Search

We introduce the notion of a partial corepresentation of a given Hopf algebra H over a coalgebra C and the closely related concept of a partial H-comodule. We prove that there exists a universal coalgebra Hpar, associated to the original Hopf algebra H, such that the category of regular partial H-comodules is isomorphic to the category of Hpar-comodules. We introduce the notion of a Hopf coalgebroid and show that the universal coalgebra Hpar has the structure of a Hopf coalgebroid over a suitable coalgebra., SCOPUS: ar.j, info:eu-repo/semantics/published

Perfluorocarbons (PFC) emissions must be reported as accurate as possible. The aluminum industry is using a consistent method to estimate high voltage PFC emissions. However, a new or improved method is needed to account for low voltage PFC emissions. Thus, equipment sensitivity and time frequency must be revised to estimate both high and low voltage emissions, during not only anode effects above 8 volts, but also during pot disturbances that affect pot noise and therefore can make the contribution of low voltage emissions significant higher. Preliminary results showing the variability of low voltage and estimation of total PFC emissions is presented from recent PFC measurement campaigns at two Alcoa smelters.

We introduce the notion of a dilation for a partial representation (that is, a partial module) of a Hopf algebra, which in case the partial representation origins from a partial action (that is, a partial module algebra) coincides with the enveloping action (or globalization). This construction leads to categorical equivalences between the category of partial H-modules, a category of (global) H-modules endowed with a projection satisfying a suitable commutation relation and the category of modules over a (global) smash product constructed upon H, from which we deduce the structure of a Hopfish algebra on this smash product. These equivalences are used to study the interactions between partial and global representation theory., SCOPUS: ar.j, info:eu-repo/semantics/published

Climate change challenge leads government to commit themselves to a greenhouse gas reduction target and to adopt Greenhouse gas (GHG) regulation including sampling and monitoring. By regulation, all the aluminum smelters in Quebec using the slope method must validate its PFC slope at least every 36 months. This is required even more often if a change occurs in the control algorithm that affects the intensity or duration of the anode effects or when a change occurs in the distribution or duration of anode effects. The three aluminum smelters operated by Alcoa located in Quebec have implemented an anode effect assessment, which includes, among others, pot start anode effect data and reviews of the distribution of anode effect duration. With the analysis of the monitoring data obtained from the anode effect sampling of pot starts, as well as with high and low voltage anode effect measurements it is the objective to seek more accurate PFC slope determination for better reporting purposes.

In this work we deal with partial (co)action of multiplier Hopf algebras on not necessarily unital algebras. Our main goal is to construct a Morita context relating the coinvariant algebra $R^{\underline{coA}}$ with a certain subalgebra of the smash product $R\#\widehat{A}$. Besides this we present the notion of partial Galois coaction, which is closely related to this Morita context., 34 pages

Perfluorocarbon (PFC) gases evolve from aluminum electrolysis pots almost continuously. They are not only emitted during anode effects (above 8 V) but also during pot instability periods where pot voltage is below 8 V. The so called “low voltage anode effects” (LVAE) can be emitted during anode changes, pot feeding underfeed cycles or pot tapping periods [1, 2, 3, 4, 5, 6, 7]. Procedures are shown how to measure and reduce LVAE. Fourier Transform Infrared (FTIR) method is reviewed to measure the very low emissions as well as together with gas bags used to measure total PFC emissions. Thus, equipment selection, measurements parameters and Quality Assurance/Quality Control (QA/QC) controls should be reinforced to comply with possible regulation change to measure total emissions. Results from feeding optimizations will be shown from three smelters with reduction on LV-PFC emissions.

In this work, we give a survey of recent developments in the theory of partial actions of groups and Hopf algebras., Comment: 31 pages

In this work, the cohomology theory for partial actions of co-commutative Hopf algebras over commutative algebras is formulated. This theory generalizes the cohomology theory for Hopf algebras introduced by Sweedler and the cohomology theory for partial group actions, introduced by Dokuchaev and Khrypchenko. Some nontrivial examples, not coming from groups are constructed. Given a partial action of a co-commutative Hopf algebra $H$ over a commutative algebra $A$, we prove that there exists a new Hopf algebra $\widetilde{A}$, over a commutative ring $E(A)$, upon which $H$ still acts partially and which gives rise to the same cochain complex as the original algebra $A$. We also study the partially cleft extensions of commutative algebras by partial actions of cocommutative Hopf algebras and prove that these partially cleft extensions can be viewed as a cleft extensions by Hopf algebroids., Comment: 49 pages, a longer version, with some detailed proofs kept in the appendix

