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Volume 6, Number 1 (2023)
q-Deformed and β-parametrized half hyperbolic tangent based Banach
space valued ordinary and fractional neural network approximation

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George A. Anastassiou
Annals of Communications in Mathematics, Vol. 6 (1) (2023), 1-16
Abstract

Here we research the univariate quantitative approximation, ordinary and fractional, of Banach space valued continuous functions on a compact interval or all the real line by quasi-interpolation Banach space valued neural network operators. These 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 of fractional derivatives. Our operators are defined by using a density function generated by a q-deformed and β-parametrized half hyperbolic tangent function, which is a sigmoid function. The approximations are pointwise and of the uniform norm. The related Banach space valued feed-forward neural networks are with one hidden layer.

GEORGE A. ANASTASSIOU
DEPARTMENT OF MATHEMATICAL SCIENCES, UNIVERSITY OF MEMPHIS, MEMPHIS, TN 38152, U.S.A.
Email: ganastss@memphis.edu

Neutrosophic Biminimal Semi-Open Sets
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S. Ganesan
Annals of Communications in Mathematics, Vol. 6 (1) (2023), 17-23
Abstract

 In this article, we introduced the notions of NjmX-semi-open sets, semiinterior and semi-closure operators in neutrosophic biminimal structures. We investigate
some basic properties of such notions. Also, we introduced the notion of NjmX-semicontinuous maps and study characterizations of NjmX-semi-continuous maps by using the
semi-interior and semi-closure operators in neutrosophic biminimal structures.

S. GANESAN
PG & RESEARCH DEPARTMENT OF MATHEMATICS, RAJA DORAISINGAM GOVERNMENT ARTS COLLEGE,
SIVAGANGAI-630561, TAMIL NADU, INDIA. (AFFILIATED TO ALAGAPPA UNIVERSITY, KARAIKUDI, TAMIL NADU, INDIA).
Email: sgsgsgsgsg77@gmail.com

On Contra nIg-Continuity in Nano Ideal Topological Spaces
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S S. Ganesan and S. S. Thakur
Annals of Communications in Mathematics, Vol. 6 (1) (2023), 24-30
Abstract

 In this paper, nIg-closed sets and nIg-open sets are used to define and investigate a new class of maps called contra nIg-continuous maps in nano ideal topological
spaces. We discuss the relationship with some other related maps.

S. S. THAKUR
FORMER PRINCIPAL AND PROFESSOR(APPLIED MATHEMATICS) JABALPUR ENGINEERING COLLEGE, JABALPUR (M. P.)- 482011, INDIA.
Email: samajh singh@rediffmail.com

Parametrized error function based Banach space valued univariate neural
network approximation

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George A. Anastassiou
Annals of Communications in Mathematics, Vol. 6 (1) (2023), 31-43
Abstract

Here we research the univariate quantitative approximation of Banach space valued continuous functions on a compact interval or all the real line by quasi-interpolation Banach space valued neural network operators. We perform also the related Banach space valued fractional approximation. These 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 derivaties. Our operators are defined by using a density function induced by a parametrized error 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 finish with a convergence analysis.

GEORGE A. ANASTASSIOU
DEPARTMENT OF MATHEMATICAL SCIENCES, UNIVERSITY OF MEMPHIS, MEMPHIS, TN 38152, U.S.A.
Email: ganastss@memphis.edu

An extension of Fermatean b-derived fuzzy soft ternary subgroup
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S.V. Manemaran, R. Nagarajan and P. Jayaraman
Annals of Communications in Mathematics, Vol. 6 (1) (2023), 44-56
Abstract

In this paper, an extension of the fermatean uncertainty soft subgroup structures under a norm. Also, the cubic fermatean uncertainty soft ideal structures and fermatean uncertainty multigroup over multi-homomorphism are discussed in detail.

P. JAYARAMAN
DEPARTMENT OF APPLIED MATHEMATICS, BHARATHIAR UNIVERSITY, COIMBATORE, INDIA.
Email: jrmsathya@gmail.com

Algebraicness properties on transitive binary relational sets and a
characterization of continuous directed complete posets

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Mohammed M. Khalaf and Esmail Hassan Abdullatif Al-Sabri
Annals of Communications in Mathematics, Vol. 6 (1) (2023), 57-66
Abstract

 In this work we introduce and study the concepts of algebraicness, and continuity on transitive binary relational sets ( so called T RS). Some interactions between these concepts are investigated. Further more a characterization of continuous directed complete posets and Algebraic T RS are studied. Our results are generalizations of corresponding results in posets.

MOHAMMED M. KHALAF
HIGH INSTITUTE OF ENGINEERING AND TECHNOLOGY KING MARIOUTT, P.O. BOX 3135, EGYPT
Email: khalfmohammed2003@yahoo.com
ESMAIL HASSAN ABDULLATIF AL-SABRI
DEPARTMENT OF MATHEMATICS, FACULTY OF SCIENCE AND ARTS, KING KHALID UNIVERSITY, MUHAYL ASSIR 61913, SAUDI ARABIA
DEPARTMENT OF MATHEMATICS AND COMPUTER, FACULTY OF SCIENCE, IBB UNIVERSITY, IBB 70270, YEMEN
Email: esmailsabria2006@gmail.com

Projective plane curves over a finite field with conical components
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Adnen SBOUI
Annals of Communications in Mathematics, Vol. 6 (1) (2023), 67-71
Abstract

We present the list of maximal projective plane curves containing conics and those which are arrangements of conics. The number of rational points and the corresponding polynomials are given. The third highest number of points of projective curves of degree d over a finite field Fq (d < [q/3]) is associated only to some linear curves. We show that for q/2 + 2 < d < q, this is no longer the case: the third highest number of points can also be obtained by some curves containing a conic. Throughout this work, we obtain some bounds concerning the number of Fq-points of curves with linear, conic and cubic factors. these bounds apply (not sharply) to irreducible curves

ADNEN SBOUI
DEPARTMENT OF MATHEMATICS, FACULTY OF SCIENCES UNIVERSITY OF TABUK, 71491 TABUK, SAUDI ARABIA KSA
IPEI EL-MANAR, UNIVERSITY OF TUNIS EL MANAR, 1068 TUNIS, TUNISIA
Email: A.Sboui@ut.edu.sa

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