A recurring question in science and engineering education is why the students do not link knowledge from theoretical classes to the real world met in laboratory courses. Mathematical models and visualisations are widely used in engineering and engineering education. Very often it is assumed that the students are familiar with the mathematical concepts used. These may be concepts taught in high school or at university level. One problem, though, is that many students have never or seldom applied their mathematical skills in other subjects, and it may be difficult for them to use their skills in a new context. Some concepts also seem to be "too difficult" to understand. One of these mathematical tools is to use Laplace Transforms to solve differential equations, and to use the derived functions to visualise transient responses in electric circuits, or control engineering. In many engineering programs at college level the application of the Laplace Transform is considered too difficult for the students to understand, but is it really, or does it depend on the teaching methods used? When applying mathematical concepts during lab work, and not teaching the mathematics and practical work in different sessions, and also using examples varied in a very systematic way, our research shows that the students approach the problem in a very different way. It shows that by developing tasks consequently according to the Theory of Variation, it is not impossible to apply the Laplace Transform already in the first year of an engineering program. The original aim of this thesis was to show: how students work with lab-tasks, especially concerning the goal to link theory to the real world how it is possible to change the ways students approach the task and thus their learning, by systematic changes in the lab-instructions During the spring 2002 students were video-recorded while working with labs in Electric Circuits. Their activity was analysed. Special focus was on what questions the students raised, and in what ways these questions were answered, and in what ways the answers were used in the further activities. This work informed the model ”learning of a complex concept”, which was used as well to analyse what students do during lab-work, and what teachers intend their students to learn. The model made it possible to see what changes in the lab-instructions that would facilitate students learning of the whole, to link theoretical models to the real world, through the labactivities. The aim of the thesis has thus become to develop a model: The learning of a complex concept show how this model can be used as well for analysis of the intended object of learning as students activities during lab-work, and thus the lived object of learning use the model in analysis of what changes in instruction that are critical for student learning. The model was used to change the instructions. The teacher interventions were included into the instructions in a systematic way, according to as well what questions that were raised by the students, as what questions that were not noticed, but expected by the teachers, as a means to form relations between theoretical aspects and measurement results. Also, problem solving sessions have been integrated into the lab sessions. Video recordings were also conducted during the spring 2003, when the new instructions were used. The students' activities were again analysed. A special focus of the thesis concerns the differences between the results from 2002 and 2003. The results are presented in four sections: Analysis of the students' questions and the teachers' answers during the lab-course 2002 Analysis of the links students need to make, the critical links for learning Analysis of the task structure before and after changes Analysis of the students' activities during the new course The thesis ends with a discussion of the conclusions which may be drawn about the possibilities to model and develop teaching sequences through research, especially concerning the aim to link theoretical models to the real world. / En stående fråga som lärare i naturvetenskapliga och tekniska utbildningar ställer är varför elever och studenter inte kopplar samman kunskaper från teoretiska kursmoment med den verklighet som möts vid laborationerna. Ett vanligt syfte med laborationer är att åstadkomma länkar mellan teori och verklighet, men dessa uteblir ofta. Många gånger används avancerade matematiska modeller och grafiska representationer, vilka studenterna lärt sig i tidigare kurser, men de har sällan eller aldrig tillämpat dessa kunskaper i andra ämnen. En av dessa matematiska hjälpmedel är Laplacetransformen, som främst används för att lösa differentialekvationer, och