Annals of Communications in Mathematics

Abstract:In our study, we propose a vector-host epidemic model with fixed-time pulse interventions guided by population size of susceptible humans and susceptible vectors. This approach aims to reflect the situation where public health interventions, namely, vaccination campaigns, mass treatments, insecticide spraying, or sterile mosquito releases, are generally implemented periodically rather than continuously. A saturated incidence function is used to fit the situation where the number of infective cases is getting larger with the limited medical facilities. The model incorporates a general rule of implementation of control measures such us vaccination, treatment and mosquitoes elimination. We theoretically investigate the dynamic behavior with the appearance of (k + m)T - periodic solutions. Firstly, we derive the existence and stability of the order-1 (k + 1)T - disease-free periodic solution with nonnegative integer k and the order-m (1 + m)T -disease-free periodic solution with m being any positive integer. Furthermore, we study the existence and stability of the disease-free (1 + 2)T -periodic solution. In addition, numerical simulations are performed to support the theoretical results. Our results indicate that there exists a critical monitoring period or vaccination rate such that the intervention strategy can successfully control the disease.

Abstract:This paper presents the notion of ideal leras topological spaces as an extension of leras topological spaces. The connections between these two classes of spaces are examined in detail. Different forms of closed sets arising in ideal leras topological spaces are introduced and their interrelations are discussed. Several characterizations and fundamental properties associated with these sets are obtained. Examples are included to clarify the introduce concepts and the corresponding results.

Abstract:This paper studies \( B \)-algebras through the Boolean-centre-valued operators \( x^\nabla = 1 \to x \) and \( x^\Delta = 0 \leftarrow x \). The operator \( {}^\Delta \) defines a centre-valued negation satisfying \( (x \vee y)^\Delta = x^\Delta \wedge y^\Delta \) for all \( x,y \in A \), together with the inequality \( x^\Delta \vee y^\Delta \leq (x \wedge y)^\Delta \). Equality in the latter holds on the Boolean centre \( B(A) \); an explicit example confirms that restricting to \( B(A) \) is necessary. The Boolean centre, equipped with the restricted operations, satisfies the equations of one standard axiomatisation of Nelson algebras [14]. An involutive distributive lattice \( \mathcal{N}(A) = A \times A \) is constructed together with an injective map \( \iota(x) = (x,x^\Delta) \). The embedding preserves joins globally and preserves meets on \( B(A) \). Prime-spectrum and prime-filter representation results are obtained for \( B \)-algebras. Under an injectivity condition on the pseudo-supplement map, an ultrafilter representation follows. The bi-implication \( x \leftrightarrow y = (x \Rightarrow y) \wedge (y \Rightarrow x) \) characterises equality and satisfies a transitivity inequality.

Abstract: The purpose of this paper is to extend the study of generalized closed sets in leras topological spaces to the ideal setting. Using the leras local function and leras \( \star \)-closure operator associated with an ideal, we introduce and investigate two new classes of sets, called \( ideal\ leras\ generalized\ closed\ sets \) (\( I_{lrg} \)-closed sets) and \( ideal\ leras\ generalized\ open\ sets \) (\( I_{lrg} \)-open sets), in ideal leras topological spaces. We show that every \( lrg \)-closed set is \( I_{lrg} \)-closed, and that every \( I^\star \)-closed set is \( I_{lrg} \)-closed, while the converses fail in general, thereby placing the new classes correctly within the existing hierarchy of sets in leras and ideal leras topological spaces. Several characterizations of \( I_{lrg} \)-closed sets are obtained, including formulations in terms of the leras \( \star \)-closure operator, the leras closures of singletons, and the non-existence of nonempty \( Ir \)-closed sets in certain associated difference sets. Additional properties, such as finite unions of \( I_{lrg} \)-closed sets being \( I_{lrg} \)-closed and sufficient conditions under which \( I_{lrg} \)-closed sets coincide with \( lrg \)-closed sets, are also established. Appropriate examples are constructed throughout to illustrate the developed concepts and to demonstrate that the implications obtained cannot, in general, be reversed.

Abstract:Let \( G \) be a connected graph. A non-empty set \( T \subseteq V(G) \) is a 2-movable total dominating set of \( G \) if \( T \) is a total dominating set and for every pair \( x,y \in T \), \( T \setminus \{x,y\} \) is a total dominating set in \( G \), or there exist \( u,v \in V(G) \setminus T \) such that \( u \) and \( v \) are adjacent to \( x \) and \( y \), respectively, and \( (T \setminus \{x,y\}) \cup \{u,v\} \) is a total dominating set in \( G \). The 2-movable total domination number of \( G \), denoted by \( \gamma_{mt}^{2}(G) \), is the minimum cardinality of a 2-movable total dominating set of \( G \). A 2-movable total dominating set with cardinality equal to \( \gamma_{mt}^{2}(G) \) is called a \( \gamma_{mt}^{2} \)-set of \( G \). This paper presents the 2-movable total domination in the join and corona of graphs.

