Topological Additive Numbering of Directed Acyclic Graphs

We propose to study a problem that arises naturally from both Topological Numbering of Directed Acyclic Graphs, and Additive Coloring (also known as Lucky Labeling). Let $D$ be a digraph and $f$ a labeling of its vertices with positive integers; denote by $S(v)$ the sum of labels over all neighbors of each vertex $v$. The labeling $f$ is called \emph{topological additive numbering} if $S(u) < S(v)$ for each arc $(u,v)$ of the digraph. The problem asks to find the minimum number $k$ for which $D$ has a topological additive numbering with labels belonging to $\{ 1, \ldots, k \}$, denoted by $\eta_t(D)$. We characterize when a digraph has topological additive numberings, give a lower bound for $\eta_t(D)$, and provide an integer programming formulation for our problem, characterizing when its coefficient matrix is totally unimodular. We also present some families for which $\eta_t(D)$ can be computed in polynomial time. Finally, we prove that this problem is \np-Hard even when its input is restricted to planar bipartite digraphs

Study of the degradation process of polyimide induced by high energetic ion irradiation

The dissertation focuses on the radiation hardness of Kapton under extreme radiation environment conditions and is motivated by the application of this polyimide as insulator in superconducting magnets for the new Facility for Antiproton and Ion Research (FAIR) planned at the Gesellschaft für Schwerionenforschnung (GSI). The new FAIR accelerators are expected to deliver protons and heavy ions of extreme energies (10 GeV/u) and unprecedented intensities (1E12 ions/pulse). Reliable data of the radiation hardness of polymers concerning mechanical, electrical, and outgassing properties are of great interest also for other facilities such as the Large Hadron Collider (LHC) of CERN. To study ion-beam induced modifications, Kapton foils were irradiated at the GSI linear accelerator UNILAC using several projectiles (e.g. Ti, Mo, Au, and U) within a large fluence regime (1E10 – 5E12 ions/cm2). The irradiated Kapton foils were analysed by means of infrared and UV/Vis spectroscopy, tensile strength measurement, mass loss analysis, and dielectric relaxation spectroscopy. For testing the radiation stability of Kapton at the cryogenic operation temperature (5-10 K) of the superconducting magnets, additional irradiation experiments were performed at the Grand Accelerateur National d’ Ions Lourds (GANIL, France) focusing on the online analysis of the outgassing process of small volatile degradation fragments. Results obtained by optical spectroscopy, tensile strength measurement and mass loss analysis show similar trends and can be scaled by the irradiation dose given by the product of fluence and energy deposited along the ion trajectory. Critical material degradation appears above a dose of 1 MGy. The investigations of the electrical properties analysed by dielectric relaxation spectroscopy exhibit a different trend: high fluence irradiations with light ions (e.g. Ti) lead to a slight increase of the conductivity, whereas heavy ions (e.g. Sm, Au) cause a drastic change already in the fluence regime of non-overlapping tracks (5E10 ions/cm2). Online analysis of the outgassing process during irradiation at cryogenic temperatures shows the release of a variety of small gaseous molecules (e.g. CO, CO2, and short hydro carbons). Also a small amount of large polymer fragments is identified and confirms the degradation mechanism of Kapton proposed in earlier studies. Simultaneous in-situ infrared spectroscopy gives evidence of accumulation of these small molecules inside the bulk polymer at cryogenic temperatures. During heat-up cycles, these fragments outgas in specific temperature zones. The results obtained by the different analytical techniques allow the following conclusions which are of special interest for the application of Kapton as insulating material in a high-energetic particle radiation environment. a) The material degradation measured with the optical spectroscopy and tensile strength tests are scalable with the dose deposited by the ions. The high correlation of the results allows the prediction of the mechanical degradation with the simple and non-destructive infrared spectroscopy. The degradation curve points to a critical material degradation which has to be expected above a dose of 1 MGy. b) The dielectric relaxation spectroscopy indicates a dramatic increase in the conductivity induced by irradiation with heavy ions which pass a threshold of mass and deposited energy (dE/dx). The phenomenon indicates that only a few hits (fluences of 1E10 ion/cm2) of a heavy high energetic ion leads to a significant increase of conductivity. c) The degradation induced formation of small molecules and their outgassing even at cryogenic temperature cause a gas release during irradiation. At temperatures below 20 K, an additional accumulation of these molecules in the bulk material occurs and leads to a critical gas evolution during heat-up cycles

Unary Primitive Recursive Functions

In this article, we study some new characterizations of primitive recursive functions based on restricted forms of primitive recursion, improving the pioneering work of R. M. Robinson and M. D. Gladstone in this area. We reduce certain recursion schemes (mixed/pure iteration without parameters) and we characterize one-argument primitive recursive functions as the closure under substitution and iteration of certain optimal sets

A DSATUR-based algorithm for the Equitable Coloring Problem

This paper describes a new exact algorithm for the Equitable Coloring Problem, a coloring problem where the sizes of two arbitrary color classes differ in at most one unit. Based on the well known DSatur algorithm for the classic Coloring Problem, a pruning criterion arising from equity constraints is proposed and analyzed. The good performance of the algorithm is shown through computational experiments over random and benchmark instances.Fil: Méndez-Díaz, Isabel. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; ArgentinaFil: Nasini, Graciela Leonor. Universidad Nacional de Rosario. Facultad de Ciencias Exactas, Ingeniería y Agrimensura; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Severin, Daniel Esteban. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Rosario. Facultad de Ciencias Exactas, Ingeniería y Agrimensura; Argentin

AUTOMORPHISMS OF ALGEBRAS AND ORTHOGONAL POLYNOMIALS

Suitable automorphisms together with complete classification of representations of some algebras can be used to generate some sets of orthogonal polynomials “at no cost”. This is also the case of nonstandard Klimyk-Gavrilik deformation Uq'(so3) which is connected to q-Racah polynomials

AUTOMORPHISMS OF ALGEBRAS AND ORTHOGONAL POLYNOMIALS

Suitable automorphisms together with complete classification of representations of some algebras can be used to generate some sets of orthogonal polynomials “at no cost”. This is also the case of nonstandard Klimyk-Gavrilik deformation Uq'(so3) which is connected to q-Racah polynomials