Tesi sul tema "Fourier multiplier"

We extend the theory of singular integral operators and multiplier theorems to the setting of anisotropic Hardy spaces. We first develop the theory of singular integral operators of convolution type in the anisotropic setting and provide a molecular decomposition on Hardy spaces that will help facilitate the study of these operators. We extend two multiplier theorems, the first by Taibleson and Weiss and the second by Baernstein and Sawyer, to the anisotropic setting. Lastly, we characterize the Fourier transforms of Hardy spaces and show that all multipliers are necessarily continuous.

Dans cette thèse, on étudie des inégalités de Carleman L^p pour des problèmes elliptiques et leurs applications à la quantification du prolongement unique par rapport aux perturbations du laplacien. On s'intéresse d'abord aux inégalités de Carleman L^p sur une bande de R^d (dgeq 3), notée mathcal{S}:= (0,1) imes R^{d-1}, pour le Laplacien. Grâce à la transformée de Fourier et une factorisation de l'opérateur conjugué, nous réduisons la démonstration de ces inégalités à la construction d'une paramétrice pour le problème du Laplacien avec des conditions au bord.En utilisant cette paramétrice, on redémontre d'abord des inégalités classiques de Carleman L^2 pour le Laplacien. Ensuite, en appliquant des techniques d'analyse harmonique, notamment le théorème de restriction de Fourier pour établir des résultats de continuité de type L^p-L^q , on obtient des estimations L^p - L^q sur cette paramétrice.On applique ensuite ces méthodes au cas qui nous intéresse, à savoir les inégalités de Carleman L^p pour le Laplacien défini sur Omega , un ouvert borné et régulier de R^d (dgeq 3) , avec un second membre f_2 + f_{2 *'} + div F , f_2 in L^2(Omega), , f_{2 *'} in L^{ frac{2d}{d+2}}(Omega), ,F in L^2(Omega; C^{d}), et une condition de Dirichlet g in H^{frac{1}{2}}(partial Omega) . On montre deux estimations de Carleman globales : une sur la norme H^1 de la solution et une sur sa norme L^{frac{2d}{d-2}} , en termes de normes L^2 à poids de f_2 et F , de la norme L^{frac{2d}{d+2}} de f_{2 *'} et de la norme H^{frac{1}{2}} de g . Cela nous permet, par exemple, d'obtenir une quantification du prolongement unique pour les solutions de Delta u = V u + W_1 cdotabla u + div(W_2 u) en fonction des normes de V dans L^{q_0}(Omega) , de W_1 dans L^{q_1}(Omega) et de W_2 dans L^{q_2}(Omega) pour q_0 in (d/2, infty] et q_1 et q_2 satisfaisant soit q_1, , q_2 > (3d-2)/2 et frac{1}{q_1} + frac{1}{q_2}< 4 (1-frac{1}{d})/(3d-2) , soit q_1, , q_2 > 3d/2 .Dans une troisième partie, on étudie une quantification du prolongement unique des solutions de l'équation Delta u = V u + W_1 cdotabla u + div(W_2 u) mais avec des potentiels d'ordre un plus singuliers dans la classe limite d'intégrabilité. En particulier, on considère le cas W_1 in L^{q_1} et W_2 in L^{q_2} , avec q_1>d et q_2 >d . En utilisant le lemme de T. Wolff sur les mesures euclidiennes et une version raffinée des estimations de Carleman, on obtient des résultats de quantification du prolongement unique pour les solutions u de Delta u = V u + W_1 cdotabla u + div (W_2 u) en fonction des normes des potentiels
In this thesis, we study L^p Carleman inequalities for elliptic problems and their applications to the quantification of unique continuation with respect to perturbations of the Laplacian. We first focus on L^p Carleman inequalities on a strip of R^d (dgeq 3) , denoted mathcal{S}:= (0,1) imes R^{d-1} , for the Laplacian. Using the Fourier transform and a factorisation of the conjugate operator, we reduce the proof of these inequalities to the construction of a parametrix for the Laplacian problem with boundary conditions. Utilising this parametrix, we first reprove classical L^2 Carleman inequalities for the Laplacian. Then, applying harmonic analysis techniques, particularly the Fourier restriction theorem to establish L^p-L^q type continuity results, we obtain L^p - L^q estimates for this parametrix.We then apply these methods to the case of interest, namely L^p Carleman inequalities for the Laplacian defined on Omega , a bounded and regular open subset of R^d (d geq 3) , with a right-hand side f_2 + f_{2 *'} + div F , f_2 in L^2(Omega), , f_{2 *'} in L^{ frac{2d}{d+2}}(Omega), ,F in L^2(Omega; C^{d}) , and a Dirichlet condition g in H^{frac{1}{2}}(partial Omega) . We establish two global Carleman estimates: one on the H^1 norm of the solution and another on its L^{frac{2d}{d-2}} norm, in terms of weighted L^2 norms of f_2 and F , the L^{frac{2d}{d+2}} norm of f_{2 *'} , and the H^{frac{1}{2}} norm of g . This allows us, for example, to obtain a quantification of unique continuation for solutions of Delta u = V u + W_1 cdotabla u + div(W_2 u) in terms of the norms of V in L^{q_0}(Omega) , W_1 in L^{q_1}(Omega) , and W_2 in L^{q_2}(Omega) for q_0 in (d/2, infty] and q_1 and q_2 satisfying either q_1, , q_2 > (3d-2)/2 and frac{1}{q_1} + frac{1}{q_2}< 4(1-frac{1}{d})/(3d-2) , or q_1, , q_2 > 3d/2 .In the third part, we study a quantification of unique continuation for solutions of the equation Delta u = V u + W_1 cdotabla u + div(W_2 u) but with first-order potentials that are more singular in the limit integrability class. In particular, we consider the case where W_1 in L^{q_1} and W_2 in L^{q_2} , with q_1 > d and q_2 > d . Using T. Wolff's lemma on Euclidean measures and a refined version of Carleman estimates, we obtain unique continuation quantification results for solutions u of Delta u = V u + W_1 cdotabla u + div(W_2 u) in terms of the norms of the potentials

We study the Lp − Lq boundedness of both spectral and Fourier multi- pliers on general locally compact separable unimodular groups G. As a consequence of the established Fourier multiplier theorem we also derive a spectral multiplier theorem on general locally compact separable uni- modular groups. We then apply it to obtain embedding theorems as well as time-asymptotics for the Lp − Lq norms of the heat kernels for general positive unbounded invariant operators on G. We illustrate the obtained results for sub-Laplacians on compact Lie groups and on the Heisenberg group, as well as for higher order operators. With minor modificaitons, our proofs of Paley-type inequalities and Lp − Lq bounds of Fourier multipliers can be adapted to the setting of compact homogeneous manifolds.