åskådliggöra transienta förlopp i ellära eller reglerteknik. På många universitet anses Laplacetransformen numera för svår för studenterna på kortare ingenjörsutbildningar, och kurser eller kursmoment som kräver denna har strukits ut utbildningsplanerna. Men, är det för svårt, eller beror det bara på hur man presenterar Laplacetransformen? Genom att låta studenterna arbeta parallellt med matematiken och de laborativa momenten, under kombinerade lab-lektionspass, och inte vid separata lektioner och laborationer, samt genom att variera övningsexemplen på ett mycket systematiskt sätt, enligt variationsteorin, visar vår forskning att studenterna arbetar med uppgifterna på ett helt annat sätt än tidigare. Det visar sig inte längre vara omöjligt att tillämpa Laplacetransformen redan under första året på civilingenjörsutbildning inom elektroteknik. Ursprungliga syftet med avhandlingen var att visa hur studenter arbetar med laborationsuppgifter, speciellt i relation till målet att länka samman teori och verklighet hur man kan förändra studenternas aktivitet, och därmed studenternas lärande, genom att förändra laborationsinstruktionen på ett systematiskt sätt. Under våren 2002 videofilmades studenter som utförde laborationer i en kurs i elkretsteori. Deras aktivitet analyserades. Speciellt studerades vilka frågor studenterna ställde till lärarna, på vilket sätt dessa frågor besvarades, och på vilket sätt svaren användes i den fortsatta aktiviteten. Detta ledde fram till en modell för lärande av sammansatta begrepp, som kunde användas både för att analysera vad studenterna gör och vad lärarna förväntar sig att studenterna ska lära sig. Med hjälp av modellen blev det då möjligt att se vad som behövde ändra i instruktionerna för att studenterna lättare skulle kunna utföra de aktiviteter som krävs för att länka teori och verklighet. Syftet med avhandlingen är därmed att ta fram en modell för lärande av ett sammansatt begrepp visa hur denna modell kan användas för såväl analys av önskat lärandeobjekt, som av studenternas aktivitet under laborationer, och därmed det upplevda lärandeobjektet använda modellen för att analysera vilka förändringar som är kritiska för  studenters lärande. Modellen användes för att förändra laborationsinstruktionerna. Lärarinterventionerna inkluderades i instruktionerna på ett systematiskt sätt utifrån dels vilka frågor som ställdes av studenterna, dels vilka frågor studenterna inte noterade, men som lärarna velat att studenterna skulle använda för att skapa relationer framför allt mellan teoretiska aspekter och mätresultat. Dessutom integrerades räkneövningar och laborationer. Videoinspelningar utfördes även våren 2003, då de nya instruktionerna användes. Även dessa analyserades med avseende på studenternas aktiviteter. Skillnader mellan resultaten från 2002 och 2003 står i fokus. Avhandlingens resultatdel består av: Analys av studenternas frågor och lärarnas svar under labkursen 2002 Analys av de länkar studenterna behöver skapa för att lära Analys av laborationsinstruktionerna före och efter förändringarna Analys av den laborationsaktivitet som blev resultatet av de nya instruktionerna, och vilket lärande som då blev möjligt Avhandlingen avlutas med en diskussion om de slutsatser som kan dras angående möjligheter att via forskning utveckla modeller av undervisningssekvenser för lärande där målet är att länka samman teori och verklighet

This thesis consists of two parts. In the first chapter, we give some results on modulation spaces. First the relationship between the classical spaces and the modulation spaces is established. It is proved that certain modulation spaces defined on R² lie in the BMO space. Another result is that the Zak transform, a discrete time-frequency transform, maps a modulation space into a higher dimensional modulation space. And by using these results, an uncertainty principle for Gabor frames via modulation spaces is obtained. In the second part, we deal with optimization of an increasing positively homogeneous functions on the unit simplex. The class of increasing positively homogeneous functions is one of the function classes obtained via min-type functions in the context of abstract convexity. The cutting angle method is used for the minimization of this type functions. The most important step of this method is the minimization of a function which is the maximum of a number of min-type functions on the unit simplex. We propose a numerical algorithm for the minimization of such functions on the unit simplex and we mathematically prove that this algorithm finds the exact solution of the minimization problem. Some experiments have been carried out and the results of the experiments have been presented.

