Rings faithfully represented on their left socle

In 1964 A. W. Goldie [1] posed the problem of determining all rings with identity and minimal condition on left ideals which are faithfully represented on the right side of their left socle. Goldie showed that such a ring which is indecomposable and in which the left and right principal indecomposable ideals have, respectively, unique left and unique right composition series is a complete blocked triangular matrix ring over a skewfield. The general problem suggested above is very difficult. We obtain results under certain natural restrictions which are much weaker than the restrictive assumptions made by Goldie.

We characterize those rings in which the principal indecomposable left ideals each contain a unique minimal left ideal (Theorem (4.2)). It is sufficient to handle indecomposable rings (Lemma (1.4)). Such a ring is also a blocked triangular matrix ring. There exist r positive integers K₁,..., K_r such that the i,j^th block of a typical matrix is a K_i x K_j matrix with arbitrary entries in a subgroup D_ij of the additive group of a fixed skewfield D. Each D_ii is a sub-skewfield of D and D_ri = D for all i. Conversely, every matrix ring which has this form is indecomposable, faithfully represented on the right side of its left socle, and possesses the property that every principal indecomposable left ideal contains a unique minimal left ideal.

The principal indecomposable left ideals may have unique composition series even though the ring does not have minimal condition on right ideals. We characterize this situation by defining a partial ordering ρ on {i, 2,...,r} where we set iρj if D_ij ≠ 0. Every principal indecomposable left ideal has a unique composition series if and only if the diagram of ρ is an inverted tree and every D_ij is a one-dimensional left vector space over D_ii (Theorem (5.4)).

We show (Theorem (2.2)) that every ring A of the type we are studying is a unique subdirect sum of less complex rings A₁,...,A_s of the same type. Namely, each A_i has only one isomorphism class of minimal left ideals and the minimal left ideals of different A_i are non-isomorphic as left A-modules. We give (Theorem (2.1)) necessary and sufficient conditions for a ring which is a subdirect sum of rings A_i having these properties to be faithfully represented on the right side of its left socle. We show ((4.F), p. 42) that up to technical trivia the rings A_i are matrix rings of the form

[...]. Each Q_j comes from the faithful irreducible matrix representation of a certain skewfield over a fixed skewfield D. The bottom row is filled in by arbitrary elements of D.

In Part V we construct an interesting class of rings faithfully represented on their left socle from a given partial ordering on a finite set, given skewfields, and given additive groups. This class of rings contains the ones in which every principal indecomposable left ideal has a unique minimal left ideal. We identify the uniquely determined subdirect summands mentioned above in terms of the given partial ordering (Proposition (5.2)). We conjecture that this technique serves to construct all the rings which are a unique subdirect sum of rings each having the property that every principal-indecomposable left ideal contains a unique minimal left ideal.

Compatibilization effect of graft copolymer on immiscible polymer blends: 1. LLDPE/SBS/LLDPE-g-PS systems

compatibilizing effect of graft copolymer, linear low density polyethylene-g-polystyrene (LLDPE-g-PS), on immiscible blends of LLDPE with styrene-butadiene-styrene triblock copolymer (SBS) has been investigated by means of C-13 CPMAS n.m.r. and d.s.c. techniques. The results indicate that LLDPE-g-PS is an effective compatibilizer for LLDPE/SBS blends. It was found that LLDPE-g-PS chains connect two immiscible components, LLDPE and SBS, through solubilization of chemically identical segments of LLDPE-g-PS into the amorphous region of LLDPE acid PS block domain of SBS, respectively. It was also found that LLDPE-g-PS chains connect the crystalline region of LLDPE by isomorphism, with serious effects on the supermolecular structure of LLDPE. The effect of LLDPE-g-PS on the supermolecular structure of LLDPE in the LLDPE/SBS blends obviously depends on the composition of the blends, but has little dependence on the PS grafting yields of LLDPE-g-PS. (C) 1998 Elsevier Science Ltd. All rights reserved.