A problem that is frequently found in large-scale multiple testing is that, in the present stage of experiment (e.g. gene microarray, functional MRI), the signals are so faint that it is impossible to attain a desired level of testing power, and one has to enroll more samples in the follow-up experiment. Suppose we are going to enlarge the sample size by a times in the follow-up experiment, where a > 1 is not necessary an integer. A problem of great interest is, given data based on the current stage of experiment, how to predict the testing power after the sample size is enlarged by a times. We consider test z-scores and model the test statistics in the current experiment as Xj ~ N(μj , 1), 1 ≤ j ≤ n. We propose a Fourier approach to predicting the testing power after n replicates. The approach produces a very accurate prediction for moderately large values of a ( a ≤ 7). Finally, we discuss potential applications of this method on real data with emphasis on gene microarray data.

In the early 1970 fs, R. Coifman and G. Weiss, generalizing the techniques introduced by A. Calderon, developed a method for transferring abstract convolution type operators, defined on general topological groups, and their respective bounds, to the so called gtransferred operators h, which are operators defined on general measure spaces. To be specific, if G is a topological group and R_x is a representation of G on some Banach space B and K is a convolution operator on G given by

Kf= çk(x-y) f(y) dy

with k an L^1 function, the transferred operator T is defined by letting

Tf= çk(x-y) R_xf(y) dy.

Transfer methods deal with the study of the preservation of properties of K that are still valid for T, mostly focusing on the preservation of boundedness on Lebesgue spaces Lp. These methods has been applied to several problems in Mathematical Analysis, and especially to the problem of restrict Fourier multipliers to closed subgroups. These techniques have been extended by other authors as N. Asmar, E. Berkson and A. Gillespie, among many others. It is worth noting however, that these prior developments have always been focused on inequalities for operators on Lebesgue spaces Lp.

In this thesis there are developed several transference techniques for quasi-Banach spaces more general than Lebesgue spaces Lp, as Lorentz spaces Lp, q, Orlicz-Lorentz, Lorentz-Zygmund spaces as well as for weighted Lebesgue spaces Lp(w). The most significant applications are obtained in the field of restriction of Fourier multipliers for rearrangement invariant spaces and weighted Lebesgue spaces Lp(w). Specifically, we get generalizations of the results obtained by K. De Leeuw for Fourier multipliers. There are also developed similar techniques in the context of multilinear operators of convolution type, where the basic example is the bilinear Hilbert transform, as well as for modular inequalities and inequalities arising in extrapolation

The main goal of this research is to design an efficient compression al~ gorithm for fingerprint images. The wavelet transform technique is the principal tool used to reduce interpixel redundancies and to obtain a parsimonious representation for these images. A specific fixed decomposition structure is designed to be used by the wavelet packet in order to save on the computation, transmission, and storage costs. This decomposition structure is based on analysis of information packing performance of several decompositions, two-dimensional power spectral density, effect of each frequency band on the reconstructed image, and the human visual sensitivities. This fixed structure is found to provide the "most" suitable representation for fingerprints, according to the chosen criteria. Different compression techniques are used for different subbands, based on their observed statistics. The decision is based on the effect of each subband on the reconstructed image according to the mean square criteria as well as the sensitivities in human vision. To design an efficient quantization algorithm, a precise model for distribution of the wavelet coefficients is developed. The model is based on the generalized Gaussian distribution. A least squares algorithm on a nonlinear function of the distribution model shape parameter is formulated to estimate the model parameters. A noise shaping bit allocation procedure is then used to assign the bit rate among subbands. To obtain high compression ratios, vector quantization is used. In this work, the lattice vector quantization (LVQ) is chosen because of its superior performance over other types of vector quantizers. The structure of a lattice quantizer is determined by its parameters known as truncation level and scaling factor. In lattice-based compression algorithms reported in the literature the lattice structure is commonly predetermined leading to a nonoptimized quantization approach. In this research, a new technique for determining the lattice parameters is proposed. In the lattice structure design, no assumption about the lattice parameters is made and no training and multi-quantizing is required. The design is based on minimizing the quantization distortion by adapting to the statistical characteristics of the source in each subimage. 11 Abstract Abstract Since LVQ is a multidimensional generalization of uniform quantizers, it produces minimum distortion for inputs with uniform distributions. In order to take advantage of the properties of LVQ and its fast implementation, while considering the i.i.d. nonuniform distribution of wavelet coefficients, the piecewise-uniform pyramid LVQ algorithm is proposed. The proposed algorithm quantizes almost all of source vectors without the need to project these on the lattice outermost shell, while it properly maintains a small codebook size. It also resolves the wedge region problem commonly encountered with sharply distributed random sources. These represent some of the drawbacks of the algorithm proposed by Barlaud [26). The proposed algorithm handles all types of lattices, not only the cubic lattices, as opposed to the algorithms developed by Fischer [29) and Jeong [42). Furthermore, no training and multiquantizing (to determine lattice parameters) is required, as opposed to Powell's algorithm [78). For coefficients with high-frequency content, the positive-negative mean algorithm is proposed to improve the resolution of reconstructed images. For coefficients with low-frequency content, a lossless predictive compression scheme is used to preserve the quality of reconstructed images. A method to reduce bit requirements of necessary side information is also introduced. Lossless entropy coding techniques are subsequently used to remove coding redundancy. The algorithms result in high quality reconstructed images with better compression ratios than other available algorithms. To evaluate the proposed algorithms their objective and subjective performance comparisons with other available techniques are presented. The quality of the reconstructed images is important for a reliable identification. Enhancement and feature extraction on the reconstructed images are also investigated in this research. A structural-based feature extraction algorithm is proposed in which the unique properties of fingerprint textures are used to enhance the images and improve the fidelity of their characteristic features. The ridges are extracted from enhanced grey-level foreground areas based on the local ridge dominant directions. The proposed ridge extraction algorithm, properly preserves the natural shape of grey-level ridges as well as precise locations of the features, as opposed to the ridge extraction algorithm in [81). Furthermore, it is fast and operates only on foreground regions, as opposed to the adaptive floating average thresholding process in [68). Spurious features are subsequently eliminated using the proposed post-processing scheme.

