Nuclear elements of degree 6 in the free alternative algebra

We construct five new elements of degree 6 in the nucleus of the free alternative algebra. We use the representation theory of the symmetric group to locate the elements. We use the computer algebra system ALBERT and an extension of ALBERT to express the elements in compact form and to show that these new elements are not a consequence of the known clegree-5 elements in the nucleus. We prove that these five new elements and four known elements form a basis for the subspace of nuclear elements of degree 6. Our calculations are done using modular arithmetic to save memory and time. The calculations can be done in characteristic zero or any prime greater than 6, and similar results are expected. We generated the nuclear elements using prime 103. We check our answer using five other primes.

A stronger Dunford-Pettis property

We discuss a strong version of the Dunford-Pettis property, earlier named (DP*) property, which is shared by both l(1) and l(infinity) It is equivalent to the Dunford-Pettis property plus the fact that every quotient map onto c(0) is completely continuous. Other weak sequential continuity results on polynomials and analytic mappings related to the (DP*) property are shown.

Finite-dimensional non-associative algebras and codimension growth

Let A be a (non-necessarily associative) finite-dimensional algebra over a field of characteristic zero. A quantitative estimate of the polynomial identities satisfied by A is achieved through the study of the asymptotics of the sequence of codimensions of A. It is well known that for such an algebra this sequence is exponentially bounded. Here we capture the exponential rate of growth of the sequence of codimensions for several classes of algebras including simple algebras with a special non-degenerate form, finite-dimensional Jordan or alternative algebras and many more. In all cases such rate of growth is integer and is explicitly related to the dimension of a subalgebra of A. One of the main tools of independent interest is the construction in the free non-associative algebra of multialternating polynomials satisfying special properties. (C) 2010 Elsevier Inc. All rights reserved.

Description of costandard modules for Schur superalgebra S(2 vertical bar 1) in positive characteristic

We describe the characters of simple modules and composition factors of costandard modules for S(2 vertical bar 1) in positive characteristics and verify a conjecture of La Scala-Zubkov regarding polynomial superinvariants for GL(2 vertical bar 1).

Nil graded self-similar algebras

In [19], [24] we introduced a family of self-similar nil Lie algebras L over fields of prime characteristic p > 0 whose properties resemble those of Grigorchuk and Gupta-Sidki groups. The Lie algebra L is generated by two derivations v(1) = partial derivative(1) + t(0)(p-1) (partial derivative(2) + t(1)(p-1) (partial derivative(3) + t(2)(p-1) (partial derivative(4) + t(3)(p-1) (partial derivative(5) + t(4)(p-1) (partial derivative(6) + ...))))), v(2) = partial derivative(2) + t(1)(p-1) (partial derivative(3) + t(2)(p-1) (partial derivative(4) + t(3)(p-1) (partial derivative(5) + t(4)(p-1) (partial derivative(6) + ...)))) of the truncated polynomial ring K[t(i), i is an element of N vertical bar t(j)(p) =0, i is an element of N] in countably many variables. The associative algebra A generated by v(1), v(2) is equipped with a natural Z circle plus Z-gradation. In this paper we show that for p, which is not representable as p = m(2) + m + 1, m is an element of Z, the algebra A is graded nil and can be represented as a sum of two locally nilpotent subalgebras. L. Bartholdi [3] andYa. S. Krylyuk [15] proved that for p = m(2) + m + 1 the algebra A is not graded nil. However, we show that the second family of self-similar Lie algebras introduced in [24] and their associative hulls are always Z(p)-graded, graded nil, and are sums of two locally nilpotent subalgebras.

Decomposability problem on branched coverings

Given a branched covering of degree d between closed surfaces, it determines a collection of partitions of d, the branch data. In this work we show that any branch data are realized by an indecomposable primitive branched covering on a connected closed surface N with chi(N) <= 0. This shows that decomposable and indecomposable realizations may coexist. Moreover, we characterize the branch data of a decomposable primitive branched covering. Bibliography: 20 titles.