Abstract: Let \( G = (V(G),E(G)) \) be a connected graph and let \( \alpha = (V_0,V_1,V_2) \) be a CvRDF on \( G \). A function \( \alpha \) is an outer-connected convex Roman dominating function (OCCvRDF) on \( G \) provided that for every \( v \in V_0 \), there exists \( u \in V_2 \) such that \( uv \in E(G) \), \( V_1 \cup V_2 \) is a convex set on \( G \), and \( \langle V_0 \rangle \) is a connected subgraph. The weight of OCCvRDF \( \alpha \) is denoted by \( \widetilde{\omega}_G^{cCvR}(\alpha) \) and is defined as \( \widetilde{\omega}_G^{cCvR}(\alpha) = \sum_{z \in V(G)} \alpha(z) = |V_1| + 2|V_2| \). The outer-connected convex Roman domination number of graph \( G \) is denoted by \( \widetilde{\gamma}_{cCvR}(G) \) and is defined as the minimum weight of an OCCvRDF \( \alpha \) on \( G \), which can be written as \( \widetilde{\gamma}_{cCvR}(G) = \min\{\widetilde{\omega}_G^{cCvR}(\alpha) : \alpha \text{ is an OCCvRDF on } G\} \). Each OCCvRDF \( \alpha \) on \( G \) satisfying the equation \( \widetilde{\omega}_G^{cCvR}(\alpha) = \widetilde{\gamma}_{cCvR}(G) \) is called a \( \widetilde{\gamma}_{cCvR} \)-function on \( G \). In this paper, we introduce a new study of convex Roman domination in graphs, called the outer-connected convex Roman dominating function, and give some of its graph-theoretic properties.

Abstract:A connected dominating set \( C \) in \( G \) is a 2-movable connected dominating set of \( G \) if for every pair \( x,y \in C \), \( C \setminus \{x,y\} \) is a connected dominating set in \( G \), or there exists \( u,v \in V(G) \setminus C \) such that \( u \) and \( v \) are adjacent to \( x \) and \( y \), respectively, and \( (C \setminus \{x,y\}) \cup \{u,v\} \) is a connected dominating set of \( G \). The minimum cardinality of a 2-movable connected dominating set of \( G \), denoted by \( \gamma_{mc}^{2}(G) \) is the 2-movable connected domination number of \( G \). A 2-movable connected dominating set with cardinality \( \gamma_{mc}^{2}(G) \) is called a minimum 2-movable connected dominating set or a \( \gamma_{mc}^{2} \)-set of \( G \). In this paper, the researcher obtained the 2-movable connected domination number of the Complete Graph \( K_n \), Join Graph \( G + H \), and Generalized Wheel Graph \( W_{m,n} \).

Abstract:In this short paper, we establish a generalization of an inequality involving the Rieman zeta function. The inequality was established by Laforgia and Natalini in 2006 and subsequently improved by other researchers. The main tools used to prove our results are the logarithmic convexity property of the Riemann zeta function and monotonicity properties of certain functions containing the Riemann zeta function.

Abstract:This study presents a semi-analytical solution for the start-up pressure-driven axial flow of an incompressible Newtonian fluid between two stationary concentric cylinders. The governing unsteady momentum equation is transformed using the Laplace technique, yielding closed-form expressions for the velocity and wall-shear distributions in terms of modified Bessel functions. The inverse transforms are evaluated by a Riemann-sum approximation, while exact steady-state solutions are derived for validation. For \( \lambda = 0.2 \), the velocities at \( R = 0.4, 0.6, \) and \( 0.8 \) reach \( 94.28\% \), \( 94.39\% \), and \( 95.06\% \) of their steady values at \( T = 0.2 \), respectively. By \( T = 0.4 \), the maximum deviation from the steady solution decreases to \( 0.41\% \), and at \( T = 10^4 \) agreement is obtained to four decimal places. Increasing the radius ratio from \( 0.4 \) to \( 0.8 \) reduces the steady inner-wall shear from \( 0.3730 \) to \( 0.1042 \), a \( 72.06\% \) decrease, while the outer-wall shear magnitude decreases from \( 0.2708 \) to \( 0.0967 \), corresponding to a \( 64.29\% \) reduction. The main contribution is a compact, root-free benchmark formulation that combines the transient axial velocity, signed wall-shear histories and exact steady-state limits within a single computational framework.

Abstract:Digital communication among individuals, institutions, and enterprises across internet-based platforms has grown substantially over the past decades. This sharp increase has greatly exposed sensitive information to adversarial attacks and to substantial data losses. Although many cryptosystems have been proposed and implemented to address these challenges, daily reports continue to reveal successful attacks. In this paper, we propose a symmetric-key cryptosystem to improve message security. The proposed system combines the classical Hill cipher with columnar transposition. It uses four distinct keys: two square key matrices and two additional keys termed ‘key-within-key’ (𝜔). The Hill cipher is enhanced by expanding the character space to include all printable ASCII characters, mitigating known-plaintext attacks. The key space is doubled by using the transpose of the key matrix as a second key. Encryption is performed in two rounds, each round employing two of the four keys; decryption follows the reverse process. Matlab simulation conducted was observed to display efficient results.

