Proyecciones (Antofagasta, On line) 2022-08-26T00:00:00+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> On the mixed multifractal formalism for vector-valued measures 2020-05-19T04:53:41+00:00 Bilel Selmi Anouar Ben Mabrouk <p>The multifractal formalism for vector-valued measures holds when-ever the existence of corresponding Gibbs-like measures, supported on the singularities sets holds. We tried through this article to improve a result developed by Menceur et al. in [29] and to suggest a new sufficient condition for a valid mixed multifractal formalism for vector-valued measures. We describe a necessary condition of validity for the formalism which is very close to the sufficient one.</p> 2022-08-26T00:00:00+00:00 Copyright (c) 2022 Bilel Selmi, Anouar Ben Mabrouk Lie (Jordan) centralizers on alternative algebras 2021-03-09T21:27:21+00:00 Aisha Jabeen Bruno Ferreira <p>In this article, we study Lie (Jordan) centralizers on alternative algebras and prove that every multiplicative Lie centralizer has proper form on alternative algebras under certain assumptions.</p> 2022-08-26T00:00:00+00:00 Copyright (c) 2022 Aisha Jabeen, Bruno Ferreira Equitable chromatic number of weak modular product of Some graphs 2022-02-20T16:21:23+00:00 K. Kaliraj R. Narmadha Devi J. Vernold Vivin <p>An equitable coloring of a graph G is a proper coloring of the vertices of G such that the number of vertices in any two color clases differ by at most one. The equitable chromatic number χ=(G) of a graph G is the minimum number of colors needed for an equitable coloring of G. In this paper, we obtain the equitable chromatic number of weak modular product of two graphs G and H, denoted by G o H.</p> <p>First, we consider the graph G o H, where G is the path graph, and H be any simple graph like the path, the cycle graph, the complete graph. Secondly, we consider G and H as the complete graph and cycle graph respectively. Finally, we consider G as the star graph and H be the complete graph and star graph.</p> 2022-08-26T00:00:00+00:00 Copyright (c) 2022 K. Kaliraj, R. Narmadha Devi, J. Vernold Vivin Spectral analysis for finite rank perturbation of diagonal operator in non-archimedean Banach space of countable type 2021-06-19T15:34:25+00:00 Abdelkhalek El amrani Aziz Blali Mohamed Amine Taybi <p>In this paper we are concerned with the spectral analysis for the classes of finte rank perturbations of diagonal operators in the form A = D +F where D is a diagonal operator and F &nbsp;is an operator of finite rank in the non archimedean Banach space of countable type. Using the theory of Fredholm operators in non archimedean setting and the concept of essential spectrum for linear operators, we compute the spectrum of A.</p> 2022-08-26T00:00:00+00:00 Copyright (c) 2022 Abdelkhalek El amrani, Aziz Blali, Mohamed Amine Taybi On the cohomological equation of a linear contraction 2020-10-30T17:08:23+00:00 Régis Leclercq Abdellatif Zeggar <p>In this paper, we study the discrete cohomological equation of a contracting linear automorphism A of the Euclidean space <strong>R</strong><sup>d</sup>. More precisely, if δ is the cobord operator defined on the Fréchet space E = C<sup>l</sup> (<strong>R</strong><sup>d</sup>) (0 ≤ l ≤ ∞) by: δ(h) = h − h ◦ A, we show that:</p> <ul> <li>If E = C<sup>0</sup>(<strong>R</strong><sup>d</sup>), the range δ (E) of δ has infinite codimension and its closure is the hyperplane E<sub>0</sub> consisting of the elements of E vanishing at 0. Consequently, H<sup>1</sup> (A, E) is infinite dimensional non Hausdorff topological vector space and then the automorphism A is not cohomologically C<sup>0</sup>-stable.</li> <li>If E = C<sup>l </sup>(<strong>R</strong><sup>d</sup>), with 1 ≤ l ≤ ∞, the space δ (E) coincides with the closed hyperplane E<sub>0</sub>. Consequently, the cohomology space H<sup>1</sup> (A, E) is of dimension 1 and the automorphism A is cohomologically C<sup>l</sup>-stable.