Most aluminum companies have initiated voluntary programs for actively reducing propagating, or above 8 volt, anode effect (AE), perfluorocarbon (PFC) emissions and all modern pre-bake smelters have automated reactive methods for terminating anode effects. The goal of these methods is to reduce cumulative anode effect minutes per cell-day. Any PFCs evolved from aluminum electrolysis pots during periods when pot voltage is below eight volts are considered non-anode effect or low voltage (LV) PFC emissions, consistent with current PFC measurement protocols.

In this work, we review some properties of twisted partial actions of Hopf algebras on unital algebras and give necessary and sufficient conditions for a twisted partial action to have a globalization. We also elaborate a series of examples., 31 pages

Motivated by partial group actions on unital algebras, in this article we extend many results obtained by Exel and Dokuchaev to the context of partial actions of Hopf algebras, according to Caenepeel and Jansen. First, we generalize the theorem about the existence of an enveloping action, also known as the globalization theorem. Second, we construct a Morita context between the partial smash product and the smash product related to the enveloping action. Third, we dualize the globalization theorem to partial coactions and finally, we define partial representations of Hopf algebras and show some results relating partial actions and partial representations., Comment: 27 pages; revised version with minor corrections, mainly typos

Perfluorocarbons (PFCs) evolved from aluminum electrolysis pots during periods when pot voltage is below eight volts are considered non-anode effect (NAE) PFC emissions, consistent with current PFC measurement protocols. NAEPFC emissions occur from all commercial smelters, regardless of plant size or technology type. This work uses historical estimations to illustrate the potential impact of including NAEPFC emissions across a portfolio of location and technology specific PFC inventories and discusses technical considerations regarding the current measurement protocol and potential modifications to include NAEPFC emissions.

The duality between partial actions (partial $H$-module algebras) and co-actions (partial $H$-comodule algebras) of a Hopf algebra $H$ is fully explored in this work. A connection between partial (co)actions and Hopf algebroids is established under certain commutativity conditions. Moreover, we continue this duality study, introducing also partial $H$-module coalgebras and their associated $C$-rings, partial $H$-comodule coalgebras and their associated cosmash coproducts, as well as the mutual interrelations between these structures., v3: strongly revised version

In this work, the notion of partial representation of a Hopf algebra is introduced and its relationship with partial actions of Hopf algebras is explored. Given a Hopf algebra $H$, one can associate it to a Hopf algebroid $H_{par}$ which has the universal property that each partial representation of $H$ can be factorized by an algebra morphism from $H_{par}$. We define also the category of partial modules over a Hopf algebra $H$, which is the category of modules over its associated Hopf algebroid $H_{par}$. The Hopf algebroid structure of $H_{par}$ enables us to enhance the category of partial $H$ modules with a monoidal structure and such that the algebra objects in this category are the usual partial actions. Some examples of categories of partial $H$ modules are explored. In particular we can describe fully the category of partially $\mathbb{Z}_2$-graded modules., 39 pages, version 2: some additions in the section on partial gradings and minor corrections elsewhere

Aluminum reduction cells use about 1.9 kg of alumina in order to produce 1 kg of aluminum. That is, for modern reduction cells operating in the 350 to 400 kA range, 5000 to 6000 kg of alumina is fed daily. Considering that 5000 to 10000 kg of molten bath is available to dissolve the alumina, the dissolution rate is an important factor in order to avoid muck and enable alumina feed control system to operate within the 2 to 5% alumina concentration. However, on top of cell status, alumina properties have an impact on alumina dissolution rate. Hence, supplier changes and/or segregation of alumina within the delivery system may have negative impact on alumina dissolution rate leading to muck and/or anode effects. This paper discusses modification to an alumina feeder pipe promoting the dissolution rate. Promising results obtained during trial in a pilot plant section are presented and discussed.

