ANNALS OF COMMUNICATIONS IN MATHEMATICS
(ISSN 2582-0818)

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.

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

This work lies in the whole biomathematics framework which has as general goal the solving of biological problems with mathematical tools. The main objective of the present paper is to predict the transmembrane helices of proteins using wavelet denoising techniques. As a case of matter, we particularly highlight the interest in solving the problem of localizing these helices. Indeed, these helices play a vital role in the human body, notably in photosynthesis, respiration, neuronal signaling, immune response, absorption of nutrition, and have an important link with drugs as receptors coupled to many proteins. However, due to technical constraints, the crystallization of these helices remains very complex, which limits the exploration of their structure [27]. To overcome these difficul- ties, different prediction tools have been developed, initially based on hydrophobicity. In this paper, we serve the Farey wavelet as a last alternative mother wavelet constructed in [4] to develop a mathematical model suitable for protein series description. We precisely apply a new type of wavelets constructed recently in [4] to localize the and/or predict the position of the transmembrane proteins alpha-helices in a coronavirus strain. The results are compared to existing works for performance, accuracy, and efficiency..

DEPARTMENT OF MATHEMATICS, FACULTY OF SCIENCES, UNIVERSITY OF TABUK, KING FAISAL
ROAD, 47512 TABUK, SAUDI ARABIA.
LABORATORY OF ALGEBRA, NUMBER THEORY AND NONLINEAR ANALYSIS LR18ES15, DEPARTMENT OF MATHEMATICS, FACULTY OF SCIENCES, UNIVERSITY OF MONASTIR, BOULEVARD OF THE ENVIRON-
MENT, 5000 MONASTIR, TUNISIA.
DEPARTMENT OF MATHEMATICS, HIGHER INSTITUTE OF APPLIED MATHEMATICS AND COMPUTER SCI-
ENCE, UNIVERSITY OF KAIROUAN, STREET OF ASSAD IBN AL FOURAT, KAIROUAN 3100, TUNISIA.
Email: 391000151@stu.ut.edu.sa; 421009239@stu.ut.edu.sa;411008509@stu.ut.edu.sa; 391000093@stu.ut.edu.sa;aalanazi@ut.edu.sa; anouar.benmabrouk@fsm.rnu.tn

Neutrosophic normed spaces, one of the recent hot issues in mathematics, are covered in this paper. The Neutrosophic approach is based on the idea that the degree of uncertainty should be taken into consideration and that it is insufficient to categorise problems in daily life as either right or wrong. This paper proposes double sequences’ rough statistical convergence in Neutrosophic Normed Spaces. It then specifies the rough statistical limit points and cluster points of a double sequence in these spaces. This paper then looks at some of their fundamental characteristics. The necessity for more research is finally covered.

P.G. AND RESEARCH DEPARTMENT OF MATHEMATICS, RAJA DORAISINGAM GOVT. ARTS COLLEGE, SIVAGANGAI,
AFFILIATED TO ALAGAPPA UNIVERSITY, KARAIKUDI, TAMILNADU, NDIA.
Email: jeya.math@gmail.com, ORCID: https://orcid.org/0000-0002-0364-1845

RESEARCH SCHOLAR, P.G. AND RESEARCH DEPARTMENT OF MATHEMATICS, RAJA DORAISINGAM GOVT. ARTS COLLEGE, SIVAGANGAI,
AFFILIATED TO ALAGAPPA UNIVERSITY, KARAIKUDI, TAMILNADU, INDIA.
Email: jeni.deepan2013@gmail.com

In this article based on trigonometric and hyperbolic type Taylor formulae we establish Poincare, Sobolev and Hilbert-Pachpatte type inequalities of different kinds specific and general.

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

The wavelet analysis of a function passes through its so-called wavelet transform. Such a transform is mathematically defined as a convolution product of the analyzed function with another analyzing function known as the mother wavelet by involving the scale and the translation parameters. This means that the mother wavelet construction is the starting and major point in the wavelet analysis. Besides, the choice of the mother wavelet remains a major problem in wavelet applications such as statistical series, time series, signal, and image processing. This needs more candidates of mother wavelets to be constructed. The main aim of the present paper is to construct a new mother wavelet by exploiting the well-known Farey map. We showed indeed that such a map may be a mother wavelet owing properties such as admissibility, moments, 2-scale relation, and reconstruction rule already necessary in the wavelet analysis of functions. By a suitable choice of translation-dilation parameters on the original Farey map, we succeeded to prove the main properties of a Farey wavelet analysis. The constructed mother looks to be suitable for many complicated applications such as hyperbolic PDEs.

SABRINE ARFAOUI
INSTITUT SUP´E RIEUR D’INFORMATIQUE DU KEF, UNIVERSIT´E DE JENDOUBA, 5 RUE SALEH AYECH, 7100 KEF, TUNISIA.
LABORATORY OF ALGEBRA, NUMBER THEORY AND NONLINEAR ANALYSIS, LR18ES15, DEPARTMENT OF MATHEMATICS, FACULTY OF SCIENCES, UNIVERSITY OF MONASTIR, BOULEVARD OF THE ENVIRONMENT, 5000 MONASTIR, TUNISIA.
Email: sabrine.arfaoui@issatm.rnu.tn

ANOUAR BEN MABROUK
LABORATORY OF ALGEBRA, NUMBER THEORY AND NONLINEAR ANALYSIS LR18ES15, DEPARTMENT OF MATHEMATICS, FACULTY OF SCIENCES, UNIVERSITY OF MONASTIR, BOULEVARD OF THE ENVIRONMENT, 5000 MONASTIR, TUNISIA.
DEPARTMENT OF MATHEMATICS, HIGHER INSTITUTE OF APPLIED MATHEMATICS AND INFORMATICS, STREET OF ASSAD IBN AL FOURAT, KAIROUAN 3100, TUNISIA.
DEPARTMENT OF MATHEMATICS, FACULTY OF SCIENCES, UNIVERSITY OF TABUK, KING FAISAL ROAD, 47512 TABUK, SAUDI ARABIA.
Email: anouar.benmabrouk@fsm.rnu.tn