976 resultados para quadratic polynomial


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The absorption spectra and upconversion fluorescence spectra of Er3+/-Yb3+-codoped natrium-gallium-germanium-bismuth glasses are measured and investigated. The intense green (533 and 549 nm) and red (672 nm) emission bands were simultaneously observed at room temperature. The quadratic dependence of the green and red emission on excitation power indicates that the two-photon absorption processes occur. The influence of Ga2C3 on upconversion intensity is investigated. The intensity of green emissions increases slowly with increasing Ga2O3 content, while the intensity of red emission increases significantly. The possible upconversion mechanisms for these glasses have also been discussed. The maximum phonon energy of the glasses determined based on the infrared (IR) spectral analysis is as low as 740 cm(-1). The studies indicate that Bi2O3-GeO2-Ga2O3-Na2O glasses may be potential materials for developing upconversion optical devices (c) 2006 Published by Elsevier B.V.

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Up-conversion luminescence characteristics under 975 nm excitation have been investigated with Tb3+/Tm3+/Yb3+ triply doped tellurite glasses. Here, green (547 nm: D-5(4) --> F-7(4)) and red (660 nm: D-5(4) --> F-7(2)) up-conversion (UC) luminescence originating from Tb3+ is observed strongly, because of the quadratic dependences of emission intensities on the excitation power. Especially, the UC luminescence was intensified violently with the energy transfer from the Tm3+ ions involves in the Tb3+ excitation. To the Tb3+/Tm3+/Yb3+ triply doped glass system, a novel up-conversion mechanism is proposed as follows: the energy of (3)G(4) level (Tm3+) was transferred to D-5(4) (Tb3+) and the 477-nm UC luminescence of Tm3+ was nearly quenched. (C) 2006 Elsevier B.V. All rights reserved.

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The Amazon river, located in northernBrazil, discharges between 80,000 and 250,000 m3s-1 of water onto the adjacent shelf, creating a plume of brackish water that extends hundreds of kilometers away from the river mouth. This river also carries a large amount of fine sediments to the ocean where fluid mud has been found in the topset and upper foreset layers of the subaqueous delta formed on the mid-shelf. One of the main goals of this dissertation is to describe how turbulence and suspended sediment concentration vary along the Northern Channel of the Amazon river. Water column measurements were carried out in October 2008 at six anchor stations (P1, P3, P5, P6, P8 e P9) located seaward of the river mouth; P1 and P9 were 125 km apart. Each station was occupied during 13 hours during which current speed and direction were continuously sampled with a 600 kHz Teledyne-RDI ADCP; hourly profiles of temperature, salinity, turbidity and depth were also obtained. Water samples were collected for determination of Suspended Particulate Matter (SPM) concentration and calibration of the turbidity sensor. Current speed reached values above 1.5 m s1 in the along-channel direction (NE-SW); a remarkable ebb-flood asymmetry was observed and flows were strongly ebb-dominated. Throughout the water column, SPM concentration at stations P1 and P3 varied between 100 and 300 mg L1 in association with the presence of freshwater. In contrast, a strong salinity gradient was observed between stations P6 and P9, coinciding with the occurrence of concentrations of SPM above 10 g L-1 (fluid mud). At stations P3, P5 and P6, interface between freshwater from the Amazon river and salt water from the continental shelf, shear stresses wereestimated through four diferents methods: Reynolds, Turbulent Kinetic Energy (TKE), modified TKE and Quadratic Law; in the nearbed region (3 mab) the computed values varied between 0 and 3 Pa. At the three stations (P3, P5 and P6) the lowest and the highest shear stress values were obtained through, respectively, the Reynolds and the TKE methods. Over the whole water column turbulence intensity was estimated through the standard deviation of the turbulent component of the along-channel current velocity (root-mean square of u); from these values, it was estimated the turbulent dissipation of energy (G), whose values at 3 mab varied between zero and 20 s1.

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The problem considered is that of minimizing the drag of a symmetric plate in infinite cavity flow under the constraints of fixed arclength and fixed chord. The flow is assumed to be steady, irrotational, and incompressible. The effects of gravity and viscosity are ignored.

Using complex variables, expressions for the drag, arclength, and chord, are derived in terms of two hodograph variables, Γ (the logarithm of the speed) and β (the flow angle), and two real parameters, a magnification factor and a parameter which determines how much of the plate is a free-streamline.

Two methods are employed for optimization:

(1) The parameter method. Γ and β are expanded in finite orthogonal series of N terms. Optimization is performed with respect to the N coefficients in these series and the magnification and free-streamline parameters. This method is carried out for the case N = 1 and minimum drag profiles and drag coefficients are found for all values of the ratio of arclength to chord.