The construction of a q-deformed N=2 superconformal algebra is proposed in terms of level 1 currents of ${\cal{U}}_{q} ({\widehat{su}}(2))$ quantum affine Lie algebra and a single real Fermi field. In particular, it suggests the expression for the q-deformed Energy-Momentum tensor in the Sugawara form. Its constituents generate two isomorphic quadratic algebraic structures. The generalization to ${\cal{U}}_{q} ({\widehat{su}}(N+1))$ is also proposed., AMSLATEX, 21pages

The effectiveness of the aplication of constructions in $G$-graded $k$-categories to the computation of the fundamental group of a finite dimensional $k$-algebra, alongside with open problems still left untouched by those methods and new problems arisen from the introduction of the concept of fundamental group of a $k$-linear category, motivated the investigation of $H$-module categories, i.e., actions of a Hopf algebra $H$ on a $k$-linear category. The $G$-graded case corresponds then to actions of the Hopf algebra $k^G$ on a $k$-linear category. In this work we take a step further and introduce partial $H$-module categories. We extend several results of partial $H$-module algebras to this context, such as the globalization theorem, the construction of the partial smash product and the Morita equivalence of this category with the smash product over a globalization. We also present a detailed description of partial actions of $k^G$., 28 pages

Aluminum reduction cells typically use about 1.9 kg of alumina in order to produce 1 kg of aluminum. Hence, for modern reduction cells operating in the 350 to 400 kA range, 5000 to 6000 kg of alumina is fed to reduction cells on a daily basis. However, no information is available in an on-line fashion about the alumina properties fed to the pot. Alumina feeding control systems assume that alumina properties are constant for all pots within a potroom and also over time. Therefore, these control systems aim at controlling alumina concentration dissolved in the bath without accounting for the time varying effects of alumina properties and/or pot condition on alumina dissolution. Based on sampling campaigns, this paper presents evidences of time varying alumina properties impacting its dissolution rate and also proposes a novel approach in order to measure on-line, at the pot, parameters that are related to alumina dissolution.

In this work, the notion of a twisted partial Hopf action is introduced as a unified approach for twisted partial group actions, partial Hopf actions and twisted actions of Hopf algebras. The conditions on partial cocycles are established in order to construct partial crossed products, which are also related to partially cleft extensions of algebras. Examples are elaborated using algebraic groups.

The topology of orientable (2 + 1)d spacetimes can be captured by certain lumps of non-trivial topology called topological geons. They are the topological analogues of conventional solitons. We give a description of topological geons where the degrees of freedom related to topology are separated from the complete theory that contains metric (dynamical) degrees of freedom. The formalism also allows us to investigate processes of quantum topology change. They correspond to creation and annihilation of quantum geons. Selection rules for such processes are derived., LaTeX file, 33 pages, 10 postscript figures, some typos corrected, references updated, and other minor changes

In this paper we employ the construction of Dirac bracket for the remaining current of $sl(2)_q$ deformed Kac-Moody algebra when constraints similar to those connecting the $sl(2)$-WZW model and the Liouville theory are imposed and show that it satisfy the q-Virasoro algebra proposed by Frenkel and Reshetikhin. The crucial assumption considered in our calculation is the existence of a classical Poisson bracket algebra induced, in a consistent manner by the correspondence principle, mapping the quantum generators into commuting objects of classical nature preserving their algebra., Comment: 6 pages, latex

