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).

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.

Aplicação de um modelo de programação linear inteira mista (PLIM) na expansão da rede de distribuição de energia elétrica em Angola

Em Angola, apenas cerca de 30% da população tem acesso à energia elétrica, nível que decresce para valores inferiores a 10% em zonas rurais mais remotas. Este problema é agravado pelo facto de, na maioria dos casos, as infraestruturas existentes se encontrarem danificadas ou não acompanharem o desenvolvimento da região. Em particular na capital angolana, Luanda que, sendo a menor província de Angola, é a que regista atualmente a maior densidade populacional. Com uma população de cerca de 5 milhões de habitantes, não só há frequentemente problemas relacionados com a falha do fornecimento de energia elétrica como há ainda uma percentagem considerável de municípios onde a rede elétrica ainda nem sequer chegou. O governo de Angola, no seu esforço de crescimento e aproveitamento das suas enormes potencialidades, definiu o setor energético como um dos fatores críticos para o desenvolvimento sustentável do país, tendo assumido que este é um dos eixos prioritários até 2016. Existem objetivos claros quanto à reabilitação e expansão das infraestruturas do setor elétrico, aumentando a capacidade instalada do país e criando uma rede nacional adequada, com o intuito não só de melhorar a qualidade e fiabilidade da rede já existente como de a aumentar. Este trabalho de dissertação consistiu no levantamento de dados reais relativamente à rede de distribuição de energia elétrica de Luanda, na análise e planeamento do que é mais premente fazer relativamente à sua expansão, na escolha dos locais onde é viável localizar novas subestações, na modelação adequada do problema real e na proposta de uma solução ótima para a expansão da rede existente. Depois de analisados diferentes modelos matemáticos aplicados ao problema de expansão de redes de distribuição de energia elétrica encontrados na literatura, optou-se por um modelo de programação linear inteira mista (PLIM) que se mostrou adequado. Desenvolvido o modelo do problema, o mesmo foi resolvido por recurso a software de otimização Analytic Solver e CPLEX. Como forma de validação dos resultados obtidos, foi implementada a solução de rede no simulador PowerWorld 8.0 OPF, software este que permite a simulação da operação do sistema de trânsito de potências.

Dimensão do sector público e crescimento económico: uma relação não linear na União Europeia dos 15?

Os Estados-Membros da União Europeia têm tido a preocupação de reduzirem a dimensão da Administração Pública na economia, a par de a tornar muito mais eficiente de forma a promover o crescimento económico. Neste artigo analisam-se as relações entre a despesa pública e o crescimento económico em 14 Estados-Membros da União Europeia dos 15, com o objectivo de determinar a dimensão óptima das Administrações Públicas, tendo por base teórica a Curva de Armey. Os resultados, para o período 1965-2007, sugerem uma dimensão do sector público maximizadora do crescimento económico de 47,37% e 22,17% do PIB, quando avaliada pelas despesas públicas totais e o consumo público, respectivamente.

Distributed Linear Precoding and User Selection in Coordinated Multicell Systems

In this manuscript we tackle the problem of semidistributed user selection with distributed linear precoding for sum rate maximization in multiuser multicell systems. A set of adjacent base stations (BS) form a cluster in order to perform coordinated transmission to cell-edge users, and coordination is carried out through a central processing unit (CU). However, the message exchange between BSs and the CU is limited to scheduling control signaling and no user data or channel state information (CSI) exchange is allowed. In the considered multicell coordinated approach, each BS has its own set of cell-edge users and transmits only to one intended user while interference to non-intended users at other BSs is suppressed by signal steering (precoding). We use two distributed linear precoding schemes, Distributed Zero Forcing (DZF) and Distributed Virtual Signalto-Interference-plus-Noise Ratio (DVSINR). Considering multiple users per cell and the backhaul limitations, the BSs rely on local CSI to solve the user selection problem. First we investigate how the signal-to-noise-ratio (SNR) regime and the number of antennas at the BSs impact the effective channel gain (the magnitude of the channels after precoding) and its relationship with multiuser diversity. Considering that user selection must be based on the type of implemented precoding, we develop metrics of compatibility (estimations of the effective channel gains) that can be computed from local CSI at each BS and reported to the CU for scheduling decisions. Based on such metrics, we design user selection algorithms that can find a set of users that potentially maximizes the sum rate. Numerical results show the effectiveness of the proposed metrics and algorithms for different configurations of users and antennas at the base stations.

Integer/fractional decomposition of the impulse response of fractional linear systems

The decomposition of a fractional linear system is discussed in this paper. It is shown that it can be decomposed into an integer order part, corresponding to possible existing poles, and a fractional part. The first and second parts are responsible for the short and long memory behaviors of the system, respectively, known as characteristic of fractional systems.

