The Annals of Communications in Mathematics (ACM) is an international, interdisciplinary, open-access journal which provides an advanced forum for studies related to mathematical sciences that has been fully refereed since 2018. It devotes exclusively to the publication of high-quality reviews, regular research papers and short communications in all areas of Pure and Applied Mathematics. ACM also publishes timely and thorough survey articles on current trends, new theoretical techniques, novel ideas, and new Mathematical tools in different branches of Mathematics.
Editorial office e-mail: editor@technoskypub.com
Editor-in-Chief: G. Muhiuddin, University of Tabuk, KSA
Article Processing Charge
There is no article processing or publication charges. The journal is free for both authors and readers.
Open Access ArticleSectional Semi-B-Near lattices: A Hierarchy, Filters, and Congruences
B. Tharuni, Naveen Kumar Kakumanu*, S. S. Raju, Y. Ravi Babu and G Laxmi Prasanna
Annals of Communications in Mathematics 2026
, 9(3)
, 15
DOI: https://doi.org/10.62072/acm.2026.09047
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.
Open Access ArticleThe Exponentiated Cosine Gompertz Distribution: Properties, Estimation, and Application to Lifetime Data
Sule Omeiza Bashiru*, Ibrahim Ali and Alhaji Modu Isa
Annals of Communications in Mathematics 2026
, 9(3)
, 14
DOI: https://doi.org/10.62072/acm.2026.09046
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.
Open Access ArticleOn topological characterizations of rough automata and their primary decomposition
Shambhu Sharan*, Nitish Kumar and Rakesh Kumar
Annals of Communications in Mathematics 2026
, 9(3)
, 13
DOI: https://doi.org/10.62072/acm.2026.09045
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.
Open Access ArticleA Note on JNB-algebras
Daniel A. Romano
Annals of Communications in Mathematics 2026
, 9(3)
, 12
DOI: https://doi.org/10.62072/acm.2026.09044
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 \( (An) \).
Open Access ArticleOn Bipolar Complex Intuitionistic Fuzzy Multi-Polygroups
A.I. Isah, P. Ayuba, N. Mubarak* and P.A. Ejegwa
Annals of Communications in Mathematics 2026
, 9(3)
, 11
DOI: https://doi.org/10.62072/acm.2026.09043
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.
Open Access ArticleA Modified Hill Cipher Cryptosystem Using Columnar Transposition for end-to-end Communication
Mohammed Ibrahim Anyass*, Mohammed Muniru Iddrisu and Peter Awon-natemi Agbedemnab
Annals of Communications in Mathematics 2026
, 9(3)
, 10
DOI: https://doi.org/10.62072/acm.2026.09042
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.
Open Access ArticleTime-dependent Axial Fluid Flow in an Annulus: A Semi-Analytical Approach
Jibrin Danjuma Yahaya*, Bamidele David Michael, Abraham Ayegba Alfa, Isaac Adaji, Aminu Ibrahim, Raji Muhammed and Agbata Benedict Celestine
Annals of Communications in Mathematics 2026
, 9(3)
, 9
DOI: https://doi.org/10.62072/acm.2026.09041
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.
Open Access ArticleGeneralization of an Inequality by Laforgia and Natalini
Kwara Nantomah
Annals of Communications in Mathematics 2026
, 9(3)
, 8
DOI: https://doi.org/10.62072/acm.2026.09040
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.
Open Access ArticleOn 2-Movable Connected Domination of Some Graphs
Grachelle M. Bangcal and Ariel C. Pedrano*
Annals of Communications in Mathematics 2026
, 9(3)
, 7
DOI: https://doi.org/10.62072/acm.2026.09039
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 \( W_{m,n} \).
Open Access ArticleOuter-connected convex Roman domination in graphs
Leomarich F. Casinillo
Annals of Communications in Mathematics 2026
, 9(3)
, 6
DOI: https://doi.org/10.62072/acm.2026.09038
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.
Open Access ArticleOn 2-Movable Total Domination in the Join and Corona of Graphs
Ariel C. Pedrano* and Rolando N. Paluga
Annals of Communications in Mathematics 2026
, 9(3)
, 5
DOI: https://doi.org/10.62072/acm.2026.09037
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.
