Completion problems for real matrices, II

Thirty years ago, G.N. de Oliveira has proposed the following completion problems: Describe the possible characteristic polynomials of [C-ij], i,j is an element of {1, 2}, where C-1,C-1 and C-2,C-2 are square submatrices, when some of the blocks C-ij are fixed and the others vary. Several of these problems remain unsolved. This paper gives the solution, over the field of real numbers, of Oliveira's problem where the blocks C-1,C-1, C-2,C-2 are fixed and the others vary.

CONTROL OF UNCERTAIN DYNAMIC-SYSTEMS USING STRICTLY POSITIVE REAL SYSTEMS

This paper presents necessary and sufficient conditions to turn a linear time-invariant system with p outputs, m inputs, p greater-than-or-equal-to m and using only inputs and outputs measurements into a Strictly Positive Real (SPR).Two results are presented. In the first, the system compensation is made by two static compensators, one of which forward feeds the outputs and the second back feeds the outputs of the nominal system.The second result presents conditions for the Walcott and Zak variable structure observer-controller synthesis. In this problem, if the nominal system is given by {A,B,C}, then the compensated system is given by {A+GC,B,FC} where F and G are the constant compensation matrices. These results are useful in the control system with uncertainties.

Determinação simultânea de ânions por eletroforese capilar: características e aplicações

Capillary electrophoresis (CE) encompasses a number of characteristics quite suitable for the simultaneous analysis of small ions such as high efficiency and resolving power, directly associated to its impressively high peak capacity, and short analysis time. In appropriate conditions, it is possible to perform the separation of approximately 36 anions in less than 3 minutes. In this work, the mechanisms by which anion analysis is performed was criteriously discussed, and a thorough review of the literature in the past 5 years, focusing mostly in applications of CE to anion analysis in real matrices, was presented.

Determinação simultânea de cátions por eletroforese capilar: fundamentos e aplicações

In this work, the analysis of cations by capillary electrophoresis is reviewed from the theoretical and practical point of view. Separation mechanisms and detection modes are discussed and illustrated. A thorough compilation of the literature over the last ten years, regarding applications of the technique to the analysis of cations in real matrices, is presented.

Optimisation of stir bar sorptive extraction and liquid desorption combined with large volume injection-gas chromatography–quadrupole mass spectrometry for the determination of volatile compounds in wines

Stir bar sorptive extraction and liquid desorption followed by large volume injection coupled to gas chromatography–quadrupole mass spectrometry (SBSE–LD/LVI-GC–qMS) had been applied for the determination of volatiles in wines. The methodology was optimised in terms of extraction time and influence of ethanol in the matrix; LD conditions, and instrumental settings. The optimisation was carried out by using 10 standards representative of the main chemical families of wine, i.e. guaiazulene, E,E-farnesol, β-ionone, geranylacetone, ethyl decanoate, β-citronellol, 2-phenylethanol, linalool, hexyl acetate and hexanol. The methodology shows good linearity over the concentration range tested, with correlation coefficients higher than 0.9821, a good reproducibility was attained (8.9–17.8%), and low detection limits were achieved for nine volatile compounds (0.05–9.09 μg L−1), with the exception of 2-phenylethanol due to low recovery by SBSE. The analytical ability of the SBSE–LD/LVI-GC–qMS methodology was tested in real matrices, such as sparkling and table wines using analytical curves prepared by using the 10 standards where each one was applied to quantify the structurally related compounds. This methodology allowed, in a single run, the quantification of 67 wine volatiles at levels lower than their respective olfactory thresholds. The proposed methodology demonstrated to be easy to work-up, reliable, sensitive and with low sample requirement to monitor the volatile fraction of wine.

Representação de linhas de transmissão, utilizando elementos discretos de circuitos, no domínio das fases

Pós-graduação em Engenharia Elétrica - FEIS

Structure of trajectories of complex-matrix eigenvalues in the Hermitian-non-Hermitian transition

The statistical properties of trajectories of eigenvalues of Gaussian complex matrices whose Hermitian condition is progressively broken are investigated. It is shown how the ordering on the real axis of the real eigenvalues is reflected in the structure of the trajectories and also in the final distribution of the eigenvalues in the complex plane.

