Invoking a cartesian product structure on social states: new resolutions of Sen's and Gibbard's impossibility theorems

The purpose of this article is to introduce a Cartesian product structure into the social choice theoretical framework and to examine if new possibility results to Gibbard's and Sen's paradoxes can be developed thanks to it. We believe that a Cartesian product structure is a pertinent way to describe individual rights in the social choice theory since it discriminates the personal features comprised in each social state. First we define some conceptual and formal tools related to the Cartesian product structure. We then apply these notions to Gibbard's paradox and to Sen's impossibility of a Paretian liberal. Finally we compare the advantages of our approach to other solutions proposed in the literature for both impossibility theorems.

‘Studies on some topics in product graphs’

For routing problems in interconnection networks it is important to find the shortest containers between any two vertices, since the w-wide diameter gives the maximum communication delay when there are up to w−1 faulty nodes in a network modeled by a graph. The concept of ‘wide diameter’ was introduced by Hsu [41] to unify the concepts of diameter and The concept of ‘domination’ has attracted interest due to its wide applications in many real world situations [38]. A connected dominating set serves as a virtual backbone of a network and it is a set of vertices that helps in routing. In this thesis, we make an earnest attempt to study some of these notions in graph products. This include, the diameter variability, the diameter vulnerability, the component factors and the domination criticality.connectivity

Factorizations of and by powers of complete graphs

Let K-k(d) denote the Cartesian product of d copies of the complete graph K-k. We prove necessary and sufficient conditions for the existence of a K-k(r)-factorization of K-pn(s), where p is prime and k > 1, n, r and s are positive integers. (C) 2002 Elsevier Science B.V. All rights reserved.

A multiplicação e a divisão de números naturais: uma análise de manuais escolares de 1.º ciclo

Dissertação apresentada à Escola Superior de Educação de Lisboa para obtenção de grau de mestre em Educação Matemática na Educação Pré-escolar e nos 1.º e 2.º ciclos do Ensino Básico

Constraint reasoning with local search for continuous optimization

Optimization is a very important field for getting the best possible value for the optimization function. Continuous optimization is optimization over real intervals. There are many global and local search techniques. Global search techniques try to get the global optima of the optimization problem. However, local search techniques are used more since they try to find a local minimal solution within an area of the search space. In Continuous Constraint Satisfaction Problems (CCSP)s, constraints are viewed as relations between variables, and the computations are supported by interval analysis. The continuous constraint programming framework provides branch-and-prune algorithms for covering sets of solutions for the constraints with sets of interval boxes which are the Cartesian product of intervals. These algorithms begin with an initial crude cover of the feasible space (the Cartesian product of the initial variable domains) which is recursively refined by interleaving pruning and branching steps until a stopping criterion is satisfied. In this work, we try to find a convenient way to use the advantages in CCSP branchand- prune with local search of global optimization applied locally over each pruned branch of the CCSP. We apply local search techniques of continuous optimization over the pruned boxes outputted by the CCSP techniques. We mainly use steepest descent technique with different characteristics such as penalty calculation and step length. We implement two main different local search algorithms. We use “Procure”, which is a constraint reasoning and global optimization framework, to implement our techniques, then we produce and introduce our results over a set of benchmarks.

The Multiple-partners assignment game with heterogeneous sales and multi-unit demands: competitive equilibria

A multiple-partners assignment game with heterogeneous sales and multiunit demands consists of a set of sellers that own a given number of indivisible units of (potentially many different) goods and a set of buyers who value those units and want to buy at most an exogenously fixed number of units. We define a competitive equilibrium for this generalized assignment game and prove its existence by using only linear programming. In particular, we show how to compute equilibrium price vectors from the solutions of the dual linear program associated to the primal linear program defined to find optimal assignments. Using only linear programming tools, we also show (i) that the set of competitive equilibria (pairs of price vectors and assignments) has a Cartesian product structure: each equilibrium price vector is part of a competitive equilibrium with all optimal assignments, and vice versa; (ii) that the set of (restricted) equilibrium price vectors has a natural lattice structure; and (iii) how this structure is translated into the set of agents' utilities that are attainable at equilibrium.