Open Access ArticleOn Ideal Leras Generalized Closed Sets in Ideal Leras Topological Spaces
I. Rajasekaran* and A. Ahamed Habeba
Annals of Communications in Mathematics 2026
, 9(3)
, 4
DOI: https://doi.org/10.62072/acm.2026.09036
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.
Open Access ArticleBoolean-Centred Negation and Involutive Envelopes in 𝐵-Algebras
Naveen Kumar Kakumanu*, B. Tharuni, S. S. Raju and Noorbasha Rafi
Annals of Communications in Mathematics 2026
, 9(3)
, 3
DOI: https://doi.org/10.62072/acm.2026.09035
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.
Open Access ArticleIdeal Structures in Leras Topological Spaces
I. Rajasekaran* and R. Jeni Siyoni
Annals of Communications in Mathematics 2026
, 9(3)
, 2
DOI: https://doi.org/10.62072/acm.2026.09034
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.
Open Access ArticleAnalysis of a host-vector disease model with fixed moments pulse interventions
Boureima Ouedraogo and Ali Traore*
Annals of Communications in Mathematics 2026
, 9(3)
, 1
DOI: https://doi.org/10.62072/acm.2026.09033
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.
Open AccessArticleAnalysis of a host-vector disease model with fixed moments pulse interventions
Boureima Ouedraogo and Ali Traore*
Annals of Communications in Mathematics 2026
, 9(3)
, 1
DOI: https://doi.org/10.62072/acm.2026.09033
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.
Open AccessArticleIdeal Structures in Leras Topological Spaces
I. Rajasekaran* and R. Jeni Siyoni
Annals of Communications in Mathematics 2026
, 9(3)
, 2
DOI: https://doi.org/10.62072/acm.2026.09034
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.
Open AccessArticleBoolean-Centred Negation and Involutive Envelopes in 𝐵-Algebras
Naveen Kumar Kakumanu*, B. Tharuni, S. S. Raju and Noorbasha Rafi
Annals of Communications in Mathematics 2026
, 9(3)
, 3
DOI: https://doi.org/10.62072/acm.2026.09035
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.
Open AccessArticleOn Ideal Leras Generalized Closed Sets in Ideal Leras Topological Spaces
I. Rajasekaran* and A. Ahamed Habeba
Annals of Communications in Mathematics 2026
, 9(3)
, 4
DOI: https://doi.org/10.62072/acm.2026.09036
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.
Open AccessArticleOn 2-Movable Total Domination in the Join and Corona of Graphs
Ariel C. Pedrano* and Rolando N. Paluga
Annals of Communications in Mathematics 2026
, 9(3)
, 5
DOI: https://doi.org/10.62072/acm.2026.09037
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.
Open AccessArticleOuter-connected convex Roman domination in graphs
Leomarich F. Casinillo
Annals of Communications in Mathematics 2026
, 9(3)
, 6
DOI: https://doi.org/10.62072/acm.2026.09038
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.
Open AccessArticleOn 2-Movable Connected Domination of Some Graphs
Grachelle M. Bangcal and Ariel C. Pedrano*
Annals of Communications in Mathematics 2026
, 9(3)
, 7
DOI: https://doi.org/10.62072/acm.2026.09039
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 \( W_{m,n} \).
Open AccessArticleGeneralization of an Inequality by Laforgia and Natalini
Kwara Nantomah
Annals of Communications in Mathematics 2026
, 9(3)
, 8
DOI: https://doi.org/10.62072/acm.2026.09040
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.
Open AccessArticleTime-dependent Axial Fluid Flow in an Annulus: A Semi-Analytical Approach
Jibrin Danjuma Yahaya*, Bamidele David Michael, Abraham Ayegba Alfa, Isaac Adaji, Aminu Ibrahim, Raji Muhammed and Agbata Benedict Celestine
Annals of Communications in Mathematics 2026
, 9(3)
, 9
DOI: https://doi.org/10.62072/acm.2026.09041
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.
Open AccessArticleA Modified Hill Cipher Cryptosystem Using Columnar Transposition for end-to-end Communication
Mohammed Ibrahim Anyass*, Mohammed Muniru Iddrisu and Peter Awon-natemi Agbedemnab
Annals of Communications in Mathematics 2026
, 9(3)
, 10
DOI: https://doi.org/10.62072/acm.2026.09042
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.