The objective of this thesis is to formulate a generic dictionary learning method with the guiding principle that states: Efficient representations lead to efficient estimations. The fundamental idea behind using transforms or dictionaries for signal representation is to exploit the regularity within data samples such that the redundancy of the representation is minimized subject to a level of fidelity. This observation translates to rate-distortion cost in compression literature, where a transform that has the lowest rate-distortion cost provides a more efficient representation than the others. In our work, rather than using as an analysis tool, the rate-distortion cost is utilized to improve the efficiency of transforms. For this, an iterative optimization method is proposed, which seeks an orthonormal transform that reduces the expected value of rate-distortion cost of an ensemble of data. Due to the generic nature of the new optimization method, one can design a set of orthonormal transforms either in the original signal domain or on the top of a transform-domain representation. To test this claim, several image codecs are designed, which use block-, lapped- and wavelet-transform structures. Significant increases in compression performances are observed compared to original methods. An extension of the proposed optimization method for video coding gave us state-of-the-art compression results with separable transforms. Also using the robust statistics, an explanation to the superiority of new design over other learning-based methods such as Karhunen-Loeve transform is provided. Finally, the new optimization method and the minimization of the "oracle" risk of diagonal estimators in signal estimation is shown to be equal. With the design of new diagonal estimators and the risk-minimization-based adaptation, a new image denoising algorithm is proposed. While these diagonal estimators denoise local image patches, by formulation the optimal fusion of overlapping local denoised estimates, the new denoising algorithm is scaled to operate on large images. In our experiments, the state-of-the-art results for transform-domain denoising are achieved.

The class of computational problems I consider in this thesis share the common trait of requiring consideration of pairs (or higher-order tuples) of data points. I focus on the problem of kernel summation operations ubiquitous in many data mining and scientific algorithms. In machine learning, kernel summations appear in popular kernel methods which can model nonlinear structures in data. Kernel methods include many non-parametric methods such as kernel density estimation, kernel regression, Gaussian process regression, kernel PCA, and kernel support vector machines (SVM). In computational physics, kernel summations occur inside the classical N-body problem for simulating positions of a set of celestial bodies or atoms. This thesis attempts to marry, for the first time, the best relevant techniques in parallel computing, where kernel summations are in low dimensions, with the best general-dimension algorithms from the machine learning literature. We provide a unified, efficient parallel kernel summation framework that can utilize: (1) various types of deterministic and probabilistic approximations that may be suitable for both low and high-dimensional problems with a large number of data points; (2) indexing the data using any multi-dimensional binary tree with both distributed memory (MPI) and shared memory (OpenMP/Intel TBB) parallelism; (3) a dynamic load balancing scheme to adjust work imbalances during the computation. I will first summarize my previous research in serial kernel summation algorithms. This work started from Greengard/Rokhlin's earlier work on fast multipole methods for the purpose of approximating potential sums of many particles. The contributions of this part of this thesis include the followings: (1) reinterpretation of Greengard/Rokhlin's work for the computer science community; (2) the extension of the algorithms to use a larger class of approximation strategies, i.e. probabilistic error bounds via Monte Carlo techniques; (3) the multibody series expansion: the generalization of the theory of fast multipole methods to handle interactions of more than two entities; (4) the first O(N) proof of the batch approximate kernel summation using a notion of intrinsic dimensionality. Then I move onto the problem of parallelization of the kernel summations and tackling the scaling of two other kernel methods, Gaussian process regression (kernel matrix inversion) and kernel PCA (kernel matrix eigendecomposition). The artifact of this thesis has contributed to an open-source machine learning package called MLPACK which has been first demonstrated at the NIPS 2008 and subsequently at the NIPS 2011 Big Learning Workshop. Completing a portion of this thesis involved utilization of high performance computing resource at XSEDE (eXtreme Science and Engineering Discovery Environment) and NERSC (National Energy Research Scientific Computing Center).

