Proyecciones (Antofagasta, On line) 2024-04-03T19:35:12+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> The Connected and Forcing Connected Restrained Monophonic Numbers of a Graph 2023-05-15T19:16:40+00:00 Ganesamoorthy K. Santhakumaran A.P. Titus P. <p>For a connected graph G = (V,E) of order at least two, a connected restrained monophonic set S of G is a restrained monophonic set such that the subgraph G[S] induced by S is connected. The minimum cardinality of a connected restrained monophonic set of G is the connected restrained monophonic number of G and is denoted by mcr(G). We determine bounds for it and find the same for some special classes of graphs. It is shown that, if a, b and p are positive integers such that 3 ≤ a ≤ b ≤ p, p−1 6= a, p−1 6= b, then there exists a connected graph G of order p, mr(G) = a and mcr(G) = b. Also, another parameter forcing connected restrained monophonic number fcrm(G) of a graph G is introduced and several interesting results and realization theorems are proved.</p> 2024-04-03T00:00:00+00:00 Copyright (c) 2024 Ganesamoorthy K., Santhakumaran A.P., Titus P. Common Multiples of Paths and Stars with Crowns 2022-11-20T12:58:47+00:00 Saritha Chandran C Reji T <p>{\footnotesize A graph $G$ is a common multiple of two graphs $H_1$ and $H_2$ if there exists a decomposition of $G$ into edge-disjoint copies of $H_1$ and also a decomposition of $G$ into edge-disjoint copies of $H_2$. If $ G $ is a common multiple of $H_1$ and $H_2$, and $ G $ has $ q $ edges, then we call $ G $ a $ (q, H_1, H_2) $ graph. Our paper deals with the following question: Given two graphs $ H_1 $ and $ H_2$, for which values of $ q $ does there exist a $ (q, H_1, H_2) $ graph? when $H_1$ is either a path or a star with $3$ or $4$ edges and $H_2$ is a crown.<br>}</p> 2024-04-03T00:00:00+00:00 Copyright (c) 2024 Saritha Chandran C, Reji T Some remarks on summability defined by invariant mean in intuitionistic fuzzy 2-normed spaces 2023-04-01T10:18:32+00:00 Sumaira Aslam Vijay Kumar Archana Sharma <div class="page" title="Page 1"> <div class="layoutArea"> <div class="column"> <p>In present paper, we aim to define a new summability method using σ-mean called σ-statistical summability in an intuitionistic fuzzy 2- normed space (briefly IF2NS). We also define σ-statistical cauchy sequence in an IF2NS and study some of their properties. We display example that shows our method of summability is more stronger in these spaces.</p> </div> </div> </div> 2024-04-03T00:00:00+00:00 Copyright (c) 2024 Sumaira Aslam, Vijay Kumar, Archana Sharma MAXIMAL GRAPHICAL REALIZATION OF A TOPOLOGY 2022-11-22T22:20:10+00:00 Ullas Thomas Sunil C Mathew <p>Given a topological space, the graphical realizations of it with as many edges as possible, called maximal graphical realizations, are studied here. Every finite topological space admits a maximal graphical realization. However, there are graphs which are not maximal graphical realizations of any topology. A tree of odd order is never a maximal graphical realization of a topological space. Maximal graphical realization of a topology is a cycle if and only if it is C_3. It is shown that chain topologies admit unique maximal graphical realizations. A lower bound for the size of a maximal graphical realization is also obtained.</p> 2024-04-03T00:00:00+00:00 Copyright (c) 2024 Ullas Thomas, Sunil C Mathew A study on derivations of inverse semirings with involution 2022-10-03T19:55:25+00:00 Dr. Madhu Dadhwal Geeta Devi <p>In this research article, &nbsp;we study the influence of derivations on semirings with involution which resembles with commutativity preserving mappings. The action of derivations on Lie ideals and some differential identities regarding Lie ideals are also investigated. It is proved that for any two derivations d1, d2 of a prime semiring S with involution ⋆ such that atleast one of d<sub>1</sub>, d<sub>2</sub> is nonzero and char(S) &nbsp;2, then the identity [d<sub>1</sub>(a), d<sub>2</sub>(a <sup>⋆</sup> )] + d<sub>2</sub>(a ◦ a <sup>⋆</sup> ) = 0, for all a ∈ L implies [L , S] = (0), where L is a Lie ideal of S.</p> 2024-04-03T00:00:00+00:00 Copyright (c) 2024 Dr. Madhu Dadhwal, Geeta Devi A semilinear non-homogeneous problem related to Korteweg-de Vries Equation 2023-06-12T13:09:41+00:00 Yassine Benia <p>In this paper, we consider a non-homogeneous generalized Korteweg-de Vries problem with some hypotheses on the right-hand side, and we give a new regularity result of the solution in an anisotropic Sobolev space. Then we apply the obtained result to a non-homogeneous KdV problem. This work is an extension of solvability results for a right-hand side f in Lebesgue space.