order six

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J. G. AL-Juaid, E.M. Elsayed and H. Malaikah

Annals of Communications in Mathematics, Vol. 6 (2) (2023), 72-85

##### Abstract

This paper is devoted to find the form of the solution of the following rational difference equations :

where the initial conditions x−5, x−4, x−3, x−2, x−1, x0 are arbitrary non zero real numbers. Also, we study the behaviour of the solutions.

**J. G. AL-JUAID**

DEPARTMENT OF MATHEMATICS, FACULTY OF SCIENCES, TAIF UNIVERSITY, P. O. BOX 11099, TAIF

21944, KSA.

DEPARTMENT OF MATHEMATICS, FACULTY OF SCIENCES, KING ABDULAZIZ UNIVERSITY, P. O. BOX

80203, JEDDAH 21589, KSA. *Email:* *jo.gh@tu.edu.sa***E. M. ELSAYED**

DEPARTMENT OF MATHEMATICS, FACULTY OF SCIENCES, KING ABDULAZIZ UNIVERSITY, P. O. BOX

80203, JEDDAH 21589, KSA.

DEPARTMENT OF MATHEMATICS, FACULTY OF SCIENCES, MANSOURA UNIVERSITY, MANSOURA 35516, EGYPT. *Email:* *emmelsayed@yahoo.com***H. MALAIKAH**

DEPARTMENT OF MATHEMATICS, FACULTY OF SCIENCES, KING ABDULAZIZ UNIVERSITY, P. O. BOX

80203, JEDDAH 21589, KSA. *Email:* *hmalaikah@kau.edu.sa*

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Daniel A. Romano

Annals of Communications in Mathematics, Vol. 6 (2) (2023), 86-98

##### Abstract

Quasi-ordered residuated systems as a generalization of both quasi-ordered commutative residuated lattices and hoop-algebras were developed in 2018 by Bonzio and Chajda. The ideas of the theory of hyper structures were applied to this algebraic structure by this author and, at the same time, developed the concepts of filters in a hyper quasi-ordered residuated system. In this paper, the conditions that determine the concept of implicative strong filters in it. Some equivalent conditions were found that also determine this concept.

**Daniel A. Romano**

International Mathematical Virtual Institute, Kordunaska Street 6, 78000 Banja Luka, Bosnia and Herzegovina.*Email: daniel.a.romano@hotmail.com*, *danielromano1949gmail.com*

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S. K. Yadav

Annals of Communications in Mathematics, Vol. 6 (2) (2023), 99-108

##### Abstract

In this work, the investigation of spacetimes admitting semiconformal curvature tensor in *f(R)*-gravity theory is the major goal. First, semiconformally flat spacetimes in the presence of *f(R)*-gravity are investigated, and the relationship between isotropic pressure and energy density is discovered. Some energy conditions are then taken into account. Finally, spacetimes with divergence-free semiconformal curvature tensors in *f(R)*-gravity are explored.

**SUNIL KUMAR YADAV**

DEPARTMENT OF APPLIED SCIENCE AND HUMANITIES, UNITED COLLEGE OF ENGINEERING & RESEARCH, A-31, UPSIDC INDUSTRIAL AREA, NAINI-211010, PRAYAGRAJ, UTTAR PRADESH, INDIA. ORCID. NO.0000-0001-6930-3585*Email: prof sky16@yahoo.com*,

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Omprakash Atale

Annals of Communications in Mathematics, Vol. 6 (2) (2023), 109-117

##### Abstract

In order theory, partially ordered sets are only equipped with one relation which decides the entire structure/Hasse diagram of the set. In this paper we have presented how partially ordered sets can be studied under simultaneous partially ordered relations which we have called binary posets. The paper is motivated by the problem of operating a set simultaneously under two distinct partially ordered relations. It has been shown that binary posets follow duality principle just like posets do. Within this framework, some new definitions concerning maximal and minimal elements are also presented. Furthermore, some theorems on order isomorphism and Galois connections are derived.

**OMPRAKASH ATALE**

SCHOOL OF MATHEMATICAL SCIENCES, MOOLJI JAITHA COLLEGE JALGAON-425001, INDIA

Email:* atale.om@outlook.com*

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Sabrine Arfaoui and Anouar Ben Mabrouk

Annals of Communications in Mathematics, Vol. 6 (2) (2023), 118-132

##### Abstract

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*