Proyecciones (Antofagasta, On line) <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> Universidad Católica del Norte. en-US Proyecciones (Antofagasta, On line) 0717-6279 <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="" data-original-title="">appropriate credit</a>, provide a link to the license, and <a id="indicate_changes_popup" class="helpLink" tabindex="0" title="" href="" 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="" data-original-title="">technological measures</a> that legally restrict others from doing anything the license permits.</li> </ul> </div> Pairwise Infra Neutrosophic Pre-Open Set in Infra Neutrosophic Bi-topological Space <p>In this article, we present the notion of infra neutrosophic bi-topological spaces (in short INBTS) as a generalization of infra neutrosophic topological space (in short INTS) and neutrosophic bi-topological space (in short NBTS). Besides, we study the different types of open and closed sets namely infra neutrosophic bi-open set (in short INBOS), infra neutrosophic bi-semi-open set (in short INBSOS), infra neutrosophic bi-pre-open set (in short INBPOS), infra neutrosophic bi-<em>b</em>-open set (in short INB<em>b-</em>OS), etc. via INBTSs. Then, we introduce the notion of pairwise infra neutrosophic bi-open set (in short PINBOS), pairwise infra neutrosophic bi-semi-open set (in short PINBSOS), pairwise infra neutrosophic bi-pre-open set (in short PINBPOS), pairwise infra neutrosophic bi-<em>b</em>-open set (in short PINB<em>b</em>-OS), and furnish few illustrative examples on them. Further, we investigate several properties of these classes of sets and establish several interesting results via INBTSs in the form of propositions, theorems, etc.</p> Suman Das Rakhal Das Copyright (c) 2024 RAKHAL DAS, Suman Das 2024-06-17 2024-06-17 43 4 793 811 10.22199/issn.0717-6279-5477 Fixed point and stability of nonlinear differential equations with variable delays <p>In this paper, we study the stability of a generalized nonlinear differential equation with variable delays via fixed point theory. An asymptotic stability theorem with sufficient conditions is proved, which improves and generalizes some previous results. Two examples are given to illustrate our results.</p> Abdelhafid Younsi Copyright (c) 2024 Abdelhafid younsi 2024-06-17 2024-06-17 43 4 813 825 10.22199/issn.0717-6279-6374 Uniform stability, boundedness and square integrability for non-autonomous third-order neutral differential equations with delay <p>The work in this article provides literature with some results concerning the exponential stability, the boundedness and the square integrability of solutions for some non autonomous equations of third order supplied with delay and neutral parameters. The main tool used in this work is the second method of Lyapunov. The article is finished by giving a concrete example that ensure the application of the obtained results.</p> Mebrouk Rahmane Fatima Abdellaoui Copyright (c) 2024 Mebrouk Rahmane, Fatima Abdellaoui 2024-06-17 2024-06-17 43 4 827 847 10.22199/issn.0717-6279-6286 Singularity of cycle-spliced signed graphs <p>We consider the adjacency spectrum of cycle-spliced signed graphs (CSSG), i.e., signed graphs whose blocks are (independent) signed cycles. For a signed graph Σ, the nullity η(Σ) is the multiplicity of the 0-eigenvalue. The adjancency spectrum of cycle-spliced (signed) graphs is studied in the literature for the relation between the nullity η and the cyclomatic number c, in particular, it is known that 0≤η(Σ) ≤ c(Σ)+1. In this paper, nonsingular cycle-spliced bipartite signed graphs are characterized. For cycle-spliced signed graphs Σ having only odd cycles, we show that η(Σ) is 0 or 1. Finally, we compute the nullity of CSSGs consisting of at most three cycles.</p> Suliman Khan Adriana Ciampella Copyright (c) 2024 Adriana Ciampella, Suliman Khan 2024-06-17 2024-06-17 43 4 849 871 10.22199/issn.0717-6279-6376 Stability and boundedness of solutions of certain Lienard-type non-autonomous differential equations <p>In this paper, the Liénard-type non-autonomous nonlinear differential equation</p> <p>ẍ+ p(t)f(x, ẋ) ẋ + q(t)g(x) = ϕ(t, x, ẋ)</p> <p>is investigated for uniform exponential asymptotic stability of solutions when ϕ(t, x, ẋ) ≡ 0, and uniform ultimate boundedness of solutions when ϕ(t, x, ẋ) ≠ 0, using the Lyapunov’s direct method</p> Abdullai Abdurasid A. L. Olutimo M. O. Omeike Copyright (c) 2024 Abdullai Abdurasid, Olutimo A.L., M. O. Omeike 2024-06-17 2024-06-17 43 4 873 882 10.22199/issn.0717-6279-6155 Coloring of Non-Zero Component Graphs <p>The non-zero component graph of finite dimensional vector space over a finite field $F$ is the graph $G = (V,E)$, where vertices of $G$ are the non-zero vectors in $V$, two of which are adjacent if they share at least one basis vector with non-zero coefficient in their basic representation. In this paper, we study the various types of colorings of non-zero component graph.