A tese introduz uma generalização do Modelo Duplo Quântico (QDM) utilizando uma estrutura algébrica chamada de Hopf group coálgebra. A nova classe de modelos é chamada de Modelo de Duplo Quântico de Grupo (G-QDM). O modelo QDM é um modelo exatamente solúvel realizado sobre uma rede 2D, obtida discretizando uma superfície orientada. O espaço de Hilbert é expresso por um sistema à muitos corpos, com grãus de liberdade associados às arestas da rede. A dinâmica, dada por um Hamiltoniano local, é construída por operadores agindo sobre primeiros vizinhos. Uma quantidade importante do QDM é a degenerescência do estado fundamental (GSD), que depende da topologia da superfície. Em outras palavras, para o QDM a GSD é um invariante quântico topológico. Mostramos uma nova prova do invariante introduzindo um novo formalismo com diagramas. No G-QDM generalizamos a teoria acrescentando elementos de um grupo finito G às arestas da rede. Isso pode ser interpretado como um campo de gauge externo definido sobre a rede. Ao contrario do QDM, o GSD do G-QDM depende de mais informação que só da topologia da superfície. Nsse caso o GSD é sensível ao campo de gauge externo aplicado na rede. Consequentemente o GSD não é mais um invariante topológico da superfície. No presente trabalho conseguimos demonstrar que o GSD é invariante por transformações locais do campo externo e por difeomorfismos da superfície. Calculamos o invariante numérico em exemplos específicos. This thesis introduces a generalization of the Quantum Double Model (QDM) using an algebraic structure called Hopf group coalgebra. We called the new class of models Group Quantum Double Model (G-QDM). The QDM is an exactly solvable model realized on a 2D lattice, made by discretizing an oriented surface. The Hilbert space expresses a quantum many body system, with independent degrees of freedom associated to the links of the lattice. The dynamics, given by a Hamiltonian, is constructed from operators acting on first neighbors. One important quantity of the QDM is the ground state degeneracy (GSD), which depends on the topology of the surface. In other words, for the QDM the GSD is a topological quantum invariant. We show a new proof of the invariant using a new diagrammatic formalism. In the G-QDM we generalize the theory by adding to the links of the lattice non-dynamical elements of a finite group G. This is interpreted as an external gauge field defined on the surface. Contrary to the QDM, the GSD of the G-QDM depends on more data than the topology of the surface. In this case the GSD is sensible to the external gauge field applied to the lattice. Therefore GSD is no longer a topological invariant of the surface. In the present work we achieved to show that the GSD in the G-QDM is invariant under local transformations of the external gauge field and under diffeomorphisms of the surface. We calculate the numerical invariant for specific examples.

O caso finito de teorias topológicas de 1-gauge, quando nenhuma simetria global está presente, é bastante bem compreendido e classificado. Nos últimos anos, as tentativas de generalizar as teorias de 1-gauge através das chamadas teorias de 2-gauge abriram a porta para novos modelos interessantes e novas fases topológicas, as quais não são descritas pelos esquemas de classificação anteriores. Nesta tese, vamos além da construção de 2-gauge, e consideramos uma classe de modelos que vivem em maiores dimensões. Esses modelos estão inseridos em uma estrutura de complexos de cadeia de grupos abelianos, forçando a generalizar o conceito usual de configurações de gauge. A vantagem de tal abordagem é que, a ordem topológica fica manifestamente explcita. Isto é feito em ter- mos de uma cohomologia com coeficientes em um complexo de cadeia finita. Além disso, mostramos que a degenerescência do estado fundamental suporta um conjunto conve- niente de números quânticos que indexam os estados e que, além, foram completamente caracterizados. Consequentemente, nós também mostramos que muitos dos exemplos abelianos de teorias de 1 -gauge 2-gauge são recuperados como casos especiais desta construção. The finite case of 1-gauge topological theories, when no global symmetries are present, is fairly well understood and classified. In recent years, attempts to generalize the latter situation through the so called 2-gauge theories have opened the door to interesting new models and new topological phases, not described by the previous schemes of classifica- tion. In this paper we go even beyond the 2-gauge construction by considering a class of models that live in arbitrary higher dimensions. These models are embedded in a structure of chain complexes of abelian groups, forcing to generalize the usual notion of gauge configurations. The advantage of such an approach is that, the topological order is explicitly manifest when the ground state space of these models is described. This is done in terms of a cohomology with coefficients in a finite chain complex. Furthermore, we show that the ground state degeneracy underpins a convenient set of quantum num- bers that label the states and that have been completely characterized. We also show that abelian examples of 1-gauge 2-gauge theories are recovered as special cases of this construction.

