Annals of Communications in Mathematics

An International Journal

(ISSN 2582-0818)
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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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There is no article processing or publication charges. The journal is free for both authors and readers.

Open AccessArticle

e⋆-local Functions and Ψe⋆ -operator in Ideal Topological Spaces

Annals of Communications in Mathematics 2024

, 7 (1)

, 1-9

DOI: https://doi.org/10.62072/acm.2024.070101

AbstractThe main goal of this paper is to introduce another local function to give the possibility of obtaining a Kuratowski closure operator. On the other hand, e⋆-local functions defined for ideal topological spaces have not been found in the current literature. e⋆-local functions for the ideal topological spaces have been described within this work. Moreover, with the help of e⋆-local functions Kuratowski closure operators cl∗e⋆ I and τ ∗e⋆ topology are obtained. Many theorems in the literature have been revised according to the definition of e⋆-local functions
Open AccessArticle

On Interval Valued Fuzzy Prime Ideals of Γ−semirings

Annals of Communications in Mathematics 2024

, 7 (1)

, 10-20

DOI: https://doi.org/10.62072/acm.2024.070102

AbstractIn this paper, we introduce the notion of interval valued fuzzy prime ideals of Γ−semirings.We study, some properties of prime ideals of a Γ−semirng in terms of interval valued fuzzy ideals.
Open AccessArticle

Quasistatic Evolution of Damage in Thermo-electro-elastic-viscoplastic Materials With Normal Compliance

Annals of Communications in Mathematics 2024

, 7 (1)

, 21-41

DOI: https://doi.org/10.62072/acm.2024.070103

AbstractWe have studied contact problem in a quasistatic process with boundary conditions, for which we couple a thermal effect and damage and electrical effect. We assume that the contact is with normal compliance in a form with a gap function and is associated to a slip rate-dependent version of Coulomb’s law of dry friction. We give the variational formulation, then the existence and the uniqueness of the weak solution. The proof is based on arguments of time-dependent variational inequalities, parabolic inequalities, and fixed points.
Open AccessArticle

Distributional Boundary Values of Analytic Functions

Annals of Communications in Mathematics 2024

, 7 (1)

, 42-46

DOI: https://doi.org/10.62072/acm.2024.070104

Abstract

Let D be a connected bounded domain in R2, S be its boundary which is closed, connected and smooth. Let Φ(z) = 1/2πi ∫S φ(s)ds/(s-z), φ ∈ X, z = x + iy, X is a Banach space of linear bounded functionals on Hμ, a Banach space of distributions, and Hμ is the Banach space of Hoelder-continuous functions on S with the usual norm. As X one can use also the space Hoelder continuous of bounded linear functionals on the Sobolev space Hℓ on S. Distributional boundary values of Φ(z) on S are studied in detail. The function Φ(t), t ∈ S, is defined in a new way. Necessary and sufficient conditions are given for φ ∈ X to be a boundary value of an analytic in D function. The Cauchy formula is generalized to the case when the boundary values of an analytic function in D are tempered distributions. The Sokhotsky-Plemelj formulas are derived for φ ∈ X.

Open AccessArticle

On Relative (2, 2)-Γ-hyperideals of 2-duo Ordered Γ-semihypergroups

Annals of Communications in Mathematics 2024

, 7 (1)

, 47-56

DOI: https://doi.org/10.62072/acm.2024.070105

AbstractIn this paper, first we obtain the necessary and sufficient condition for an ordered Γ-semihypergroup H to be a relative completely regular 2-duo ordered Γ-semihypergroup for any relative (2, 2)-Γ-hyperideal as well as for any relative (2, 2)-quasi-Γ-hyperideal of H. Then, we find the necessary and sufficient condition that Q = (Q2]S for every relative (2, 2)-Γ-hyperideal Q of H to be a relative quasi-Γ-prime with S ⊆ H. Finally, we prove the necessary and sufficient condition for relative (2, 2)-Γ-hyperideal to be a relative quasi-Γ-prime for a relative completely regular and relative (2, 2)-Γ-hyperideal of H making a chain with inclusive relation.
Open AccessArticle

Common Limit Range Property in Neutrosophic Menger Spaces

Annals of Communications in Mathematics 2024

, 7 (1)

, 57-70

DOI: https://doi.org/10.62072/acm.2024.070106

AbstractThe aim of this paper is to prove some common fixed-point theorems for weakly compatible mappings in Neutrosophic Menger Spaces satisfying common limit range property. Some examples are also given which demonstrate the validity of our results. As an application of our main result, we present a common fixed point theorems for four finite families of self-mappings in Menger spaces.
Open AccessArticle

Ordered Γ-semihypergroup of the Associated Γ-semihypergroup with All Relative Bi-Γ-hyperideals

Annals of Communications in Mathematics 2024

, 7 (1)

, 71-79

DOI: https://doi.org/10.62072/acm.2024.070107

AbstractIn this paper, the main goal is to study an ordered Γ-semihypergroup H in the context of the characterizations of the associated Γ-semihypergroup B(H) of all bi-Γ-hyperideals of H. We show that an ordered Γ-semihypergroup H is a Clifford ordered Γ-semihypergroup if and only if B(H) is a semilattice. We also show that a Γsemihypergroup B(H) is a normal band if and only if the ordered Γ-semihypergroup H is simultaneously regular and intra regular. Furthermore, for each subclass S with many bands, we prove that for an ordered Γ-semihypergroup H, the conditional inclusion B(H) ∈ S holds true.
Open AccessArticle

Some New Results on JU-algebras

Annals of Communications in Mathematics 2024

, 7 (1)

, 80-90

DOI: https://doi.org/10.62072/acm.2024.070108

AbstractJU-algebra (or weak KU-algebra) is a generalization of a KU-algebra. The concepts of atoms in JU-algebras are introduced and their important basic properties are registered. In addition to the previous one, an extension of a (weak) KU-algebra A to the JU-algebra A ∪ {w} was designed.
Open AccessArticle

q-Deformed and L-parametrized hyperbolic tangent function relied complex valued multivariate trigonometric and hyperbolic neural network approximations

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.
Open AccessArticle

Quotient quasi-ordered residuated systems induced by quasi-valuation maps

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.

Open AccessArticle

Trigonometric generated Lp degree of approximation

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.
Open AccessArticle

New definition of a singular integral operator

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.
Open AccessArticle

Fuzzy soft tri-ideals over Gamma-semirings

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.

Open AccessArticle

q-Deformed and L-parametrized hyperbolic tangent function relied complex valued multivariate trigonometric and hyperbolic neural network approximations

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.
Open AccessArticle

Quotient quasi-ordered residuated systems induced by quasi-valuation maps

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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