A generalization of the optimal diagonal approximate inverse preconditioner

[EN ]The classical optimal (in the Frobenius sense) diagonal preconditioner for large sparse linear systems Ax = b is generalized and improved. The new proposed approximate inverse preconditioner N is based on the minimization of the Frobenius norm of the residual matrix AM − I, where M runs over a certain linear subspace of n × n real matrices, defined by a prescribed sparsity pattern. The number of nonzero entries of the n×n preconditioning matrix N is less than or equal to 2n, and n of them are selected as the optimal positions in each of the n columns of matrix N. All theoretical results are justified in detail…

Sviluppo di biosensori: modifiche di superfici elettrodiche e sistemi di immobilizzazione enzimatica

An amperometric glucose biosensor was developed using an anionic clay matrix (LDH) as enzyme support. The enzyme glucose oxidase (GOx) was immobilized on a layered double hydroxide Ni/Al-NO3 LDH during the electrosynthesis, which was followed by crosslinking with glutaraldehyde (GA) vapours or with GA and bovine serum albumin (GABSA) to avoid the enzyme release. The electrochemical reaction was carried out potentiostatically, at -0.9V vs. SCE, using a rotating disc Pt electrode to assure homogeneity of the electrodeposition suspension, containing GOx, Ni(NO3)2 and Al(NO3)3 in 0.3 M KNO3. The mechanism responsible of the LDH electrodeposition involves the precipitation of the LDH due to the increase of pH at the surface of the electrode, following the cathodic reduction of nitrates. The Pt surface modified with the Ni/Al-NO3 LDH shows a much reduced noise, giving rise to a better signal to noise ratio for the currents relative to H2O2 oxidation, and a linear range for H2O2 determination wider than the one observed for bare Pt electrodes. We pointed out the performances of the biosensor in terms of sensitivity to glucose, calculated from the slope of the linear part of the calibration curve for enzimatically produced H2O2; the sensitivity was dependent on parameters related to the electrodeposition in addition to working conditions. In order to optimise the glucose biosensor performances, with a reduced number of experimental runs, we applied an experimental design. A first screening was performed considering the following variables: deposition time (30 - 120 s), enzyme concentration (0.5 - 3.0 mg/mL), Ni/Al molar ratio (3:1 or 2:1) of the electrodeposition solution at a total metals concentration of 0.03 M and pH of the working buffer solution (5.5-7.0). On the basis of the results from this screening, a full factorial design was carried out, taking into account only enzyme concentration and Ni/Al molar ratio of the electrosynthesis solution. A full factorial design was performed to study linear interactions between factors and their quadratic effects and the optimal setup was evaluated by the isoresponse curves. The significant factors were: enzyme concentration (linear and quadratic terms) and the interaction between enzyme concentration and Ni/Al molar ratio. Since the major obstacle for application of amperometric glucose biosensors is the interference signal resulting from other electro-oxidizable species present in the real matrices, such as ascorbate (AA), the use of different permselective membranes on Pt-LDHGOx modified electrode was discussed with the aim of improving biosensor selectivity and stability. Conventional membranes obtained using Nafion, glutaraldehyde (GA) vapours, GA-BSA were tested together with more innovative materials like palladium hexacyanoferrate (PdHCF) and titania hydrogels. Particular attention has been devoted to hydrogels, because they possess some attractive features, which are generally considered to favour biosensor materials biocompatibility and, consequently, the functional enzyme stability. The Pt-LDH-GOx-PdHCF hydrogel biosensor presented an anti-interferant ability so that to be applied for an accurate glucose analysis in blood. To further improve the biosensor selectivity, protective membranes containing horseradish peroxidase (HRP) were also investigated with the aim of oxidising the interferants before they reach the electrode surface. In such a case glucose determination was also accomplished in real matrices with high AA content. Furthermore, the application of a LDH containing nickel in the oxidised state was performed not only as a support for the enzyme, but also as anti-interferant sistem. The result is very promising and it could be the starting point for further applications in the field of amperometric biosensors; the study could be extended to other oxidase enzymes.

