Proyecciones (Antofagasta, On line) 2023-09-13T19:29:25+00:00 Ricardo Soto Montero Open Journal Systems <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> An inverse source time-fractional diffusion problem via an input-output mapping 2020-08-09T02:02:31+00:00 Rahima Atmania Loubna Settara <p>In this paper, we investigate an inverse source problem involving a one-dimensional diffusion equation of a time-fractional RiemannLiouville derivative with 0 &lt; α &lt; 1. First, results on the existence and regularity of the weak solution of the direct problem are obtained. For the determination of the unknown time-dependent source term, we use a monotone and distinguishable input-output mapping defined by the additional over-determination integral data for the considered sub-diffusion problem. Finally, the uniqueness of the solution of the inverse problem is proved.</p> 2023-09-13T00:00:00+00:00 Copyright (c) 2023 Rahima Atmania, Loubna Settara Study of some algebraic and topological properties of difference gai sequence of interval numbers 2022-01-24T04:43:47+00:00 Achyutananda Baruah <p>Here we have studied some algebraic and topological properties of Difference Gai Sequence of Interval numbers. We study the Completeness, Solidness, Symmetricity and Convergence free.</p> 2023-09-13T00:00:00+00:00 Copyright (c) 2023 Achyutananda Baruah Analytic odd mean labeling of union and identification of some graphs 2023-05-07T22:28:32+00:00 P. Jeyanthi R. Gomathi G. C. Lau W. C. Shiu <p>A graph G is analytic odd mean if there exist an injective function <em>f</em> : V → {0, 1, 3, . . . , 2q − 1} with an induced edge labeling <em>f</em><sup>∗</sup> : E → Z such that for each edge uv with f(u) &lt; f(v),</p> <p><img src="" /></p> <p>is injective. Clearly the values of f<sup>∗</sup> are odd. We say that f is an analytic odd mean labeling of G. In this paper, we show that the union and identification of some graphs admit analytic odd mean labeling by using the operation of joining of two graphs by an edge.</p> 2023-09-13T00:00:00+00:00 Copyright (c) 2023 P. Jeyanthi, R. Gomathi, G. C. Lau, W. C. Shiu Hyers-Ulam-Rassias stability of some perturbed nonlinear second order ordinary differential equations 2023-02-28T13:08:10+00:00 Ilesanmi Fakunle Peter Olutola Arawomo <p>In this paper we investigate the Hyers-Ulam-Rassias stability of a perturbed nonlinear second order ordinary differential equation using Gronwall-Bellman-Bihari type integral inequalities. Further, the paper also investigates the Hyers-Ulam-Rassias stability of four different cases of a perturbed nonlinear second order differential equation.</p> 2023-09-13T00:00:00+00:00 Copyright (c) 2023 Ilesanmi Fakunle, Peter Olutola Arawomo Grundy number of corona product of some graphs 2022-10-26T14:00:20+00:00 R. Stella Maragatham A. Subramanian <p>The Grundy number of a graph G is the maximum number k of colors used to color the vertices of G such that the coloring is proper and every vertex u colored with color i, 1 ≤ i ≤ k, is adjacent to i – 1 vertices colored with each color j, 1 ≤ j ≤ i − 1. In this paper we obtain the Grundy number of corona product of some graphs, denoted by G ◦ H. First, we consider the graph G be 2-regular graph and H be a cycle, complete bipartite, ladder graph and fan graph. Also we consider the graph G and H be a complete bipartite graphs, fan graphs.</p> 2023-09-13T00:00:00+00:00 Copyright (c) 2023 R. Stella Maragatham, A. Subramanian Nonlocal partial fractional evolution equations with state dependent delay 2022-10-24T13:10:11+00:00 Nardjis Lachachi-Merad Selma Baghli-Bendimerad Mouffak Benchohra Erdal Karapınar <p>In this work, we propose sufficient conditions guaranteeing an existence result of mild solutions by using the nonlinear Leray-Schauder alternative in Banach spaces combined with the semigroup theory for the class of Caputo partial semilinear fractional evolution equations with finite state-dependent delay and nonlocal conditions.