Nonhomogeneous subalgebras of Lie and special Jordan superalgebras

We consider polynomial identities satisfied by nonhomogeneous subalgebras of Lie and special Jordan superalgebras: we ignore the grading and regard the superalgebra as an ordinary algebra. The Lie case has been studied by Volichenko and Baranov: they found identities in degrees 3, 4 and 5 which imply all the identities in degrees <= 6. We simplify their identities in degree 5, and show that there are no new identities in degree 7. The Jordan case has not previously been studied: we find identities in degrees 3, 4, 5 and 6 which imply all the identities in degrees <= 6, and demonstrate the existence of further new identities in degree 7. our proofs depend on computer algebra: we use the representation theory of the symmetric group, the Hermite normal form of an integer matrix, the LLL algorithm for lattice basis reduction, and the Chinese remainder theorem. (C) 2009 Elsevier Inc. All rights reserved.

A Character Formula for the Category (O)over-tilde of Modules for Affine sl(2)

One may construct, for any function on the integers, an irreducible module of level zero for affine sl(2) using the values of the function as structure constants. The modules constructed using exponential-polynomial functions realize the irreducible modules with finite-dimensional weight spaces in the category (O) over tilde of Chari. In this work, an expression for the formal character of such a module is derived using the highest weight theory of truncations of the loop algebra.

A Harmonized Vocabulary For Water Quality

Interoperability of water quality data depends on the use of common models, schemas and vocabularies. However, terms are usually collected during different activities and projects in isolation of one another, resulting in vocabularies that have the same scope being represented with different terms, using different formats and formalisms, and published in various access methods. Significantly, most water quality vocabularies conflate multiple concepts in a single term, e.g. quantity kind, units of measure, substance or taxon, medium and procedure. This bundles information associated with separate elements from the OGC Observations and Measurements (O&M) model into a single slot. We have developed a water quality vocabulary, formalized using RDF, and published as Linked Data. The terms were extracted from existing water quality vocabularies. The observable property model is inspired by O&M but aligned with existing ontologies. The core is an OWL ontology that extends the QUDT ontology for Unit and QuantityKind definitions. We add classes to generalize the QuantityKind model, and properties for explicit description of the conflated concepts. The key elements are defined to be sub-classes or sub-properties of SKOS elements, which enables a SKOS view to be published through standard vocabulary APIs, alongside the full view. QUDT terms are re-used where possible, supplemented with additional Unit and QuantityKind entries required for water quality. Along with items from separate vocabularies developed for objects, media, and procedures, these are linked into definitions in the actual observable property vocabulary. Definitions of objects related to chemical substances are linked to items from the Chemical Entities of Biological Interest (ChEBI) ontology. Mappings to other vocabularies, such as DBPedia, are in separately maintained files. By formalizing the model for observable properties, and clearly labelling the separate concerns, water quality observations from different sources may be more easily merged and also transformed to O&M for cross-domain applications.

Optimal Rehabilitation Strategy In Water Distribution Systems Considering Reduction In Greenhouse Gas Emissions

Most of water distribution systems (WDS) need rehabilitation due to aging infrastructure leading to decreasing capacity, increasing leakage and consequently low performance of the WDS. However an appropriate strategy including location and time of pipeline rehabilitation in a WDS with respect to a limited budget is the main challenge which has been addressed frequently by researchers and practitioners. On the other hand, selection of appropriate rehabilitation technique and material types is another main issue which has yet to address properly. The latter can affect the environmental impacts of a rehabilitation strategy meeting the challenges of global warming mitigation and consequent climate change. This paper presents a multi-objective optimization model for rehabilitation strategy in WDS addressing the abovementioned criteria mainly focused on greenhouse gas (GHG) emissions either directly from fossil fuel and electricity or indirectly from embodied energy of materials. Thus, the objective functions are to minimise: (1) the total cost of rehabilitation including capital and operational costs; (2) the leakage amount; (3) GHG emissions. The Pareto optimal front containing optimal solutions is determined using Non-dominated Sorting Genetic Algorithm NSGA-II. Decision variables in this optimisation problem are classified into a number of groups as: (1) percentage proportion of each rehabilitation technique each year; (2) material types of new pipeline for rehabilitation each year. Rehabilitation techniques used here includes replacement, rehabilitation and lining, cleaning, pipe duplication. The developed model is demonstrated through its application to a Mahalat WDS located in central part of Iran. The rehabilitation strategy is analysed for a 40 year planning horizon. A number of conventional techniques for selecting pipes for rehabilitation are analysed in this study. The results show that the optimal rehabilitation strategy considering GHG emissions is able to successfully save the total expenses, efficiently decrease the leakage amount from the WDS whilst meeting environmental criteria.

