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

Some New Coincidence Point Results in B-Metric Spaces using a Simulation Function

Abderrahmane Boudraa, Taieb Hamaizia*

Annals of Communications in Mathematics 2025

, 8 (3)

, Pages: 343-349

DOI: https://doi.org/10.62072/acm.2025.080301

ABSTRACT. In this paper, we prove a coincidence point theorem in the context of b-metric spaces. The result is achieved by extending the known conditions of existence and uniqueness through the use of simulation functions. An example is also provided to support the obtained result.

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Open AccessArticle

Inferior Semigroups and Ideals

G. Muhiuddin*, Young Bae Jun

Annals of Communications in Mathematics 2025

, 8 (3)

, Pages: 350-362

DOI: https://doi.org/10.62072/acm.2025.080302

ABSTRACT. Inferior semigroups, left (right) inferior ideals and inferior quasi-ideals in semi-groups are introduced, and several properties are investigated. Characterizations of inferior semigroups and ideals are considered, and relations between inferior semigroups, inferior ideals and inferior quasi-ideals are discussed. Characteristic inferior mappings and inferior products of inferior mappings are introduced. Using these notions, related properties on inferior semigroups, left (right) inferior ideals and inferior quasi-ideals are investigated. A regular semigroup is characterized by an inferior quasi-ideal.

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Open AccessArticle

On Some Connections Between Hilbert and Hardy Type Integral Inequalities

Christophe Chesneau

Annals of Communications in Mathematics 2025

, 8 (3)

, Pages: 363-378

DOI: https://doi.org/10.62072/acm.2025.080303

ABSTRACT. This article investigates some new connections between the Hilbert and Hardy integral inequalities. In particular, two general theorems are established, both based on integral terms derived from those used in these two famous inequalities. They have the property of depending on two functions and one modulable parameter. Applications and examples are given to specific cases combining Hilbert and Hardy type integral inequalities. Emphasis is placed on a particular weighted integral term, showing how our results can be used to improve what can be obtained with some classical integral inequalities in the literature.

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Open AccessArticle

Exploring Ideals of Semiring with Involution

M. Murali Krishna Rao, Noorbhasha Rafi*

Annals of Communications in Mathematics 2025

, 8 (3)

, Pages: 379-385

DOI: https://doi.org/10.62072/acm.2025.080304

ABSTRACT. In this paper, we introduce the notion of involution in semirings. We define bi-ideal, quasi ideal, interior ideal, bi-quasi interior ideal, and bi-interior ideals of semirings with involution and study their properties.

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Open AccessArticle

On Some Trigonometric and Inverse Trigonometric Integral Formulas

Christophe Chesneau

Annals of Communications in Mathematics 2025

, 8 (3)

, Pages: 386-392

DOI: https://doi.org/10.62072/acm.2025.080305

ABSTRACT. This paper presents a new collection of trigonometric and inverse trigonometric integral formulas based on a known integral result. Some of these formulas evaluate to zero, while others are notable for their connection to well-known mathematical constants, such as π,√ 2, and the Catalan constant. Comprehensive proofs are provided for all results, and an open problem is posed to inspire further investigation.

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Open AccessArticle

Tribonacci Cordial Labeling of Some Snake Graphs

Ariel C. Pedrano*, Melaine Vieve S. Gudin

Annals of Communications in Mathematics 2025

, 8 (3)

, Pages: 393-405

DOI: https://doi.org/10.62072/acm.2025.080306

ABSTRACT. An injective function f : V (G) → {T0, T1, T2, . . . , Tn}, where n = |V (G)| − 1, is said to be a Tribonacci cordial labeling if the induced function f ∗ E(G) →{0, 1} defined by f∗(uv) = (f(u) + f(v)) mod 2 satisfies the condition |ef (0) − ef (1)| ≤ 1 where ef (0) is the number of edges with label 0 and ef (1) is the number of edges with label 1. A graph that admits a tribonacci cordial labeling is called a Tribonacci cordial graph. In this paper, we determined the Tribonacci Cordial Labeling of Triangular Snake Graph T Sn, Double Triangular Snake Graph D(T Sn), Quadrilateral Snake Graph QSn, Double Quadrilateral Snake Graph D(QSn), and Cycle Quadrilateral Snake Graph C(QSn).