L'éclatement en géométrie algébrique, différentielle et symplectique

L'éclatement est une transformation jouant un rôle important en géométrie, car il permet de résoudre des singularités, de relier des variétés birationnellement équivalentes, et de construire des variétés possédant des propriétés inédites. Ce mémoire présente d'abord l'éclatement tel que développé en géométrie algébrique classique. Nous l'étudierons pour le cas des variétés affines et (quasi-)projectives, en un point, et le long d'un idéal et d'une sous-variété. Nous poursuivrons en étudiant l'extension de cette construction à la catégorie différentiable, sur les corps réels et complexes, en un point et le long d'une sous-variété. Nous conclurons cette section en explorant un exemple de résolution de singularité. Ensuite nous passerons à la catégorie symplectique, où nous ferons la même chose que pour le cas différentiable complexe, en portant une attention particulière à la forme symplectique définie sur la variété. Nous terminerons en étudiant un théorème dû à François Lalonde, où l'éclatement joue un rôle clé dans la démonstration. Ce théorème affirme que toute 4-variété fibrée par des 2-sphères sur une surface de Riemann, et différente du produit cartésien de deux 2-sphères, peut être équipée d'une 2-forme qui lui confère une structure symplectique réglée par des courbes holomorphes par rapport à sa structure presque complexe, et telle que l'aire symplectique de la base est inférieure à la capacité de la variété. La preuve repose sur l'utilisation de l'éclatement symplectique. En effet, en éclatant symplectiquement une boule contenue dans la 4-variété, il est possible d'obtenir une fibration contenant deux sphères d'auto-intersection -1 distinctes: la pré-image du point où est fait l'éclatement complexe usuel, et la transformation propre de la fibre. Ces dernières sont dites exceptionnelles, et donc il est possible de procéder à l'inverse de l'éclatement - la contraction - sur chacune d'elles. En l'accomplissant sur la deuxième, nous obtenons une variété minimale, et en combinant les informations sur les aires symplectiques de ses classes d'homologies et de celles de la variété originale nous obtenons le résultat.

Antimedian graphs

Antimedian graphs are introduced as the graphs in which for every triple of vertices there exists a unique vertex x that maximizes the sum of the distances from x to the vertices of the triple. The Cartesian product of graphs is antimedian if and only if its factors are antimedian. It is proved that multiplying a non-antimedian vertex in an antimedian graph yields a larger antimedian graph. Thin even belts are introduced and proved to be antimedian. A characterization of antimedian trees is given that leads to a linear recognition algorithm.

Fair Sets of Some Classes of Graphs

Given a non empty set S of vertices of a graph, the partiality of a vertex with respect to S is the di erence between maximum and minimum of the distances of the vertex to the vertices of S. The vertices with minimum partiality constitute the fair center of the set. Any vertex set which is the fair center of some set of vertices is called a fair set. In this paper we prove that the induced subgraph of any fair set is connected in the case of trees and characterise block graphs as the class of chordal graphs for which the induced subgraph of all fair sets are connected. The fair sets of Kn, Km;n, Kn e, wheel graphs, odd cycles and symmetric even graphs are identi ed. The fair sets of the Cartesian product graphs are also discussed

The Eccentric Connectivity Polynomial of some Graph Operations

The eccentric connectivity index of a graph G, ξ^C, was proposed by Sharma, Goswami and Madan. It is defined as ξ^C(G) = ∑ u ∈ V(G) degG(u)εG(u), where degG(u) denotes the degree of the vertex x in G and εG(u) = Max{d(u, x) | x ∈ V (G)}. The eccentric connectivity polynomial is a polynomial version of this topological index. In this paper, exact formulas for the eccentric connectivity polynomial of Cartesian product, symmetric difference, disjunction and join of graphs are presented.

ANOSOV MAPS, POLYCYCLIC GROUPS AND HOMOLOGY

Many manifolds that do not admit Anosov diffeomorphisms are constructed. For example: the Cartesian product of the Klein bottle and a torus.

Calculating the tetrahedral bond angle using spherical polars and the dot product

A proof using the methane tetrahedroid bond angle can be obtained by using spherical polar coordinates to calculate the Cartesian coordinates of the hydrogen atoms, then using the dot product of vectors.

