $L^{p(\cdot)}(E‎, ‎X)$‎. ‎We establish that $L^{p(\cdot)}(E‎, ‎X)$ has the Radon-Nikodym property (RNP) if and only if $X$ does‎, ‎under the condition $p_m > 1$‎. ‎We investigate dentability of specific subsets‎, ‎showing that while the unit ball inherits dentability from $X$‎, ‎the set of simple functions may remain nondentable even when the space possesses RNP‎. ‎The perseverance of uniform convexity and smoothness are shown when both $X$ and $L^{p(\cdot)}(E)$ have these properties‎. ‎We introduce quantitative dentability moduli and relate the dentability modulus of $L^{p(\cdot)}(E,X)$ to that of $X$‎, ‎showing the relevance to the measure of $E$‎, ‎and the oscillation of $p(\cdot)$‎. ‎The paper reveals how variable exponents create hybrid geometries mixing $L^1$ and $L^p$ behaviors‎, ‎with implications for PDE theory‎, ‎optimization‎, ‎and geometric analysis‎. https://jims.ims.ir/article_239013.html A 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_240124.html Let $G=(V‎, ‎E)$ 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_239596.html In this paper‎, ‎we introduce the concepts of Cesàro hypercyclicity and Cesàro transitivity for $C_0$-semigroups‎. ‎We prove that a $C_0$-semigroup is Cesàro transitive if and only if it possesses a dense set of Cesàro hypercyclic vectors‎. ‎Subsequently‎, ‎we demonstrate that Cesàro transitive $C_0$-semigroups are hypercyclic‎. ‎Also‎, ‎we provide an example of a Cesàro hypercyclic $C_0$-semigroup that is not hypercyclic‎. ‎We establish that if a $C_0$-semigroup contains a Cesàro hypercyclic operator‎, ‎then the entire semigroup is Cesàro hypercyclic‎. ‎Furthermore‎, ‎we characterize the structure of Cesàro hypercyclic vectors‎. ‎Additionally‎, ‎we define sequentially Cesàro mixing $C_0$-semigroups that is a subset of Cesàro hypercyclic $C_0$-semigroups‎. ‎We provide certain criteria for sequential Cesàro mixing‎, ‎and use them to make an example of a Cesàro mixing $C_0$-semigroup‎. https://jims.ims.ir/article_240303.html The 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_242204.html In 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 I2-convergence for double sequences‎. ‎We compare (uniformly) almost surely I2-convergence with convergence in measure‎, ‎in mean‎, ‎and in distribution‎. ‎In each case‎, ‎we either show a deductive relation or provide a counterexample‎.