Proyecciones (Antofagasta, On line) https://www.revistaproyecciones.cl/index.php/proyecciones <p align="justify">La revista&nbsp;Proyecciones. Journal of Mathematics es una publicación científica, sin fines de lucro, oficial de la Universidad Católica del Norte, Antofagasta, Chile. Fue fundada en 1982 y depende del Departamento de Matemáticas de la Universidad Católica del Norte.<br>Proyecciones. Journal of Mathematics edita un volumen con 5 números al año.</p> en-US <div id="deed-conditions" class="row"> <ul class="license-properties col-md-offset-2 col-md-8" dir="ltr"> <li class="license by"> <p><strong>Attribution</strong> — You must give <a id="appropriate_credit_popup" class="helpLink" tabindex="0" title="" href="https://creativecommons.org/licenses/by/4.0/deed.en" data-original-title="">appropriate credit</a>, provide a link to the license, and <a id="indicate_changes_popup" class="helpLink" tabindex="0" title="" href="https://creativecommons.org/licenses/by/4.0/deed.en" data-original-title="">indicate if changes were made</a>. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.<span id="by-more-container"></span></p> </li> </ul> </div> <div class="row"> <ul id="deed-conditions-no-icons" class="col-md-offset-2 col-md-8"> <li class="license"><strong>No additional restrictions</strong> — You may not apply legal terms or <a id="technological_measures_popup" class="helpLink" tabindex="0" title="" href="https://creativecommons.org/licenses/by/4.0/deed.en" data-original-title="">technological measures</a> that legally restrict others from doing anything the license permits.</li> </ul> </div> rsoto@ucn.cl (Ricardo Soto Montero) revproy@ucn.cl (Proyecciones) Thu, 02 May 2024 00:00:00 +0000 OJS 3.2.0.3 http://blogs.law.harvard.edu/tech/rss 60 On the incomplete fourth Appell hypergeometric matrix functions Υ₄ and Γ₄ https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/5891 <p>In this paper, we define the incomplete fourth Appell hypergeometric matrix functions Υ₄ and Γ₄ through application of the incomplete Pochhammer matrix symbols. We also give certain properties such as matrix differential equation, integral formula, recursion formula, differentiation formula of the incomplete fourth Appell hypergeometric matrix functions Υ₄ and Γ₄, where not all the matrices involved are commuting matrices.</p> Ashish Verma, Komal Singh Yadav, Raj Karan Patel Copyright (c) 2024 Ashish Verma, Komal Singh Yadav, Raj Karan Patel https://creativecommons.org/licenses/by/4.0 https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/5891 Thu, 02 May 2024 00:00:00 +0000 A variant of Banach’s contraction principle in ordered Banach spaces https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/6128 <p>In this article we establish a version of Banach’s contraction principle in ordered Banach spaces. This version is adapted to prove existence and uniqueness results for an integral equation or a boundary value problem depending on the derivative.</p> Abdelhamid Benmezai Copyright (c) 2024 Abdelhamid Benmezai https://creativecommons.org/licenses/by/4.0 https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/6128 Thu, 02 May 2024 00:00:00 +0000 On graded 1 -absorbing δ -primary ideals https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/6190 <p>Let G be an abelian group with identity 0 and let R be a commutative graded ring of type G with nonzero unity. Let I(R) be the set of all ideals of R and let δ: I(R)⟶I(R) be a function. Then, according to (R. Abu-Dawwas, M. Refai, Graded δ-Primary Structures, Bol. Soc. Paran. Mat., 40 (2022), 1-11), δ is called a graded ideal expansion of a graded ring R if it assigns to every graded ideal I of R another graded ideal δ(I) of R with I ⊆ δ(I), and if whenever I and J are graded ideals of R with J ⊆ I, we have δ (J) ⊆ δ(I). Let δ be a graded ideal expansion of a graded ring R. In this paper, we introduce and investigate a new class of graded ideals that is closely related to the class of graded δ-primary ideals. A proper graded ideal I of R is said to be a graded 1-absorbing δ-primary ideal if whenever nonunit homogeneous elements a,b,c ∊ R with abc ∊ I, then ab ∊ I or c ∊ δ(I). After giving some basic properties of this new class of graded ideals, we generalize a number of results about 1-absorbing δ-primary ideals into these new graded structure. Finally, we study the graded 1-absorbing δ-primary ideals of the localization of graded rings and of the trivial graded ring extensions.