Open AccessArticleOn Bipolar Complex Intuitionistic Fuzzy Multi-Polygroups
A.I. Isah, P. Ayuba, N. Mubarak* and P.A. Ejegwa
Annals of Communications in Mathematics 2026
, 9(3)
, 11
DOI: https://doi.org/10.62072/acm.2026.09043
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.
Open AccessArticleA Note on JNB-algebras
Daniel A. Romano
Annals of Communications in Mathematics 2026
, 9(3)
, 12
DOI: https://doi.org/10.62072/acm.2026.09044
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 \( (An) \).
Open AccessArticleOn topological characterizations of rough automata and their primary decomposition
Shambhu Sharan*, Nitish Kumar and Rakesh Kumar
Annals of Communications in Mathematics 2026
, 9(3)
, 13
DOI: https://doi.org/10.62072/acm.2026.09045
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.
Open AccessArticleThe Exponentiated Cosine Gompertz Distribution: Properties, Estimation, and Application to Lifetime Data
Sule Omeiza Bashiru*, Ibrahim Ali and Alhaji Modu Isa
Annals of Communications in Mathematics 2026
, 9(3)
, 14
DOI: https://doi.org/10.62072/acm.2026.09046
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.
Open AccessArticleSectional Semi-B-Near lattices: A Hierarchy, Filters, and Congruences
B. Tharuni, Naveen Kumar Kakumanu*, S. S. Raju, Y. Ravi Babu and G Laxmi Prasanna
Annals of Communications in Mathematics 2026
, 9(3)
, 15
DOI: https://doi.org/10.62072/acm.2026.09047
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.
Open Access ArticleOn Five Original Integral Inequalities of the Hardy-Hilbert Type
Christophe Chesneau
Annals of Communications in Mathematics 2025
, 8 (4)
, Pages: 431-441
DOI: https://doi.org/10.62072/acm.2025.080401
Abstract:This article is devoted to five distinct integral inequalities of the Hardy-Hilbert type, each possessing its own originality. In particular, we highlight new trigonometric variants that yield sharp upper bounds involving weighted integral norms of the underlying functions. Complete and rigorous proofs are provided in detail.
Open Access ArticleOn Logarithmic Cordial Labelling of Some Graphs
Jason D. Andoyo
Annals of Communications in Mathematics 2025
, 8 (4)
, Pages: 459-471
DOI: https://doi.org/10.62072/acm.2025.080404
Abstract:Let \( n \ge 3 \) be an integer with primitive root \( \varpi \). For a simple connected graph \( G \) of order \( n \), a bijective function \( f : V(G) \to \{1,2,\ldots,n\} \) is called a logarithmic cordial labeling to the base \( \varpi \) modulo \( n \) if the induced function \( f_{\varpi,n}^{*} : E(G) \to \{0,1\} \) is defined by\[f_{\varpi,n}^{*}(ab)=\begin{cases}0, \text{ if } \mathrm{ind}_{\varpi,n}(f(a)+f(b)) \equiv 0 \pmod 2 \text{ or } \gcd(f(a)+f(b),n)\neq 1, \\1, \text{ if } \mathrm{ind}_{\varpi,n}(f(a)+f(b)) \equiv 1 \pmod 2,\end{cases}\]and satisfies the condition \( |e_{f_{\varpi,n}}(0) - e_{f_{\varpi,n}}(1)| \le 1 \), where \( e_{f_{\varpi,n}}(i) \) is the number of edges with label \( i \ (i=0,1) \).