隨著網際網路的盛行，網路不但改變一般人的資訊收集方式、訊息閱讀方式、交友方式、娛樂方式，也影響企業研究顧客需要、銷售商品、打造品牌、服務客戶的方式。過去依靠讀者閱讀所帶來的發行收入，及廣告收入所創造營收的報紙、雜誌平面媒體，現在卻因為發行收入的減少，及廣告收入的滑落，而面臨了有史以來最嚴峻的挑戰。如果平面媒體因應大勢所趨轉型為數位媒體，應該採取哪種轉型策略模式？ 本研究採文獻分析、觀察研究、專家深度訪談，及個案分析法，針對目前平面媒體轉型為數位媒體的策略模式，及美國Advertising Age與 AD WEEK這兩本行銷傳播專業雜誌，轉型為數位媒體的策略模式研究結論如下： 一、平面媒體轉型為數位媒體的三種轉型策略模式中，目前運用「產品延伸變革型」的最多，運用「市場開發變革型」、「多角整合變革型」的較少。 二、把原先平面的內容，移到數位媒體上的「產品延伸變革型」，是種比較安全，也很容易在激烈媒體競爭中，被各式各樣對手所取代的模式。 三、「市場開發變革型」是以網路閱讀者為主要對象，完全以網路為工具提供的服務，所開發出的模式。這種模式除了服務原有的顧客，也可能創造原來不是顧客的顧客而開創新市場。這種轉型模式雖有風險，美國幾家服務青少年的雜誌媒體經營者在衡量得失後，仍大膽採行這種模式。 四、在數位媒體上整合各種服務，提供讀者一指搞定所有需求的「多角整合變革型」模式，除了提供資訊服務，也整合目標對象的其他需求，一次完整提供。換句話說，過去平面媒體是把資訊印在紙上傳送給讀者，未來應該是透過更有效率、又互動的媒體工具，把讀者所需的各種服務傳送到讀者眼前，幫助讀者在工作上、生活上更成功。這種模式大部分是先建構一個平台，並結合同業、異業夥伴，甚至讓過去只是被動接收訊息的讀者，現在也参與一起創造內容。這種轉型模式由於收入多元化，成功機率也較高。 五、許多平面媒體在面對網路時代的衝擊，在轉型過程中，大多會先採取安全保險的做法，運用「產品延伸變革」轉型策略模式。也有的在觀察一段時間後，慢慢摸索朝「市場開發變革」模式、「多角整合變革」模式發展。但是現階段已有越來越多的平面媒體，在轉型初期就立即採取市場開發變革模式、多角整合變革模式，搶佔市場先機。而許多平面媒體與數位媒體的關係，一開始是平面為主附加數位媒體，接著是虛實共生，部分媒體是從平面換手由數位媒體接續經營。 關鍵字：平面媒體、數位媒體、轉型策略模式 / As use of the Internet has become more popular, it has not only changed the way people gather information, read messages, meet new friends and entertain each other; it has also changed the way companies carry out market researches on their customers, sell products, create brands and service their clients. In the past, newspaper and other print media have relied heavily on the revenues generated by publishing and advertising -. Revenues have now dropped dramatically, and the print media are facing their biggest challenge yet. Therefore the question has become obvious; if the print media are to keep up with the trends to evolve to digital, what strategic solution should they adapt? In finding a solution to this problem, this study uses the technique of case-study analysis of two American marketing and advertising magazines (Advertising Age and AD WEEK) to understand the strategies involved in their decision-making to evolve into the digital media. The findings are listed below: 1.Of the three ways of evolving into a digital medium, the product-extension transformation strategy model is the most commonly used, while market exploration and the diversified-integration transformation strategy models are less commonly used. 2. Shifting content into digital media from print. This product-extension transformation strategy model is a safer way, yet it cannot breach boundaries and can be easily wiped out from the market by a wide variety of competitors. (In the Internet age there are no differences between print and digital media.) 3. Market exploration focuses on Internet readers as their target group. This is purely a solution based on providing services using the Internet as a tool. In this way, besides providing services to customers, it is possible to create a new market for those who are not existing customers. Although risks are involved in this solution, some companies in the US that target teen-agers have gone this way after evaluating their situation. In combining all kinds of services, and offering to help their readers to solve all their need with the click of a mouse, the diversified-integration transformation strategy model not only offers information but also loops in target audiences' other needs, to provide a one-stop-shopping solution. For most of the companies that operate under this concept, they have created a platform and work together with other companies and even their readers could create contents. As their services are charged through different channels, this has a higher rate of success. Faced with the impact of ‘Internet Age’, many print media are taking the safest way to evolve into the digital media and choosing the product-extension transformation strategy model. While some others have decided to gradually ease their way toward a market development-transformation strategy model or a diversified-integration transformation strategy model. But more and more print media have decided to put their efforts into the market-development transformation strategy model and the diversified-integration transformation strategy model in the process of evolving into digital media. This puts them in the right spot in the market and protects them from the fate of elimination. The connections between many print media and digital media have changed from focusing on the print sector accompanied by digital means to both equally important. For some media, they have converted completely to the digital media. Key words: printed media, digital media, transforms strategy model

