Scielo RSS <![CDATA[Proyecciones (Antofagasta)]]> vol. 37 num. 2 lang. es <![CDATA[SciELO Logo]]> <![CDATA[Super vertex mean labeling of cycles through different ways]]> Abstract: A super vertex mean labeling 𝑓 of a (p,q) - graph G = (V,E) is defined as an injection from E to the set {1,2,3,···,p+q} that induces for each vertex v the label defined by the rule , where Ev denotes the set of edges in G that are incident at the vertex v, such that the set of all edge labels and the induced vertex labels is {1,2,3,···,p+q}. In this paper, we investigate the super vertex mean labeling behavior of cycles by giving various ways by which they can be labeled. <![CDATA[On estimates for the generalized Fourier-Bessel transform]]> Abstract: Two estimates useful in applications are proved for the generalized Fourier-Bessel transform in the space as applied to some classes of functions characterized by a generalized modulus of continuity. <![CDATA[Saturations of submodules with respect to subsets of a ring]]> Abstract Let R be a commutative ring with identity and M a unital R-module. For any submodule N of M and non-empty subset T of R, let (N)={m ∈ M : rm∈ N for some r∈ R\T}. In this article we study conditions under which (N) is a submodule of M and investigate when it is a union of prime submodules. <![CDATA[Generalised Closed Sets in Multiset Topological Space]]> Abstract: In this article, we introduce the notion of generalized closed sets and generalized open sets in multiset topological spaces. We investigate their different properties. We have introduced the notion of some separation axioms and discussed some examples. <![CDATA[A new family of chromatically unique 6-bridge graph]]> Abstract: For a graph G, let P(G,λ) denote the chromatic polynomial of G. Two graphs G and H are chromatically equivalent (or simply χ-equivalent), denoted by G∼ H, if P(G,λ)=P(H,λ). A graph G is chromatically unique (or simply χ-unique) if for any graph H such as H∼ G, we have H≅ G, i.e, H is isomorphic to G. In this paper, the chromatic uniqueness of a new family of 6-bridge graph θ (a,a,b,b,b,c) where 2≤ a≤ b≤ c, is investigated. <![CDATA[A general method for to decompose modular multiplicative inverse operators over Group of units]]> Abstract: In this article, the notion of modular multiplicative inverse operator (MMIO): where ϱ=b × d &gt;3 with b, d ∈ N, is introduced and studied. A general method to decompose (MMIO) over group of units of the form (Z/ϱZ)* is also discussed through a new algorithmic functional version of Bezout's theorem. As a result, interesting decomposition laws for (MMIO)'s over (Z/ϱZ)* are obtained. Several numerical examples confirming the theoretical results are also reported. <![CDATA[Upper double monophonic number of a graph]]> Abstract: A set S of a connected graph G of order n is called a double monophonic set of G if for every pair of vertices x, y in G there exist vertices u, v in S such that x, y lie on a u-v monophonic path. The double monophonic number dm(G) of G is the minimum cardinality of a double monophonic set. A double monophonic set S in a connected graph G is called a minimal double monophonic set if no proper subset of S is a double monophonic set of G. The upper double monophonic number of G is the maximum cardinality of a minimal double monophonic set of G, and is denoted by dm+(G). Some general properties satisfied by upper double monophonic sets are discussed. It is proved that for a connected graph G of order n, dm(G)=n if and only if dm+(G)=n. It is also proved that dm(G)=n-1 if and only if dm+(G)=n-1 for a non-complete graph G of order n with a full degree vertex. For any positive integers 2 ≤ a ≤ b, there exists a connected graph G with dm(G)= a and dm+(G)=b. <![CDATA[Bound on H3(1) Hankel determinant for pre-starlike functions of order α]]> Abstract: The objective of this paper is to obtain best possible upper bound to the third Hankel determinant for the pre-starlike functions of order α(0≤α&lt;1), using Toeplitz determinants. <![CDATA[Solutions and stability of a variant of Wilson's functional equation]]> Abstract: In this paper we will investigate the complex-valued solutions and stability of the generalized variant of Wilson's functional equation (E): 𝑓(xy)+χ(y)𝑓(σ(y)x)=2𝑓(x)g(y), x,y ∈ G, where G is a group, σ is an involutive morphism of G and χ is a character of G. (a) We solve (E) when σ is an involutive automorphism, and we obtain some properties about solutions of (E) when σ is an involutive anti-automorphism. (b) We obtain the Hyers Ulam stability of equation (E). As an application, we prove the superstability of the functional equation (xy)+χ(y) 𝑓(σ(y)x)=2 𝑓(x) 𝑓(y), x,y ∈ G. <![CDATA[Riemann-Liouville fractional trapezium-like inequalities via generalized (m, h <sub>1</sub> , h <sub>2</sub> )-preinvexity]]> Abstract: In this paper, we derive a fractional integral identity concerning three times differentiable generalized preinvex mappings defined on m-invex set. By using of this identity, we obtain new estimates on generalization of trapezium-like inequalities for functions whose third order derivatives are generalized (m,h1,h2)-preinvex via Riemann-Liouville fractional integrals. Some interesting special cases of our main result are also considered and shown to be connected with certain known ones. <![CDATA[On velocity bimagnetic biharmonic particles with energy on Heisenberg space]]> Abstract: In this work, we consider velocity bimagnetic biharmonic particle on 3D Heisenberg space in the magnetic field ℬ and we give the concept of energy. Moreover, we characterize energy conditions of velocity bimagnetic biharmonic particles with Frenet vector field. Therefore, we obtain energy results for bimagnetic particles by Frenet fields in the Heisenberg space. <![CDATA[Fuzzy normed linear sequence space]]> Abstract. In this article we introduce the notion of class of sequences noindent , 1 ≤ p &lt; ∞ with the concept of fuzzy norm. We study some of its properties such as completeness, solidness, symmeticity and convergence free. Also, we establish some inclusion results.