Spectral and weak polynomial completeness for the porduct of nonsingular matrices

Let F be a field with at least four elements. In this paper, we identify all the pairs (A, B) of n x n nonsingular matrices over F , satisfying the following property: for every monic polynomial f(x) = xn + an-1xn-1 + … +a1x + aο over F, with a root in F and aο = (-1)n det(AB), there are nonsingular matrices X, Y ϵ Fnxn such that X A X-1 Y BY-1 has characteristic polynomial f (x). © 2014 © 2014 Taylor & Francis.

Spectral and weak polynomial completeness for the product of nonsingular matrices

Let F be a field with at least four elements. In this paper, we identify all the pairs (A, B) of n x n nonsingular matrices over F, satisfying the following property: for every monic polynomial f (x) = x(n) + a(n-1)x(n-1) +... + a(1)x + a(0) over F, with a root in F and a(0) = (-1)(n) det(AB), there are nonsingular matrices X, Y is an element of F-nxn such that XAX(-1)Y BY-1 has characteristic polynomial f (x).

Avaliação da exposição de crianças a material particulado em suspensão

Este trabalho teve como principal objectivo caracterizar a exposição de crianças a partículas atmosféricas e aos elementos químicos que as constituem. Pretendeu-se também determinar as fontes e processos que afectam os níveis e composição das partículas em suspensão no ar ambiente e no interior de salas de aula de escolas do 1º ciclo localizadas no centro de Lisboa. Os efeitos das partículas atmosféricas na saúde humana manifestam-se sobretudo ao nível do aparelho respiratório, dependendo da sua composição química, e principalmente da sua dimensão. As partículas inaláveis (PM10) podem depositar-se nas unidades funcionais do sistema respiratório. O PM2,5 podem atingir os alvéolos pulmonares e penetrar no sistema circulatório. As crianças são um dos principais grupos de risco, visto que os seus órgãos e tecidos ainda estão em desenvolvimento, ficando mais susceptíveis à exposição de partículas. A recolha de material particulado foi realizada no ar ambiente recorrendo a um colector PARTISOL e no interior e exterior das escolas usando amostradores GENT. A concentração total de partículas em suspensão foi determinada por gravimetria. A caracterização química da matéria particulada foi efectuada por Análise por Activação com Neutrões (INAA) para a determinação da concentração dos elementos e por Cromatografia Iónica para a quantificação de iões solúveis em água. Em 2007, a concentração média anual de PM2,5 no Centro de Lisboa foi de 18µg/m3. Através da Análise de Componentes Principais e Regressão Multilinear verificou-se que a massa das partículas da fracção fina resulta essencialmente da produção de aerossóis secundários (35%) de uma fonte de cálcio (28%) e da emissão de poluentes por veículos motorizados (23%). No interior das escolas verificou-se que as concentrações de partículas são mais elevadas comparativamente com o ambiente exterior, principalmente no PM2,5-10 (74µg/m3). A ressuspensão de partículas causada pelas actividades desempenhadas no interior das salas e a suspensão de poeiras do solo transportada pelas crianças, são as principais causas apontadas. O Ca é o elemento maioritário no interior das escolas. Os resultados obtidos neste trabalho não excederam os limites estabelecidos pela Legislação Portuguesa.

Unified min-max and interlacing theorems for linear operators

There exist striking analogies in the behaviour of eigenvalues of Hermitian compact operators, singular values of compact operators and invariant factors of homomorphisms of modules over principal ideal domains, namely diagonalization theorems, interlacing inequalities and Courant-Fischer type formulae. Carlson and Sa [D. Carlson and E.M. Sa, Generalized minimax and interlacing inequalities, Linear Multilinear Algebra 15 (1984) pp. 77-103.] introduced an abstract structure, the s-space, where they proved unified versions of these theorems in the finite-dimensional case. We show that this unification can be done using modular lattices with Goldie dimension, which have a natural structure of s-space in the finite-dimensional case, and extend the unification to the countable-dimensional case.

