Ordinary mod p representations of the metaplectic cover of p-adic SL_2

We classify the genuine ordinary mod p representations of the metaplectic group SL(2,F)-tilde, where F is a p-adic field, and compute its genuine mod p spherical and Iwahori Hecke algebras. The motivation is an interest in a possible correspondence between genuine mod p representations of SL(2,F)-tilde and mod p representations of the dual group PGL(2,F), so we also compare the two Hecke algebras to the mod p spherical and Iwahori Hecke algebras of PGL(2,F). We show that the genuine mod p spherical Hecke algebra of SL(2,F)-tilde is isomorphic to the mod p spherical Hecke algebra of PGL(2,F), and that one can choose an isomorphism which is compatible with a natural, though partial, correspondence of unramified ordinary representations via the Hecke action on their spherical vectors. We then show that the genuine mod p Iwahori Hecke algebra of SL(2,F)-tilde is a subquotient of the mod p Iwahori Hecke algebra of PGL(2,F), but that the two algebras are not isomorphic. This is in contrast to the situation in characteristic 0, where by work of Savin one can recover the local Shimura correspondence for representations generated by their Iwahori fixed vectors from an isomorphism of Iwahori Hecke algebras.

Geometric integration applied to moving mesh methods and degenerate Lagrangians

Moving mesh methods (also called r-adaptive methods) are space-adaptive strategies used for the numerical simulation of time-dependent partial differential equations. These methods keep the total number of mesh points fixed during the simulation, but redistribute them over time to follow the areas where a higher mesh point density is required. There are a very limited number of moving mesh methods designed for solving field-theoretic partial differential equations, and the numerical analysis of the resulting schemes is challenging. In this thesis we present two ways to construct r-adaptive variational and multisymplectic integrators for (1+1)-dimensional Lagrangian field theories. The first method uses a variational discretization of the physical equations and the mesh equations are then coupled in a way typical of the existing r-adaptive schemes. The second method treats the mesh points as pseudo-particles and incorporates their dynamics directly into the variational principle. A user-specified adaptation strategy is then enforced through Lagrange multipliers as a constraint on the dynamics of both the physical field and the mesh points. We discuss the advantages and limitations of our methods. The proposed methods are readily applicable to (weakly) non-degenerate field theories---numerical results for the Sine-Gordon equation are presented.

In an attempt to extend our approach to degenerate field theories, in the last part of this thesis we construct higher-order variational integrators for a class of degenerate systems described by Lagrangians that are linear in velocities. We analyze the geometry underlying such systems and develop the appropriate theory for variational integration. Our main observation is that the evolution takes place on the primary constraint and the 'Hamiltonian' equations of motion can be formulated as an index 1 differential-algebraic system. We then proceed to construct variational Runge-Kutta methods and analyze their properties. The general properties of Runge-Kutta methods depend on the 'velocity' part of the Lagrangian. If the 'velocity' part is also linear in the position coordinate, then we show that non-partitioned variational Runge-Kutta methods are equivalent to integration of the corresponding first-order Euler-Lagrange equations, which have the form of a Poisson system with a constant structure matrix, and the classical properties of the Runge-Kutta method are retained. If the 'velocity' part is nonlinear in the position coordinate, we observe a reduction of the order of convergence, which is typical of numerical integration of DAEs. We also apply our methods to several models and present the results of our numerical experiments.

Multiscale model reduction methods for deterministic and stochastic partial differential equations

Partial differential equations (PDEs) with multiscale coefficients are very difficult to solve due to the wide range of scales in the solutions. In the thesis, we propose some efficient numerical methods for both deterministic and stochastic PDEs based on the model reduction technique.

For the deterministic PDEs, the main purpose of our method is to derive an effective equation for the multiscale problem. An essential ingredient is to decompose the harmonic coordinate into a smooth part and a highly oscillatory part of which the magnitude is small. Such a decomposition plays a key role in our construction of the effective equation. We show that the solution to the effective equation is smooth, and could be resolved on a regular coarse mesh grid. Furthermore, we provide error analysis and show that the solution to the effective equation plus a correction term is close to the original multiscale solution.

For the stochastic PDEs, we propose the model reduction based data-driven stochastic method and multilevel Monte Carlo method. In the multiquery, setting and on the assumption that the ratio of the smallest scale and largest scale is not too small, we propose the multiscale data-driven stochastic method. We construct a data-driven stochastic basis and solve the coupled deterministic PDEs to obtain the solutions. For the tougher problems, we propose the multiscale multilevel Monte Carlo method. We apply the multilevel scheme to the effective equations and assemble the stiffness matrices efficiently on each coarse mesh grid. In both methods, the $\KL$ expansion plays an important role in extracting the main parts of some stochastic quantities.