(2) The variational method. A variational calculus method for minimizing integral functionals of a function and its finite Hilbert transform is introduced, This method is applied to functionals of quadratic form and a necessary condition for the existence of a minimum solution is derived. The variational method is applied to the minimum drag problem and a nonlinear integral equation is derived but not solved.

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The microwave response of the superconducting state in equilibrium and non-equilibrium configurations was examined experimentally and analytically. Thin film superconductors were mostly studied in order to explore spatial effects. The response parameter measured was the surface impedance.

For small microwave intensity the surface impedance at 10 GHz was measured for a variety of samples (mostly Sn) over a wide range of sample thickness and temperature. A detailed analysis based on the BCS theory was developed for calculating the surface impedance for general thickness and other experimental parameters. Experiment and theory agreed with each other to within the experimental accuracy. Thus it was established that the samples, thin films as well as bulk, were well characterised at low microwave powers (near equilibrium).

Thin films were perturbed by a small dc supercurrent and the effect on the superconducting order parameter and the quasiparticle response determined by measuring changes in the surface resistance (still at low microwave intensity and independent of it) due to the induced current. The use of fully superconducting resonators enabled the measurement of very small changes in the surface resistance (< 10-9 Ω/sq.). These experiments yield information regarding the dynamics of the order parameter and quasiparticle systems. For all the films studied the results could be described at temperatures near Tc by the thermodynamic depression of the order parameter due to the static current leading to a quadratic increase of the surface resistance with current.

For the thinnest films the low temperature results were surprising in that the surface resistance decreased with increasing current. An explanation is proposed according to which this decrease occurs due to an additional high frequency quasiparticle current caused by the combined presence of both static and high frequency fields. For frequencies larger than the inverse of the quasiparticle relaxation time this additional current is out of phase (by π) with the microwave electric field and is observed as a decrease of surface resistance. Calculations agree quantitatively with experimental results. This is the first observation and explanation of this non-equilibrium quasiparticle effect.

For thicker films of Sn, the low temperature surface resistance was found to increase with applied static current. It is proposed that due to the spatial non-uniformity of the induced current distribution across the thicker films, the above purely temporal analysis of the local quasiparticle response needs to be generalised to include space and time non-equilibrium effects.

The nonlinear interaction of microwaves arid superconducting films was also examined in a third set of experiments. The surface impedance of thin films was measured as a function of the incident microwave magnetic field. The experiments exploit the ability to measure the absorbed microwave power and applied microwave magnetic field absolutely. It was found that the applied surface microwave field could not be raised above a certain threshold level at which the absorption increased abruptly. This critical field level represents a dynamic critical field and was found to be associated with the penetration of the app1ied field into the film at values well below the thermodynamic critical field for the configuration of a field applied to one side of the film. The penetration occurs despite the thermal stability of the film which was unequivocally demonstrated by experiment. A new mechanism for such penetration via the formation of a vortex-antivortex pair is proposed. The experimental results for the thinnest films agreed with the calculated values of this pair generation field. The observations of increased transmission at the critical field level and suppression of the process by a metallic ground plane further support the proposed model.

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Topography of a granite surface has an effect on the vertical positioning of a wafer stage in a lithographic tool, when the wafer stage moves on the granite. The inaccurate measurement of the topography results in a bad leveling and focusing performance. In this paper, an in situ method to measure the topography of a granite surface with high accuracy is present. In this method, a high-order polynomial is set up to express the topography of the granite surface. Two double-frequency laser interferometers are used to measure the tilts of the wafer stage in the X- and Y-directions. From the sampling tilts information, the coefficients of the high-order polynomial can be obtained by a special algorithm. Experiment results shows that the measurement reproducibility of the method is better than 10 nm. (c) 2006 Elsevier GmbH. All rights reserved.

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The centralized paradigm of a single controller and a single plant upon which modern control theory is built is no longer applicable to modern cyber-physical systems of interest, such as the power-grid, software defined networks or automated highways systems, as these are all large-scale and spatially distributed. Both the scale and the distributed nature of these systems has motivated the decentralization of control schemes into local sub-controllers that measure, exchange and act on locally available subsets of the globally available system information. This decentralization of control logic leads to different decision makers acting on asymmetric information sets, introduces the need for coordination between them, and perhaps not surprisingly makes the resulting optimal control problem much harder to solve. In fact, shortly after such questions were posed, it was realized that seemingly simple decentralized optimal control problems are computationally intractable to solve, with the Wistenhausen counterexample being a famous instance of this phenomenon. Spurred on by this perhaps discouraging result, a concerted 40 year effort to identify tractable classes of distributed optimal control problems culminated in the notion of quadratic invariance, which loosely states that if sub-controllers can exchange information with each other at least as quickly as the effect of their control actions propagates through the plant, then the resulting distributed optimal control problem admits a convex formulation.