Ordem topológica descreve fases da matéria que não são caracterizadas apenas pelo esquema de quebra de simetria de Landau. Em 2-dimensões ordem topológica é caracterizada, entre outras propriedades, pela existência de uma degenerescência do estado fundamental que é robusta sobre perturbações locais arbitrarias. Com o proposito de entender o que caracteriza e classifica ordem topológica 3-dimensional o presente trabalho apresenta um modelo quântico exatamente solúvel em 3-dimensões que generaliza os modelos em 2-dimensões baseados em teorias de gauge. No modelo proposto o grupo de gauge é substituído por um 2-grupo. A Hamiltonia, que é dada por uma soma de operadores locais, é livre de frustrações. Provamos que a degenerescência do estado fundamental nesse modelo é dado pelo invariante de Yetter da variedade 4-dimensional Sigma × S¹, onde Sigma é a variedade 3-dimensional onde o modelo está definido. Topological order describes phases of matter that cannot be described only by the symmetry breaking theory of Landau. In 2-dimensions topological order is characterized, among other properties, by the presence of a ground state degeneracy that is robust to arbitrary local perturbations. With the purpose of understanding what characterizes and classify 3-dimensional topological order this works presents an exactly soluble quantum model in 3-dimensions that generalize 2-dimensional models constructed using gauge theories. In the model we propose the gauge group is replaced by a 2-group. The Hamiltonian, that is given by a sum of local commuting operators, is frustration free. We prove that the ground state degeneracy of this model is given by the Yetters invariant of the 4-dimensional manifold Sigma × S¹, where Sigma is the 3-dimensional manifold the model is defined.

Made available in DSpace on 2015-02-02T12:39:17Z (GMT). No. of bitstreams: 0 Previous issue date: 2014-09-01Bitstream added on 2015-02-02T13:08:12Z : No. of bitstreams: 1 S0100-83582014000300002.pdf: 461600 bytes, checksum: 3450bbcf252098e36a9d801eb350c7e0 (MD5) Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) O reservatório de Aimorés é formado pelo represamento do Rio Doce e tem duas partes distintas: uma porção do rio que foi alagada e um canal de adução formado pelo desvio do rio em direção à usina geradora de energia elétrica. O levantamento das populações de macrófitas aquáticas presentes e o dimensionamento da área infestada são de suma importância para estabelecimento e avaliação do plano de manejo do reservatório e foi o objetivo deste trabalho. A colonização do reservatório cresceu de 39,2 para 92,5 hectares entre os meses de março e junho de 2009, decrescendo paulatinamente no período posterior, até atingir 39,9 hectares em janeiro de 2010. Esse decréscimo foi atribuído à implementação de plano de manejo, especialmente pela destruição de habitats para crescimento de Eichhornia crassipes. A comunidade de macrófitas aquáticas apresentou 31 espécies, pertencentes a 16 famílias botânicas. As espécies mais frequentes foram E.crassipes, Salvinia molesta, Paspalum repens, Oxycaryum cubense, Urochloa subquadripara e Hymenachne amplexicaulis. A família botânica mais representativa em termos de riqueza em espécies foi Poaceae, com seis representantes, seguida por Cyperaceae, com três. The Aimorés reservoir is formed by the construction of a dam across a river called Rio Doce It is divided into two different portions, one that was flooded, and another consisting of an adduction channel formed by the deviation of the river towards a power plant. It is of paramount importance to estimate the populations of aquatic macrophytes and determine which areas have been infested, in order to employ and assess a management plan for this reservoir, thus, this was the main objective of this work. Colonization rates have increased from 39.2 to 92.5hectares from March to June in 2009, and have gradually decreased on the following season, reaching down to 39.9hectares in January 2010. Such decrease was associated with the implementation of a management plan, especially due to the destruction of habitats that provide the growth of Eichhornia crassipes. In the macrophytes community, 31species belonging to 16botanical families were identified. The most commonly found species were E. crassipes, Salvinia molesta, Paspalum repens, Oxycaryum cubense, Urochloa subquadripara, and Hymenachne amplexicaulis. The most representative botanical family in terms of species richness was Poaceae with six representatives, followed by Cyperaceae with three representatives. ECOSAFE Agricultura e Meio Ambiente SS Ltda Universidade Estadual Paulista Usina de Aimorés - Hidrelétrica Eliezer Batista Universidade Estadual Paulista