For both the deterministic and stochastic PDEs, numerical results are presented to demonstrate the accuracy and robustness of the methods. We also show the computational time cost reduction in the numerical examples.

Influência do sistema de cimentação e do modo de ativação na resistência ao push-out de pinos de fibra de vidro

O objetivo deste estudo foi avaliar a influência do tipo de sistema de cimentação (condicionamento ácido total ou autoadesivo), do modo de ativação (autoativado ou dual), do terço do conduto radicular (cervical, médio ou apical) e da espessura do filme de cimento sobre a resistência de união de pinos de fibra de vidro cimentados em dentes humanos. Quarenta raízes foram incluídas em resina epóxi, submetidas a tratamento endodôntico e obturadas com guta percha e cimento endodôntico sem eugenol. Decorridos sete dias, os condutos foram preparados a uma profundidade de 10mm com brocas padronizadas do sistema dos pinos de fibra (WhitePost DC #2) e aleatoriamente divididos em 4 grupos, conforme o sistema de cimentação e o modo de ativação: (G1) RelyX ARC/Adper Scotchbond Multi-Purpose Plus (condicionamento ácido total), ativação dual, (G2) RelyX ARC/Adper Scotchbond Multi-Purpose Plus, autoativado, (G3) RelyX U100 (autoadesivo), dual e (G4) RelyX U100, autoativado. Após uma semana, cada raiz foi seccionada em máquina de corte, originando 6 fatias de 1 mm de espessura (n=60). Antes do ensaio de push-out cada fatia foi fotografada em ambas as faces, para determinação do raio dos pinos e da espessura do filme de cimento. Após o ensaio mecânico, novas imagens foram capturadas para determinação do modo de falha. Para automatizar a determinação da espessura de cimento, foi desenvolvida uma macro no software KS 400. Os dados foram estatisticamente analisados com ANOVA 3 fatores (resistência de união) e teste de Kruskall-Wallis (espessura do cimento). Comparações múltiplas foram realizadas com o teste Student-Newman-Keuls. Análise de regressão, modelo linear, foi empregada para verificar a correlação entre espessura do cimento e resistência de união. Todos os testes foram aplicados com α = 0,05. O fator cimento exerceu influência significativa para a resistência de união (p = 0,0402): o RelyX U100 apresentou a maior média. A ativação dual elevou os valores de resistência de união em comparação ao modo quimicamente ativado (p < 0,0001). Houve diferenças significantes entre os grupos, sendo G1 (22,4 4,0 MPa) > G3 (20,4 3,6 MPa) > G4 (17,8 5,2 MPa) > G2 (13,5 4,3 MPa). O terço do conduto não exerceu influência significativa sobre a resistência adesiva (p = 0,4749). As espessuras dos filmes de cimento foram estatisticamente diferentes nos diferentes terços: cervical (102 45 m) > médio (75 29 m) > apical (52 28m). Não foi observada forte correlação entre os valores de espessura e os de resistência ao push-out (r = - 0,2016, p = 0,0033). O tipo de falha predominante foi a mista, exceto para o G2, que apresentou 74% das falhas na interface cimento-pino. Dessa forma, o cimento autoadesivo apresentou melhor desempenho que o convencional, e ambos os sistemas duais, sobretudo o RelyX ARC, apresentaram dependência da fotoativação para atingirem maiores valores de resistência de união.

The isolation and partial biochemical analysis of Sindbis virus proteins

Recently, the amino acid sequences have been reported for several proteins, including the envelope glycoproteins of Sindbis virus, which all probably span the plasma membrane with a common topology: a large N-terminal, extracellular portion, a short region buried in the bilayer, and a short C-terminal intracellular segment. The regions of these proteins buried in the bilayer correspond to portions of the protein sequences which contain a stretch of hydrophobic amino acids and which have other common characteristics, as discussed. Reasons are also described for uncertainty, in some proteins more than others, as to the precise location of some parts of the sequence relative to the membrane.

The signal hypothesis for the transmembrane translocation of proteins is briefly described and its general applicability is reviewed. There are many proteins whose translocation is accurately described by this hypothesis, but some proteins are translocated in a different manner.