The identification of quadratic invariance as an appropriate means of "convexifying" distributed optimal control problems led to a renewed enthusiasm in the controller synthesis community, resulting in a rich set of results over the past decade. The contributions of this thesis can be seen as being a part of this broader family of results, with a particular focus on closing the gap between theory and practice by relaxing or removing assumptions made in the traditional distributed optimal control framework. Our contributions are to the foundational theory of distributed optimal control, and fall under three broad categories, namely controller synthesis, architecture design and system identification.

We begin by providing two novel controller synthesis algorithms. The first is a solution to the distributed H-infinity optimal control problem subject to delay constraints, and provides the only known exact characterization of delay-constrained distributed controllers satisfying an H-infinity norm bound. The second is an explicit dynamic programming solution to a two player LQR state-feedback problem with varying delays. Accommodating varying delays represents an important first step in combining distributed optimal control theory with the area of Networked Control Systems that considers lossy channels in the feedback loop. Our next set of results are concerned with controller architecture design. When designing controllers for large-scale systems, the architectural aspects of the controller such as the placement of actuators, sensors, and the communication links between them can no longer be taken as given -- indeed the task of designing this architecture is now as important as the design of the control laws themselves. To address this task, we formulate the Regularization for Design (RFD) framework, which is a unifying computationally tractable approach, based on the model matching framework and atomic norm regularization, for the simultaneous co-design of a structured optimal controller and the architecture needed to implement it. Our final result is a contribution to distributed system identification. Traditional system identification techniques such as subspace identification are not computationally scalable, and destroy rather than leverage any a priori information about the system's interconnection structure. We argue that in the context of system identification, an essential building block of any scalable algorithm is the ability to estimate local dynamics within a large interconnected system. To that end we propose a promising heuristic for identifying the dynamics of a subsystem that is still connected to a large system. We exploit the fact that the transfer function of the local dynamics is low-order, but full-rank, while the transfer function of the global dynamics is high-order, but low-rank, to formulate this separation task as a nuclear norm minimization problem. Finally, we conclude with a brief discussion of future research directions, with a particular emphasis on how to incorporate the results of this thesis, and those of optimal control theory in general, into a broader theory of dynamics, control and optimization in layered architectures.

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The coupled differential recurrence equations for the corrections to the paraxial approximation solutions in transversely nonuniform refractive-index media are established in terms of the perturbation method. All the corrections (including the longitudinal field corrections) to the paraxial approximation solutions are presented in the weak-guidance approximation. As a concrete application, the first-order longitudinal field correction and the second-order transverse field correction to the paraxial approximation of a Gaussian beam propagating in a transversely quadratic refractive index medium are analytically investigated. (C) 1999 Optical Society of America [S0740-3232(99)00310-5].

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[EN] This study analyzes the relationship between board size and economic-financial performance in a sample of European firms that constitute the EUROSTOXX50 Index. Based on previous literature, resource dependency and agency theories, and considering regulation developed by the OECD and European Union on the normative of corporate governance for each country in the sample, the authors propose the hypotheses of both positive linear and quadratic relationships between the researched parameters. Using ROA as a benchmark of financial performance and the number of members of the board as measurement of the board size, two OLS estimations are performed. To confirm the robustness of the results the empirical study is tested with two other similar financial ratios, ROE and Tobin s Q. Due to the absence of significant results, an additional factor, firm size, is employed in order to check if it affects firm performance. Delving further into the nature of this relationship, it is revealed that there exists a strong and negative relation between firm size and financial performance. Consequently, it can be asseverated that the generic recommendation one size fits all cannot be applied in this case; which conforms to the Recommendations of the European Union that dissuade using generic models for all countries.

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O presente trabalho propõe analisar metodologias para o cálculo do gradiente em malhas não-estruturadas do tipo Voronoi que são utilizadas no método de Volumes Finitos. Quatro metodologias para o cálculo do gradiente são testadas e comparadas com soluções analíticas. As técnicas utilizadas são: Método do Balanço de Forças, Método do Mínimo Resíduo Quadrático, Método da Média dos Gradientes Projetos e Método da Média dos Gradientes Projetados Corrigidos. Uma análise por série de Taylor também foi feita, e as equações analíticas comparadas com resultados numéricos. Os testes são realizados em malhas cartesianas e malhas triangulares, que em um trabalho anterior apresentaram alguns resultados inconsistentes. A influência do ponto gerador e do ângulo de rotação é analisada. É verificado que a posição do ponto gerador e a metodologia utilizada em cada malha influencia no cálculo do gradiente. Dependendo da malha e da metodologia utilizada, as equações analíticas indicaram que existem erros associados, que prejudicam o cálculo do gradiente.

