Proyecciones (Antofagasta, On line)

On r- Dynamic coloring of the gear graph families

2020-04-21T17:18:24+00:00

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 ∈ 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.

Another example of the mutual singularity of multifractal measures

2020-05-14T03:26:26+00:00

We propose an example for which the multifractal Hausdorff and packing measures are mutually singular.

H-supplemented modules with respect to images of fully invariant submodules

2020-04-29T04:25:32+00:00

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_F -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_F -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_F –H supplemented modules is not in general I_F -H-supplemented. Some sufficient conditions such that the direct sum of I_F -H-supplemented modules is I_F -H-supplemented are given

Stability of a general p-radical functional equation related to additive mappings in 2-Banach spaces

2019-07-21T10:39:38+00:00

In this paper, we introduce and solve a new general p-radical functional equation

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

Remarks on the mutual singularity of multifractal measures

2020-06-22T02:42:06+00:00

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.

New algebraic properties of middle Bol loops II

2019-08-05T18:41:32+00:00

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.

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

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 D. We derive upper bounds for the second and third coefficients and solve Fekete-Szegö problem of functions belongs to this family.

A Moreau-Yosida regularization for Markov decision processes

2020-07-01T16:20:08+00:00

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.

Existence and uniqueness of positive solutions for nonlinear Caputo-Hadamard fractional differential equations

2020-07-17T18:57:37+00:00

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.

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

The aim of this paper is to introduce and solve the following p-radical functional equation related to Drygas mappings

f is a mapping from R into a vector space X and p ≥ 3 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 p-radical functional equation related to Drygas mappings

Minimal and maximal solutions to first-order differential equations with piecewise constant generalized delay

2019-11-26T18:05:36+00:00

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).

New approach for Somos’s Dedekind eta-function identities of level 6

2020-04-29T05:40:08+00:00

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.

Some trapezoid and midpoint type inequalities for newly defined quantum integrals

2020-04-30T04:37:18+00:00

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.

Relating centralities in graphs and the principal eigenvector of its distance matrix

2020-05-13T21:32:05+00:00

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.

On a bi-nonlocal fourth order elliptic problem

2020-08-19T20:59:11+00:00

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.

Diagonal entries of the combined matrix of sign regular matrices of order three

2020-09-03T10:40:15+00:00

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.