</p> 2023-09-13T00:00:00+00:00 Copyright (c) 2023 Nardjis Lachachi-Merad, Selma Baghli-Bendimerad, Mouffak Benchohra, Erdal Karapınar An application of the Stone-Weierstrass Theorem 2022-08-01T17:44:54+00:00 Adalberto García-Máynez Margarita Gary Adolfo Pimienta <p>Let (X, τ) be a topological space, we will denote by |X|,|X|<sub>K</sub>, |X|τ and |X|<sub>δ</sub>, the cardinalities of X; the family of compacts in X; the family of closed in X, and the family of G<sub>δ</sub>-closed in X, respectively. The purpose of this work is to establish relationships between these four numbers and conditions under which two of them coincide or one of them is ≤ c, where c denotes, as usual, the cardinality of the set of real numbers <strong>R</strong>. We will use the Stone-Weierstrass theorem to prove that: Let (X, τ) be a compact Hausdorff topological space, then |X|<sub>δ</sub> ≤ |X|<sup>ℵ</sup><sup>0</sup></p> 2023-09-13T00:00:00+00:00 Copyright (c) 2023 Adalberto García-Máynez, Margarita Gary, Adolfo Pimienta Some extensions of the Hermite-Hadamard inequalities for quasi-convex functions via weighted integral 2022-08-28T14:03:02+00:00 Bahtiyar Bayraktar Juan Eduardo Napoles Florencia Rabossi Aylen Samaniego <div>In this note, starting with a lemma, we obtain several extensions of the</div> <div>well-known Hermite-Hadamard inequality for convex functions, using</div> <div>generalized weighted integral operators.</div> 2023-09-13T00:00:00+00:00 Copyright (c) 2023 Bahtiyar Bayraktar, Juan Eduardo Napoles, Florencia Rabossi, Aylen Samaniego K-Riesz bases and K-g-Riesz bases in Hilbert C∗-module 2022-11-03T09:31:23+00:00 Abdelkhalek El amrani Mohamed Rossafi Tahar El Krouk <p>This paper is devoted to studying the K-Riesz bases and the K-g-Riesz bases in Hilbert C<sup>∗</sup>-modules; we characterize the concept of K-Riesz bases by a bounded below operator and the standard orthonormal basis for Hilbert C<sup>∗</sup>-modules <em>H</em>. Also We give some properties and characterization of K-g-Riesz bases by a bounded surjective operator and g-orthonormal basis for H. Finally we consider the relationships between K-Riesz bases and K-g-Riesz bases.</p> 2023-09-13T00:00:00+00:00 Copyright (c) 2023 Abdelkhalek El amrani, Mohamed Rossafi, Tahar El Krouk Note on modified generalized Bessel function 2022-12-26T08:27:03+00:00 Farhatbanu H. Patel Ranjan Jana Ajay Shukla <p>An attempt is made to define Modified Generalized Bessel Function, and Modified Generalized Bessel Matrix Function. Some properties have also been discussed.</p> 2023-09-13T00:00:00+00:00 Copyright (c) 2023 Farhatbanu H. Patel, Ranjan Jana, Ajay Shukla Characterization of prime rings having involution and centralizers 2023-02-22T13:09:12+00:00 Nadeem Ahmad Dar Adnan Abbasi Claus Haetinger Arshad Madni Muzibur Rahman Mozumder <p>The major goal of this paper is to study the commutativity of prime rings with involution that meet specific identities using left centralizers. The results obtained in this paper are the generalization of many known theorems. Finally, we provide some examples to show that the conditions imposed in the hypothesis of our results are not superfluous.</p> 2023-09-13T00:00:00+00:00 Copyright (c) 2023 Nadeem Ahmad Dar, Adnan Abbasi, Claus Haetinger, Arshad Madni, Muzibur Rahman Mozumder On weakly (m, n)−closed δ−primary ideals of commutative rings 2022-11-25T12:43:27+00:00 Mohammad Hamoda Mohammed Issoual <p>Let R be a commutative ring with 1 ̸= 0. In this article, we introduce the concept of weakly (m, n)−closed δ−primary ideals of R and explore its basic properties. We show that a proper ideal I of R is a weakly (m, n)−closed γ ◦ δ−primary ideal of R if and only if I is an (m, n)−closed γ ◦ δ−primary ideal of R, where δ and γ are expansions ideals of R with δ(0) is an (m, n)−closed γ−primary ideal of R. Furthermore, we provide examples to demonstrate the validity and applicability of our results.