The capability to detect, track and monitor human activities behind building walls and other non-line-of-sight environments is an important component of security and surveillance operations. Over the years, both ultrawideband and Doppler based radar techniques have been researched and developed for tracking humans behind walls. In particular, Doppler radars capture some interesting features of the human radar returns called microDopplers that arise from the dynamic movements of the different body parts. All the current research efforts have focused on building hardware sensors with very specific capabilities. This dissertation focuses on developing a physics based Doppler radar simulator to generate the dynamic signatures of complex human motions in nonline-of-sight environments. The simulation model incorporates dynamic human motion, electromagnetic scattering mechanisms, channel propagation effects and radar sensor parameters. Detailed, feature-by-feature analyses of the resulting radar signatures are carried out to enhance our fundamental understanding of human sensing using radar. First, a methodology for simulating the radar returns from complex human motions in free space is presented. For this purpose, computer animation data from motion capture technologies are exploited to describe the human movements. Next, a fast, simple, primitive-based electromagnetic model is used to simulate the human body. The microDopplers of several human motions such as walking, running, crawling and jumping are generated by integrating the animation models of humans with the electromagnetic model of the human body. Next, a methodology for generating the microDoppler radar signatures of humans moving behind walls is presented. This involves combining wall propagation functions derived from the finite-difference time-domain (FDTD) simulation with the free space radar simulations of humans. The resulting hybrid simulator of the human and wall is used to investigate the effects of both homogeneous and inhomogeneous walls on human microDopplers. The results are further corroborated by basic point-scatterer analysis of different wall effects. The wall studies are followed by an analysis of the effects of flat grounds on human radar signatures. The ground effect is modeled using the method of images and a ground reflection coefficient. A suitable Doppler radar testbed is developed in the laboratory for simulation validation. Measured data of different human activities are collected in both line-of-sight and through-wall environments and the resulting microDoppler signatures are compared with the simulation results. The human microDopplers are best observed in the joint timefrequency space. Hence, suitable joint time-frequency transforms are investigated for improving the display and the readability of both simulated and measured spectrograms. Finally, two new Doppler radar paradigms are considered. First, a scenario is considered where multiple, spatially distributed Doppler radars are used to measure the microDopplers of a moving human from different viewing angles. The possibility of using these microDoppler data for estimating the positions of different point scatterers on the human body is investigated. Second, a scenario is considered where multiple Doppler radars are collocated in a two-dimensional (2-D) array configuration. The possibility of generating frontal images of human movements using joint Doppler and 2-D spatial beamforming is considered. The performance of this concept is compared with that of conventional 2-D array processing without Doppler processing. / text

Derivative pricing, and in particular the pricing of options, is an important area of current research in financial mathematics. Experts debate on the best method of pricing and the most appropriate model of a price process to use. In this thesis, a ``Switching Black-Scholes'' model of a price process is proposed. This model is based on the standard geometric Brownian motion (or Black-Scholes) model of a price process. However, the drift and volatility parameters are permitted to vary between a finite number of possible values at known times, according to the state of a hidden Markov chain. This type of model has been found to replicate the Black-Scholes implied volatility smiles observed in the market, and produce option prices which are closer to market values than those obtained from the traditional Black-Scholes formula. As the Markov chain incorporates a second source of uncertainty into the Black-Scholes model, the Switching Black-Scholes market is incomplete, and no unique option pricing methodology exists. In this thesis, we apply the methods of mean-variance hedging, Esscher transforms and minimum entropy in order to price options on assets which evolve according to the Switching Black-Scholes model. C programs to compute these prices are given, and some particular numerical examples are examined. Finally, filtering techniques and reference probability methods are applied to find estimates of the model parameters and state of the hidden Markov chain. / Thesis (Ph.D.)--Applied Mathematics, 2003.