Antioxidant And Antiproliferative Activities Of Methanolic Extract From A Neglected Agricultural Product: Corn Cobs.

Neglected agricultural products (NAPs) are defined as discarded material in agricultural production. Corn cobs are a major waste of agriculture maize. Here, a methanolic extract from corn cobs (MEC) was obtained. MEC contains phenolic compounds, protein, carbohydrates (1.4:0.001:0.001). We evaluated the in vitro and in vivo antioxidant potential of MEC. Furthermore, its antiproliferative property against tumor cells was assessed through MTT assays and proteins related to apoptosis in tumor cells were examined by western blot. MEC showed no hydroxyl radical scavenger capacity, but it showed antioxidant activity in Total Antioxidant Capacity and DPPH scavenger ability assays. MEC showed higher Reducing Power than ascorbic acid and exhibited high Superoxide Scavenging activity. In tumor cell culture, MEC increased catalase, metallothionein and superoxide dismutase expression in accordance with the antioxidant tests. In vivo antioxidant test, MEC restored SOD and CAT, decreased malondialdehyde activities and showed high Trolox Equivalent Antioxidant Capacity in animals treated with CCl4. Furthermore, MEC decreased HeLa cells viability by apoptosis due an increase of Bax/Bcl-2 ratio, caspase 3 active. Protein kinase C expression increased was also detected in treated tumor cells. Thus, our findings pointed out the biotechnological potential of corn cobs as a source of molecules with pharmacological activity.

Systematic Management of Variability in UML-based Software Product Lines

This paper presents SMarty, a variability management approach for UML-based software product lines (PL). SMarty is supported by a UML profile, the SMartyProfile, and a process for managing variabilities, the SMartyProcess. SMartyProfile aims at representing variabilities, variation points, and variants in UML models by applying a set of stereotypes. SMartyProcess consists of a set of activities that is systematically executed to trace, identify, and control variabilities in a PL based on SMarty. It also identifies variability implementation mechanisms and analyzes specific product configurations. In addition, a more comprehensive application of SMarty is presented using SEI's Arcade Game Maker PL. An evaluation of SMarty and related work are discussed.

Direct evidence of singlet molecular oxygen generation from peroxynitrate, a decomposition product of peroxynitrite

The decomposition of peroxynitrite to nitrite and dioxygen at neutral pH follows complex kinetics, compared to its isomerization to nitrate at low pH. Decomposition may involve radicals or proceed by way of the classical peracid decomposition mechanism. Peroxynitrite (ONOOH/ONOO(-)) decomposition has been proposed to involve formation of peroxynitrate (O(2)NOOH/O(2)NOO(-)) at neutral pH (D. Gupta, B. Harish, R. Kissner and W. H. Koppenol, Dalton Trans., 2009, DOI: 10.1039/b905535e, see accompanying paper in this issue). Peroxynitrate is unstable and decomposes to nitrite and dioxygen. This study aimed to investigate whether O(2)NOO(-) formed upon ONOOH/ONOO(-) decomposition generates singlet molecular oxygen [O(2) ((1)Delta(g))]. As unequivocally revealed by the measurement of monomol light emission in the near infrared region at 1270 nm and by chemical trapping experiments, the decomposition of ONOO(-) or O(2)NOOH at neutral to alkaline pH generates O(2) ((1)Delta(g)) at a yield of ca. 1% and 2-10%, respectively. Characteristic light emission, corresponding to O(2) ((1)Delta(g)) monomolecular decay was observed for ONOO(-) and for O(2)NOOH prepared by reaction of H(2)O(2) with NO(2)BF(4) and of H(2)O(2) with NO(2)(-) in HClO(4). The generation of O(2) ((1)Delta(g)) from ONOO(-) increased in a concentration-dependent manner in the range of 0.1-2.5 mM and was dependent on pH, giving a sigmoid pro. le with an apparent pK(a) around pD 8.1 (pH 7.7). Taken together, our results clearly identify the generation of O(2) ((1)Delta(g)) from peroxynitrate [O(2)NOO(-) -> NO(2)(-) + O(2) ((1)Delta(g))] generated from peroxynitrite and also from the reactions of H(2)O(2) with either NO(2)BF(4) or NO(2)(-) in acidic media.