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Open AccessArticle

Solution of the Millennium Problem for the Navier-Stokes Equations

Alexander G. Ramm

Annals of Communications in Mathematics 2025

, 8 (2)

, Pages: 406-409

DOI: https://doi.org/10.62072/acm.2025.080307

ABSTRACT. One of the millennium problems can be stated as follows: can there be smooth, not vanishing identically initial data for the Navier-Stokes equations in R such that the corresponding solution to the NSP (Navier-Stokes problem) exists for all times t ≥ 0? We prove that such a solution does not exist.

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Open AccessArticle

Fuzzy Bi-Quasi-Interior Ideals of Semirings

Ganesh Kumar Reddi, M. Murali Krishna Rao, Rajendra Kumar Kona*, Vineela B

Annals of Communications in Mathematics 2025

, 8 (3)

, Pages: 410-424

DOI: https://doi.org/10.62072/acm.2025.080308

ABSTRACT.In this paper, we introduce the notion of a fuzzy bi-quasi interior ideal as a generalization of fuzzy ideals, fuzzy bi-quasi ideals, fuzzy quasi-interior ideals and fuzzy bi-interior ideals of a semiring. We prove that every fuzzy right quasi-interior ideal of a semiring is a fuzzy bi-quasi interior ideal and a fuzzy bi-quasi interior ideal is a fuzzy right tri-ideal of a semiring. We characterize the regular semiring in terms of fuzzy bi-quasi interior ideals and study some of the properties.

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Open AccessArticle

Subexponential Computation of Truncated Theta Series

Francesco Sica

Annals of Communications in Mathematics 2025

, 8 (3)

, Pages: 425-430

DOI: https://doi.org/10.62072/acm.2025.080309

ABSTRACT. We describe an algorithm to compute in $O(e^{c\sqrt{ k\log k}})$ binary operations, for some absolute constant $c>0$, expressions like $\sum_{1\leq n\leq 2^\alpha} e^{\frac{2\pi i n^2}{2^k}} n^a$ and $\sum_{\substack{1\leq n\leq 2^\alpha\\ 1\leq m\leq 2^\beta}} e^{\frac{2\pi i nm}{2^k}} n^a m^b$ where $\alpha,\beta= O(k)$ and $a,b$ are fixed (small) nonnegative integers. The error terms in these computations are $O(e^{-c k})$.

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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

AbstractLet D be a connected bounded domain in R^2, S be its boundary which is closed, connected, and smooth, or S=(-∞,∞). Let Φ(z) be the function defined as Φ(z)=1/(2πi) ∫S(f(s)ds)/(s-z), where f∈L^1(S) and z=x+iy. The singular integral operator Af is defined as Af: =1/(iπ) ∫S(f(s)ds)/(s-t), where t∈S. This new definition simplifies the proof of the existence of Φ(t). Necessary and sufficient conditions are given for f∈L^1(S) to be the boundary value of an analytic function in D. The Sokhotsky-Plemelj formulas are derived for f∈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, Rajendra Kumar Kona*

Annals of Communications in Mathematics 2023

, 6 (4)

, Pages: 225-237

DOI: https://doi.org/10.62072/acm.2023.060403

AbstractIn this paper, we introduce the notion of a fuzzy soft tri-ideal over Γ−semiring. We characterize the regular Γ−semiring in terms of fuzzy soft tri-ideals, and study some of the properties. M is a regular Γ−semiring, E be a parameters set and A ⊆ E. If (µ, A) is a fuzzy soft left tri-ideal over M, then (µ, A) is a fuzzy soft right ideal over M.

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Open AccessArticle