[pt] Este trabalho tem como objetivo analisar o problema das perdas por absorção dos dados de reflexão sísmica, bem como testar três métodos disponíveis na literatura para sua correção. Utilizamos a modelagem da absorção apresentada por Romanelli Rosa, com a noção de frequência instantânea, e analisamos os seguintes métodos de correção: a Compensação Q, o método de Varela et al. e o método de Duarte, que é um filtro recursivo. Observamos que o método de Duarte é computacionalmente mais rápido que os demais. Ainda assim, podemos utilizar a Transformada de Fourier para torná-lo mais rápido nos casos em que a recursão é interrompida em uma etapa M, menor que o número de amostras N do dado sísmico e maior que lnN. Por fim, testamos o desempenho dos métodos em uma linha de reflexão sísmica marítima da Bacia de Sergipe-Alagoas, fornecida pela Agência Nacional do Petróleo, Gás Natural e Biocombustíveis (ANP). A linha foi reprocessada, com a correção das perdas por absorção aplicada antes do empilhamento, para cada método estudado. Para comparar os resultados, o dado também foi processado sem correção da absorção. Verificamos que houve um aumento da resolução das camadas geológicas de subsuperfície em todos os métodos testados em comparação com o dado sem correção, porém o método de Duarte mostrou-se mais rápido que os demais. / [en] This work aims at analyzing the problem of losses by absorption in seismic reflection data and test three correction methods available in the literature. We use the modeling of the absorption presented by Romanelli Rosa, with the concept of instantaneous frequency, and analyzed the following correction methods: Q compensation, Varela s method and Duarte s method, which is a recursive filter. We note that Duarte s method is computationally faster than the others. However, we can use the Fourier Transform to make it faster in cases where the recursion is interrupted at a step M, smaller than the number of samples N in the seismic data and greater than ln N. Finally, we test the performance of the methods in a marine seismic line in Sergipe-Alagoas Basin, provided by the Agência Nacional do Petróleo, Gás Natural e Biocombustíveis (ANP). The line was reprocessed, with the correction of the losses by absorption applied before stacking, for each method studied. In order to compare the results, the data was also processed without correction of absorption. We observe an increase in the resolution of the geological subsurface in all methods tested in comparison with the data without correction. We also observe the computational advantage of Duarte s method.

The Fourier transform (spectrum) of a signal is a complex function and is characterized by the magnitude and phase spectra. Phase retrieval is the reconstruction of the phase spectrum from the measurements of the magnitude spectrum. Such problems are encountered in imaging modalities such as X-ray crystallography, frequency-domain optical coherence tomography (FDOCT), quantitative phase microscopy, digital holography, etc., where only the magnitudes of the wavefront are detected by the sensors. The phase retrieval problem is ill-posed in general, since an in nite number of signals can have the same magnitude spectrum. Typical phase retrieval techniques rely on certain prior knowledge about the signal, such as its support or sparsity, to reconstruct the signal. A classical result in phase retrieval is that minimum-phase signals have log-magnitude and phase spectra that satisfy the Hilbert integral equations, thus facilitating exact phase retrieval. In this thesis, we demonstrate that there exist larger classes of signals beyond minimum-phase signals, for which exact phase retrieval is possible. We generalize Hilbert integral equations to 2-D, and also introduce a variant that we call the composite Hilbert transform in the context of 2-D periodic signals. Our first extension pertains to a particular type of parametric modelling of 2-D signals. While 1-D minimum-phase signals have a parametric representation, in terms of poles and zeros, there exists no such 2-D counterpart. We introduce a new class of parametric 2-D signals that possess the exact phase retrieval property, that is, their magnitude spectrum completely characterizes the signal. Starting from the magnitude spectrum, a sequence of non-linear operations lead us to a sum-of-exponentials signal, from which the parameters are computed employing concepts from high-resolution spectral estimation such as the annihilating filter and algebraically coupled matrix-pencil methods. We demonstrate that, for this new class of signals, our method outperforms existing techniques even in the presence of noise. Our second extension is to continuous-domain signals that lie in a principal shift-invariant space spanned by a known basis. Such signals are characterized by the basis combining coefficients. These signals need not be minimum-phase, but certain conditions on the coefficients lead to exact phase retrieval of the continuous-domain signal. In particular, we introduce the concept of causal, delta dominant (CDD) sequences, and show that such signals are characterized by their magnitude spectra. This condition pertains to the