Open Access Article(a, b)-Fibonacci–Legendre Cordial Graphs and k-Pisano–Legendre Primes
Jason D. Andoyo
Annals of Communications in Mathematics 2026
, 9(1)
, Pages: 11
DOI: https://doi.org/10.62072/acm.2026.09011
Abstract:Let \( p \) be an odd prime and let \( F_i \) be the \( i \)th \( (a,b) \)-Fibonacci number with initial values \( F_0 = a \) and \( F_1 = b \). For a simple connected graph \( G = (V,E) \), define a bijective function \( f : V(G) \rightarrow \{0,1,\ldots,|V|-1\} \). If the induced function \( f_p^* : E(G) \rightarrow \{0,1\} \), defined by \( f_p^*(uv) = \frac{1+((F_{f(u)}+F_{f(v)})/p)}{2} \) whenever \( F_{f(u)} + F_{f(v)} \not\equiv 0 \; (\text{mod } p) \) and \( f_p^*(uv) = 0 \) whenever \( F_{f(u)} + F_{f(v)} \equiv 0 \; (\text{mod } p) \), satisfies the condition \( |e_f^*(0) - e_f^*(1)| \leq 1 \) where \( e_f^*(i) \) is the number of edges labeled \( i \) (\( i = 0,1 \)), then \( f \) is called a \( (a,b) \)-Fibonacci-Legendre cordial labeling modulo \( p \). In this paper, the \( (a,b) \)-Fibonacci-Legendre cordial labeling of path graphs, star graphs, wheel graphs, and graphs under the operations join, corona, lexicographic product, cartesian product, tensor product, and strong product is explored in relation to \( k \)-Pisano-Legendre primes relative to \( (a,b) \). We also present some properties of \( k \)-Pisano-Legendre primes relative to \( (a,b) \) and numerical observations on its distribution, leading to several conjectures concerning their density and growth behavior.
Open Access ArticleCorrection of a Proof of an Inequality Involving the Polygamma Function
Kwara Nantomah
Annals of Communications in Mathematics 2026
, 9(1)
, Pages: 16
DOI: https://doi.org/10.62072/acm.2026.09016
Abstract:The proof of Lemma 5 in the paper ”Corrigendum to A Harmonic Mean Inequality for the Polygamma Function” [Math. Inequal. Appl., 27(2)(2024), 273-274] contains an error. The purpose of this paper is to correct the error.
Open Access ArticleStatistical Gauge Convergence and Its Induced Topology in Metric Spaces
İsmail Osmanoğlu
Annals of Communications in Mathematics 2026
, 9(2)
, Pages: 2
DOI: https://doi.org/10.62072/acm.2026.09018
Abstract:This paper introduces statistical gauge convergence as a refinement of statistical convergence in metric spaces, where deviations from the limit are controlled by positive continuous functions rather than fixed constants. We provide equivalent density based characterizations and examine their relationship with both classical and statistical convergence, showing that the corresponding implications are strict in general. Further more, we investigate the topology generated by this convergence and prove that it is typically finer than the underlying metric topology. Several examples are included to clarify the hierarchical structure among the considered notions of convergence.
Open Access ArticleOn a new logarithmic modification of the Hilbert integral inequality
Christophe Chesneau
Annals of Communications in Mathematics 2026
, 9(2)
, Pages: 6
DOI: https://doi.org/10.62072/acm.2026.09022
Abstract:The Hilbert integral inequality is a well-known and widely studied result in analysis that has inspired many refinements and modifications. In this paper, we present a new logarithmic modification of this inequality. Our approach is based on a trigonometric method that offers a fresh perspective on existing standard techniques. As a consequence, we also derive another integral inequality. All arguments are presented in full detail.
Open Access ArticleOn Total Product Cordial Labeling of Some Snake Graphs
Ariel C. Pedrano* and Rex Ryan A. Marquez
Annals of Communications in Mathematics 2026
, 9(2)
, Pages: 8
DOI: https://doi.org/10.62072/acm.2026.09024
Abstract:A total product cordial labeling of a graph \( G \) is a function \( f : V \rightarrow \{0,1\} \). For each \( xy \), assign the label \( f(x)f(y) \); \( f \) is called total product cordial labeling of \( G \) if it satisfies the condition that \( |v_f(0)+e_f(0)-v_f(1)-e_f(1)| \leq 1 \) where \( v_f(i) \) and \( e_f(i) \) denote the set of vertices and edges which are labeled with \( i = 0,1 \), respectively. A graph with a total product cordial labeling defined on it is called a total product cordial graph. In this paper, we determined the total product cordial labeling of the snake graphs \( T_n \), \( A(T_n) \), \( D(T_n) \), \( DA(T_n) \), \( Q_n \), \( A(Q_n) \), \( D(Q_n) \), and \( DA(Q_n) \).