Compatibilization effect of graft copolymer on immiscible polymer blends .2. LLDPE/PS/LLDPE-g-PS systems

The compatibilizing effect of graft copolymer, linear low density polyethylene-g-polystyrene (LLDPE-g-PS), on immiscible LLDPE/PS blends has been studied by means of C-13 CP-MAS NMR and DSC techniques. The results indicate that LLDPE-g-PS is an effective compatibilizer for LLDPE/PS blends, and the compatibilizing effect of LLDPE-g-PS on LLDPE/PS blends depends on the PS grafting yield and molecular structure of the compatibilizers and also on the composition of the blends. It was found that LLDPE-g-PS chains connect two immiscible components, LLDPE and PS, through solubilization of chemically identical segments of LLDPE-g-PS into the noncrystalline region of the LLDPE and PS domain, respectively. Meanwhile, LLDPE-g-PS chains connect the crystalline region of LLDPE by isomorphism, resulting in an obvious change in the crystallization behavior of LLDPE. (C) 1996 John Wiley & Sons, Inc.

Type-alpha DPLs

This paper introduces Denotational Proof Languages (DPLs). DPLs are languages for presenting, discovering, and checking formal proofs. In particular, in this paper we discus type-alpha DPLs---a simple class of DPLs for which termination is guaranteed and proof checking can be performed in time linear in the size of the proof. Type-alpha DPLs allow for lucid proof presentation and for efficient proof checking, but not for proof search. Type-omega DPLs allow for search as well as simple presentation and checking, but termination is no longer guaranteed and proof checking may diverge. We do not study type-omega DPLs here. We start by listing some common characteristics of DPLs. We then illustrate with a particularly simple example: a toy type-alpha DPL called PAR, for deducing parities. We present the abstract syntax of PAR, followed by two different kinds of formal semantics: evaluation and denotational. We then relate the two semantics and show how proof checking becomes tantamount to evaluation. We proceed to develop the proof theory of PAR, formulating and studying certain key notions such as observational equivalence that pervade all DPLs. We then present NDL, a type-alpha DPL for classical zero-order natural deduction. Our presentation of NDL mirrors that of PAR, showing how every basic concept that was introduced in PAR resurfaces in NDL. We present sample proofs of several well-known tautologies of propositional logic that demonstrate our thesis that DPL proofs are readable, writable, and concise. Next we contrast DPLs to typed logics based on the Curry-Howard isomorphism, and discuss the distinction between pure and augmented DPLs. Finally we consider the issue of implementing DPLs, presenting an implementation of PAR in SML and one in Athena, and end with some concluding remarks.

Learning by Failing to Explain

Explanation-based Generalization requires that the learner obtain an explanation of why a precedent exemplifies a concept. It is, therefore, useless if the system fails to find this explanation. However, it is not necessary to give up and resort to purely empirical generalization methods. In fact, the system may already know almost everything it needs to explain the precedent. Learning by Failing to Explain is a method which is able to exploit current knowledge to prune complex precedents, isolating the mysterious parts of the precedent. The idea has two parts: the notion of partially analyzing a precedent to get rid of the parts which are already explainable, and the notion of re-analyzing old rules in terms of new ones, so that more general rules are obtained.

Deciding Isomorphisms of Simple Types in Polynomial Time

The isomorphisms holding in all models of the simply typed lambda calculus with surjective and terminal objects are well studied - these models are exactly the Cartesian closed categories. Isomorphism of two simple types in such a model is decidable by reduction to a normal form and comparison under a finite number of permutations (Bruce, Di Cosmo, and Longo 1992). Unfortunately, these normal forms may be exponentially larger than the original types so this construction decides isomorphism in exponential time. We show how using space-sharing/hash-consing techniques and memoization can be used to decide isomorphism in practical polynomial time (low degree, small hidden constant). Other researchers have investigated simple type isomorphism in relation to, among other potential applications, type-based retrieval of software modules from libraries and automatic generation of bridge code for multi-language systems. Our result makes such potential applications practically feasible.

A critical examination of node-similarity based graph matching algorithms

In this paper, we shall critically examine a special class of graph matching algorithms that follow the approach of node-similarity measurement. A high-level algorithm framework, namely node-similarity graph matching framework (NSGM framework), is proposed, from which, many existing graph matching algorithms can be subsumed, including the eigen-decomposition method of Umeyama, the polynomial-transformation method of Almohamad, the hubs and authorities method of Kleinberg, and the kronecker product successive projection methods of Wyk, etc. In addition, improved algorithms can be developed from the NSGM framework with respects to the corresponding results in graph theory. As the observation, it is pointed out that, in general, any algorithm which can be subsumed from NSGM framework fails to work well for graphs with non-trivial auto-isomorphism structure.

