https://www.revistaproyecciones.cl/index.php/proyecciones/issue/feed Proyecciones (Antofagasta, On line) 2021-02-01T00:00:00+00:00 Ricardo Soto Montero rsoto@ucn.cl 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> https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/3767 On r- Dynamic coloring of the gear graph families 2020-04-21T17:18:24+00:00 T. Deepa deepathangavelu88@gmail.com M. Venkatachalam venkatmaths@gmail.com D. Dafik d.dafik@unej.ac.id <p><em>An r-dynamic coloring of a graph G is a proper coloring c of the vertices such that |c(N(v))| ≥ min {r, d(v)}, for each v </em><em>∈</em><em> V (G). The r-dynamic chromatic number of a graph G is the minimum k such that G has an r-dynamic coloring with k colors. In this paper, we obtain the r−dynamic chromatic number of the middle, central and line graphs of the gear graph.</em></p> 2021-01-06T00:00:00+00:00 Copyright (c) 2021 T. Deepa, M. Venkatachalam, D. Dafik https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/4012 Another example of the mutual singularity of multifractal measures 2020-05-14T03:26:26+00:00 Zied Douzi zied.douzi@fsm.rnu.tn Amal Samti amal_samti@yahoo.fr Bilel Selmi bilel.selmi@fsm.rnu.tn <p><em>We propose an example for which the multifractal Hausdorff and packing measures are mutually singular. </em></p> 2021-01-06T00:00:00+00:00 Copyright (c) 2021 Zied Douzi, Amal Samti, Bilel Selmi https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/3507 H-supplemented modules with respect to images of fully invariant submodules 2020-04-29T04:25:32+00:00 A. R. Moniri Hamzekolaee a.monirih@umz.ac.ir Tayyebeh Amouzegar t.amoozegar@yahoo.com <p><em>Lifting modules plays important roles in module theory. H-supplemented modules are a nice generalization of lifting modules which have been studied extensively recently. In this article, we introduce a proper generalization of H-supplemented modules via images of fully invariant submodules. Let F be a fully invariant submodule of a right Rmodule M. We say that M is I<sub>F</sub> -H-supplemented in case for every endomorphism φ of M, there is a direct summand D of M such that φ(F) + X = M if and only if D + X = M, for every submodule X of M. It is proved that M is I<sub>F</sub> -H-supplemented if and only if F is a dual Rickart direct summand of M for a fully invariant noncosingular submodule F of M. It is shown that the direct sum of I<sub>F</sub> –H supplemented modules is not in general I<sub>F</sub> -H-supplemented. Some sufficient conditions such that the direct sum of I<sub>F</sub> -H-supplemented modules is I<sub>F</sub> -H-supplemented are given </em></p> 2021-01-06T00:00:00+00:00 Copyright (c) 2021 A. R. Moniri Hamzekolaee, Tayyebeh Amouzegar https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/3671 Stability of a general p-radical functional equation related to additive mappings in 2-Banach spaces 2019-07-21T10:39:38+00:00 Sadeq A. A. AL Ali sadeqalali2018@gmail.com Muaadh Almahalebi muaadh1979@hotmail.fr Youssfi Elkettani elkettani@ui-ibntofail.ac.ma <p>In this paper, we introduce and solve a new general p-radical functional equation</p> <p><img src="https://www.revistaproyecciones.cl/public/site/images/rvidal/imagen1.png" alt="" width="257" height="81" /></p> <p>Also, we investigate some stability and hyperstability results for the considered equation in 2-Banach spaces. In addition, we prove the hyperstability of the inhomogeneous p-radical functional equation</p> <p><img src="https://www.revistaproyecciones.cl/public/site/images/rvidal/imagen2.png" alt="" width="307" height="81" /></p> 2021-01-06T00:00:00+00:00 Copyright (c) 2021 Sadeq A. A. AL Ali, Muaadh Almahalebi, Youssfi Elkettani https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/4121 Remarks on the mutual singularity of multifractal measures 2020-06-22T02:42:06+00:00 Bilel Selmi bilel.selmi@fsm.rnu.tn <p><em>In the present work, we study the mutual singularity of multifractal Hausdorff and packing measures which provide a positive answer to Olsen’s questions in a more general framework. Our main results apply to a family of measures supported by the full 5-adic grid of [0, 1], namely the quasi-Bernoulli measures.