Harmonization Of Vocabularies For Water Data

Observational data encodes values of properties associated with a feature of interest, estimated by a specified procedure. For water the properties are physical parameters like level, volume, flow and pressure, and concentrations and counts of chemicals, substances and organisms. Water property vocabularies have been assembled at project, agency and jurisdictional level. Organizations such as EPA, USGS, CEH, GA and BoM maintain vocabularies for internal use, and may make them available externally as text files. BODC and MMI have harvested many water vocabularies alongside others of interest in their domain, formalized the content using SKOS, and published them through web interfaces. Scope is highly variable both within and between vocabularies. Individual items may conflate multiple concerns (e.g. property, instrument, statistical procedure, units). There is significant duplication between vocabularies. Semantic web technologies provide the opportunity both to publish vocabularies more effectively, and achieve harmonization to support greater interoperability between datasets. - Models for vocabulary items (property, substance/taxon, process, unit-of-measure, etc) may be formalized OWL ontologies, supporting semantic relations between items in related vocabularies; - By specializing the ontology elements from SKOS concepts and properties, diverse vocabularies may be published through a common interface; - Properties from standard vocabularies (e.g. OWL, SKOS, PROV-O and VAEM) support mappings between vocabularies having a similar scope - Existing items from various sources may be assembled into new virtual vocabularies However, there are a number of challenges: - use of standard properties such as sameAs/exactMatch/equivalentClass require reasoning support; - items have been conceptualised as both classes and individuals, complicating the mapping mechanics; - re-use of items across vocabularies may conflict with expectations concerning URI patterns; - versioning complicates cross-references and re-use. This presentation will discuss ways to harness semantic web technologies to publish harmonized vocabularies, and will summarise how many of the challenges may be addressed.

O gás ionizado em galáxias ativas

Foram analisados espectros óticos de fenda longa de 29 galáxias que hospedam núcleos ativos (AGNs), sendo 6 galáxias Seyfert 1, 18 galáxias Seyfert 2, 4 Rádio-galáxias de linhas estreitas (NLRG) e 1 Rádio-galáxia de linhas largas (BLRG). Estas galáxias apresentam emissão por gás de alta excitação que se estende em alguns casos a 10 kpc do núcleo. O objetivo do presente trabalho consiste em estudar e caracterizar as propriedades físicas da região estendida de linhas estreitas (ENLR) destes objetos bem como propriedades da fonte central. A distribuição radial de parâmetros que caracterizam o gás emissor em cada galáxia, tais como brilho superficial das linhas de emissão, densidade do gás, massa, extinção e excitação são obtidos. Estes valores característicos são comparados entre as diferentes classes de atividade nuclear presentes em nossa amostra, bem como às propriedades de galáxias normais com o mesmo tipo de Hubble quando possível. Nós encontramos que a massa de gás ionizado é consistente com a hipótese de que o gás é “originado” na fotoionização pela fonte central das nuvens de HI préexistentes na galáxia hospedeira. Os valores observados das razões entre as linhas estreitas de emissão são comparados com os obtidos através de modelos de fotoionização gerados com o código MAPPINGS Ic, obtendo os parâmetros do modelo – densidade, índice espectral da distribuição de energia e da metalicidade do gás – que melhor reproduzem as observações. Observamos que a variação da abundância química do gás é necessária para explicar o espalhamento nos valores observados. Adicionalmente, comparamos os valores observados com os obtidos com modelos de choques gerados por Dopita & Sutherland. Investigamos também a influência da emissão proveniente de regiões HII ao espectro observado – a qual concluímos ser importante particularmente nas regiões emissoras mais distantes do que 2 kpc do núcleo. Nós determinamos a luminosidade ionizante da fonte central nos AGNs usando a aproximação de que as nuvens de gás são limitadas por radiação, e obtivemos os correspondentes valores para o fator de cobertura do gás. Esta luminosidade ionizante foi então comparada com a luminosidade observada em raios-X na banda 2 –10 keV, através de aproximações para a distribuição espectral de energia (SED). Para 9 galáxias Seyfert 2 a luminosidade observada está disponível, e verificamos que nosso método recupera a luminosidade do AGN em raios-X – assim como obtida dos dados do satélite ASCA – bem como identifica os 3 casos Compton espessos. Por fim, investigamos a natureza do contínuo infravermelho (IR) médio e distante – comparandose a luminosidade observada no IR, calculada a partir dos fluxos IRAS, com a luminosidade predita para um toro que envolve a fonte central absorvendo a radiação incidente e re-emitindo esta no infravermelho. Encontramos que a luminosidade observada no IR é consistente com a luminosidade predita para o torus.