On the derived category of a regular toric scheme

Let X be a quasi-compact scheme, equipped with an open covering by affine schemes U s = Spec A s . A quasi-coherent sheaf on X gives rise, by taking sections over the U s , to a diagram of modules over the coordinate rings A s , indexed by the intersection poset S of the covering. If X is a regular toric scheme over an arbitrary commutative ring, we prove that the unbounded derived category of quasi-coherent sheaves on X can be obtained from a category of Sop-diagrams of chain complexes of modules by inverting maps which induce homology isomorphisms on hyper-derived inverse limits. Moreover, we show that there is a finite set of weak generators, one for each cone in the fan S. The approach taken uses the machinery of Bousfield–Hirschhorn colocalisation of model categories. The first step is to characterise colocal objects; these turn out to be homotopy sheaves in the sense that chain complexes over different open sets U s agree on intersections up to quasi-isomorphism. In a second step it is shown that the homotopy category of homotopy sheaves is equivalent to the derived category of X.

Double complexes and vanishing of Novikov cohomology

We consider non-standard totalisation functors for double complexes, involving left or right truncated products. We show how properties of these imply that the algebraic mapping torus of a self map h of a cochain complex of finitely presented modules has trivial negative Novikov cohomology, and has trivial positive Novikov cohomology provided h is a quasi-isomorphism. As an application we obtain a new and transparent proof that a finitely dominated cochain complex over a Laurent polynomial ring has trivial (positive and negative) Novikov cohomology.

Práticas de contabilidade e controlo de gestão no setor automóvel

Dissertação apresentada para obtenção do Grau de Mestre em Contabilidade e Finanças, sob orientação de: Amélia Ferreira da Silva José António Fernandes Lopes Oliveira Vale

O ensino profissional de nível secundário em Portugal, 2000-2014

O presente estudo aborda a forma como as escolas secundárias públicas com ensino profissional (cursos profissionais) de qualificação profissional de nível 4, se têm vindo a adaptar às novas configurações do sistema educativo, na integração desta oferta educativa. Esta via de ensino tem contribuído de forma expressiva para o aumento da escolarização do ensino secundário nos últimos anos em Portugal. Tendo presentes estas novas configurações institucionais que resultaram em mudanças no sistema educativo, o Estado parece agora legitimar e apelar ao comportamento competitivo, numa ação conduzida por lógicas de mercado (quase-mercado). Destacamos aspetos fundamentais como os reflexos da crise económica e financeira no desemprego e na formulação de quadros de incerteza, o reforço do regime de autonomia, a imposição de condições de administração e gestão participativa, a estrutura e organização desta via de ensino, e o planeamento da oferta formativa como contextos centrais para a reflexão e identificação da ação estratégica. Recorremos ao conceito de instituição, o qual define o ambiente organizacional como um espaço de trocas de recursos económicos e simbólicos, e enfatiza que as estruturas organizacionais são o resultado de pressões exercidas pelo ambiente institucional em que estão inseridas, e não entidades passivas, pois desenvolvem práticas e estratégias consideradas apropriadas para assegurar o seu poder, legitimidade e sobrevivência. Através da análise da evolução das ofertas de cursos às escalas nacional e regional e de entrevistas com escolas públicas e municípios da rede EXCEL, bem como de escolas privadas dos mesmos concelhos, concluímos que numa primeira fase as escolas públicas pautaram as suas ofertas por estratégias defensivas, face à dependência de recursos, à procura de estabilidade organizativa e de afetação do corpo docente instalado e à perceção duvidosa sobre a autonomia. A segunda fase, a partir de 2011, carateriza-se pelo reforço da centralidade do Estado que passou a determinar as ofertas agindo como representante único da procura pública, ao mesmo tempo que se manteve a pressão concorrencial sobre as escolas como atores da oferta, estruturando um quase-mercado aproximado a um monopsónio.

Rings, Group Rings, and Their Graphs

We associate some graphs to a ring R and we investigate the interplay between the ring-theoretic properties of R and the graph-theoretic properties of the graphs associated to R. Let Z(R) be the set of zero-divisors of R. We define an undirected graph ᴦ(R) with nonzero zero-divisors as vertices and distinct vertices x and y are adjacent if xy=0 or yx=0. We investigate the Isomorphism Problem for zero-divisor graphs of group rings RG. Let Sk denote the sphere with k handles, where k is a non-negative integer, that is, Sk is an oriented surface of genus k. The genus of a graph is the minimal integer n such that the graph can be embedded in Sn. The annihilating-ideal graph of R is defined as the graph AG(R) with the set of ideals with nonzero annihilators as vertex such that two distinct vertices I and J are adjacent if IJ=(0). We characterize Artinian rings whose annihilating-ideal graphs have finite genus. Finally, we extend the definition of the annihilating-ideal graph to non-commutative rings.