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Based on the Collins integral formula, the analytic expressions of propagation of the coherent and the incoherent off-axis Hermite-cosh-Gaussian (HChG) beam combinations with rectangular symmetry passing through a paraxial first-order optical system are derived, and corresponding numerical examples are given and analysed. The resulting beam quality is discussed in terms of power in the bucket (PIB). The study suggests that the resulting beam cannot keep the initial intensity shape during the propagation and the beam quality for coherent mode is not always better than that for incoherent mode. Reviewing the numerical simulations of Gaussian, Hermite-Gaussian (HG) and cosh Gaussian (ChG) beam combinations indicates that the Hermite polynomial exerts a chief influence on the irradiance profile of composite beam and far field power concentration.

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Esta dissertação apresenta um estudo da modelagem de experimentos aplicados a um processo industrial de tratamento térmico. A motivação deste trabalho surgiu diante das dificuldades associadas aos processos de recozimento industrial de aços do tipo baixa liga, na tentativa de encontrar temperaturas nas quais as durezas superficiais dos aços atingissem valores suficientemente baixos, adequados para etapas posteriores de fabricação, em especial a usinagem. Inicialmente forem realizados diversos experimentos com diferentes aços, onde a dureza superficial é obtida em função da temperatura de recozimento e dos teores de carbono e silício das amostras utilizadas. Em seguida propôs-se um modelo quadrático para modelar a dureza superficial como função dessas três variáveis. A estimação de parâmetros do modelo proposto foi realizada com o emprego do algoritmo Simulated Annealing, uma meta-heurística para otimização global que procura imitar o processo de recozimento de um material sólido. Finalmente, usando-se o modelo proposto, foi resolvido o chamado problema inverso, o qual consiste na estimação da temperatura de recozimento em função dos teores de carbono e silício e da dureza desejada.

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Infrared-to-visible upconversion fluorescence of Er(3+)/Yb(3+) co-doped lithium-strontium-lead-bismuth (LSPB) glasses for developing potential upconversion lasers has been studied under 975-nm excitation. Based on the results of energy transfer efficiency and upconversion spectra, the optimal Yb(3+)-Er(3+) concentration ratio is found to be 5:1. Intense green and red emissions centered at 525, 546, and 657 nm, corresponding to the transitions 2H_(11/2)-->4I_(15/2), 4S_(3/2)-->4I_(15/2), and 4F_(9/2)-->4I_(15/2), respectively, were observed. The quadratic dependence of the 525-, 546-, and 657-nm emissions on excitation power indicates that a two-photon absorption process occurs under 975-nm excitation. The high-populated 4I_(11/2) level is supposed to serve as the intermediate state responsible for the upconversion processes. The intense upconversion luminescence of Er(3+)/Yb(3+) co-doped LSPB glasses may be a potentially useful material for developing upconversion optical devices.

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We report on the energy transfer and frequency upconversion spectroscopic properties of Er3+-doped and Er3+/Yb3+-codoped TeO2-ZnO-Na2O-PbCl2 halide modified tellurite glasses upon excitation with 808 and 978 nm laser diode. Three intense emissions centered at around 529, 546 and 657 nm, alongwith a very weak blue emission at 4 10 nm have clearly been observed for the Er3+/Yb3+-codoped halide modified tellurite glasses upon excitation at 978 nm and the involved mechanisms are explained. The quadratic dependence of fluorescence on excitation laser power confirms the fact that the two-photon contribute to the infrared to green-red upconversion emissions. And the blue upconversion at 410 nm involved a sequential three-photon absorption process. (c) 2005 Elsevier Ltd. All rights reserved.

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This paper reports on the successful preparation and a detailed study on the up-conversion properties of Er3+ -doped TeO2-ZnO-PbCl2 oxylialide tellurite glasses. Three intense emissions centered at around 527, 549 and 666 nm have been clearly observed under 977 nm excitation and the involved mechanisms have been explained. The green emissions centered at 527 and 549 nin are due to the H-2(11/2 ->) I-4(15/2) and S-4(3/2) -> I-4(15/2) transitions, and the red up-conversion emission centered at 666 nm is associated with the F-4(9/2) -> I-4(15/2) transitions of Er3+ ions, respectively. The quadratic dependence of fluorescence on excitation laser power confirm that two-photons contribute to up-conversion of the green-red emissions. (c) 2005 Elsevier B.V. All rights reserved.