</em></p> 2021-01-06T00:00:00+00:00 Copyright (c) 2021 Bilel Selmi https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/3694 New algebraic properties of middle Bol loops II 2019-08-05T18:41:32+00:00 Temitope Gbolahan Jaiyeola tjayeola@oauife.edu.ng S. P. David davidsp4ril@yahoo.com O. O. Oyebola oyebolaoo@funaab.edu.ng <p><em>A loop (Q, ·, \, /) is called a middle Bol loop (MBL) if it obeys the identity x(yz\x)=(x/z)(y\x). To every MBL corresponds a right Bol loop (RBL) and a left Bol loop (LBL). In this paper, some new algebraic properties of a middle Bol loop are established in a different style. Some new methods of constructing a MBL by using a non-abelian group, the holomorph of a right Bol loop and a ring are described. Some equivalent necessary and sufficient conditions for a right (left) Bol loop to be a middle Bol loop are established. A RBL (MBL, LBL, MBL) is shown to be a MBL (RBL, MBL, LBL) if and only if it is a Moufang loop.</em></p> 2021-01-06T00:00:00+00:00 Copyright (c) 2021 Temitope Gbolahan Jaiyeola, S. P. David, O. O. Oyebola https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/3936 Horadam polynomials and their applications to new family of bi-univalent functions with respect to symmetric conjugate points 2020-05-04T22:15:50+00:00 Abbas Kareem Wanas abbas.kareem.w@qu.edu.iq Sibel Yalçın syalcin@uludag.edu.tr <p><em>In the current paper, by making use of the Horadam polynomials, we introduce and investigate a new family of holomorphic and biunivalent functions with respect to symmetric conjugate points defined in the open unit disk <strong>D</strong>. We derive upper bounds for the second and third coefficients and solve Fekete-Szegö problem of functions belongs to this family<strong>.</strong></em></p> <p align="LEFT"><span style="font-family: CMR10; font-size: small;">.</span></p> 2021-01-08T00:00:00+00:00 Copyright (c) 2021 Abbas Kareem Wanas, Sibel Yalçın https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/4020 A Moreau-Yosida regularization for Markov decision processes 2020-07-01T16:20:08+00:00 Israel Ortega-Gutiérrez rei_israel@yahoo.com.mx Hugo Cruz-Suárez hcs@fcfm.buap.mx <p><em>This paper addresses a class of sequential optimization problems known as Markov decision processes. These kinds of processes are considered on Euclidean state and action spaces with the total expected discounted cost as the objective function. The main goal of the paper is to provide conditions to guarantee an adequate Moreau-Yosida regularization for Markov decision processes (named the original process). In this way, a new Markov decision process that conforms to the Markov control model of the original process except for the cost function induced via the Moreau-Yosida regularization is established. Compared to the original process, this new discounted Markov decision process has richer properties, such as the differentiability of its optimal value function, strictly convexity of the value function, uniqueness of optimal policy, and the optimal value function and the optimal policy of both processes, are the same. To complement the theory presented, an example is provided.</em></p> 2021-01-08T00:00:00+00:00 Copyright (c) 2021 Israel Ortega-Gutiérrez, Hugo Cruz-Suárez https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/4350 Existence and uniqueness of positive solutions for nonlinear Caputo-Hadamard fractional differential equations 2020-07-17T18:57:37+00:00 Abdelouaheb Ardjouni abd_ardjouni@yahoo.fr <p><em>We prove the existence and uniqueness of a positive solution of nonlinear Caputo-Hadamard fractional differential equations. In the process we employ the Schauder and Banach fixed point theorems and the method of upper and lower solutions to show the existence and uniqueness of a positive solution. Finally, an example is given to illustrate our results.</em></p> 2021-01-13T00:00:00+00:00 Copyright (c) 2021 Abdelouaheb Ardjouni https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/3862 Some hyperstability results of a p-radical functional equation related to Drygas mappings in non-Archimedean Banach spaces 2020-06-24T19:24:25+00:00 Mostapha Esseghyr Hryrou hryrou.mustapha@hotmail.com Ahmed Nuino ahmed.nuino2015@gmail.com Samir Kabbaj samkabbaj@yahoo.fr <p>The aim of this paper is to introduce and solve the following <em>p</em>-radical functional equation related to Drygas mappings</p> <p> </p> <p><img src="https://www.revistaproyecciones.cl/public/site/images/rvidal/imagen1-art10.png" alt="" width="419" height="25" /></p> <p><em>f</em> is a mapping from <strong>R </strong>into a vector space <em>X</em> and <em>p ≥ 3</em> is an odd natural number. Using an analogue version of Brzdȩk’sfixed point theorem [12], we establish some hyperstability results for the considered equation in non-Archimedean Banach spaces. Also, we give some hyperstability results for the inhomogeneous <em>p</em>-radical functional equation related to Drygas mappings<br /><br /></p> <p><img src="https://www.revistaproyecciones.cl/public/site/images/rvidal/imagen2-art10.png" alt="" width="416" height="25" /></p> 2021-01-13T00:00:00+00:00 Copyright (c) 2021 Mostapha Esseghyr Hryrou, Ahmed Nuino, Samir Kabbaj https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/3869 Minimal and maximal solutions to first-order differential equations with piecewise constant generalized delay 2019-11-26T18:05:36+00:00 Kuo-Shou Chiu kschiu@umce.cl <p><em>In this paper we employ the method of maximal and minimal solutions coupled with comparison principles and the monotone iterative technique to obtain results of existence and approximation of solutions for differential equations with piecewise constant delay of generalized type (DEPCAG).