Criteria for the validation of specialized verb equivalents : application in bilingual terminography

Multilingual terminological resources do not always include valid equivalents of legal terms for two main reasons. Firstly, legal systems can differ from one language community to another and even from one country to another because each has its own history and traditions. As a result, the non-isomorphism between legal and linguistic systems may render the identification of equivalents a particularly challenging task. Secondly, by focusing primarily on the definition of equivalence, a notion widely discussed in translation but not in terminology, the literature does not offer solid and systematic methodologies for assigning terminological equivalents. As a result, there is a lack of criteria to guide both terminologists and translators in the search and validation of equivalent terms. This problem is even more evident in the case of predicative units, such as verbs. Although some terminologists (L‘Homme 1998; Lerat 2002; Lorente 2007) have worked on specialized verbs, terminological equivalence between units that belong to this part of speech would benefit from a thorough study. By proposing a novel methodology to assign the equivalents of specialized verbs, this research aims at defining validation criteria for this kind of predicative units, so as to contribute to a better understanding of the phenomenon of terminological equivalence as well as to the development of multilingual terminography in general, and to the development of legal terminography, in particular. The study uses a Portuguese-English comparable corpus that consists of a single genre of texts, i.e. Supreme Court judgments, from which 100 Portuguese and 100 English specialized verbs were selected. The description of the verbs is based on the theory of Frame Semantics (Fillmore 1976, 1977, 1982, 1985; Fillmore and Atkins 1992), on the FrameNet methodology (Ruppenhofer et al. 2010), as well as on the methodology for compiling specialized lexical resources, such as DiCoInfo (L‘Homme 2008), developed in the Observatoire de linguistique Sens-Texte at the Université de Montréal. The research reviews contributions that have adopted the same theoretical and methodological framework to the compilation of lexical resources and proposes adaptations to the specific objectives of the project. In contrast to the top-down approach adopted by FrameNet lexicographers, the approach described here is bottom-up, i.e. verbs are first analyzed and then grouped into frames for each language separately. Specialized verbs are said to evoke a semantic frame, a sort of conceptual scenario in which a number of mandatory elements (core Frame Elements) play specific roles (e.g. ARGUER, JUDGE, LAW), but specialized verbs are often accompanied by other optional information (non-core Frame Elements), such as the criteria and reasons used by the judge to reach a decision (statutes, codes, previous decisions). The information concerning the semantic frame that each verb evokes was encoded in an xml editor and about twenty contexts illustrating the specific way each specialized verb evokes a given frame were semantically and syntactically annotated. The labels attributed to each semantic frame (e.g. [Compliance], [Verdict]) were used to group together certain synonyms, antonyms as well as equivalent terms. The research identified 165 pairs of candidate equivalents among the 200 Portuguese and English terms that were grouped together into 76 frames. 71% of the pairs of equivalents were considered full equivalents because not only do the verbs evoke the same conceptual scenario but their actantial structures, the linguistic realizations of the actants and their syntactic patterns were similar. 29% of the pairs of equivalents did not entirely meet these criteria and were considered partial equivalents. Reasons for partial equivalence are provided along with illustrative examples. Finally, the study describes the semasiological and onomasiological entry points that JuriDiCo, the bilingual lexical resource compiled during the project, offers to future users.

La structure de Jordan des matrices de transfert des modèles de boucles et la relation avec les hamiltoniens XXZ