A three-channel Frequency Response Function (FRF) estimator is discussed and statistical relations developed. Methods for estimating the variance of the FRF magnitude and levels of uncorrelated content in the test signals are developed. FRF magnitude variance estimates allow ’confidence bands’ to be placed on FRF magnitude estimates, giving an indication of the variability of the result. Uncorrelated content estimates indicate sources and magnitudes of noise in the measurement system. Both Monte Carlo simulations and experimental work are used to verify the statistical and uncorrelated content estimates. Relations to extend the three-channel FRF estimator to multiple input-multiple output measurements are developed and verified through simulations.
Ph. D.

Of the wide variety of existing optical techniques for non-contact 3D surface mapping, Fourier Transform Interferometry (FTI) is the method that most elegantly combines simplicity with high speed and high resolution. FTI generates continuous-phase surface maps from a projected optical interference pattern, which is generated with a simple double-pinhole source and collected in a single snapshot using conventional digital camera technology. For enhanced stability and reduced system size, the fringe source can be made from a fiber optic coupler. Unfortunately, many applications require mapping of surfaces that contain challenging features not ideally suited for reconstruction using FTI. Rough and discontinuous surfaces, commonly seen in applications requiring imaging of rock particles, present a unique set of obstacles that cannot be overcome using existing FTI techniques. This work is based on an original analysis of the limitations of FTI and the means in which errors are generated by the particular features encountered in the aggregate mapping application. Several innovative solutions have been developed to enable the use of FTI on rough and discontinuous surfaces. Through filter optimization and development of a novel phase unwrapping and referencing technique, the Method of Multiple References (MoMR), this work has enabled surface error correction and simultaneous imaging of multiple particles using FTI. A complete aggregate profilometry system has been constructed, including a MoMR-FTI software package and graphical user interface, to implement these concepts. The system achieves better than 22µm z-axis resolution, and comprehensive testing has proven it capable to handle a wide variety of particle surfaces. A range of additional features have been developed, such as error correction, particle boundary mapping, and automatic data quality windowing, to enhance the usefulness of the system in its intended application. Because of its high accuracy, high speed and ability to map varied particles, the developed system is ideally suited for large-scale aggregate characterization in highway research laboratories. Additionally, the techniques developed in this work are potentially useful in a large number of applications in which surface roughness or discontinuities pose a challenge.
Ph. D.

This work concentrates on the application of diversity techniques and space time block coding for future high speed mobile wireless communications on multicarrier systems. At first, alternative multicarrier kernels robust for high speed doubly-selective fading channel are sought. They include the comparisons of discrete Fourier transform (DFT), fractional Fourier transform (FrFT) and wavelet transform (WT) multicarrier kernels. Different wavelet types, including the raised-cosine spectrum wavelets are implemented, evaluated and compared. From different wavelet families, orthogonal wavelets are isolated from detailed evaluations and comparisons as suitable for multicarrier applications. The three transforms are compared over a doubly-selective channel with the WT significantly outperforming all for high speed conditions up to 300 km/hr. Then, a new wavelet is constructed from an ideal filter approximation using established wavelet design algorithms to match any signal of interest; in this case under bandlimited criteria. The new wavelet showed better performance than other traditional orthogonal wavelets. To achieve MIMO communication, orthogonal space-time block coding, OSTBC, is evaluated next. First, the OSTBC is extended to assess the performance of the scheme over extended receiver diversity order. Again, with the extended diversity conditions, the OSTBC is implemented for a multicarrier system over a doubly-selective fading channel. The MIMO-OFDM systems (implemented using DFT and WT kernels) are evaluated for different operating frequencies, typical of LTE standard, with Doppler effects. It was found that, during high mobile speed, it is better to transmit OFDM signals using lower operating frequencies. The information theory for the 2-transmit antenna OSTBC does not support higher order implementation of multi-antenna systems, which is required for the future generation wireless communications systems. Instead of the OSTBC, the QO-STBC is usually deployed to support the design of higher order multi-antenna systems other than the 2-transmit antenna scheme. The performances of traditional QO-STBC methods are diminished by some off-diagonal (interference) terms such that the resulting system does not attain full diversity. Some methods for eliminating the interference terms have earlier been discussed. This work follows the construction of cyclic matrices with Hadamard matrix to derive QO-STBC codes construction which are N-times better than interference free QO-STBC, where N is the number of transmit antenna branches.

This work concentrates on the application of diversity techniques and space time block coding for future high speed mobile wireless communications on multicarrier systems. At first, alternative multicarrier kernels robust for high speed doubly-selective fading channel are sought. They include the comparisons of discrete Fourier transform (DFT), fractional Fourier transform (FrFT) and wavelet transform (WT) multicarrier kernels. Different wavelet types, including the raised-cosine spectrum wavelets are implemented, evaluated and compared. From different wavelet families, orthogonal wavelets are isolated from detailed evaluations and comparisons as suitable for multicarrier applications. The three transforms are compared over a doubly-selective channel with the WT significantly outperforming all for high speed conditions up to 300 km/hr. Then, a new wavelet is constructed from an ideal filter approximation using established wavelet design algorithms to match any signal of interest; in this case under bandlimited criteria. The new wavelet showed better performance than other traditional orthogonal wavelets. To achieve MIMO communication, orthogonal space-time block coding, OSTBC, is evaluated next. First, the OSTBC is extended to assess the performance of the scheme over extended receiver diversity order. Again, with the extended diversity conditions, the OSTBC is implemented for a multicarrier system over a doubly-selective fading channel. The MIMO-OFDM systems (implemented using DFT and WT kernels) are evaluated for different operating frequencies, typical of LTE standard, with Doppler effects. It was found that, during high mobile speed, it is better to transmit OFDM signals using lower operating frequencies. The information theory for the 2-transmit antenna OSTBC does not support higher order implementation of multi-antenna systems, which is required for the future generation wireless communications systems. Instead of the OSTBC, the QO-STBC is usually deployed to support the design of higher order multi-antenna systems other than the 2-transmit antenna scheme. The performances of traditional QO-STBC methods are diminished by some off-diagonal (interference) terms such that the resulting system does not attain full diversity. Some methods for eliminating the interference terms have earlier been discussed. This work follows the construction of cyclic matrices with Hadamard matrix to derive QO-STBC codes construction which are N-times better than interference free QO-STBC, where N is the number of transmit antenna branches.