The transmembraneous glycoproteins E1 and E2 of Sindbis virus, as well as the only other virion protein, the capsid protein, were purified in amounts sufficient for biochemical analysis using sensitive techniques. The amino acid composition of each protein was determined, and extensive N-terminal sequences were obtained for E1 and E2. By these techniques E1 and E2 are indistinguishable from most water soluble proteins, as they do not contain an obvious excess of hydrophobic amino acids in their N-terminal regions or in the intact molecule.

The capsid protein was found to be blocked, and so its N-terminus could not be sequenced by the usual methods. However, with the use of a special labeling technique, it was possible to incorporate tritiated acetate into the N-terminus of the protein with good specificity, which was useful in the purification of peptides from which the first amino acids in the N-terminal sequence could be identified.

Nanomole amounts of PE2, the intracellular precursor of E2, were purified by an immuno-affinity technique, and its N-terminus was analyzed. Together with other work, these results showed that PE2 is not synthesized with an N-terminal extension, and the signal sequence for translocation is probably the N-terminal amino acid sequence of the protein. This N-terminus was found to be 80-90% blocked, also by Nacetylation, and this acetylation did not affect its function as a signal sequence. The putative signal sequence was also found to contain a glycosylated asparagine residue, but the inhibition of this glycosylation did not lead to the cleavage of the sequence.

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.

A influência do corte com diferentes discos e velocidades na integridade dos espécimes e na resistência adesiva de uma cerâmica a um cimento resinoso dual em ensaio de microtração

Esta pesquisa estudou a influência de diferentes velocidades de corte e marcas de discos diamantados nos valores de resistência adesiva, durante a preparação dos espécimes a serem submetidos à microtração, e na integridade das amostras por meio do microscópio eletrônico de varredura (MEV). Vinte blocos da cerâmica à base de dissilicato de lítio (IPS e.max Press) foram unidos com cimento resinoso (Rely X ARC) a blocos de compósito (Z100), construídos incrementalmente. Foram seguidas as recomendações dos fabricantes no tratamento da superfície da cerâmica e aplicação do cimento resinoso. Após 24 horas em água destilada a 37C, os espécimes foram divididos em dois grupos de discos: marcas Buehler e Extec e subdivididos nas velocidades de 200rpm e 400rpm (B2; E2; B4 e E4, respectivamente). Cada espécime foi cortado em dois eixos perpendiculares para obtenção de palitos com área adesiva de 1,0mm. Para cada condição experimental, os palitos foram separados, aleatoriamente, 15 palitos para análise ao MEV e 30 palitos para serem submetidos à força de tração. As médias de resistência adesiva em MPa foram E4=20,312 ; B4= 24,2 11,3 ; B2= 25,2 9,0 e E2= 28,6 10,4. Na análise estatística, observou-se que os valores de resistência adesiva na velocidade de 200rpm foram significativamente maiores comparados a velocidade de 400rpm, independente do disco empregado. Ao MEV, observou-se melhor integridade dos palitos na velocidade de 200rpm com presença de trincas menos extensas nas bordas externas. Constatou-se também que o disco Extec na velocidade de 400rpm apresentou movimentos excêntricos ao corte e obteve-se maior número de perdas prematuras, uma diminuição significante na média da área total de união (p<0,05), além de diferença significativa nos valores de resistência comparada a velocidade de 200rpm. Concluiu-se que a utilização de diferentes velocidades e sua interação com o disco empregado interfere na integridade dos espécimes e nos valores de resistência adesiva, sendo mais acentuada ao se utilizar o disco da marca Extec.

Class two p groups as fixed point free automorphism groups

Suppose that AG is a solvable group with normal subgroup G where (|A|, |G|) = 1. Assume that A is a class two odd p group all of whose irreducible representations are isomorphic to subgroups of extra special p groups. If p^c ≠ r^d + 1 for any c = 1, 2 and any prime r where r^2d+1 divides |G| and if C_G(A) = 1 then the Fitting length of G is bounded by the power of p dividing |A|.

The theorem is proved by applying a fixed point theorem to a reduction of the Fitting series of G. The fixed point theorem is proved by reducing a minimal counter example. IF R is an extra spec r subgroup of G fixed by A₁, a subgroup of A, where A₁ centralizes D(R), then all irreducible characters of A₁R which are nontrivial on Z(R) are computed. All nonlinear characters of a class two p group are computed.