</p> Rashid Abu-Dawwas, Anass Assarrar, Jebrel M Habeb, Najib Mahdou Copyright (c) 2024 Rashid Abu-Dawwas, Anass Assarrar, Jebrel M Habeb, Najib Mahdou https://creativecommons.org/licenses/by/4.0 https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/6190 Thu, 02 May 2024 00:00:00 +0000 Edge metric dimension of some Cartesian product of graphs https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/5770 <p>The edge metric dimension edim(G)of a connected graph G is the minimum cardinality of a set S of vertices such that each edge is uniquely determined by its distance from the vertices of the set S. In this work, the edge metric dimension of the prism over a graph G(G◻K<sub>2</sub>), cylinder graphs(C<sub>m</sub>◻P<sub>n</sub>)and torus graphs(C<sub>m</sub>◻ C<sub>n</sub>)are determined</p> Saritha Chandran C., Reji T. Copyright (c) 2024 Saritha Chandran C, Reji T https://creativecommons.org/licenses/by/4.0 https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/5770 Tue, 14 May 2024 00:00:00 +0000 On the existence of solutions for a class of nonlinear fully fourth-order differential systems https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/5813 <p>This paper discusses the existence of solutions to fourth order nonlinear boundary value problem involving systems of differential equations and two point boundary conditions. The nonlinearity f ∈ C ([0,1] × R<sup>n</sup><sub>+</sub> × R<sup>n</sup> × R<sup>n</sup> × R<sup>n</sup>, R<sup>n</sup>)considered in this paper includes derivatives up to order three. Using recent fixed point results for the sum of two operators, we impose a growth condition on f to establish a new existence criteria that ensure the existence of at least one and the existence of at least two nonnegative solutions.</p> Lydia Bouchal, Karima Mebarki, Svetlin Georgiev Georgiev Copyright (c) 2024 Lydia Bouchal, Karima Mebarki, Svetlin Georgiev Georgiev https://creativecommons.org/licenses/by/4.0 https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/5813 Tue, 14 May 2024 00:00:00 +0000 On graded pseudo 2-prime ideals https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/5394 <p>In this paper, we study graded pseudo 2-prime ideals of graded commutative rings with nonzero identities. Let G be a commutative additive monoid with an identity element 0, and R=⊕<sub>g∈G</sub> R<sub>g </sub>be a commutative graded ring with a nonzero identity element. A proper graded ideal I of R is said to be a graded pseudo 2-prime ideal if whenever ab ∈ I for some homogeneous elements a,b ∈ R, then a²ⁿ ∈ Iⁿ or b²ⁿ ∈ Iⁿ for some n ∈ ℕ. Besides giving many properties of graded pseudo 2-prime ideals, we characterize graded almost valuation domains in terms of our new concept.</p> Anass Assarrar, Najib Mahdou, Muroj Al-Shboul, Ünsal Tekïr, Suat Koç Copyright (c) 2024 Anass Assarrar, Najib Mahdou, Muroj Al-Shboul, Unsal Tekir, Suat Koç https://creativecommons.org/licenses/by/4.0 https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/5394 Tue, 14 May 2024 00:00:00 +0000 Ball convergence of derivative free iterative methods with or without memory using weight operator technique https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/4928 <div class="page" title="Page 1"> <div class="layoutArea"> <div class="column"> <p>A method without memory as well as a method with memory are developed free of derivatives for solving Banach space valued equations. Their ball convergence analysis is provided using only the derivative and the divided difference of order one in contrast to earlier works on the real line using the fifth as well as the seventh derivative. This way the applicability is expanded for these methods.</p> </div> </div> </div> Ioannis Argyros, Santhosh George, Christopher Argyros Copyright (c) 2024 IOANNIS ARGYROS, Dr. George, Christopher Argyros https://creativecommons.org/licenses/by/4.0 https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/4928 Tue, 14 May 2024 00:00:00 +0000 Existence of nonnegative solution for a boundary value problem via upper and lower method on the half-line https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/5202 <p>In this paper, we provide existence results to the following boundary value problem</p> <p><img src="https://www.revistaproyecciones.cl/public/site/images/rvidal/mceclip0.png" width="200" height="33" /></p> <div>where q ∈ L<sup>1</sup> ((0, +∞), R) and the nonlinearity f: [0, +∞ [×R×R→ R is continuous.</div> <p> </p> <p> </p> Ziad Youcef, Kamal Bachouche, Toufik Moussaoui Copyright (c) 2024 Toufik Moussaoui, Ziad Youcef, Kamal Bachouche https://creativecommons.org/licenses/by/4.0 https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/5202 Wed, 15 May 2024 00:00:00 +0000 Equitable Irregular Edge-Weighting of Polar Grid Graph and Mongolian Tent Graph https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/4677 <div>An k-edge-weighting of a graph G=(V,E) is a map φ: E(G) → {1, 2, 3, ..., k} where k ≥ 1 is an integer. Denote S<sub>φ</sub>(v) is the sum of edge-weights appearing on the edges incident at the vertex v under φ. An k-edge-weighting of G is equitable irregular if |S<sub>φ </sub>(u)−S<sub>φ</sub> (v)| ≤ 1, for every pair of adjacent vertices u and v in G. Theequitable irregular strength of an equitable irregular graph G is the smallest positive integer k such that there is a k-edge weighting of G and is denoted by S<sub>e</sub> (G). In this paper, we discuss the equitable irregularity of Polar grid and Mongolian tent graphs</div> C. Gayathri, S. Saravanakumar Copyright (c) 2024 Gayathri C https://creativecommons.org/licenses/by/4.0 https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/4677 Mon, 20 May 2024 00:00:00 +0000 On graded 2-absorbing primal ideals https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/5695 <p>Let R be G-graded ring. In this paper, we introduce and devoted to the concept of graded 2-absorbing primal ideal of R which is a generalization of graded primal ideal. These ideals and their homogeneous components are given some features and characterizations.