Le sujet de cette thèse est le développement de méthodes itératives permettant la résolution degrands systèmes linéaires creux d'équations présentant plusieurs seconds membres simultanément. Ces méthodes seront en particulier utilisées dans le cadre d'une application géophysique : la migration sismique visant à simuler la propagation d'ondes sous la surface de la terre. Le problème prend la forme d'une équation d'Helmholtz dans le domaine fréquentiel en trois dimensions, discrétisée par des différences finies et donnant lieu à un système linéaire creux, complexe, non-symétrique, non-hermitien. De plus, lorsque de grands nombres d'onde sont considérés, cette matrice possède une taille élevée et est indéfinie. Du fait de ces propriétés, nous nous proposons d'étudier des méthodes de Krylov préconditionnées par des techniques hiérarchiques deux niveaux. Un tel pre-conditionnement s'est montré particulièrement efficace en deux dimensions et le but de cette thèse est de relever le défi de l'adapter au cas tridimensionel. Pour ce faire, des méthodes de Krylov sont utilisées à la fois comme lisseur et comme méthode de résolution du problème grossier. Ces derniers choix induisent l'emploi de méthodes de Krylov dites flexibles
The topic of this PhD thesis is the development of iterative methods for the solution of large sparse linear systems of equations with possibly multiple right-hand sides given at once. These methods will be used for a specific application in geophysics - seismic migration - related to the simulation of wave propagation in the subsurface of the Earth. Here the three-dimensional Helmholtz equation written in the frequency domain is considered. The finite difference discretization of the Helmholtz equation with the Perfect Matched Layer formulation produces, when high frequencies are considered, a complex linear system which is large, non-symmetric, non-Hermitian, indefinite and sparse. Thus we propose to study preconditioned flexible Krylov subspace methods, especially minimum residual norm methods, to solve this class of problems. As a preconditioner we consider multi-level techniques and especially focus on a two-level method. This twolevel preconditioner has shown efficient for two-dimensional applications and the purpose of this thesis is to extend this to the challenging three-dimensional case. This leads us to propose and analyze a perturbed two-level preconditioner for a flexible Krylov subspace method, where Krylov methods are used both as smoother and as approximate coarse grid solver

Properties of aggregates are affected by their morphological characteristics, including shape factors, angularity and texture. These morphological characteristics influence the aggregate's mutual interactions and strengths of bonds between the aggregates and the binder. The interactions between aggregates and bond strengths between the aggregate and the binder are vital to rheological properties, related to workability and friction resistance of mixtures. As a consequence, quantification of the aggregate's morphological characteristics is essential for better quality control and performance improvement of aggregates. With advancement of hardware and software, the computation capability has reached the stage to rapidly quantify morphological characteristics at multiple scales using digital imaging techniques. Various computational algorithms have been developed, including Hough transform, Fourier transform, and wavelet analysis, etc. Among the aforementioned computational algorithms, Fourier transform has been implemented in various areas by representing the original image/signal in the spatial domain as a summation of representing functions of varying magnitudes, frequencies and phases in the frequency domain. This dissertation is dedicated to developing the two-dimensional Fourier transform (FFT2) method using the Fourier Transform Interferometry (FTI) system that is capable to quantify aggregate morphological characteristics at different scales. In this dissertation, FFT2 method is adopted to quantify angularity and texture of aggregates based on surface coordinates acquired from digital images in the FTI system. This is followed by a comprehensive review on prevalent aggregate imaging techniques for the quantification of aggregate morphological characteristics, including the second generation of Aggregate Image Measurement System (AIMS II), University of Illinois Aggregate Image Analyzer (UIAIA), the FTI system, etc. Recommendations are made on the usage of aggregate imaging system in the measurements of morphological parameters that are interested. After that, the influence of parent rock, crushing, and abrasion/polishing on aggregate morphological characteristics are evaluated. Atomic-scale roughness is calculated for crystal structures of five representative minerals in four types of minerals (i.e., α-quartz for quartzite/granite/gravel/aplite, dolomite for dolomite, calcite for limestone, haematite and magnetite for iron ore); roughness ranking at atomic-scale is further compared with surface texture ranking at macroscale based on measurement results using the FTI system and AIMS II. Morphological characteristics of aggregates before and after crushing test and micro-deval test are measured to quantitatively evaluate the influences of the crushing process and the abrasion/polishing process on morphological characteristics of aggregates, respectively.
Ph. D.