Retenção em canais amplos de núcleos confeccionados por diferentes técnicas com pinos fibro resinosos

O propósito desse trabalho foi verificar a retenção de pinos fibro resinosos cimentados em canais radiculares alargados simulando raízes extensamente comprometidas, fabricados por duas técnicas usadas para diminuir sua desadaptação; comparando-as ao pino fixado somente com cimento. Foram utilizados vinte e quatro raízes de dentes humanos unirradiculares, padronizadas com 15.0 mm de comprimento e 5.0 0.3 mm de diâmetro. As raízes foram incluídas em resina acrílica e divididas em grupos de acordo com a técnica usada: grupo I - pino DC White Post no2 cimentado com sistema adesivo quimicamente ativado e com cimento resinoso dual; grupo II mesmo pino reanatomizado com resina composta para copiar a anatomia do canal radicular, cimentado da mesma forma; e grupo III mesmo pino associado a três pinos acessórios, cimentados do mesmo modo. O canal radicular teve seu diâmetro padronizado pela broca no2 para o pino DC em uma profundidade de 12.0 mm e alargado com uma broca tronco cônica em uma profundidade de 10.0 mm. As oito raízes de cada grupo foram seccionadas transversalmente em três discos de 3.0 mm, a partir da cervical para a execução de um ensaio de extrusão, descartando-se os últimos 2.0 mm, que serviram somente para centralizar o pino. Os valores de retenção foram registrados e tratados estatisticamente por ANOVA e pelo teste SNK (p<0.05). Diferenças significativas foram observadas entre três porções radiculares investigadas em todos os grupos, com os valores de retenção diminuindo da cervical para apical. A retenção na porção apical do grupo com pinos customizado com resina foi estatisticamente maior que na mesma região dos demais grupos. Nenhuma diferença foi encontrada entre o grupo com pinos acessórios e o grupo somente com pino e cimento nessa parte da raiz. Nenhuma diferença foi observada comparando as porções cervical e média dos diferentes grupos. Os tipos de falha após o teste de extrusão foram observados em microscópio eletrônico de varredura com aumento de 200, 600 e 1000 vezes. Elas ocorreram exclusivamente entre o pino e o cimento ou a resina composta. A camada de adesão (camada híbrida) foi mais facilmente observada nas porções cervical e média de todos os grupos. Isso sugere que a retenção nas porções apicais da raiz é predominantemente friccional. Uma vez que pinos acessórios somente alcançam até a porção média do canal radicular, a retenção do pino não é aumentada com essa técnica.

The rate and mechanism of the partial oxidation of acetaldehyde by PPM concentrations of nitrogen dioxide

The thermal reaction between nitrogen dioxide and acetaldehyde in the gas phase was investigated at room temperature and atmospheric pressure. The initial rate of disappearance of nitrogen dioxide was 1.00 ± 0.03 order with respect to nitrogen dioxide and 1.00 ± 0.07 order with respect to acetaldehyde. An initial second order rate constant of (8.596 ± 0.189) x 10^-3 1.mole^-1 sec^-1 was obtained at 22.0 ± 0.1 °C and a total pressure of one atmosphere. The activation energy of the reaction was 12,900 cal/mole in the temperature range between 22°C and 122°C.

The products of the reaction were nitric oxide, carbon dioxide, methyl nitrite, nitromethane and a trace amount of trans-dimeric nitrosomethane. The addition of nitric oxide increased the rate of formation of nitromethane and decreased the rate of formation of methyl nitrite. There were no measurable surface effects due to the addition of glass wool or glass beads to the reactor.

Reactants and products were analyzed by gas chromatography. A mechanism was proposed incorporating the principal features of the reaction.

Elimination of parity doublets in Regge amplitudes

In Part I, the common belief that fermions lying on linear trajectories must have opposite-parity partners is shown to be false. Reggeization of a sequence of positive-parity fermion resonance is carried out in the Van Hove model. As a consequence of the absence of negative-parity states, the partial-wave amplitudes must have a fixed cut in the J plane. This fixed cut, in conjunction with the moving Regge pole, provides a new parametrization for fermion-exchange reactions, which is in qualitative agreement with the data.

In Part II, the spin structure of three particle vertices is determined from the quark model. Using these SU(6)_W vertices in the Van Hove model, we derive a Reggeized scattering amplitude. In addition to Regge poles there are necessarily fixed Regge cuts in both fermion and boson exchange amplitudes. These fixed cuts are similar to those found in Part I, and may be viewed as a consequence of the absence of parity doubled quarks. The magnitudes of the pole and cut terms in an entire class of SU(6) related reactions are determined by their magnitudes in a single reaction. As an example we explain the observed presence or absence of wrong-signature nonsense dips in a class of reactions involving vector meson exchange.