</li> </ul> 2022-09-13T00:00:00+00:00 Copyright (c) 2022 Régis Leclercq, Abdellatif Zeggar I-convergent triple fuzzy normed spaces 2021-06-15T07:03:26+00:00 Tanweer Jalal Ishfaq Ahmad Malik <p>In this paper we introduce the lacunary ideal convergence of triple sequences in fuzzy normed spaces and the relation between lacunary convergence and lacunary ideal convergence is investigated for triple sequences in fuzzy normed spaces. Concept of limit point and cluster point for triple sequences in fuzzy normed spaces and theorems related to these concepts are also given.</p> 2022-09-13T00:00:00+00:00 Copyright (c) 2022 Tanweer Jalal, Ishfaq Ahmad Malik Stratonovich-Henstock integral for the operator-valued stochastic process 2021-07-12T07:54:25+00:00 Recson Canton Mhelmar Labendia Tin Lam Toh <p>In this paper, we introduce the Stratonovich-Henstock integral of an operator-valued stochastic process with respect to a Q-Wiener process. We also formulate a version of Ito's formula for this integral.</p> 2022-09-13T00:00:00+00:00 Copyright (c) 2022 Recson Canton, Mhelmar Labendia, Tin Lam Toh Implications of Some Types of Pairwise Closed Graphs 2022-04-15T10:46:52+00:00 Hend Bouseliana Adem Kılıçman <p>The main goal of this paper is to introduce and look into some of the fundamental properties of pairwise strongly closed, pairwise strongly -closed and pairwise quasi -closed graphs. Some characterizations and several properties concerning these graphs are obtained. We also investigate relationships between&nbsp; (i,j)-strongly alpha -closed graph&nbsp; G(f) and&nbsp; (i,j)-weakly alpha -continuous. We study relationships between&nbsp; (i,j) strongly alpha -closed&nbsp; (i,j)-quasi alpha-closed graphs with covering properties. The concepts of pairwise -closed and pairwise quasi H-closed relatively are stated.</p> 2022-09-13T00:00:00+00:00 Copyright (c) 2022 Hend Bouseliana, Adem Kılıçman Some characterizations of frames in ℓ²(I; H) and topological applications 2020-03-19T23:43:10+00:00 Nizar El Idrissi Samir Kabbaj Brahim Moalige <p>We propose in this article some characterizations of the notion of frame in ℓ<sup>²</sup>(<em>I</em>; <em>H</em>). The first one is general, and depends on a procedure of inserting a family of vectors instead of x in the definition of a frame. This allows us to define the analysis, synthesis and frame operator on the space ℓ<sup>²</sup>(<em>I</em>; <em>H</em>) instead of <em>H</em>. The second one is specific to ℓ<sup>²</sup> (<em>I</em>; <em>C</em><sup>k</sup>) and relate it to the freeness of the finite set of components of the frame. The third one concerns normalised tight frames in ℓ<sup>²</sup>(<em>I</em>; <em>C</em><sup>k</sup>). Afterwards, we give an example of a frame in ℓ<sup>²</sup>(<em>I</em>; <em>C</em><sup>²</sup>) using another sufficient condition in dimension 2. We conclude with some topological applications of these characterizations.</p> 2022-09-13T00:00:00+00:00 Copyright (c) 2022 Nizar El Idrissi, Samir Kabbaj, Brahim Moalige Combination labelings of graphs related to several cycles and paths 2022-03-30T11:42:43+00:00 Aiewcharoen Busakorn Ratinan Boonklurb Sakulwat Promvichitkul <p>Suppose that G = (V (G), E(G)) is a graph and |V (G)| = p. If there exists a bijective function <em>f</em> : V (G) → {1, 2, 3, ..., p} such that an <em>f</em> <sup>c</sup> : E(G) → N defined by <em>f</em> <sup>c</sup>(uv) = (<sup>f(u)</sup><sub>f(v)</sub>)when <em>f</em> (u) &gt; f(v) and <em>f </em><sup>c</sup>(uv) = (<sup>f(u)</sup><sub>f(v)</sub>)when <em>f </em>(v) &gt; <em>f</em> (u) is an injection function, then <em>f</em> is called a combination labelings and G is called a combination graph.</p> <p>This article considers a suitable bijective function f and prove that G(C<sub>n</sub>, C<sub>m</sub>, P<sub>k</sub>) which are graphs related to two cycles and one path containing three parameters, are combination graphs.