Made available in DSpace on 2022-04-29T11:29:23Z (GMT). No. of bitstreams: 0 Previous issue date: 2014-07-01 The Aimorés reservoir is formed by the construction of a dam across a river called Rio Doce It is divided into two different portions, one that was flooded, and another consisting of an adduction channel formed by the deviation of the river towards a power plant. It is of paramount importance to estimate the populations of aquatic macrophytes and determine which areas have been infested, in order to employ and assess a management plan for this reservoir, thus, this was the main objective of this work. Colonization rates have increased from 39.2 to 92.5 hectares from March to June in 2009, and have gradually decreased on the following season, reaching down to 39.9 hectares in January 2010. Such decrease was associated with the implementation of a management plan, especially due to the destruction of habitats that provide the growth of Eichhornia crassipes. In the macrophytes community, 31 species belonging to 16 botanical families were identified. The most commonly found species were E. crassipes, Salvinia molesta, Paspalum repens, Oxycaryum cubense, Urochloa subquadripara, and Hymenachne amplexicaulis. The most representative botanical family in terms of species richness was Poaceae with six representatives, followed by Cyperaceae with three representatives. ECOSAFE – Agricultura e Meio Ambiente SS Ltda Universidade Estadual Paulista Usina de Aimorés - Hidrelétrica Eliezer Batista Universidade Estadual Paulista

Estudamos a Mecânica Quântica não-relativística de sistemas físicos caracterizados pela presença de um grau de liberdade extra, que não comuta com a coordenada temporal. Na linguagem da Geometria Não-Comutativa, tratamos de sistemas descritos por uma álgebra da forma F(Q) X \"A IND.\"teta\"\"(R X \"S POT.1\"), onde F(Q) é a álgebra de funções sobre o espaço de configurações usual \"Q\" e \"A IND.\"teta\"\"(R X \"S POT.1\") é uma deformação de F(R X \"S POT.1\"), conhecida como cilindro não-comutativo. Do ponto de vista geométrico, os geradores do cilindro não-comutativo correspondem à coordenada temporal e a uma coordenada espacial (extra) compacta, em analogia com o caso das teorias do tipo Kaluza-Klein. Mostramos que, como resultado da não-comutatividade entre o tempo e a dimensão extra, a evolução temporal dos sistemas descritos por F(Q) X \"A_t(R X S 1) é discretizada. Ao desenvolver a teoria de espalhamento para sistemas definidos nesse espaço-tempo, verificamos o aparecimento de um efeito inexistente no caso usual: transições entre um estado \"in\" com energia \"E IND.\"alfa\"\" e um estado \"out\" com energia \"E IND.\"beta\"\" (diferente de \"E IND.\"alfa\"\") passam a ser possíveis. Mais especificamente, transições serão possíveis sempre que \"E IND.\"beta\" -\" E IND.\"alfa\" = 2\"pi\"/\"teta\"n, com n \'PERTENCE A\' aos inteiros. As conseqüências desse fato são investigadas de maneira qualitativa, no caso específico de uma barreira uni-dimensional do tipo delta. Essa análise é baseada na aproximação de Born para a matriz de transição We study the nonrelativistic Quantum Mechanics of physical systems characterized F(Q) X \"A IND.\"teta\"\"(R X \"S POT.1\"), by the presence of an extra degree of freedom which does not commute with the time coordinate. In the language of Noncommutative Geometry, we deal with systems described by an algebra of the form F(Q) X \"A IND.\"teta\"\"(R X \"S POT.1\"),, where F(Q) is the algebra of functions over the usual con¯guration space \"Q\" e \"A IND.\"teta\"\"(R X\"S POT.1\") is a deformation of F(R X \"S POT.1\"), known as noncommutative cylinder. From a geometric viewpoint, the generators of the noncommutative cylinder correspond to the time coordinate and to an extra compact spatial coordinate, just like in Kaluza-Klein theories. We show that because of the noncommutativity between the time coordinate and the extra degree of freedom, the time evolution of systems described by F(Q) X \"A_t(R X S 1) is discretized. We develop the scattering theory for such systems, and verify the presence of a new e®ect: transitions from an in state with energy \"E IND.\"alfa\"\" and an out state with energy \"E IND.\"beta\"\" (diferente de \"E IND.\"alfa\"\") are now allowed, in contrast to the usual case. In fact, transitions take place whenever \"E IND.\"beta\" -\" E IND.\"alfa\" = 2\"pi\"/\"teta\"n,, with n \'PERTENCE A\'. The consequences of this result are investigated in the case of a one-dimensional delta barrier. Our analysis is based on the Born approximation for the transition matrix.