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In this paper we present a new algorithm for solving polynomial equations based on the Taylor series of the inverse function of a polynomial, fP(y). The foundations of the computing of such series have been previously developed by the authors in some recent papers, proceeding as follows: given a polynomial function y = P(x) = a0 + a1x +···+ amxm, with ai ∈ R, 0 ≤ i ≤ m, and a real number u so that P (u) = 0, we have got an analytic function fP(y) that satisfies x = fP(P(x)) around x = u. Besides, we also introduce a new proof (completely different) of the theorems involves in the construction of fP(y), which provide a better radius of convergence of its Taylor series, and a more general perspective that could allow its application to other kinds of equations, not only polynomials. Finally, we illustrate with some examples how fP(y) could be used for solving polynomial systems. This question has been already treated by the authors in preceding works in a very complex and hard way, that we want to overcome by using the introduced algorithm in this paper.

In this paper, we determine list-chromatic number and characterize chromatically unique of the graph G = Kr2 +Ok. We shall prove that ch(G) = r + 1 if 1

espanolSe estima una cota superior para el numero de puntos criticos de la solucion de un problema semilineal eliptico con condicion de Dirichlet nula en el borde de un dominio planar. El resultado se obtiene en dominios simetricos con respecto a una recta y convexos en la direccion ortogonal a la misma. MSC2010: 35J25, 35J91, 74K15. EnglishIn this paper we estimate an upper bound for the number of critical points of the solution to a semilinear elliptic problem with vanishing Dirichlet condition on a bounded planar domain. The result is obtained assuming that the domain is symmetric with respect to a line and convex in the orthogonal direction to the line of symmetry.

The weighted distributions are used when the sampling mechanism records observations according to a nonnegative weight function. Sometimes the form of the weighted distribution is the same as the original distribution except possibly for a change in the parameters that is called the form-invariant weighted distribution. In this paper, by identifying a general class of weight functions, we introduce an extended class of form-invariant weighted distributions belonging to the non-regular exponential family which included two common families of distribution: exponential family and non-regular family as special cases. Some properties of this class of distributions such as the sufficient and minimal sufficient statistics, maximum likelihood estimation and the Fisher information matrix are studied. Las distribuciones ponderadas son usadas cuando el mecanismo de muestreo registra observaciones de acuerdo a una función no negativa. En ocasiones la forma de la función ponderada es igual a la original, excepto, posiblemente, en un cambio de parámetros y se denominan distribuciones ponderadas de forma invariante. En este artículo identificamos una clase general de funciones ponderadas e introducimos una forma extendida de distribuciones ponderadas de forma invariante, la cual incluye dos familias comunes: la familia exponencial y la familia no regular como caso particular. Algunas propiedades de estas distribuciones como las estadísticas suficientes y máximas suficientes, la estimación de máxima verosimilitud y la matriz de información de Fisher son estudiadas.

In this paper, we proposes an algorithm to approximate the Euclidean distance between points p and q of plane, by doing a search of geodesic that depart from the point p and arrive to a neighborhood of the point q . This search is done through the numerical solution of initial value problems associated with the system of ordinary differential equations of the geodesics; for this is choose a set of directions in the plane. En este artículo, se plantea un algoritmo para aproximar la distancia Euclidiana entre los puntos p y q del plano, mediante la búsqueda de geodésicas que salen del punto p y llegan a una vecindad del punto q. Esta búsqueda se hace a través de la solución numérica de problemas de valor inicial asociados a sistemas de ecuaciones diferenciales ordinarias de las geodésicas; para lo cual se elige un conjunto de direcciones en el plano.

ResumenEl objetivo principal de este trabajo es introducir la especie de los pulpos en combinatoria enumerativa. Demostraremos además la validez de ciertas ecuaciones combinatorias sugeridas por Bergeron et al. en [3]. AbstractThe main goal of this paper is introduce the species of octopuse in enumerative combinatoricss. We also prove the validity of some combinatorial equations suggested by Bergeron et al. in [3].

espanolEn este articulo estudiamos algunas propiedades asintoticas de la sucesion de polinomios monicos ortogonales con respecto a la medida dµ = x 2+a x2+b e −x 2 dx, donde a, b > 0 y a 6= b. En este sentido, estudiamos la asintotica relativa exterior con respecto a los polinomios clasicos de Hermite, ademas son analizadas formulas tipo Mehler-Heine. EnglishIn this paper we study some asymptotic properties of the sequence of monic polynomials orthogonal with respect to the measure dµ = x 2+a x2+b e −x 2 dx, where a, b > 0 and a 6= b. In this way we study the outer relative asymptotic with respect to the classical Hermite polynomials; besides, Mehler-Heine type formulas are analyzed.

A set of positive integers A is called a g-Golomb ruler if the difference between two distinct elements of A is repeated at most g times. This definition is a generalization of the Golomb ruler (g = 1). In this paper we construct g-Golomb ruler from Golomb ruler and we prove two theorems about extremal functions associated with this sets. Keywords: Sidon sets, B2 sets, Golomb ruler. To cite this article: Y. Caicedo, C.A. Martos, C.A. Trujillo, g-Golomb, Rev. Integr. Temas Mat. 33 (2015), No. 2, 161–172.

A remarkable achievement of algorithmic topology is A.A.Markov’s theorem on the unsolvability of the homeomorphism problem for manifolds. Boone, Haken and Poenaru extended Markov’s original proof to the case of closed smooth manifolds. One of their initial difficulties was the introduction of a natural finite representation of a differentiable and/or combinatorial manifold. In this paper we extend this representation to compact smooth manifolds and propose an extension to smooth manifolds. Keywords : Computability and recursion theory, algorithmic topology, smooth manifolds. To cite this article: C.M Parra, J. Suarez Ramirez, Representacion finita de variedades compactas, Rev. Integr. Temas Mat. 33 (2015), No. 2, 97–105.