An Extension of Estimation of Domain of Attraction for Fractional Order Linear System Subject to Saturation Control

This paper employs the Lyapunov direct method for the stability analysis of fractional order linear systems subject to input saturation. A new stability condition based on saturation function is adopted for estimating the domain of attraction via ellipsoid approach. To further improve this estimation, the auxiliary feedback is also supported by the concept of stability region. The advantages of the proposed method are twofold: (1) it is straightforward to handle the problem both in analysis and design because of using Lyapunov method, (2) the estimation leads to less conservative results. A numerical example illustrates the feasibility of the proposed method.

Utilidade do Doppler Tecidular na Predição de Eventos Arrítmicos em Adultos com Tetralogia de Fallot Corrigida

INTRODUCTION: Adults with repaired tetralogy of Fallot (TOF) may be at risk for progressive right ventricular (RV) dilatation and dysfunction, which is commonly associated with arrhythmic events. In frequently volume-overloaded patients with congenital heart disease, tissue Doppler imaging (TDI) is particularly useful for assessing RV function. However, it is not known whether RV TDI can predict outcome in this population. OBJECTIVE: To evaluate whether RV TDI parameters are associated with supraventricular arrhythmic events in adults with repaired TOF. METHODS: We studied 40 consecutive patients with repaired TOF (mean age 35 +/- 11 years, 62% male) referred for routine echocardiographic exam between 2007 and 2008. The following echocardiographic measurements were obtained: left ventricular (LV) ejection fraction, LV end-systolic volume, LV end-diastolic volume, RV fractional area change, RV end-systolic area, RV end-diastolic area, left and right atrial volumes, mitral E and A velocities, RV myocardial performance index (Tei index), tricuspid annular plane systolic excursion (TAPSE), myocardial isovolumic acceleration (IVA), pulmonary regurgitation color flow area, TDI basal lateral, septal and RV lateral peak diastolic and systolic annular velocities (E' 1, A' 1, S' 1, E' s, A' s, S' s, E' rv, A' rv, S' rv), strain, strain rate and tissue tracking of the same segments. QRS duration on resting ECG, total duration of Bruce treadmill exercise stress test and presence of exercise-induced arrhythmias were also analyzed. The patients were subsequently divided into two groups: Group 1--12 patients with previous documented supraventricular arrhythmias (atrial tachycardia, fibrillation or flutter) and Group 2 (control group)--28 patients with no previous arrhythmic events. Univariate and multivariate analysis was used to assess the statistical association between the studied parameters and arrhythmic events. RESULTS: Patients with previous events were older (41 +/- 14 vs. 31 +/- 6 years, p = 0.005), had wider QRS (173 +/- 20 vs. 140 +/- 32 ms, p = 0.01) and lower maximum heart rate on treadmill stress testing (69 +/- 35 vs. 92 +/- 9%, p = 0.03). All patients were in NYHA class I or II. Clinical characteristics including age at corrective surgery, previous palliative surgery and residual defects did not differ significantly between the two groups. Left and right cardiac chamber dimensions and ventricular and valvular function as evaluated by conventional Doppler parameters were also not significantly different. Right ventricular strain and strain rate were similar between the groups. However, right ventricular myocardial TDI systolic (Sa: 5.4+2 vs. 8.5 +/- 3, p = 0.004) and diastolic indices and velocities (Ea, Aa, septal E/Ea, and RV free wall tissue tracking) were significantly reduced in patients with arrhythmias compared to the control group. Multivariate linear regression analysis identified RV early diastolic velocity as the sole variable independently associated with arrhythmic history (RV Ea: 4.5 +/- 1 vs. 6.7 +/- 2 cm/s, p = 0.01). A cut-off for RV Ea of < 6.1 cm/s identified patients in the arrhythmic group with 86% sensitivity and 59% specificity (AUC = 0.8). CONCLUSIONS: Our results suggest that TDI may detect RV dysfunction in patients with apparently normal function as assessed by conventional echocardiographic parameters. Reduction in RV early diastolic velocity appears to be an early abnormality and is associated with occurrence of arrhythmic events. TDI may be useful in risk stratification of patients with repaired tetralogy of Fallot.