Abstract:This paper introduces the idea of complex numbers to intuitionistic fuzzy sets which enhances the representation of uncertain, hesitant and ambiguous data. By integrating the complex-valued intuitionistic fuzzy membership and non-membership functions with the algebraic structure of multi-polygroups known as Complex Intuitionistic Fuzzy Multi-Polygroups (CIFMPGs). This extension addresses the limitations of classical fuzzy and intuitionistic fuzzy multi-polygroups by introducing both amplitude and phase into the representation of membership values. The basic operations and structural properties were studied such as complement, intersection, containment and cartesian product. Their closure properties on those operations were also established. Furthermore, the concept of Bipolar Complex Intuitionistic Fuzzy Multi-Polygroups (BCIFMPGs) was introduced by integrating the degrees of positive and negative complex-valued membership and non-membership into the multi-polygroups structure. The bipolar extension leads to an algebraic representation of positive and negative information together with amplitude and phase. Basic operations on BCIFMPGs such as intersection and complement were defined, and their closure properties. The introduced structures generalize intuitionistic fuzzy multi-polygroups to complex-valued settings, opening the way for further theoretical study of fuzzy algebraic structures.

Abstract: As a generalization of the self-distributive BE-algebra, the concept of JNB-algebras is introduced in 2025 by Y. B. Jun et al., and its basic properties are investigated. In this short note, we show that in every JNB-algebra \( A = (A, \ast, 1) \), the natural congruence relation \( \equiv \) can be determined such that the factor-algebra \( A/\equiv \) is an aBE-algebra, that is, it is a JNB-algebra that additionally satisfies the conditions \( (Ex) \) and \( (An) \).

Abstract:This paper presents a topological approach to the study of rough automata.We introduce the core of a rough automaton and show that it naturally induces a topology on the state set. We show that this topology is preserved under the product of rough automata. We further establish topological characterizations of definite and possible primary subautomata in terms of regular closed sets. Based on these characterizations, we prove primary decomposition theorems for compact rough automata. Overall, this work clarifies the theoretical interplay among rough sets, topology, and automata.

Abstract:The cosine Gompertz distribution has been proposed as an extension of the classical Gompertz model; however, its hazard rate is restricted to an increasing shape. To overcome this limitation, we introduce the Exponentiated Cosine Gompertz Distribution (ECGD) by applying the exponentiated family approach to the cosine Gompertz distribution. The proposed model offers greater flexibility in describing different hazard-rate patterns, including decreasing, increasing, and bathtub-shaped behaviors. Some mathematical properties of the ECGD are derived, and its parameters are estimated using the methods of maximum likelihood, maximum product of spacings, Anderson–Darling, and Cramér–von Mises. A simulation study is conducted to assess the performance of these estimation methods, with the results indicating satisfactory estimation performance across the considered scenarios. The practical applicability of the ECGD is demonstrated using a real-world dataset, where it provides a better fit than several competing models. These results indicate that the proposed distribution is a useful and flexible model for reliability analysis.

Abstract: Near-Heyting algebras generalise Heyting algebras to distributive nearlattices, linking each principal upset’s Heyting structure by a global identity. Sectional Hilbert nearlattices [23] drop this identity and instead build a filter and congruence theory from sectional residuation alone. We extend this programme to the Epstein–Horn \( B \)-algebra setting [11,24]. A sectional semi-\( B \)-nearlattice (SSBN-algebra) is a distributive nearlattice \( (A,\vee,1) \) whose implication \( \Rightarrow \) restricts, on every principal upset \( [a) \), to a semi-\( B \)-algebra satisfying the Birkhoff-center adjunction \( x \wedge_a b \leq z \Longleftrightarrow b \leq x \Rightarrow z \). SSBN-algebras sit in a hierarchy \( \mathbf{N_sB} \subseteq \mathbf{SSBN} \subset \mathbf{DNSB} \) between near-semi-\( B \)-algebras and the strictly larger class of distributive nearlattice semi-\( B \)-algebras. Within this hierarchy, ordinary (non-sectional) semi-\( B \)-algebras and near-semi-\( B \)-algebras turn out to be incomparable classes, with neither containing the other. For downward-directed SSBN-algebras, we build a complete lattice of implicative semi-\( B \)-filters and characterise generated filters through a sectional meet; this repairs a natural implication-based formula that fails when the adjoined element is not a Birkhoff element. From this characterisation we obtain an unconditional prime extension theorem, a separation theorem, a prime-spectrum embedding, and a congruence-and-quotient theory for the semi-\( B \)-algebra reduct.