Open Access ArticleInfinitely many Concrete Multiple-Composite and Amplified Fuzzy ordinary and Fractional Neural Network Approximations
George A. Anastassiou
Annals of Communications in Mathematics 2026
, 9(2)
, Pages: 10
DOI: https://doi.org/10.62072/acm.2026.09026
Abstract:Here we investigate further the univariate fuzzy ordinary and fractional quantitative approximation of fuzzy real valued functions on a compact interval. This is done by quasi-interpolation sigmoid multicomposite activation functions based infinitely many specific and amplified multicomposite fuzzy neural network operators. These approximations are derived by establishing fuzzy multicomposite Jackson type inequalities involving the fuzzy moduli of continuity of the function, or of the right and left Caputo fuzzy fractional derivatives of the involved function. The approximations are fuzzy pointwise and fuzzy uniform. The related feed-forward fuzzy multicomposite neural networks are with one hidden layer. We study in particular the fuzzy integer derivative and just fuzzy continuous cases. Our fuzzy fractional multicomposite approximation result using higher order fuzzy differentiation converges better than in the multicomposite fuzzy just continuous case. All these approximations are generated by 7 specific and basic activation functions.
Open Access
Article
q-Deformed and L-parametrized hyperbolic tangent function relied complex valued multivariate trigonometric and hyperbolic neural network approximations
George A. Anastassiou
Annals of Communications in Mathematics 2023
, 6 (3)
, Pages: 141-164
DOI: https://doi.org/10.62072/acm.2023.060301
Abstract:Here we study the multivariate quantitative approximation of complex valued continuous functions on a box of RN , N ∈ N, by the multivariate normalized type neural network operators. We investigate also the case of approximation by iterated multilayer neural network operators. These approximations are achieved by establishing multidimen-sional Jackson type inequalities involving the multivariate moduli of continuity of the en- gaged function and its partial derivatives. Our multivariate operators are defined by using a multidimensional density function induced by a q-deformed and λ-parametrized hyper-bolic tangent function, which is a sigmoid function. The approximations are pointwise and uniform. The related feed-forward neural network are with one or multi hidden layers. The basis of our theory are the introduced multivariate Taylor formulae of trigonometric and hyperbolic type.
Open Access
Article
Quotient quasi-ordered residuated systems induced by quasi-valuation maps
Daniel A. Romano
Annals of Communications in Mathematics 2023
, 6 (3)
, Pages: 199-208
DOI: https://doi.org/10.62072/acm.2023.060305
Abstract:The concept of quasi-ordered residuated systems was introduced in 2018 by Bonzio and Chajda as a generalization both of commutative residuated lattices and hoopalgebras. Then this author investigated the substructures of ideals and filters in these algebraic structures. As a continuation of these research, in this article we design the concept of quotient quasi-ordered residuated systems induced by a quasi-valuation on it. Additionally, we prove some important properties of the thus constructed quotient structure.
Open Access
Article
On Some Results about Bipolar Soft Ideals of Gamma Near-rings
Filiz Çitak* and Seher Kahraman Erturk
Annals of Communications in Mathematics 2025
, 8 (2)
, Pages: 163-172
DOI: https://doi.org/10.62072/acm.2025.080201
Abstract:With the advancement of scientific studies, problems involving uncertainty have emerged. Classical mathematics needed to be more robust to model or make sense of these uncertain problems. Due to this insufficiency, scientists have put forward new theories. One of them is the soft set theory, which Molodtsov first studied. Then, many researchers have done various studies in different fields using soft sets. In this study, bipolar soft ideals of a gamma near-ring were defined. Some basic properties of this algebraic structure have been analyzed. The bipolar soft coset set was determined with the help of bipolar soft ideals, and this set was shown to be a gamma near-ring. Finally, a function was defined with the help of bipolar soft ideals of a gamma near-ring, and this study concluded by showing that this function is a gamma near-ring epimorphism.
Open Access
Article
On Jerusalem Square Fractal, Its Construction and Properties
Akhlaq Husain
Annals of Communications in Mathematics 2025
, 8 (2)
, Pages: 293-298
DOI: https://doi.org/10.62072/acm.2025.080211
Abstract:This short communication proposes a novel Iterated Function System (IFS) to construct the Jerusalem square fractal, a two-dimensional projection of the Jerusalem cube, characterized by its cross-like self-similar structure. We provide a step-by-step con- struction, a proof of its fractal nature, and Python code for visualization. Properties such as self-similarity, fractal dimension, and connectivity are analyzed with formal proofs. The IFS offers a new perspective on Jerusalem square fractal generation. Results demonstrate the fractal’s intricate geometry, with applications in computer graphics and geometric mod- eling.