</em></p> 2021-01-16T00:00:00+00:00 Copyright (c) 2021 Kuo-Shou Chiu https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/4127 New approach for Somos’s Dedekind eta-function identities of level 6 2020-04-29T05:40:08+00:00 D. Anu Radha anurad13@gmail.com B. R. Srivatsa Kumar sri_vatsabr@yahoo.com Shruthi shruthikarranth@gmail.com <p><em>In the present work, we prove few new Dedekind eta-function identities of level 6 discovered by Somos in two different methods. Also during this process, we give an alternate method to Somos’s Dedekind eta-function identities of level 6 proved by B. R. Srivatsa Kumar et al. As an application of this, we establish colored partition identities.</em></p> 2021-01-16T00:00:00+00:00 Copyright (c) 2021 D. Anu Radha, B. R. Srivatsa Kumar, Shruthi https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/4135 Some trapezoid and midpoint type inequalities for newly defined quantum integrals 2020-04-30T04:37:18+00:00 Hüseyin Budak hsyn.budak@gmail.com <p><em>In this paper, we first obtain prove two new identities for the quantum integrals. Then we establish Trapezoid and Midpoint type inequalities for quantum integrals defined by Bermudo et al. in [3]. The inequalities in this study generalize some results obtained in earlier works.</em></p> 2021-01-16T00:00:00+00:00 Copyright (c) 2021 Hüseyin Budak https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/4178 Relating centralities in graphs and the principal eigenvector of its distance matrix 2020-05-13T21:32:05+00:00 Celso Marques da Silva Jr. celsomjr@gmail.com Renata R. Del-Vecchio rrdelvecchio@id.uff.br Bruno B. Monteiro brunobm@id.uff.br <p><em>In this work a new centrality measure of graphs is presented, based on the principal eigenvector of the distance matrix: spectral closeness. Using spectral graph theory, we show some of its properties and we compare the results of this new centrality with closeness centrality. In particular, we prove that for threshold graphs these two centralities always coincide. In addition we construct an infinity family of graphs for which these centralities never coincide.</em></p> 2021-01-16T00:00:00+00:00 Copyright (c) 2021 Celso Marques da Silva Junior, Renata R. Del-Vecchio, Bruno B. Monteiro https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/4416 On a bi-nonlocal fourth order elliptic problem 2020-08-19T20:59:11+00:00 Fatna F. Jaafri jaafri.fatna.sma@gmail.com Abdesslem Ayoujil abayoujil@gmail.com Mohamed Berrajaa berrajaamo@yahoo.fr <p><em>This paper is aiming at obtaining weak solution for a bi-nonlocal fourth order elliptic problem with Navier boundary condition. Our approach is based on variational methods and critical point theory. </em></p> 2021-01-16T00:00:00+00:00 Copyright (c) 2021 Fatna F. Jaafri, Abdesslem Ayoujil, Mohamed Berrajaa https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/4437 Diagonal entries of the combined matrix of sign regular matrices of order three 2020-09-03T10:40:15+00:00 Maria T. Gassó mgasso@mat.upv.es Iv´an Gil 100082928@est.uasd.edu.do Isabel Giménez igimenez@imm.upv.es M´aximo Santana msantana22@uasd.edu.do Elaine Segura esegura@uasd.edu.do <div class="page" title="Page 1"> <div class="layoutArea"> <div class="column"> <p><em>The study of the diagonal entries of the combined matrix of a nonsingular matrix A has been considered by different authors for the classes of M—matrices, positive definite matrices and totally positive (negative) matrices. This problem appears to be difficult as the results have been done only for matrices of order three. In this work, we continue to give the characterization of the diagonal entries of the combined matrix of the remainder sign regular matrices. Thus, the problem is closed for all possible sign regular matrices of order three.</em></p> </div> </div> </div> 2021-01-16T00:00:00+00:00 Copyright (c) 2021 Maria T. Gassó, Iv´an Gil, Isabel Giménez, M´aximo Santana, Elaine Segura