A new “best match” match model has been developed to account for adduct formation on multiply charged peptides observed in negative ion electrospray mass spectrometry. To obtain a stable adduct, the model necessitates an approximate matching of apparent gas-phase basicity (GBapp) of a given proton bearing site on the peptide with the gas-phase basicity (GB) of the anion attaching at that site. Evidence supporting the model is derived from the fact that singly charged adducts were only observed for lower GB anions: HSO4-, I-, CF3COO-. Ions that have medium GBs (NO3-, Br-, H2PO4-) only form adducts having -2 charge states, whereas Cl- (higher GB) can form adducts having -3 charge states. Hydrogen bonds are the main interactions pertinent to the “Best Match” model, however, ion-ion interactions formed between peptides ([Glu]Fibrinopeptide B, Angiotensin I or [Asn1,Val5]-Angiotensin II) and low GB anions (ClO4- or HSO4-) have been established by CID-MS/MS. Evidence for ion-ion interactions comes especially from product ions formed during the first dissociation step, where, in addition to the expected loss of the anion or neutral acid, other product ions that require covalent bond cleavage (i.e., H2O or NH3 loss) are also observed. In this study, the “Best Match” model is further supported by the decomposition behavior of adducts formed when Na+/H+ exchange has occurred on peptides. Na+/H+ exchanges were found to occur preferentially at higher acidity sites. Without any Na+/H+ exchange, F- and CH3COO- can hardly form observable adducts with [Glu]Fibrinopeptide B. However, after multiple Na+/H+ exchanges, F- and CH3COO- do form stable adducts. This phenomenon can be rationalized by considering that Na+ cations serve to “block” the highly acidic sites, thereby forcing them to remain overall neutral. This leaves the less acidic protons available to match with higher GB anions. According to the "best match" model, high GB anions will match with high GBapp sites on the peptide, whereas low GB anions will match with low GBapp peptide sites. High charge states readily augment GBapp of the peptide (through-space effect). Na+/H+ exchanges substantially decrease GBapp by neutralizing charged sites, while slightly increasing intrinsic GBs by the inductive effect.

The purpose of this study was to explore what contributes to resilience in females diagnosed with Fragile X Syndrome. Fragile X Syndrome can be defined as an inherited (genetic) condition that causes mental impairment, attention deficit and hyperactivity, anxiety and unstable mood, autistic behaviours, hyper-extensible joints, and seizures. I became aware of Fragile X Syndrome during my time as a live-in caretaker to an adolescent female who was diagnosed with Fragile X Syndrome. Because she coped with her disability so resiliently, I was encouraged to explore what contributes to resilience in females diagnosed with Fragile X Syndrome. I followed a qualitative approach, anchored in the interpretivist paradigm. This means that I tried to understand the resilience of females diagnosed with Fragile X Syndrome through the meanings that the participants in my study assigned to them. Furthermore, I worked from a transformative paradigm, which meant that I was interested in changing the traditionally negative ways in which females diagnosed with Fragile X Syndrome are seen. I followed a multiple case study approach, which included four case studies. I conveniently selected the first participant, but realised that convenience sampling was not very credible for a qualitative case study. An Advisory Panel was then used to purposefully recruit three more participants. In order to explore what contributed to their resilience, I made use of interviews, observations, and visual data collection. I also interviewed adults (e.g. parents, teachers and consulting psychologists) who were significantly involved in the lives of my participants. My findings suggest that resilience in females with Fragile X Syndrome is rooted in protective processes within the individual as well as within her family and environment. Because my findings do not point to one specific resource, my study underscores newer understandings of resilience as an Eco systemic transaction. Most of the resilience-promoting resources noted by the participants in my study as contributing to their resilience have been identified as resilience-promoting in previous studies. Although the themes that emerged in my study have been reported in resilience previously, I make a contribution to theory because I link traditional resilience-promoting resources to resilience in females diagnosed with Fragile X Syndrome. Peer support was previously reported as a resilience-promoting resource, but in my study I noticed that the main source of peer support came from peers who were also disabled. Furthermore, my study transforms how we see females diagnosed with Fragile X Syndrome. This transformation encourages communities and families to work together towards resilience in females diagnosed with Fragile X Syndrome.
Ph.D, North-West University, Vaal Triangle Campus, 2011

Cette thèse étudie quelques problèmes d’analyse harmonique sur les groupes quantiques compacts. Elle consiste en trois parties. La première partie présente la théorie Lp élémentaire des transformées de Fourier, les convolutions et les multiplicateurs sur les groupes quantiques compacts, y compris la théorie de Hausdorff-Young et les inégalités de Young.Dans la seconde partie, nous caractérisons les opérateurs de convolution positifs sur un groupe quantique fini qui envoient Lp dans L2, et donnons aussi quelques constructions sur les groupes quantiques compacts infinis. La méthode pour étudier les états non-dégénérés fournit une formule générale pour calculer les états idempotents associés aux images deHopf, qui généralise un travail de Banica, Franz et Skalski. La troisième partie est consacrée à l’étude des ensembles de Sidon, des ensembles _(p) et des notions associées pour les groupes quantiques compacts. Nous établissons différentes caractérisations des ensembles de Sidon, et en particulier nous démontrons que tout ensemble de Sidon est un ensemble de Sidon fort au sens de Picardello. Nous donnons quelques liens entre les ensembles de Sidon, les ensembles _(p) et les lacunarités pour les multiplicateurs de Fourier sur Lp, généralisant un travail de Blendek et Michali˘cek. Nous démontrons aussi l’existence des ensembles de type _(p) pour les systèmes orthogonaux dans les espaces Lp non commutatifs, et déduisons les propriétés correspondantes pour les groupes quantiques compacts. Nous considérons aussi les ensembles de Sidon centraux, et nous prouvons que les groupes quantiques compacts ayant les mêmes règles de fusion et les mêmes fonctions de dimension ont des ensemble de Sidon centraux identiques. Quelques exemples sont aussi étudiés dans cette thèse. Les travaux présentés dans cette thèse se basent sur deux articles de l’auteur. Le premier s’intitule “Lp-improving convolution operators on finite quantum groups” et a été accepté pour publication dans Indiana University Mathematics Journal, et le deuxième est un travail intitulé “Lacunary Fourier series for compact quantum groups” et a été publié en ligne dans Communications in Mathematical Physics
This thesis studies some problems in the theory of harmonic analysis on compact quantum groups. It consists of three parts. The first part presents some elementary Lp theory of Fourier transforms, convolutions and multipliers on compact quantum groups, including the Hausdorff-Young theory and Young’s inequalities. In the second part, we characterize positive convolution operators on a finite quantum group G which are Lp-improving, and also give some constructions on infinite compact quantum groups. The methods for ondegeneratestates yield a general formula for computing idempotent states associated to Hopf images, which generalizes earlier work of Banica, Franz and Skalski. The third part is devoted to the study of Sidon sets, _(p)-sets and some related notions for compact quantum groups. We establish several different characterizations of Sidon sets, and in particular prove that any Sidon set in a discrete group is a strong Sidon set in the sense of Picardello. We give several relations between Sidon sets, _(p)-sets and lacunarities for Lp-Fourier multipliers, generalizing a previous work by Blendek and Michali˘cek. We also prove the existence of _(p)-sets for orthogonal systems in noncommutative Lp-spaces, and deduce the corresponding properties for compact quantum groups. Central Sidon sets are also discussed, and it turns out that the compact quantum groups with the same fusion rules and the same dimension functions have identical central Sidon sets. Several examples are also included. The thesis is principally based on two works by the author, entitled “Lp-improvingconvolution operators on finite quantum groups” and “Lacunary Fourier series for compact quantum groups”, which have been accepted for publication in Indiana University Mathematics Journal and Communications in Mathematical Physics respectively