Formulação fisicamente não - linear da teoria generalizada de vigas

Dissertação para obtenção do grau de Mestre em Engenharia Civil

Optimização estrutural na análise não linear dos modelos de escoras e tirantes

Dissertação para obtenção do Grau de Mestre em Engenharia Civil - Perfil Estruturas

Contributo para a modelização de magnetos supercondutores de fluxo residual: aplicação a um motor linear todo supercondutor

Dissertação para obtenção do Grau de Mestre em Engenharia Electrotécnica e de Computadores

Effects of Acute Autonomic Modulation on Atrial Conduction Delay and Local Electrograms Duration in Paroxysmal Atrial Fibrillation

Slowed atrial conduction may contribute to reentry circuits and vulnerability for atrial fibrillation (AF). The autonomic nervous system (ANS) has modulating effects on electrophysiological properties. However, complex interactions of the ANS with the arrhythmogenic substrate make it difficult to understand the mechanisms underlying induction and maintenance of AF. AIM: To determine the effect of acute ANS modulation in atrial activation times in patients (P) with paroxysmal AF (PAF). METHODS AND RESULTS: 16P (9 men; 59±14years) with PAF, who underwent electrophysiological study before AF ablation, and 15P (7 men; 58±11years) with atrioventricular nodal reentry tachycardia, without documentation or induction of AF (control group). Each group included 7P with arterial hypertension but without underlying structural heart disease. The study was performed while off drugs. Multipolar catheters were placed at the high right atrium (HRA), right atrial appendage (RAA), coronary sinus (CS) and His bundle area (His). At baseline and with HRA pacing (600ms, shortest propagated S2) we measured: i) intra-atrial conduction time (IACT, between RAA and atrial deflection in the distal His), ii) inter-atrial conduction time (interACT, between RAA and distal CS), iii) left atrial activation time (LAAT, between atrial deflection in the distal His and distal CS), iv) bipolar electrogram duration at four atrial sites (RAA, His, proximal and distal CS). In the PAF group, measurements were also determined during handgrip and carotid sinus massage (CSM), and after pharmacological blockade of the ANS (ANSB). AF was induced by HRA programmed stimulation in 56% (self-limited - 6; sustained - 3), 68.8% (self-limited - 6; sustained - 5), and 50% (self-limited - 5; sustained - 3) of the P, in basal, during ANS maneuvers, and after ANSB, respectively (p=NS). IACT, interACT and LAAT significantly lengthened during HRA pacing in both groups (600ms, S2). P with PAF have longer IACT (p<0.05), a higher increase in both IACT, interACT (p<0.01) and electrograms duration (p<0.05) with S2, and more fragmented activity, compared with the control group. Atrial conduction times and electrograms duration were not significantly changed during ANS stimulation. Nevertheless, ANS maneuvers increased heterogeneity of the local electrograms duration. Also, P with sustained AF showed longer interACT and LAAT during CSM. CONCLUSION: Atrial conduction times, electrograms duration and fractionated activity are increased in PAF, suggesting a role for conduction delays in the arrhythmogenic substrate. Acute vagal stimulation is associated with prolonged interACT and LAAT in P with inducible sustained AF and ANS modulation may influence the heterogeneity of atrial electrograms duration.

On the analysis of data emerging in non-linear and complex systemscomparison of two X-Ray prony spectra

New arguments proving that successive (repeated) measurements have a memory and actually remember each other are presented. The recognition of this peculiarity can change essentially the existing paradigm associated with conventional observation in behavior of different complex systems and lead towards the application of an intermediate model (IM). This IM can provide a very accurate fit of the measured data in terms of the Prony's decomposition. This decomposition, in turn, contains a small set of the fitting parameters relatively to the number of initial data points and allows comparing the measured data in cases where the “best fit” model based on some specific physical principles is absent. As an example, we consider two X-ray diffractometers (defined in paper as A- (“cheap”) and B- (“expensive”) that are used after their proper calibration for the measuring of the same substance (corundum a-Al2O3). The amplitude-frequency response (AFR) obtained in the frame of the Prony's decomposition can be used for comparison of the spectra recorded from (A) and (B) - X-ray diffractometers (XRDs) for calibration and other practical purposes. We prove also that the Fourier decomposition can be adapted to “ideal” experiment without memory while the Prony's decomposition corresponds to real measurement and can be fitted in the frame of the IM in this case. New statistical parameters describing the properties of experimental equipment (irrespective to their internal “filling”) are found. The suggested approach is rather general and can be used for calibration and comparison of different complex dynamical systems in practical purposes.

Contributo para o estudo do motor linear síncrono supercondutor

Dissertação para obtenção do Grau de Mestre em Engenharia Electrotécnica e de Computadores

Non-linear time series models

The last three decades have seen quite dramatic changes the way we modeled time dependent data. Linear processes have been in the center stage in modeling time series. As far as the second order properties are concerned, the theory and the methodology are very adequate.However, there are more and more evidences that linear models are not sufficiently flexible and rich enough for modeling purposes and that failure to account for non-linearities can be very misleading and have undesired consequences.