Complexity of distance paired-domination problem in graphs

Suppose G = (V, E) is a simple graph and k is a fixed positive integer. A subset D subset of V is a distance k-dominating set of G if for every u is an element of V. there exists a vertex v is an element of D such that d(G)(u, v) <= k, where d(G)(u, v) is the distance between u and v in G. A set D subset of V is a distance k-paired-dominating set of G if D is a distance k-dominating set and the induced subgraph GD] contains a perfect matching. Given a graph G = (V, E) and a fixed integer k > 0, the MIN DISTANCE k-PAIRED-DOM SET problem is to find a minimum cardinality distance k-paired-dominating set of G. In this paper, we show that the decision version of MIN DISTANCE k-PAIRED-DOM SET iS NP-complete for undirected path graphs. This strengthens the complexity of decision version Of MIN DISTANCE k-PAIRED-DOM SET problem in chordal graphs. We show that for a given graph G, unless NP subset of DTIME (n(0)((log) (log) (n)) MIN DISTANCE k-PAIRED-Dom SET problem cannot be approximated within a factor of (1 -epsilon ) In n for any epsilon > 0, where n is the number of vertices in G. We also show that MIN DISTANCE k-PAIRED-DOM SET problem is APX-complete for graphs with degree bounded by 3. On the positive side, we present a linear time algorithm to compute the minimum cardinality of a distance k-paired-dominating set of a strongly chordal graph G if a strong elimination ordering of G is provided. We show that for a given graph G, MIN DISTANCE k-PAIRED-DOM SET problem can be approximated with an approximation factor of 1 + In 2 + k . In(Delta(G)), where Delta(G) denotes the maximum degree of G. (C) 2012 Elsevier B.V All rights reserved.

Da superação da monogamia como princípio estruturante do estatuto jurídico da família

A tese propõe novos fundamentos para a abordagem da conjugalidade contemporânea, tendo como eixo de referência a superação da monogamia como princípio estruturante do estatuto jurídico da família. Alguns fios condutores perpassam a tese e norteiam o tratamento do tema: (i) o princípio jurídico da monogamia como mecanismo legitimador da dominação masculina; (ii) a preocupação com a construção de lugares de não-direito e de invisibilidade jurídica de determinadas pessoas, mormente, as concubinas, excluídas da condição de sujeito de direito; (iii) o concubinato, campo privilegiado de estudo, é referido e analisado como estatuto de exclusão; (iv) os fatores decisivos para a reconfiguração da conjugalidade contemporânea: a democracia, o pluralismo cultural e a laicização do Direito; (v) a perspectiva do Direito Civil constitucionalizado é tomada como referência para a problematização da questão central da tese, e os princípios constitucionais da dignidade humana, solidariedade, igualdade, liberdade e democracia prestam-se ao estabelecimento de um banco de provas a que é submetida a assertiva que constitui o enunciado da própria tese: a superação da monogamia como princípio estruturante do estatuto jurídico das famílias contemporâneas. O tratamento dado à matéria é necessariamente interdisciplinar, tendo-se mostrado indispensável a interlocução, ainda que pontual, com historiadores, antropólogos, e sociólogos e mesmo com autores das ciências naturais. O princípio da monogamia consolidado no Ocidente, por força do monopólio da regulação das relações familiares pelo Direito Canônico, especialmente, pelos decretos e cânones tridentinos, e transposto ao domínio jurídico do Estado, a partir das revoluções burguesas experimenta, na reconfiguração da conjugalidade contemporânea, efetivo arrefecimento. Fatores, como a superação da dominação masculina, a laicização do Estado e do Direito, a primazia alcançada pela autonomia privada no campo das situações subjetivas existenciais e coexistenciais, a consagração do princípio do pluralismo das entidades familiares, nítida expressão da democratização da intimidade, são indicados como razões decisivas para a superação da monogamia como princípio jurídico.

An analysis of masculine and feminine writings in postings within a series of health and social care online undergraduate courses

This study aims to extend understanding of pedagogic dialogue by analysing the effect that the gender of the student has on interaction within a selection of ordinary health and social care on line courses.