OBJETIVO: Utilizar a tomografia de coerência óptica (TCO) de domínio Fourier para avaliar as camadas internas da retina de olhos de pacientes com esclerose múltipla (EM) ou neuromielite óptica (NMO), com ou sem história de neurite óptica (NO), e compará-los entre si e com os olhos de controles normais. Investigar a correlação entre os achados da TCO e os achados do campo visual nesse grupo de pacientes. MÉTODOS: Cento e oitenta e dois indivíduos foram estudados incluindo 74 com diagnóstico de EM, 33 com NMO, 30 com mielite transversa aguda longitudinal extensa (MTALE) e 45 controles normais. Todos os indivíduos foram submetidos a exame oftalmológico completo incluindo a perimetria computadorizada e a TCO de domínio Fourier. Os olhos estudados foram divididos em 5 grupos: olhos de pacientes com EM e episódio prévio de neurite óptica (EM-NO) olhos de pacientes com EM sem episódio prévio de neurite óptica (EM-sNO), olhos de pacientes com NMO e história de neurite olhos de pacientes com MTALE e olhos de controles normais. Foram analisadas as seguintes medidas obtidas pela TCO: a espessura da camada de fibras nervosas retiniana (CFNR) peri-papilar, a espessura macular total (EMT) avaliada em 8 setores de acordo com o mapa do \"Early Treatment Diabetes Retinopathy Treatment Trial\" e medidas segmentadas da CFNR na mácula, da camada de células ganglionares (CCG), camada nuclear interna (CNI). Os resultados da perimetria foram avaliados levando em consideração o \" mean deviation ( desvio médio)\" (MD) e os valores de diferentes regiões do campo visual divididos de acordo com a sua correspondência no disco óptico seguindo o mapa de Garway-Heath. A comparação dos achados entre os diferentes grupos foi feita usando modelos \"generalized estimated equations\" (GEE) de tal forma a fazer a compensação pela interdependência dos dois olhos de um mesmo indivíduo. Foram também calculadas e comparadas as áreas sob as áreas sob as curvas ROC (\"Receiver operating characteristics\") nos diferentes grupos. Foram calculadas as correlações de Spearman ou Pearson dependendo da distribuição dos valores. RESULTADOS: Não houve diferença significativa em relação à idade média e à distribuição dos pacientes quanto ao sexo nos 5 grupos estudados. Quando comparados ao grupo controle, os 4 grupos de olhos dos doentes apresentaram a espessura da CFNR peri-papilar e a CFNR macular significativamente menor que as medidas dos controles normais. Em relação à CCG e à EMT, os grupos NMO, EM-NO e EM-sNO apresentaram espessura estatisticamente menor que os controles enquanto que no grupo MTALE esta diferença não foi evidenciada. Quando a CNI foi estudada não houve diferença entre os controles e os 2 grupos com EM, enquanto que os grupos NMO e MTALE apresentaram espessura estatisticamente maior que os controles. Os dois grupos com história prévia de NO (NMO e EM-NO) apresentaram a espessura da CFNR peri-papilar e macular, da CCG e da EMT menores do que seus grupos correspondentes sem história prévia de NO (respectivamente MTALE e EM-sNO). Quando os grupos NMO e EM-NO foram comparados entre si não houve diferença de espessura em nenhuma camada exceto na CNI onde o grupo NMO foi estatisticamente mais espesso. Houve correlação entre os achados do TCO e aqueles da campimetria para ambas as doenças e esta correlação foi maior na NMO do que na EM, em especial quando a EMT foi o parâmetro do TCO utilizado na comparação. CONCLUSÕES: A TCO é capaz de demonstrar a perda neural nos doentes com EM ou NMO e evidencia perda neural subclínica tanto em olhos com MTALE como em pacientes com EM, sem história de NO prévia e demonstra aumento da CNI nos olhos de pacientes com NMO ou MTALE. Além do já conhecido mecanismo de lesão do nervo óptico por desmielinização o fato da CNI estar alterada no espectro NMO mostra que outros processos podem estar envolvidos na patogênese destas doenças e que esta camada pode ajudar na diferenciação entre as duas doenças, EM e NMO
PURPOSE: To evaluate, by the using of Fourier domain optical coherence tomography (OCT) the retinal inner layers of eyes with or without previous history of optic neuritis (ON) in multiple sclerosis (MS) or neuromyelitis optica (NMO) patients and compare them with normal controls. To investigate the correlation between the OCT and the visual field fidings. METHODS: One hundred two subjects were studied, 74 diagnosed as MS, 33 as NMO, 30 as longitudinally extensive transverse myelitis (LETM) and 45 nolmal controls. All patients were submitted to a complete ophthalmic evaluation including automated perimetry and Fourier domain OCT. The studied eyes were divided in 5 groups: eyes of MS patients with previous episodes of optic neuritis (MS-ON, group 1), eyes of MS patients without previous episodes of optic neuritis (MS-nON, group 2), eyes of NMO patients (group 3), eyes of LETM patients (group 4) and eyes of normal controls (group 5). The retinal layers measured by OCT were from the optic nerve, peri-papillary retinal nerve fiber layer (RNFL) and from the macula: the total macular thickness (TMT), which was sub-divided in 8 sectors according to \"Early treatment diabetic retinopathy study\", and the segmented inner macula layers, RNFL, ganglion cell layer (CGL) and inner nuclear layer (INL). Regard to automated perimetry we analyzed the \"mean deviation\" (MD) and different sectors of the visual field according to their correspondence to Garway-Heath optic nerve map. Generalized estimation equation (GEE) models accounting for age and within-patient, inter-eye correlations, were used to compare the results among different groups. We also compare the area under ROC (receiver operating charactheristics) curve among the different groups. We also compute either Spearman or Pearson correlation according to values distributions. RESULTS: There was no statistical difference among the groups regard to sex or mean age. All 4 diseased groups presented peri-papillary RNFL and macular RNFL thicknesses statistically thinner than normal controls. Regarding to GCL thickness and TMT, the NMO, MS-ON and MS-nON groups were statistically thinner than controls, on the other hand the LETM group was not statistically different. When the INL thickness was studied, there was no statistical difference between controls and both MS groups, whereas the NMO and LETM groups were statistically thicker than controls. Both groups with previous history of ON (NMO and MS-ON) presented peri-papillary RNFL, macular RNFL, GCL and TMT thinner than theirs corresponding groups without previous history of ON (LETM and MS-nON, respectively). When NMO and MS-ON were compared, there was no statistical difference in any layer, except the INL, which was thicker in NMO group. There was statistical correlation between OCT and automated perimetry findings for both, MS and NMO, diseases and the correlation was bigger in NMO, particularly when TMT was the OCT parameter used. CONCLUSION: The OCT is able to demonstrate the neural loss in MS and NMO patients and it also shows sub-clinical neural loss in LETM and MS-nON patients. Besides the already known mechanism of optic nerve injury caused by demyelination, the presence of a abnormal INL in the NMO and LETM patients suggest that different processes may be involved in the pathogenesis of these diseases and also that the INL may help differentiating between NMO and MS