</p> 2024-04-03T00:00:00+00:00 Copyright (c) 2024 Yassine Benia An optimization model for fuzzy nonlinear programming with Beale's conditions using trapezoidal membership functions 2024-01-28T10:34:55+00:00 Palanivel Kaliyaperumal Muralikrishna P <p>Non-linear Programming (NLP) is an optimization technique&nbsp;for determining the optimum solution to a broad range of research issues. Many times, the objective function is non-linear, owing to various economic behaviors such as demand, cost, and many others. Since the appearance of Kuhn and Tucker's fundamental theoretical work, a general NLP problem can be resolved using many methods to find the optimum solution. In this chapter, a fuzzy mathematical model based on Beale's condition is proposed to address NLP with inequality constraints in terms of fuzziness. Furthermore, the model demonstrates how quadratic programming problems can be solved using membership functions. The model also describes three stages: that is, mathematical formulation, computational procedures, and numerical illustration with comparative analysis. Likewise, the model illustrates the considered problem using two distinct approaches, namely membership functions (MF) and robust ranking index. Finally, the comparison analysis provides detailed results and discussion that justify the optimal outcome in order to address the vagueness of certain NLPPs.</p> 2024-04-05T00:00:00+00:00 Copyright (c) 2024 Palanivel Kaliyaperumal, Muralikrishna P A note on local edge antimagic chromatic number of graphs 2023-07-20T21:58:07+00:00 Fawwaz Fakhrurrozi Hadiputra Tita Khalis Maryati <p>Let $G$ be a finite, undirected and simple graph. A bijection $f : V(G) \to [1,|V(G)|]$ is called a local edge antimagic labeling if for any two adjacent edges $uv,vw \in E(G), f(u) \ne f(w)$. The local edge antimagic chromatic number $\ch(G)$ is the minimum number of colors taken over all colorings induced by local edge antimagic labeling of $G$. In this paper, we investigate characterization of graphs $G$ with small number $\ch(G)$, relationship between local edge antimagic chromatic number $\ch(G)$ and edge independence number $\alpha'(G)$, and bounds of $\ch(G)$ for any graphs.</p> 2024-04-03T00:00:00+00:00 Copyright (c) 2024 Fawwaz Fakhrurrozi Hadiputra, Tita Khalis Maryati On derivations over trivial extensions 2023-11-20T15:16:58+00:00 brahim boudine Mohammed Zerra <pre>In this paper, we investigate the structure of derivations over trivial extensions. We provide a detailed analysis of the structure of derivations on trivial extensions, the centre of trivial extensions, and the conditions for a trivial extension to be prime. Additionally, we examine the structure of derivations on trivial extensions when the underlying ring, $R$, is a prime ring, under the conditions of Herstein's Theorem, Posner's Theorem, and Bell's theorem.</pre> 2024-04-03T00:00:00+00:00 Copyright (c) 2024 brahim boudine, Mohammed Zerra On local distance antimagic chromatic number of graphs disjoint union with 1-regular graphs 2023-08-08T12:46:32+00:00 Nalliah M <p>Let $G$ be a graph on $p$ vertices and $q$ edges with no isolated vertices. A bijection $f: V\rightarrow \{1,2,3,...,p\}$ is called local distance antimagic labeling, if for any two adjacent vertices $u$ and $v$, we have $w(u) \neq w(v)$, where $w(u)=\sum_{x\epsilon N(u)} {f(x)}$. The local distance antimagic chromatic number $\chi_{lda}(G)$ is defined to be the minimum number of colors taken over all colorings of $G$ induced by local distance antimagic labelings of $G$. In this paper, we obtained the necessary and sufficient condition for the local distance antimagic chromatic number of some disjoint union of graphs with 1-regular graphs equal to the number of distinct neighbors of its pendant vertices. We also gave a correct result in [Local Distance Antimagic Vertex Coloring of Graphs,].%magic Vertex Coloring of Graphs,</p> 2024-04-03T00:00:00+00:00 Copyright (c) 2024 Nalliah M Higher order mKdV breathers: nonlinear stability 2023-06-13T01:56:22+00:00 MIGUEL A ALEJO <p>We are interested in stability results for breather solutions of the 5th, 7th and 9th order mKdV equations.<br>We show that these higher order mKdV breathers are stable in $H^2(\R)$, in the same way as \emph{classical} mKdV breathers. <br>We also show that breather solutions of the 5th, 7th and 9th order mKdV equations satisfy the same stationary fourth order<br>nonlinear elliptic equation as the mKdV breather, independently of the order, 5th, 7th or 9th, considered.</p> 2024-04-03T00:00:00+00:00 Copyright (c) 2024 MIGUEL A ALEJO Antimagic Labeling for Some Snake Graphs 2023-10-06T13:21:15+00:00 Chirag Barasara Palak Prajapati <p>A graph with q edges is called antimagic if its edges can be labeled with 1, 2, 3, ..., q without repetition such that the sums of the labels of the edges incident to each vertex are distinct. In this paper we study antimagic labeling of double triangular snake, alternate triangular snake, double alternate triangular snake, quadrilateral snake, double quadrilateral snake, alternate quadrilateral snake, double alternate quadrilateral snake.</p> 2024-04-05T00:00:00+00:00 Copyright (c) 2024 Chirag Barasara, Palak Prajapati