On Nilpotent Subsemigroups in some Matrix Semigroups

2000 Mathematics Subject Classification: 20M20, 20M10.

Single real transformation matrices applied to double three-phase transmission lines

Single real transformation matrices are tested as phase-mode transformation matrices of typical symmetrical systems with double three-phase and two parallel double three-phase transmission lines. These single real transformation matrices are achieved from eigenvector matrices of the mentioned systems and they are based on Clarke's matrix. Using linear combinations of the Clarke's matrix elements, the techniques applied to the single three-phase lines are extended to systems with 6 or 12 phase conductors. For transposed double three-phase lines, phase Z and Y matrices are changed into diagonal matrices in mode domain. Considering non-transposed cases of double three-phase lines, the results are not exact and the error analyses are performed using the exact eigenvalues. In case of two parallel double three-phase lines, the exact single real transformation matrix has not been obtained yet. Searching for this exact matrix, the analyses are based on a single homopolar reference. For all analyses in this paper, the homopolar mode is used as the only homopolar reference for all phase conductors of the studied system. (C) 2008 Elsevier B.V. All rights reserved.

Muestras de los nuevos punzones y matrices para la letra de imprenta executados por orden de S.M. y de su caudal destinado a la dotacion de su Real Biblioteca.

Palau,

Inspeção e diagnóstico de edifícios recentes: estudo de um caso real

Trabalho de Projeto para obtenção do grau de Mestre em Engenharia Civil na Área de Especialização em Edificações

Real-time simulation of multibody systems with applications for working mobile vehicles

This dissertation describes an approach for developing a real-time simulation for working mobile vehicles based on multibody modeling. The use of multibody modeling allows comprehensive description of the constrained motion of the mechanical systems involved and permits real-time solving of the equations of motion. By carefully selecting the multibody formulation method to be used, it is possible to increase the accuracy of the multibody model while at the same time solving equations of motion in real-time. In this study, a multibody procedure based on semi-recursive and augmented Lagrangian methods for real-time dynamic simulation application is studied in detail. In the semirecursive approach, a velocity transformation matrix is introduced to describe the dependent coordinates into relative (joint) coordinates, which reduces the size of the generalized coordinates. The augmented Lagrangian method is based on usage of global coordinates and, in that method, constraints are accounted using an iterative process. A multibody system can be modelled as either rigid or flexible bodies. When using flexible bodies, the system can be described using a floating frame of reference formulation. In this method, the deformation mode needed can be obtained from the finite element model. As the finite element model typically involves large number of degrees of freedom, reduced number of deformation modes can be obtained by employing model order reduction method such as Guyan reduction, Craig-Bampton method and Krylov subspace as shown in this study The constrained motion of the working mobile vehicles is actuated by the force from the hydraulic actuator. In this study, the hydraulic system is modeled using lumped fluid theory, in which the hydraulic circuit is divided into volumes. In this approach, the pressure wave propagation in the hoses and pipes is neglected. The contact modeling is divided into two stages: contact detection and contact response. Contact detection determines when and where the contact occurs, and contact response provides the force acting at the collision point. The friction between tire and ground is modelled using the LuGre friction model, which describes the frictional force between two surfaces. Typically, the equations of motion are solved in the full matrices format, where the sparsity of the matrices is not considered. Increasing the number of bodies and constraint equations leads to the system matrices becoming large and sparse in structure. To increase the computational efficiency, a technique for solution of sparse matrices is proposed in this dissertation and its implementation demonstrated. To assess the computing efficiency, augmented Lagrangian and semi-recursive methods are implemented employing a sparse matrix technique. From the numerical example, the results show that the proposed approach is applicable and produced appropriate results within the real-time period.

Caractère intrinsèque des matrices de Stokes

Il est connu qu’une équation différentielle linéaire, x^(k+1)Y' = A(x)Y, au voisinage d’un point singulier irrégulier non-résonant est uniquement déterminée (à isomorphisme analytique près) par : (1) sa forme normale formelle, (2) sa collection de matrices de Stokes. La définition des matrices de Stokes fait appel à un ordre sur les parties réelles des valeurs propres du système, ordre qui peut être perturbé par une rotation en x. Dans ce mémoire, nous avons établi le caractère intrinsèque de cette relation : nous avons donc établi comment la nouvelle collection de matrices de Stokes obtenue après une rotation en x qui change l’ordre des parties réelles des valeurs propres dépend de la collection initiale. Pour ce faire, nous donnons un chapitre de préliminaires généraux sur la forme normale des équations différentielles ordinaires puis un chapitre sur le phénomène de Stokes pour les équations différentielles linéaires. Le troisième chapitre contient nos résultats.