O contínuo e a região estendida de linhas estreitas das galáxias ativas ESO 362-G18 e ESO 362-G8

Foram analisados espectros óticos de fenda longa das galáxias Seyfert 1 ESO362-G18 e Seyfert 2 ESO362-G8. Estas duas galáxias apresentam emissão por gás de alta excitação em forma anisotrópica, possivelmente devido a colimação por um tóro de poeira. O objetivo do presente trabalho consiste em estudar o contínuo e a região estendida de linhas de emissão (ENLR) destes objetos. Este trabalho constitui-se no primeiro estudo detalhado realizado sobre estas galáxias. A população estelar em cada galáxia e caracterizada em função da distância ao núcleo. O contínuo nuclear e estudado em termos de duas componentes: a população estelar e a componente AGN (\Active Galatic Nuclei"). Observa-se a presença desta componente AGN na gal axia Seyfert 1 ESO362-G18. A galáxia Seyfert 2 não permite observar esta componente AGN mesmo depois de subtraída a componente de população estelar. Nas duas galáxias observa-se importante contribuição de população de idade intermediária ( 5 108 anos). A partir das linhas estreitas de emissão, mapeamos a excitação do gás interestelar ao longo da ENLR. As razões entre estas linhas de emissão são reproduzidas a partir de um modelo de fotoionização de duas componentes - uma componente limitada por matéria ("matter-bounded") e uma componente limitada por ionização ("ionization-bounded"). Este modelo, construído utilizando o código de fotoionização MAPPINGS Ic, se propõe a resolver os problemas apresentados pelos modelos tradicionais de uma componente apenas. A partir dos resultados obtidos com o modelo de duas componentes, determinamos o fator de preenchimento e o fator de cobertura do gás em função da distância ao núcleo. Utilizamos estes parâmetros para testar a consistência do modelo proposto. Por fim realizase o cálculo de balanço de fótons e estuda-se a natureza do contínuo infravermelho (IR) médio e distante - comparando-se a luminosidade observada no IR, calculada a partir dos fluxos IRAS, com a luminosidade predita para um tóro que envolve a fonte modelada e re-emite a radiação incidente no infravermelho.

Estimação em classes de processos estocásticos com decaimento hiperbólico da função de autocorrelação

Neste trabalho analisamos processos estocásticos com decaimento polinomial (também chamado hiperbólico) da função de autocorrelação. Nosso estudo tem enfoque nas classes dos Processos ARFIMA e dos Processos obtidos à partir de iterações da transformação de Manneville-Pomeau. Os objetivos principais são comparar diversos métodos de estimação para o parâmetro fracionário do processo ARFIMA, nas situações de estacionariedade e não estacionariedade e, além disso, obter resultados similares para o parâmetro do processo de Manneville-Pomeau. Entre os diversos métodos de estimação para os parâmetros destes dois processos destacamos aquele baseado na teoria de wavelets por ser aquele que teve o melhor desempenho.

Beyond indifferent players: on the existence of prisoners dilemmas in games with amicable and adversarial preferences

Why don’t agents cooperate when they both stand to gain? This question ranks among the most fundamental in the social sciences. Explanations abound. Among the most compelling are various configurations of the prisoner’s dilemma (PD), or public goods problem. Payoffs in PD’s are specified in one of two ways: as primitive cardinal payoffs or as ordinal final utility. However, as final utility is objectively unobservable, only the primitive payoff games are ever observed. This paper explores mappings from primitive payoff to utility payoff games and demonstrates that though an observable game is a PD there are broad classes of utility functions for which there exists no associated utility PD. In particular we show that even small amounts of either altruism or enmity may disrupt the mapping from primitive payoff to utility PD. We then examine some implications of these results.