</p> 2022-09-27T00:00:00+00:00 Copyright (c) 2022 Aiewcharoen Busakorn, Ratinan Boonklurb, Sakulwat Promvichitkul Orbit equivalence of linear systems on manifolds and semigroup actions on homogeneous spaces 2021-10-28T14:35:48+00:00 João Augusto Navarro Cossich R. M. Hungaro O. G. Rocio A. J. Santana <p>In this paper we introduce the notion of orbit equivalence for semi-<br>group actions and the concept of generalized linear control system on<br>smooth manifold. The main goal is to prove that, under certain condi-<br>tions, the semigroup system of a generalized linear control system on a<br>smooth manifold is orbit equivalent to the semigroup system of a linear<br>control system on a homogeneous space.</p> 2022-09-27T00:00:00+00:00 Copyright (c) 2022 João Augusto Navarro Cossich, R. M. Hungaro, O. G. Rocio, A. J. Santana Fractional metric dimension of generalized prism graph 2022-02-21T18:24:32+00:00 Nosheen Goshi Sohail Zafar Tabasam Rashid <p>Fractional metric dimension of connected graph $G$ was introduced by Arumugam et al. in [Discrete Math. 312, (2012), 1584-1590] as a natural extension of metric dimension which have many applications in different areas of computer sciences for example optimization, intelligent systems, networking and robot navigation. In this paper fractional metric dimension of generalized prism graph $P_{m}\times C_{n}$ is computed using combinatorial criterion devised by Liu et al. in [ Mathematics, 7(1), (2019), 100].</p> 2022-09-27T00:00:00+00:00 Copyright (c) 2022 Nosheen Goshi, Sohail Zafar, Tabasam Rashid On even-odd meanness of super subdivision of some graphs 2022-01-18T14:57:37+00:00 Mohamed Basher Muhammad Kamran Siddiqui <p>Graph Labeling is a significant area of graph theory that is used in a variety of applications like coding hypothesis, x-beam crystallography, radar, cosmology, circuit design, correspondence network tending to, and database administration. This study provides a general overview of graph naming in heterogeneous fields, however it primarily focuses on graph subdivision. The even vertex odd meanness of super subdivide of various graphs is discussed in this study. The graphs generated by super subdivided of path, cycle, comb, crown, and planar grid are even-odd mean graphs, according to our proof.</p> 2022-09-27T00:00:00+00:00 Copyright (c) 2022 Mohamed Basher, Muhammad Kamran Siddiqui Bounds for absolute values and imaginary parts of matrix eigenvalues via traces 2022-02-14T15:15:48+00:00 Michael Gil' <p>Let λ<sub>1</sub>(A), λ<sub>2</sub>(A), ..., λ<sub>n</sub>(A) be the eigenvalues of an n × n-matrix A taken with their algebraic multiplicities. We suggest new bounds for |λ<sub>j</sub> (A) − <sup>trace(A)/ n</sup> | and |Im λ<sub>j</sub> (A) − <sup>Im trace(A)/n</sup> | (j = 1, ..., n), which refine the previously published results.</p> <p> </p> 2022-09-27T00:00:00+00:00 Copyright (c) 2022 Michael Gil' Decomposition dimension of corona product of some classes of graphs 2022-05-13T09:33:29+00:00 T. Reji R. Ruby <p>For an ordered <em>k</em>-decomposition <em>D</em> = {G<sub>1</sub>, G<sub>2</sub>,...,G<sub>k</sub>} of a connected graph G = (V,E), the <em>D</em>-representation of an edge e is the k-tuple γ(e/D)=(d(e, G<sub>1</sub>), d(e, G<sub>2</sub>), ...,d(e, G<sub>k</sub>)), where d(e, G<sub>i</sub>) represents the distance from e to G<sub>i</sub>. A decomposition D is resolving if every two distinct edges of G have distinct representations. The minimum k for which G has a resolving k-decomposition is its decomposition dimension dec(G). In this paper, the decomposition dimension of corona product of the path P<sub>n</sub> and cycle C<sub>n</sub> with the complete graphs K<sub>1</sub> and K<sub>2</sub> are determined.</p> 2022-09-27T00:00:00+00:00 Copyright (c) 2022 T. Reji , R. Ruby