The accuracy and efficiency of computing multiple integrals is a very important problem that arises in many scientific, financial and engineering applications. The research conducted in this thesis is designed to build on past work and develop and analyze new numerical methods to evaluate double integrals efficiently. The fundamental aim is to develop and assess techniques for (numerically) evaluating double integrals with high accuracy. The general approach presented in this thesis involves the development of new multivariate approximations from a generalaised Taylor perspective in terms of Appell type polynomials and to study their use in multi-dimensional integration. The expectation is that the new methods will provide polynomial and polynomial-like approximations that can be used for application in a straight forward manner with better accuracy. That is, we aim to devise and investigate new multiple integration formulae and as well as provide information on a priori error bounds. A further major contribution of the work builds on the research conducted in the field of Grüss type inequalities and leads to a new approximation of the one and two dimensional finite Fourier transform. The approximations are in terms of the complex exponential mean and estimate of the error of approximation for different classes of functions of bounded variation defined on finite intervals. It is believed that this work will also have an impact in the area of numerical multidimensional integral evaluation for other integral operators.

Cette thèse a pour but d'étudier les architectures de circuits intégrés pour le traitement numérique de l'OFDM avancé, très haut débit et multi-standard. Ces architectures visent à développer à la fois des puissances de calculs plus élevées pour répondre aux exigences de débit, ainsi que des capacités de reconfiguration pour des applications multi-standard. Elles doivent aussi respecter une contrainte de consommation réduite du fait de l'environnement embarqué des terminaux mobiles. En termes de solutions avancées, nous considérons deux schémas différents de la modulation OFDM, l'OFDM/QAM et l'OFDM/OQAM. Nous proposons une architecture à base de mémoires utilisant un multiplexage temporel des opérations sur une matrice de calcul à gros grain optimisée pour le traitement de la transformée de Fourier rapide et le filtrage polyphase. Nous proposons aussi une stratégie pour la gestion des mémoires
Most current wireless LANs and future Beyond 3G and 4G mobile networks involve the multicarrier OFDM transmission, based itself on the digital processing of the fast Fourier transform. These systems should cover bandwidths in the order of several tens or even hundreds of MHz. The aim of this thesis was to study the architectures of integrated circuit for a high speed and multi-standard OFDM digital processing. These architectures require both higher speed processing to meet the required throughput, and reconfiguration for multi-standard applications. Moreover, these architectures should meet the requirement of reduced power consumption due to the embedded environment of mobile terminals. In terms of advanced solutions, one considers two different OFDM modulation patterns, the OFDM/ QAM and OFDM/OQAM. This latter requires a pulse shaping polyphase filter implemented in our study on the IOTA prototype function. One considers also SISO/MIMO functionalities. A comparative analysis of various FFT algorithms and architectures has led to identify the best approach which gives a good algorithm architecture adequation. This solution also incorporates the pulse shaping filter, more precisely implementing the IOTA function. One has therefore proposed a memory-based architecture using a time multiplexed operations on a coarse grained matrix optimized for the treatment of the FFT and of the pulse shaping filtering. This time approach allows a realization of advanced OFDM modulation for values of the parameter N, the number of subcarrier, from 64 to 8192 and the parameter L, the truncation length for pulse shaping filter, equal to 2, 4 and 8. The architecture of the matrix applies the same treatment on two or four streams of different samples, for modes MIMO 2x2 and 4x4 respectively. A strategy to manage memories has also been proposed. It is based on a memory banks approach to obtain various memory sizes and to enable the turn of the unnecessary memories. A first FPGA prototyping and an ASIC layout design have validated the functioning and the feasibility of the architecture. The FPGA prototyping platform used was the ML402 from Xilinx incorporating the FPGA XC4VSX35 from the Virtex-4 family. The ASIC layout design has been done using the submicronic 65 nm CMOS technology from STMicroelectronics. The performances obtained out of this architecture makes it a good candidate to cover the different standards based on OFDM modulation

The accuracy and efficiency of computing multiple integrals is a very important problem that arises in many scientific, financial and engineering applications. The research conducted in this thesis is designed to build on past work and develop and analyze new numerical methods to evaluate double integrals efficiently. The fundamental aim is to develop and assess techniques for (numerically) evaluating double integrals with high accuracy. The general approach presented in this thesis involves the development of new multivariate approximations from a generalaised Taylor perspective in terms of Appell type polynomials and to study their use in multi-dimensional integration. The expectation is that the new methods will provide polynomial and polynomial-like approximations that can be used for application in a straight forward manner with better accuracy. That is, we aim to devise and investigate new multiple integration formulae and as well as provide information on a priori error bounds. A further major contribution of the work builds on the research conducted in the field of Grüss type inequalities and leads to a new approximation of the one and two dimensional finite Fourier transform. The approximations are in terms of the complex exponential mean and estimate of the error of approximation for different classes of functions of bounded variation defined on finite intervals. It is believed that this work will also have an impact in the area of numerical multidimensional integral evaluation for other integral operators.