In this paper we construct a family of spin Lie groups G with an outer automorphism of order three (triality automorphism) and we describe the subgroups of fixed points for this kind of automorphisms. We will take advantage of this work to study the action of the group of outer automorphisms of G on the moduli space of principal G-bundles and describe the subvariety of fixed points in M(G) for the action of the outer automorphism of order three of G. Finally, we further study the case of Spin(8, C). Resumen En este artículo construimos una familia de grupos de Lie espinoriales G dotados de un automorfismo externo de orden tres (trialidad) y describimos los subgrupos de puntos fijos para esta clase de automorfismos. Usaremos esto para estudiar la acción del grupo de automorfismos externos de G en el espacio de moduli de G-fibrados principales y describir la subvariedad de puntos fijos en M(G) para la acción del automorfismo externo de orden tres de G. Finalmente, profundizaremos en el estudio del caso Spin(8, C).

In this paper we prove that the generalized functions d (k) (P+) - d (k) (P), d (k) (P-)-d (k) (-P) and d 1 (k) (P)-d 2 (k) (P)d are concentrated in the vertex of the cone P=0 and we find their relationship with the ultrahyperbolic operator iterated (k +1 -n/2 ) times under condition k ³ n/2-1. En este trabajo se prueba que las funciones generalizadas d (k) (P+) - d (k) (P), d (k) (P-)-d (k) (-P) and d 1 (k) (P)-d 2 (k) (P)destán concentradas en el vértice del cono P=0 y encontramos sus relaciones con el operador ultrahperbólico iterado (k +1 -n/2 ) veces bajo la condición k ³ n/2-1.

En Ramírez (2001) se introdujo el problema de coloracion robusta generalizado (PCRG), el cual resuelve problemas de horarios que consideran restricciones del tipo: dos eventos no pueden realizarse a la misma hora y debe haber al menos d días entre dos eventos. El PCRG es una coloración robusta, en que dada una gráfica y un número fijo de colores, no necesariamente el número cromático, considera la distancia entre colores como penalización de las aristas complementarias. Se demostró que el problema es NP-Completo, por lo que es necesario utilizar métodos aproximados para encontrar buenas soluciones en un tiempo razonable. En este trabajo se presenta un híbrido de un algoritmo genético con uno de búsqueda local para casos de 30 a 120 horas por semana, se demuestra que para algunos la solución es óptima y en otros se encuentran soluciones muy prometedoras. Ramírez (2001) introduced the generalized robust coloring problem (GRCP), this problem lets solve timetabling problems which considers constraints such as: two events can not be assigned at the same time and there must be at least d days between two events. The GRCP deals with a robust coloring for a given graph with a fixed number of colors, not necessarily the chromatic number and considers the distance between colors as the penalization of complementary edges. It was shown that the problem is NP-complete, so it is necessary to use approximate methods to find good solutions in a reasonable time. This paper presents a hybrid of a genetic algorithm with a local search for cases of 30-120 hours per week; it is shown that for some cases the found solution is optimal and in other cases the solutions are very promising.

In this paper we relate the Matrix Theory and the Graphs Theory, particularlly we work with the characteristic polynomial of precedence matrix with the spectrum of (h, j) adjoint digraphs. The object of this work is to enunciate and demonstrate, with adequate matrix representations, a theorem that allows to determinate the eigenvalues of an (h, j) adjoin digraph of a multidigraph k–regular, resulting the respective multiplicities and also the shape of the eigenvectors associated. En este trabajo se vincula la Teoría de Matrices con la Teoría de Grafos, en particular se trabaja con polinomios característicos de matrices de precedencia y con el espectro de digrafos (h, j) adjuntos. El mismo tiene como objetivo enunciar y demostrar, mediante representaciones matriciales adecuadas, un teorema que permite determinar los autovalores de un digrafo (h, j) adjunto de un multidigrafo k–regular, dándose las respectivas multiplicidades y también la forma de los autovectores asociados.

Problems related to the random approximation of convex bodies fall into the field of integral geometry and geometric probabilities. The aim of this paper is to give a survey of known results about the stochastic model that has received special attention in the literature and that can be described as follows: Let K be a d-dimensional convex body in Eucliden space Rd, d = 2. Denote by Hn the convex hull of n independent random points X1, ..., Xn distributed identically and uniformly in the interior of K. If f is a random variable on d-dimensional polytopes on Rd, we define the random variable fn by: fn = f (conv {X1, ..., Xn}), where conv denotes the convex hull. Typical random variables studied in the literature are numbers of vertices and facets, volume, surface area and mean width. Our main interest concerns the study of the mathematical expectation E(fn) of fn. Some further stochastic models and other problems related to random points studied in the literature will be presented.

This paper shows some deficiences of the Spanish Standard Method UNE 7245 and the corresponding deficiences of the Spanish Concrete Code EH-SO adopting it. According to the actual Method, erroneous low values may result in determining sulphides and in general sulphur compounds in cocrete aggregates. Attention is drawn to the convenience of revising the limit of 1.2 per cent for the admissible maximum value of such compounds, particularly if they are exclusively formed by pyrites., Se ponen de relieve en este trabajo ciertas definiciones de la Norma UNE 7245 y las correspondientes de la Instrucción EH-80 que la adopta, en cuanto que la citada Norma puede dar valores erróneos por defecto en la determinación de sulfures y, en general, de compuestos de azufre en áridos para hormigón. Se llama la atención sobre la conveniencia de revisar el límite de 1,2 por ciento para el contenido máximo tolerable de dichos compuestos, particularmente si están constituidos en exclusiva por piritas.