Les modèles sur réseau comme ceux de la percolation, d’Ising et de Potts servent à décrire les transitions de phase en deux dimensions. La recherche de leur solution analytique passe par le calcul de la fonction de partition et la diagonalisation de matrices de transfert. Au point critique, ces modèles statistiques bidimensionnels sont invariants sous les transformations conformes et la construction de théories des champs conformes rationnelles, limites continues des modèles statistiques, permet un calcul de la fonction de partition au point critique. Plusieurs chercheurs pensent cependant que le paradigme des théories des champs conformes rationnelles peut être élargi pour inclure les modèles statistiques avec des matrices de transfert non diagonalisables. Ces modèles seraient alors décrits, dans la limite d’échelle, par des théories des champs logarithmiques et les représentations de l’algèbre de Virasoro intervenant dans la description des observables physiques seraient indécomposables. La matrice de transfert de boucles D_N(λ, u), un élément de l’algèbre de Temperley- Lieb, se manifeste dans les théories physiques à l’aide des représentations de connectivités ρ (link modules). L’espace vectoriel sur lequel agit cette représentation se décompose en secteurs étiquetés par un paramètre physique, le nombre d de défauts. L’action de cette représentation ne peut que diminuer ce nombre ou le laisser constant. La thèse est consacrée à l’identification de la structure de Jordan de D_N(λ, u) dans ces représentations. Le paramètre β = 2 cos λ = −(q + 1/q) fixe la théorie : β = 1 pour la percolation et √2 pour le modèle d’Ising, par exemple. Sur la géométrie du ruban, nous montrons que D_N(λ, u) possède les mêmes blocs de Jordan que F_N, son plus haut coefficient de Fourier. Nous étudions la non diagonalisabilité de F_N à l’aide des divergences de certaines composantes de ses vecteurs propres, qui apparaissent aux valeurs critiques de λ. Nous prouvons dans ρ(D_N(λ, u)) l’existence de cellules de Jordan intersectorielles, de rang 2 et couplant des secteurs d, d′ lorsque certaines contraintes sur λ, d, d′ et N sont satisfaites. Pour le modèle de polymères denses critique (β = 0) sur le ruban, les valeurs propres de ρ(D_N(λ, u)) étaient connues, mais les dégénérescences conjecturées. En construisant un isomorphisme entre les modules de connectivités et un sous-espace des modules de spins du modèle XXZ en q = i, nous prouvons cette conjecture. Nous montrons aussi que la restriction de l’hamiltonien de boucles à un secteur donné est diagonalisable et trouvons la forme de Jordan exacte de l’hamiltonien XX, non triviale pour N pair seulement. Enfin nous étudions la structure de Jordan de la matrice de transfert T_N(λ, ν) pour des conditions aux frontières périodiques. La matrice T_N(λ, ν) a des blocs de Jordan intrasectoriels et intersectoriels lorsque λ = πa/b, et a, b ∈ Z×. L’approche par F_N admet une généralisation qui permet de diagnostiquer des cellules intersectorielles dont le rang excède 2 dans certains cas et peut croître indéfiniment avec N. Pour les blocs de Jordan intrasectoriels, nous montrons que les représentations de connectivités sur le cylindre et celles du modèle XXZ sont isomorphes sauf pour certaines valeurs précises de q et du paramètre de torsion v. En utilisant le comportement de la transformation i_N^d dans un voisinage des valeurs critiques (q_c, v_c), nous construisons explicitement des vecteurs généralisés de Jordan de rang 2 et discutons l’existence de blocs de Jordan intrasectoriels de plus haut rang.

Analyse de l'évolution de l'Administration canadienne de la sûreté du transport aérien

La présente étude a analysé l’évolution de l’Administration Canadienne de la Sureté du Transport Aérien (ACSTA) depuis sa mise en place jusqu’aujourd’hui, ainsi que les acteurs individuels ou institutionnels impliqués dans ce processus. L’ACSTA gravite dans un champ organisationnel ‐ensemble d’organisations qui constituent un domaine reconnu de la vie institutionnelle (DiMaggio et Powell, 1983)-­ au sein duquel agissent différents acteurs qui ont influencé non seulement sa création, mais qui ont continué à jouer un rôle important tout au long de son évolution. Nous avons défini le champ de la sûreté aérienne et au sein de celui‐ci, nous avons analysé les mécanismes institutionnels, tout en identifiant et définissant le rôle des différents acteurs en présence. Il ressort de nos analyses que principalement deux types de contraintes institutionnelles (DiMaggio et Powell, 1983) ont influencé la création et le développement de l’ACSTA. Premièrement, mis à part les contraintes coercitives émanant de la règlementation internationale de l’Organisation de l’Aviation Civile Internationale, il apparait que d’autres contraintes du même type proviennent du gouvernement américain, par le biais de pressions visant à la mise en place de mesures sécuritaires, tant au moment de la création que tout le long de l’évolution de l’organisation. Il est à noter, cependant, le rôle du terrorisme et des tentatives d’attentat comme provocant de telles contraintes. Deuxièmement, nous avons identifié des contraintes du type normatif, c’est-à‐dire celles qui proviennent des valeurs, des normes et du bagage professionnel lié à la sécurité et à la sureté aérienne. Il apparait que les contraintes normatives agissent constamment alors que les contraintes coercitives surgissent ponctuellement tout au long de la période analysée.