Annals of Communications of Mathematics

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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

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Open AccessArticle

On 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.

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Open AccessArticle

On Pendant Domination Polynomial in the Corona of Some Graphs

Ariel C. Pedrano* and Christine R. Giganto

Annals of Communications in Mathematics 2025

, 8 (4)

, Pages: 442-450

DOI: https://doi.org/10.62072/acm.2025.080402

ABSTRACT.A dominating set \( S \) in \( G \) is called a pendant dominating set if \( \langle S \rangle \) contains at least one pendant vertex. The minimum cardinality of a pendant dominating set is called the pendant domination number, denoted by \( \gamma_{pe}(G) \). The pendant domination polynomial of \( G \) is denoted by \( D_{pe}(G,x) \) and is defined as\[D_{pe}(G,x)=\sum_{i=\gamma_{pe}(G)}^{n} d_{pe}(G,i)\,x^{i},\]where \( d_{pe}(G,i)x^{i} \) is the number of pendant dominating sets of size \( i \). In this paper, we obtained the pendant domination number and pendant domination polynomial of the corona of some graphs, namely, \( P_m \circ K_n \), \( C_m \circ K_n \), and \( K_m \circ K_n \).

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Open AccessArticle

On Lucas Cordial Labeling of Some Snake Graphs

Ariel C. Pedrano* and Ernesto R. Salise Jr.

Annals of Communications in Mathematics 2025

, 8 (4)

, Pages: 451-458

DOI: https://doi.org/10.62072/acm.2025.080403

ABSTRACT. An injective function \( f : V(G) \to \{L_1, L_2, \ldots, L_n\} \), where \( L_j \) is the \( j^{\text{th}} \) Lucas number \( (j=1,2,\ldots,n) \), is said to be a Lucas cordial labeling if the induced function \( f^{*} : E(G) \to \{0,1\} \) defined by \( f^{*}(uv) = (f(u)+f(v)) \pmod 2 \) satisfies \( |e_f(0)-e_f(1)| \le 1 \). A graph admitting such labeling is called a Lucas cordial graph.

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Open AccessArticle

On 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 \( i \ (i=0,1) \).

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Open AccessArticle

A Review of Recent Generalized Probability Distribution Families: Advances and Applications

Sule Omeiza Bashiru

Annals of Communications in Mathematics 2025

, 8 (4)

, Pages: 472-485

DOI: https://doi.org/10.62072/acm.2025.080405

ABSTRACT. Probability distributions are essential tools for modeling, prediction, and statistical inference. In recent years, several generalized families of distributions have been proposed to extend classical models and increase their flexibility in capturing complex data behaviors. This paper reviews selected generalized families published between 2023 and 2025, focusing on their construction mechanisms, statistical properties, estimation methods, and real-world applications. The families discussed include trigonometric-based, inverse, Lomax-generated, Topp–Leone, and hybrid forms. To illustrate their performance, five families were combined with the exponential distribution and fitted to a real dataset. The comparison shows that all extended models provide an adequate fit, while the standard exponential model performs poorly. The findings confirm the practical value of generalized families in improving data modeling.

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Open AccessArticle

On a Generalized Hardy Integral Inequality

Christophe Chesneau

Annals of Communications in Mathematics 2025

, 8 (4)

, Pages: 486-500

DOI: https://doi.org/10.62072/acm.2025.080406

ABSTRACT. In this article, we present a new generalized version of the Hardy integral inequality. It has the property of depending on an auxiliary function. Thanks to this function, numerous variants are examined. The theory is complemented by two secondary results, one showing that the main inequality can be improved under additional assumptions, and another giving a valuable lower bound for the main integral term. Several examples are given for illustration.

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Open AccessArticle

General Multi-Composite Sigmoid Relied Banach Space Valued Univariate Neural Network Approximation

George A. Anastassiou

Annals of Communications in Mathematics 2025

, 8 (4)

, Pages: 501-514

DOI: https://doi.org/10.62072/acm.2025.080407

ABSTRACT. Here we research the univariate multi-composite sigmoid activated quantitative approximation of Banach space valued continuous functions on a compact interval or all the real line by quasi-interpolation Banach space valued multi-composite sigmoid activated neural network operators. We perform also the related Banach space valued multi-composite sigmoid activated fractional approximation. These multi-composite sigmoid acti-vated approximations are derived by establishing Jackson type inequalities involving the modulus of continuity of the engaged function or its Banach space valued high order derivative or fractional derivatives. Our operators are deÖned by using a multi-composite density function induced by a gen- eral multi-composite sigmoid function. The approximations are pointwise and with respect to the uniform norm. The related Banach space valued feed-forward neural networks are with one hidden layer. We Önish with a convergence analysis.

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Open AccessArticle

Properties of Hybrid Structures in Groupoids

B. Elavarasan, G. Muhiuddin*, K. Porselvi, Mohamed E. Elnair and Taif Alshehri

Annals of Communications in Mathematics 2025

, 8 (4)

, Pages: 515-529

DOI: https://doi.org/10.62072/acm.2025.080408

ABSTRACT. Classical mathematical methods are insufficient for resolving certain issues in real-life human problems due to the uncertainty of the data. Researchers from around the world have created innovative mathematical models, like soft and fuzzy set theories, to model the uncertainties that arise in different areas. Jun recently developed a hybrid structure that combined fuzzy and soft set concepts. The hybrid structure principle is applied to groupoids in this paper, and the properties of hybrid ideals and hybrid subgroupoids in groupoids are also described. Furthermore, the notions of hybrid subgroups, hybrid normal subgroups, and hybrid cosets in a group, as well as their key properties, are discussed. In addition, we show that any member of the collection of hybrid cut sets of a hybrid normal subgroup of a group G is a normal subgroup of G in the traditional sense. Finally, we obtain a finite-group hybrid version of Lagrange’s theorem.

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Open AccessArticle

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

AbstractHere 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.

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Open AccessArticle

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

AbstractThe 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.

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Open AccessArticle

Trigonometric generated Lp degree of approximation

George A. Anastassiou

Annals of Communications in Mathematics 2023

, 6 (4)

, Pages: 209-219

DOI: https://doi.org/10.62072/acm2023060401

AbstractIn this article we continue the study of smooth Picard singular integral operators that started in [3], see there chapters 10-14. This time the foundation of our research is a trigonometric Taylor’s formula. We establish the Lp convergence of our operators to the unit operator with rates via Jackson type inequalities engaging the first Lp modulus of continuity. Of interest here is a residual appearing term. Note that our operators are not positive.

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Open AccessArticle

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.

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Open AccessArticle

Fuzzy soft tri-ideals over Gamma-semirings

M. Murali Krishna Rao, Noorbhasha 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 \( M \).

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Open AccessArticle