</p> 2023-09-13T00:00:00+00:00 Copyright (c) 2023 Mohammad Hamoda, Mohammed Issoual On local antimagic chromatic numbers of circulant graphs join with null graphs or cycles 2023-01-16T20:38:38+00:00 G. C. Lau K. Premalatha W. C. Shiu M. Nalliah <p>An edge labeling of a graph G = (V,E) is said to be local antimagic if there is a bijection f : E → {1,..., |E|} such that for any pair of adjacent vertices x and y, <em>f</em> <sup>+</sup>(x) ≠ <em>f </em><sup>+</sup>(y), where the induced vertex label is <em>f</em> <sup>+</sup>(x) = 𝜮 f(e), with e ranging over all the edges incident to x. The local antimagic chromatic number of G, denoted by χ<sub>la</sub>(G), is the minimum number of distinct induced vertex labels over all local antimagic labelings of G. For a bipartite circulant graph G, it is known that χ(G)=2 but χ<sub>la</sub>(G) ≥ 3. Moreover, χ<sub>la</sub>(C<sub>n</sub> ∨ K<sub>1</sub>)=3 (respectively 4) if n is even (respectively odd). Let G be a graph of order m ≥ 3. In [Affirmative solutions on local antimagic chromatic number, Graphs Combin., 36 (2020), 1337—1354], the authors proved that if m ≡ n (mod 2) with χ<sub>la</sub>(G) = χ(G), m&gt;n ≥ 4 and m ≥ n<sup>2</sup>/2, then χ<sub>la</sub>(G∨O<sub>n</sub>) = χ<sub>la</sub>(G)+1. In this paper, we show that the conditions can be omitted in obtaining χ<sub>la</sub>(G∨H) for some circulant graph G, and H is a null graph or a cycle. The local antimagic chromatic number of certain wheel related graphs are also obtained.</p> 2023-09-13T00:00:00+00:00 Copyright (c) 2023 G. C. Lau, K. Premalatha, W. C. Shiu, M. Nalliah On fuzzy congruence relation in residuated lattices 2022-03-20T08:56:22+00:00 S. Khosravi Shoar A. Borumand Saeid <p>In this paper, we characterize some properties of fuzzy congruence relations and obtain a fuzzy congruence relation generated by a fuzzy relation in residuated lattices. For this purpose, two various types of fuzzy relations (regular and irregular) are introduced. In order to obtain a fuzzy congruence relation generated by an irregular fuzzy relation it must convert to a regular fuzzy relation.</p> 2023-09-13T00:00:00+00:00 Copyright (c) 2023 S. Khosravi Shoar, A. Borumand Saeid Fractional ordered Euler Riesz difference sequence spaces 2022-10-08T08:53:47+00:00 Diptimayee Jena Salila Dutta <p>In this article we introduce new sequence spaces c<sub>0 </sub>(<sup>τ</sup>), c(<sup>τ</sup>) and l<sub>∞</sub>(<sup>τ</sup>) of fractional order τ , consisting of an operator which is a composition of Euler-Riesz operator and fractional difference operator. Certain topological properties of these spaces are investigated along with Schauder basis and α−, β− and γ−duals.</p> 2023-09-13T00:00:00+00:00 Copyright (c) 2023 Diptimayee Jena, Salila Dutta On universal realizability in the left half-plane 2023-06-23T07:28:05+00:00 Jaime H. Alfaro Ricardo L. Soto <p>A list Λ = {λ<sub>1</sub>, λ<sub>2</sub>,..., λn} of complex numbers is said to be realizable if it is the spectrum of a nonnegative matrix. Λ is said to be universally realizable (UR) if it is realizable for each possible Jordan canonical form allowed by Λ. In this paper, using companion matrices and applying a procedure by Šmigoc, we provide sufficient conditions for the universal realizability of left half-plane spectra, that is, spectra Λ = {λ<sub>1</sub>,...,λ<sub>n</sub>} with λ<sub>1</sub> &gt; 0, Re λ<sub>i</sub> ≤ 0, i = 2, . . . , n. It is also shown how the effect of adding a negative real number to a not UR left half-plane list of complex numbers, makes the new list UR, and a family of left half-plane lists that are UR is characterized.</p> 2023-09-13T00:00:00+00:00 Copyright (c) 2023 Jaime H. Alfaro, Ricardo L. Soto