Impact of maritime air mass trajectories on the Western European coast urban aerosol

Lisbon is the largest urban area in the Western European coast. Due to this geographical position the Atlantic Ocean serves as an important source of particles and plays an important role in many atmospheric processes. The main objectives of this study were to (1) perform a chemical characterization of particulate matter (PM2.5) sampled in Lisbon, (2) identify the main sources of particles, (3) determine PM contribution to this urban area, and (4) assess the impact of maritime air mass trajectories on concentration and composition of respirable PM sampled in Lisbon. During 2007, PM2.5 was collected on a daily basis in the center of Lisbon with a Partisol sampler. The exposed Teflon filters were measured by gravimetry and cut into two parts: one for analysis by instrumental neutron activation analysis (INAA) and the other by ion chromatography (IC). Principal component analysis (PCA) and multilinear regression analysis (MLRA) were used to identify possible sources of PM2.5 and determine mass contribution. Five main groups of sources were identified: secondary aerosols, traffic, calcium, soil, and sea. Four-day backtracking trajectories ending in Lisbon at the starting sampling time were calculated using the HYSPLIT model. Results showed that maritime transport scenarios were frequent. These episodes were characterized by a significant decrease of anthropogenic aerosol concentrations and exerted a significant role on air quality in this urban area.

The usefulness of ultrasound in the classification of chronic liver disease

Chronic Liver Disease is a progressive, most of the time asymptomatic, and potentially fatal disease. In this paper, a semi-automatic procedure to stage this disease is proposed based on ultrasound liver images, clinical and laboratorial data. In the core of the algorithm two classifiers are used: a k nearest neighbor and a Support Vector Machine, with different kernels. The classifiers were trained with the proposed multi-modal feature set and the results obtained were compared with the laboratorial and clinical feature set. The results showed that using ultrasound based features, in association with laboratorial and clinical features, improve the classification accuracy. The support vector machine, polynomial kernel, outperformed the others classifiers in every class studied. For the Normal class we achieved 100% accuracy, for the chronic hepatitis with cirrhosis 73.08%, for compensated cirrhosis 59.26% and for decompensated cirrhosis 91.67%.

Efficient Implementation Of A Single-Precision Floating-Point Arithmetic Unit on FPGA

This paper presents a single precision floating point arithmetic unit with support for multiplication, addition, fused multiply-add, reciprocal, square-root and inverse squareroot with high-performance and low resource usage. The design uses a piecewise 2nd order polynomial approximation to implement reciprocal, square-root and inverse square-root. The unit can be configured with any number of operations and is capable to calculate any function with a throughput of one operation per cycle. The floatingpoint multiplier of the unit is also used to implement the polynomial approximation and the fused multiply-add operation. We have compared our implementation with other state-of-the-art proposals, including the Xilinx Core-Gen operators, and conclude that the approach has a high relative performance/area efficiency. © 2014 Technical University of Munich (TUM).

Densities and refractive indices for the ternary mixture methanol/propan-1-Ol/acetonitrile

Refractive indices, n(D), and densities, rho, at 298.15 K were measured for the ternary mixture methanol (MeOH)/propan-1-ol (1-PrOH)/acetonitrile (MeCN) for a total of 22 mole fractions, along with 18 mole fractions of each of the corresponding binary mixtures, methanol/propan-1-ol, propan-1-ol/acetonitrile and methanol/acetonitrile. The variation of excess refractive indices and excess molar volumes with composition was modeled by the Redlich-Kister polynomial function in the case of binary mixtures and by the Cibulka equation for the ternary mixture. A thermodynamic approach to excess refractive indices, recently proposed by other authors, was applied for the first time to ternary liquid mixtures. Structural effects were identified and interpreted both in the binary and ternary systems. A complex relationship between excess refractive indices and excess molar volumes was identified, revealing all four possible sign combinations between these two properties. Structuring of the mixtures was also discussed on the basis of partial molar volumes of the binary and ternary mixtures.

Avaliação do potencial eólico para geração de energia eléctrica

Trabalho Final de Mestrado para a obtenção do grau de Mestre em Engenharia Mecânica /Energia

On the requirements of interpolating polynomials for path motion constraints

In the framework of multibody dynamics, the path motion constraint enforces that a body follows a predefined curve being its rotations with respect to the curve moving frame also prescribed. The kinematic constraint formulation requires the evaluation of the fourth derivative of the curve with respect to its arc length. Regardless of the fact that higher order polynomials lead to unwanted curve oscillations, at least a fifth order polynomials is required to formulate this constraint. From the point of view of geometric control lower order polynomials are preferred. This work shows that for multibody dynamic formulations with dependent coordinates the use of cubic polynomials is possible, being the dynamic response similar to that obtained with higher order polynomials. The stabilization of the equations of motion, always required to control the constraint violations during long analysis periods due to the inherent numerical errors of the integration process, is enough to correct the error introduced by using a lower order polynomial interpolation and thus forfeiting the analytical requirement for higher order polynomials.

Weakly spectrally complete pair of matrices

Let and be matrices over an algebraically closed field. Let be elements of such that and . We give necessary and sufficient condition for the existence of matrices and similar to and, respectively, such that has eigenvalues.