The Masculine Habitus as 'Distributed Cognition': A Case Study of 5- to 6-Year-Old Boys in an English Inner-City, Multi-Ethnic Primary School

This article provides a case study demonstrating the active role that 5- to 6-year-old boys in an English inner-city, multi-ethnic primary school play in the appropriation and reproduction of their masculine identities. It is argued that the emphasis on physicality, violence and racism found among the boys cannot be understood without reference to the immediate contexts of the local community and the school within which they are located. In making this argument the article draws upon and applies the concept of the habitus and develops this with the notion of 'distributed cognition' as proposed in sociocultural theory. Some of the implications of this analysis for working with boys in early years settings are discussed in the conclusion.

Finite domination and Novikov rings. Iterative approach

Suppose C is a bounded chain complex of finitely generated free modules over the Laurent polynomial ring L = R[x,x -1]. Then C is R-finitely dominated, i.e. homotopy equivalent over R to a bounded chain complex of finitely generated projective R-modules if and only if the two chain complexes C ? L R((x)) and C ? L R((x -1)) are acyclic, as has been proved by Ranicki (A. Ranicki, Finite domination and Novikov rings, Topology 34(3) (1995), 619–632). Here R((x)) = R[[x]][x -1] and R((x -1)) = R[[x -1]][x] are rings of the formal Laurent series, also known as Novikov rings. In this paper, we prove a generalisation of this criterion which allows us to detect finite domination of bounded below chain complexes of projective modules over Laurent rings in several indeterminates.

Racism, masculine peer-group relations and the schooling of African/Caribbean infant boys

The past decade has witnessed the publication of a growing number of important ethnographic studies investigating the schooling experiences of Black students. Their focus has largely been upon student-teacher relations during the students' last few years of compulsory schooling. What they have highlighted is the complexity of racism and the varied nature of Black students' experiences of schooling. Drawing upon data from a year-long ethnographic study of an inner-city, multi-ethnic primary school, this paper aims to compliment these studies in two ways. Firstly the paper will broaden the focus to examine how student peer-group relations play an integral role, within the context of student-teacher relations, in shaping many Black students' schooling experiences. By focussing on African/Caribbean infant boys, it will be shown how student-teacher relations on the one hand, and peer-group relations on the other, form a continuous feed-back loop; the products of each tending to exacerbate and inflate the other. Secondly, by concentrating on infant children, the paper will assess the extent to which these resultant processes and practices are also evident for Black pupils at the beginning of their school careers - at the ages of five and six.

Discursive Control, Non-Domination and Hegelian Recognition Theory: Marrying Pettit’s Account(s) of Freedom with a Pippinian/Brandomian Reading of Hegelian Agency

The aim of this article is to combine Pettit’s account(s) of freedom, both his work on discursive control and on non-domination, with Pippin’s and Brandom’s reinterpretation of Hegelian rational agency and the role of recognition theory within it. The benefits of combining these two theories lie, as the article hopes to show, in three findings: first, re-examining Hegelian agency in the spirit of Brandom and Pippin in combination with Pettit’s views on freedom shows clearly why and in which way a Hegelian account of rational agency can ground an attractive socio-political account of freedom; second, the reconciling of discursive control and non-domination with Hegelian agency shows how the force and scope of recognition become finally tangible, without either falling into the trap of overburdening the concept, or merely reducing it to the idea of simple respect; third, the arguments from this article also highlight the importance of freedom as non-domination and how this notion is, indeed, as Pettit himself claims, an agency-freedom which aims at successfully securing the social, political, economic and even (some) psychological conditions for free and autonomous agency.

Finite domination and Novikov rings: Laurent polynomial rings in two variables

Let C be a bounded cochain complex of finitely generatedfree modules over the Laurent polynomial ring L = R[x, x−1, y, y−1].The complex C is called R-finitely dominated if it is homotopy equivalentover R to a bounded complex of finitely generated projective Rmodules.Our main result characterises R-finitely dominated complexesin terms of Novikov cohomology: C is R-finitely dominated if andonly if eight complexes derived from C are acyclic; these complexes areC ⊗L R[[x, y]][(xy)−1] and C ⊗L R[x, x−1][[y]][y−1], and their variants obtainedby swapping x and y, and replacing either indeterminate by its inverse.

Vector bundles on the projective line and finite domination of chain complexes

We present an algebro-geometric approach to a theorem on finite domination of chain complexes over a Laurent polynomial ring. The approach uses extension of chain complexes to sheaves on the projective line, which is governed by a K-theoretical obstruction.