</p> Vrinda Mary Mathew Sudev Naduvath Copyright (c) 2024 Vrinda, Sudev Naduvath 2024-06-19 2024-06-19 43 4 883 898 10.22199/issn.0717-6279-5962 A note on P-Sasakian manifolds satisfying certain conditions <p>In the present paper, we have studied the curvature tensors of PSasakian manifold. For a P-Sasakian manifold, W1 ·S = 0, W1 ·Ze = 0 and W9 · W1 = 0 cases are considered. According these cases, PSasakian manifolds have been characterized such as η-Einstein and Einstein. In addition, we research W1-flat and W9-flat for a PSasakian manifold. The results are interesting and give an idea about the geometry of P-Sasakian manifold.</p> pakize uygun Mehmet Atceken Copyright (c) 2024 pakize uygun, Mehmet Atceken 2024-06-19 2024-06-19 43 4 899 910 10.22199/issn.0717-6279-6158 A study on deg-centric graphs <p>The deg-centric graph of a simple, connected graph $G$, denoted by $G_d$, is a graph constructed from $G$ such that, $V(G_d) = V(G)$ and $E(G_d) = \{v_iv_j: d_G(v_i,v_j) \leq deg_G(v_i)\}$. In this paper, the concepts of deg-centric graphs and iterated deg-centrication of a graph are introduced and discussed.</p> Sudev Naduvath Timmy Tomy Thalavayalil Johan Kok Copyright (c) 2024 Sudev Naduvath, Timmy, Johan 2024-06-24 2024-06-24 43 4 911 926 10.22199/issn.0717-6279-6174 Cayley fuzzy graphs on groups <p>We investigate some properties of Cayley fuzzy graphs on groups in terms of algebraic structures. And we also discuss the connectedness on it. In this paper, we prove that the Cayley fuzzy graph induced by (Zm × Zn, +, ν) is the disjoint union of Cay(aH, R) provided ν(h) &gt; 0 ∀ h ∈ H and ν(h′) =0 ∀ h′∈ Zm × Zn\H, where H is the cyclic subgroup of order n in Zm × Zn.</p> JISHA MARY JOHN KAIMALIL HOUSE A RIYAS K GEETHA Copyright (c) 2024 JISHA MARY JOHN KAIMALIL HOUSE, A RIYAS, K GEETHA 2024-06-19 2024-06-19 43 4 927 933 10.22199/issn.0717-6279-5828 On the right automorphic generalised Bol loops <p>This study centers on right automophic generalised Bol loops. Having established the generators of inner mapping group of generalised Bol loops, some properties of generalised Bol loops, in terms of right translation map, are obtained. These properties are later used to established a condition under which right automorphic generalised Bol loop is a generalised Moufang loop.</p> Abdulafeez Abdulkareem Y.T Oyebo J. O. Adeniran Copyright (c) 2024 Dr. Abdulkareem A.O., Y.T Oyebo, J. O. Adeniran 2024-06-24 2024-06-24 43 4 935 946 10.22199/issn.0717-6279-5862 Induced Dominating Sequence and ESD Graphs <p>A vertex subset D of a graph G = (V,E) is said to be a dominating<br>set if every vertex in G is either in D or adjacent to some vertex in D.<br>The minimum cardinality of such a set is the domination number, which<br>is denoted as γ(G). In this paper, we define a sequence associated with<br>the domination concept in graphs and studied the basic properties of the<br>sequence in terms of various parameters of graphs. Using this sequence<br>we order the vertices of a dominating set according its significance and<br>propose Equally Significant Dominating (ESD) graphs. We also introduced<br>domination related topological indices and compute their lower bounds for<br>trees, unicyclic graphs and bicyclic graphs. All the graphs attaining the<br>bounds are characterized.</p> Indulal Gopalapilla Liju Alex John Joy Mulloor Copyright (c) 2024 Indulal Gopalapilla, Liju Alex, John Joy 2024-06-19 2024-06-19 43 4 947 964 10.22199/issn.0717-6279-6179 A CHARACTERIZATION OF σ-PRIME RINGS INVOLVING GENERALIZED DERIVATIONS <p><strong>This paper’s major goal is to work on commutativity of σ-prime rings<br>with second kind involution σ, involving generalized derivation satisfy the<br>certain differential identities. Finally, we provide some examples to demonstrate<br>that the conditions assumed in our results are not unnecessary</strong></p> Wasim Ahmed Md. Arshad Madni Muzibur Rahman Mozumder Abu Zaid Ansari Copyright (c) 2024 Wasim Ahmed, Md. Arshad Madni, Muzibur Rahman Mozumder, Abu Zaid Ansari 2024-06-24 2024-06-24 43 4 965 983 10.22199/issn.0717-6279-6412