Open Access
Article
α-product Soft Matrices
Amutha. K, P. Balaji* and S. Sivaramakrishnan
Annals of Communications in Mathematics 2025
, 8 (2)
, Pages: 225-233
DOI: https://doi.org/10.62072/acm.2025.080207
AbstractIn this paper, we define α-Product Soft Matrices which generalize the Product Soft Matrices. Further, we also provide a decision theory using these α-Product Soft Matrices. As a practical application, we formulate a novel approach to environmental toxicology by modeling multi-layered chemical interactions in aquatic ecosystems.
Open Access
Article
New definition of a singular integral operator
Alexander G. Ramm
Annals of Communications in Mathematics 2023
, 6 (4)
, Pages: 220-224
DOI: https://doi.org/10.62072/acm.2023.060402
Abstract:Let \( D \) be a connected bounded domain in \( \mathbb{R}^{2} \), \( S \) be its boundary which is closed, connected and smooth or \( S = (-\infty,\infty) \). Let\[\Phi(z) = \frac{1}{2\pi i}\int_{S} \frac{f(s)\, ds}{s - z}, \qquad f \in L^{1}(S), \; z = x + iy.\]The singular integral operator\[Af := \frac{1}{\pi i}\int_{S} \frac{f(s)\, ds}{s - t}, \qquad t \in S,\]is defined in a new way. This definition simplifies the proof of the existence of \( \Phi(t) \). Necessary and sufficient conditions are given for \( f \in L^{1}(S) \) to be a boundary value of an analytic function in \( D \). The Sokhotsky–Plemelj formulas are derived for \( f \in L^{1}(S) \). Our new definition allows one to treat singular boundary values of analytic functions.
Open Access
Article
Fuzzy soft tri-ideals over Gamma-semirings
M. Murali Krishna Rao, Noorbasha Rafi and Rajendra Kumar Kona*
Annals of Communications in Mathematics 2023
, 6 (4)
, Pages: 225-237
DOI: https://doi.org/10.62072/acm.2023.060403
Abstract:In this paper, we introduce the notion of a fuzzy soft tri-ideal over \( \Gamma \)-semiring. We characterize the regular \( \Gamma \)-semiring in terms of fuzzy soft tri-ideals, and study some of the properties. \( M \) is a regular \( \Gamma \)-semiring, \( E \) be a parameters set and \( A \subseteq E \). If \( (\mu, A) \) is a fuzzy soft left tri-ideal over \( M \), then \( (\mu, A) \) is a fuzzy soft right ideal over \( M \).
Open Access
Article
Fuzzy Weak-interior Ideals of Semirings
Marapureddy Murali Krishna Rao
Annals of Communications in Mathematics 2025
, 8 (2)
, Pages: 188-195
DOI: https://doi.org/10.62072/acm.2025.080204
Abstract:In this paper, we introduce the notion of a fuzzy weak interior ideal as a generalization of a fuzzy ideal of a semiring. We characterize the regular semiring in terms of fuzzy weak interior ideals of a semiring.
Open Access
Article
Revisiting an Existing Integral Inequality
Christophe Chesneau
Annals of Communications in Mathematics 2025
, 8 (2)
, Pages: 173-183
DOI: https://doi.org/10.62072/acm.2025.080202
Abstract:In this article, we revisit a well-known result from the literature that can be considered a variant of the Hardy integral inequality. First, we present a counterexample to demonstrate the invalidity of the current formulation. We then revise the result by identifying and addressing a gap in the original proof. Finally, as an additional contribution, we derive a new integral inequality.
Open Access
Article
A K-analogue of the Lambda Gamma Function and its Properties
Kwara Nantomah, Mohammed Muniru Iddrisu and Sunday Sandow*
Annals of Communications in Mathematics 2025
, 8 (2)
, Pages: 209-224
DOI: https://doi.org/10.62072/acm.2025.080206
AbstractThis paper establishes a k-analogue of the lambda gamma function and in troduces a k-Riemann zeta function and a k-lambda Riemann zeta function. In addition, the paper establishes a relationship between the k-analogue of the lambda gamma function, the k-Riemann zeta function and the k-lambda Riemann zeta function. Finally, the paper establishes some properties of the k-analogue of the lambda gamma function similar to existing properties satisfied by the classical gamma function, the k-analogue of the gamma function and the lambda gamma function.