time/spatial-domain description of the signal, in contrast to the minimum-phase condition, which is described in the spectral domain. We show that there exist CDD sequences that are not minimum-phase, and vice versa. However, finite-length CDD sequences are always minimum-phase. Our method reconstructs the signal from the magnitude spectrum up to ma-chine precision. We thus have a class of continuous-domain signals that are neither causal nor minimum phase, and yet allow for exact phase retrieval. The shift-invariant structure is applicable to modelling signals encountered in imaging modalities such as FDOCT. We next present an application of 2-D phase retrieval to continuous-domain CDD signals in the context of quantiative phase microscopy. We develop sufficient conditions on the interfering reference wave for exact phase retrieval from magnitude measurements. In particular, we show that when the reference wave is a plane wave with magnitude greater that the intensity of the object wave, and when the carrier frequency is larger than the band-width of the object wave, we can reconstruct the object wave exactly. We demonstrate high-resolution reconstruction of our method on USAF target images. Our final and perhaps the most unifying contribution is in developing Hilbert integral equations for 2-D first-quadrant signals and in introducing the notion of generalized minimum-phase signals for both 1-D and 2-D signals. For 2-D continuous-domain, first-quadrant signals, we establish partial Hilbert transform relations between the real and imaginary parts of the spectrum. In the context of 2-D discrete-domain signals, we show that the partial Hilbert transform does not suffice and introduce the notion of composite Hilbert transform and establish the integral equations. We then introduce four classes of signals (combinations of 1-D/2-D and continuous/discrete-domain) that we call generalized minimum-phase signals, which satisfy corresponding Hilbert integral equations between log-magnitude and phase spectra, hence facilitating exact phase retrieval. This class of generalized minimum-phase signals subsumes the well known class of minimum-phase signals. We further show that, akin to minimum-phase signals, these signals also have stable inverses, which are also generalized minimum-phase signals.

Submitted by Cristhiane Guerra (cristhiane.guerra@gmail.com) on 2017-01-26T13:30:08Z No. of bitstreams: 1 arquivototal.pdf: 7840328 bytes, checksum: 74229a382309ea0fcf42de5818cc899a (MD5) / Made available in DSpace on 2017-01-26T13:30:08Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 7840328 bytes, checksum: 74229a382309ea0fcf42de5818cc899a (MD5) Previous issue date: 2016-08-25 / The aim of this work deals with the analysis of the mutual interaction between flow and magnetic fields that develops in a parallel-plate channel as soon as an external magnetic field is applied transversely to the plates. The fluid, electrically conductive, enters the channel under any velocity profile and will have its natural development within the channel changed by the applied magnetic field. With a coupled two-way interaction, the field will also be affected by the flow. The study of these interactions will be made from the two-dimensional version of the steady-state Navier-Stokes equations in the stream function formulation, coupled with the transport equation of the magnetic field. The solution of the governing equations will be obtained by the Generalized Integral Transform Technique (GITT). The results obtained for the velocity field, magnetic field and temperature field, as well as the associated scalar functions, are produced and compared with the literature on the basis of the main parameters of government: Reynolds number (Re), magnetic Reynolds number (Rem) and Hartmann number (Ha). In order to illustrate the consistency of the generalized integral transform technique, convergence analysis, are also performed and presented. / O objetivo do presente trabalho trata da análise da interação mútua escoamento/campo magnético que se desenvolve no interior de um canal de placas planas e paralelas ao se aplicar um campo magnético externo transversal. O fluido, eletricamente condutor, entra no canal sob um perfil qualquer de velocidade, e terá seu desenvolvimento natural afetado pelo campo magnético aplicado. Com uma interação acoplada de duas vias, o campo também será afetado pelo escoamento. O estudo dessas interações será efetuado a partir de uma formulação bidimensional das equações de Navier-Stokes, na formulação em função corrente, para escoamento em regime permanente, acoplada à equação de transporte do campo magnético. A solução das equações governantes será obtida através da Técnica da Transformada Integral Generalizada (GITT). Os resultados obtidos para o campo de velocidade e campo magnético, bem como suas funções escalares associadas, são produzidos e comparados aos da literatura em função dos principais parâmetros de governo: número de Reynolds (Re), número de Reynolds magnético (Rem) e número de Hartmann (Ha). Com o objetivo de ilustrar a consistência da técnica da transformada integral generalizada, análises de convergência são também efetuadas e apresentadas.