</p> Tamem Al-shorman, Malik Bataineh Copyright (c) 2024 Tamem Al-shorman, Malik Bataineh https://creativecommons.org/licenses/by/4.0 https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/5695 Mon, 20 May 2024 00:00:00 +0000 Generalized Balancing and Balancing-Lucas numbers https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/5712 <p>In this paper, we introduce a generalization of Balancing and Balancing-Lucas numbers. We describe some of their properties also we give the related matrix representation and divisibility properties.</p> Hasan Al-Zoubi, Alaa Al-Kateeb Copyright (c) 2024 Alaa Al-Kateeb, Hasan Al-Zoubi https://creativecommons.org/licenses/by/4.0 https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/5712 Mon, 20 May 2024 00:00:00 +0000 On edge irregularity strength of cycle-star graphs https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/5801 <p>For a simple graph G, a vertex labeling ϕ : V (G) → {1, 2, . . . , k} is called k-labeling. The weight of an edge uv in G, written wϕ(uv), is the sum of the labels of end vertices u and v, i.e., wϕ(uv) = ϕ(u) + ϕ(v). A vertex k-labeling is defined to be an edge irregular k-labeling of the graph G if for every two distinct edges u and v, wϕ(u) ̸= wϕ(v). The minimum k for which the graph G has an edge irregular k-labeling is called the edge irregularity strength of G, written es(G). In this paper, we study the edge irregular k-labeling for cycle-star graph CSk,n−k and determine the exact value for cycle-star graph for 3 ≤ k ≤ 7 and n − k ≥ 1. Finally, we make a conjecture for the edge irregularity strength of CSk,n−k for k ≥ 8 and n − k ≥ 1.</p> Umme Salma, H. M. Nagesh, Narahari Nittur Copyright (c) 2024 Umme Salma, H.M. Nagesh, N Narahari https://creativecommons.org/licenses/by/4.0 https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/5801 Mon, 20 May 2024 00:00:00 +0000 Some bounds onfirst degcity index https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/5928 <p>The first degcity index DC<sub>1</sub>(G) of a connected graph G is defined as the sum of the terms [e<sub>x</sub>+e<sub>y</sub>][d<sub>x</sub>+d<sub>y</sub>] over all the lines xy of G, where d<sub>x</sub> and e<sub>x</sub> represents the degree and eccentricity of a point x in G respectively. In this article, we have obtained some lower and upper bounds of first degcity index.</p> P. S. Guruprasad, K. B. Sudhakara , M. A. Sriraj Copyright (c) 2024 P. S. Guruprasad, K. B. Sudhakara , M. A. Sriraj https://creativecommons.org/licenses/by/4.0 https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/5928 Wed, 22 May 2024 00:00:00 +0000 Further studies on circulant completion of graphs https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/6034 <p>A circulant graph C(n,S) is a graph having its adjacency matrix as a circulant matrix. It can also be intrepreted as a graph with vertices v<sub>0</sub>,v<sub>1</sub>,...,v<sub>n-1</sub> that are in one to one correspondence with the members of <strong>Z</strong><sub>n</sub> and with edge set {v<sub>i</sub>v<sub>j</sub>:i-j ∈ S}, where S known as the connection set or symbol, is a subset of non-identity members of <strong>Z</strong><sub>n</sub> that is closed under inverses. This work extends the study of circulant completion and general formulae for calculating circulant completion number in two different perspectives, one in terms of circulant span and the other in terms of adjacency matrix.</p> Tony Antony, Sudev Naduvath Copyright (c) 2024 Sudev Naduvath, Toby https://creativecommons.org/licenses/by/4.0 https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/6034 Sun, 26 May 2024 00:00:00 +0000 Neutrosophic equivalence relation applied onincline algebra https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/5281 <div>Researchers have great interest in working in the fields of fuzzy algebra and its substructure. Nowadays, the work on fuzzy algebra has attained the greatest height. Considering the incline algebra in this study, the concept of the neutrosophic equivalence relation in incline algebra and its related properties are introduced. Furthermore, the characteristic function and chain conditions are also analyzed, with some results.</div> Prakasam Muralikrishna, Surya Manokaran Copyright (c) 2024 Muralikrishna Prakasam, Surya M https://creativecommons.org/licenses/by/4.0 https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/5281 Sun, 26 May 2024 00:00:00 +0000