Resolving sets for breaking symmetries of graphs

This paper deals with the maximum value of the difference between the determining number and the metric dimension of a graph as a function of its order. Our technique requires to use locating-dominating sets, and perform an independent study on other functions related to these sets. Thus, we obtain lower and upper bounds on all these functions by means of very diverse tools. Among them are some adequate constructions of graphs, a variant of a classical result in graph domination and a polynomial time algorithm that produces both distinguishing sets and determining sets. Further, we consider specific families of graphs where the restrictions of these functions can be computed. To this end, we utilize two well-known objects in graph theory: $k$-dominating sets and matchings.Comment: 24 pages, 12 figure

Introducció: El debat entre W.K. Clifford i William James

Introducció al debat entre Cliiford i James i a la traducció dels seus articles "L'ètica de la creença" i "La voluntat de creure"

Graph theory with an introduction to algebraic graph theory

Firstly, we shall start with an introduction to the main topics in Graph Theory with special emphasis in connectivity, colorability and planarity. The, we shall continue with the firsts concepts in Algebraic Graph Theory. Algebraic Graph Theory uses algebraic techniques to study properties of graphs. We shall see several examples of those techniques, covering, for instance the fundamental group of a graph, several polynomials associated to graphs, and the spectra of a graph. seeing how those algebraic tools provide information about the properties of the graph.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Vibrational assignments of two polymorphic forms of metaxolone by using DFT calculations and the SQM methodology

A theoretical study has been performed on the musclerelaxant 5-[(3, 5-dimethylphenoxy)methyl]-1,3-oxazolidin-2-one, of generic name metaxolone (MTX), by using the hybridB3LYP/6-31G calculations in the gas phase and theexperimental available infrared and Raman spectra in thesolid phase. Three C1, C2 and C3 isomers were found in thepotential energy surface (PES) but only two of them, C1 andC2 correspond to those experimentally reported polymorphicforms A and B, respectively. The absence of C3 isomer couldbe easily explained by the quite high values in the dihedralC5-C7-O2-C9 and O1-C5-C7-O2 angles different from thoseexperimental structures reported for the two polymorphicforms A and B of MTX. On the other hand, the higher bondorders values together with the high topological propertiesobserved for the oxazolidinone ring of C1 could possiblysupport their existence despite this isomer has highest energythan C2 and C3. The natural bond orbital (NBO) analysesreveal the high stabilities of C1 and C2 while the atoms inmolecules(AIM) study suggests that the ringdimethylphenoxy-methyl practically do not have influence onthe properties of MTX. The frontier orbitals show that theisomers of MTX have reactivities and electrophilicity indexessimilar to antiviral thymidine while their nucleophilicityindexes present values closer to antimicrobial thione. Inaddition, the complete vibrational assignments of those twostable isomers were performed by using the experimentalavailable FT-IR and FT-Raman spectra, their normal internalcoordinates,the scaled quantum mechanical force field(SQMFF) methodology and the Molvib program.Theharmonic force fields for the two isomers and theircorresponding force constants were also reported. The forceconstants values are in agreement with values reported in theliterature for species with similar groups.Fil: Iramain, Maximiliano Alberto. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Tucumán. Facultad de Bioquímica, Química y Farmacia. Instituto de Química Inorgánica; ArgentinaFil: Márquez, María J.. Universidad Nacional de Tucumán. Facultad de Bioquímica, Química y Farmacia. Instituto de Química Inorgánica; ArgentinaFil: Ledesma, Ana Estela. Universidad Nacional de Santiago del Estero. Facultad de Cs.exactas y Tecnologías. Departamento de Física y Química; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Brandan, Silvia Antonia. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Tucumán. Facultad de Bioquímica, Química y Farmacia. Instituto de Química Inorgánica; Argentin

“DISTANCIA DE LA PIEL AL ESPACIO PERIDURAL SEGÚN EL INDICE DE MASA CORPORAL EN EL PACIENTE PROGRAMADO PARA CIRUGIA ELECTIVA EN CENTRO MEDICO ISSEMYM ECATEPEC EN EL PERIODO DE MAYO DEL 2012 A SEPTIEMBRE DEL 2012”

La Anestesia Neuroaxial es una técnica ampliamente utilizada, debido a las numerosas ventajas que esta ofrece. El Bloqueo Peridural o Epidural también conocido, presenta diversas aplicaciones: para anestesia quirúrgica, analgesia postoperatoria y para manejo de dolor crónico casos donde la anestesia general balanceada se encuentra contraindicada

An aperiodic tiles machine

The results we introduce in this work lead to get an algorithm which produces aperiodic sets of tiles using Voronoi diagrams. This algorithm runs in optimal worst-case time O(nlogn). Since a wide range of new examples can be obtained, it could shed some new light on non-periodic tilings. These examples are locally isomorphic and exhibit the 5-fold symmetry which appears in Penrose tilings and quasicrystals. Moreover, we outline a similar construction using Delaunay triangulations and propose some related open problems

Ptychadena in Mauritania and the first record of Ptychadena schillukorum

The study of specimens of the genus Ptychadena of the herpetological collection of the Museo Nacional de Ciencias Naturales de Madrid reveals the first record of Ptychadena schillukorum from Mauritania, extending the known distribution range of the species in West Africa more than 450 km northwards. A key is provided for the four Mauritanian species of Ptychadena to solve problems in identification encountered in previous studies.This research was partially funded by project TATANKA (CGL2011-25062) obtained from Ministerio de Ciencia e Innovación, Spain.Peer reviewe