Thesis (MScEng)--Stellenbosch University, 2012.
ENGLISH ABSTRACT: In the wool trade the mean diameter of wool is a primary indicator of wool quality. It is currently standard practice for a wool grower to send samples to a laboratory for classification before and after shearing. The devices used to make measurements on samples are often big and bulky and sensitive to the environment, thus they are not ideally suited for on site testing. A brief discussion of the industry is given with background information on existing devices as well as information about organic fibres in general. We test an experimental device which has the potential to be robust and compact based on the Fourier optical principle. Two initial designs are considered and the transmission design is further developed into a working system. The working system is evaluated in a sample measurement experiment. In our sample measurement experimentwe determine the mean diameter of a set of samples which has been analysed by an external testing body such that the measurements could be compared.
AFRIKAANSE OPSOMMING: In diewol bedryfword die gemiddelde diameter vanwol as ’n primêre kwaliteitindeks gebruik. Dit is tans gebruiklik om wol monsters na ’n laboratorium te stuur vir klassifikasie voor en na die skape geskeer word. Die toestel wat gebruik word om die wol monsters te klassifiseer is geneig om groot, lomp en sensitief vir die omgewing te wees en is sodoende nie ideaal vir veld gebruik nie. ’n Kort uitleg van die industrie word gegee tesame met agtergrond inligting van bestaande toestelle asook agtergrond oor organiese vesels in die algemeen. Ons toets ’n eksperimentele toestel wat potensieel kompak en aanpasbaar kan wees en gebaseer is op die Fourier optiese prinsiep. Twee aanvanklike ontwerpe word oorweeg en eindelik word die transmissie ontwerp verder ontwikkel tot ’n werkende sisteem. Die sisteem word geëvalueer in ’n monster meting eksperiment. In die monster meting eksperiment bepaal ons die gemiddelde diameter van ’n stel monsters waarvan die gemiddelde diameter deur ’n eksterne liggaam bepaal is om sodoende die metings te kan vergelyk.

A multiple-sensor optical shape measurement system (SMS) based on the principle of white-light fringe projection has been developed and commercialised by Loughborough University and Phase Vision Ltd for over 10 years. The use of the temporal phase unwrapping technique allows precise and dense shape measurements of complex surfaces; and the photogrammetry-based calibration technique offers the ability to calibrate multiple sensors simultaneously in order to achieve 360° measurement coverage. Nevertheless, to enhance the applicability of the SMS in industrial environments, further developments are needed (i) to improve the calibration speed for quicker deployment, (ii) to broaden the application range from shape measurement to deformation field measurement, and (iii) to tackle practically-challenging surfaces of which specular components may disrupt the acquired data and result in spurious measurements. The calibration process typically requires manual positioning of an artefact (i.e., reference object) at many locations within the view of the sensors. This is not only timeconsuming but also complicated for an operator with average knowledge of metrology. This thesis introduces an automated artefact positioning system which enables automatic and optimised distribution of the artefacts, automatic prediction of their whereabouts to increase the artefact detection speed and robustness, and thereby greater overall calibration performance. This thesis also describes a novel technique that integrates the digital image correlation (DIC) technique into the present fringe projection SMS for the purpose of simultaneous shape and deformation field measurement. This combined technique offers three key advantages: (a) the ability to deal with geometrical discontinuities which are commonly present on mechanical surfaces and currently challenging to most deformation measurement methods, (b) the ability to measure 3D displacement fields with a basic single-camera single-projector SMS with no additional hardware components, and (c) the simple implementation on a multiple-sensor hardware platform to achieve complete coverage of large-scale and complex samples, with the resulting displacement fields automatically lying in a single global coordinate system. A displacement measurement accuracy of ≃ 1/12,000 of the measurement volume, which is comparable to that of an industry-standard DIC system, has been achieved. The applications of this novel technique to several structural tests of aircraft wing panels on-site at the research centre of Airbus UK in Filton are also presented. Mechanical components with shiny surface finish and complex geometry may introduce another challenge to present fringe projection techniques. In certain circumstances, multiple reflections of the projected fringes on an object surface may cause ambiguity in the phase estimation process and result in incorrect coordinate measurements. This thesis presents a new technique which adopts a Fourier domain ranging (FDR) method to correctly identifying multiple phase signals and enables unambiguous triangulation for a measured coordinate. Experiments of the new FDR technique on various types of surfaces have shown promising results as compared to the traditional phase unwrapping techniques.

Cette thèse présente quelques résultats de la théorie des probabilités quantiques et de l'analyse harmonique à valeurs operateurs. La thèse est composée des trois parties.Dans la première partie, on démontre la décomposition atomique des espaces de Hardy de martingales non commutatives. On identifie aussi les interpolés complexes et réels entre les versions conditionnelles des espaces de Hardy et BMO de martingales non commutatives.La seconde partie est consacrée à l'étude des espaces de Hardy à valeurs opérateursvia la méthode d'ondellettes. Cette approche est similaire à celle du cas des martingales non commutatives. On démontre que ces espaces de Hardy sont équivalents à ceux étudiés par Tao Mei. Par conséquent, on donne une base explicite complètement inconditionnelle pour l'espace de Hardy H1(R), muni d'une structure d'espace d'opérateurs naturelle. La troisième partie porte sur l'analyse harmonique sur le tore quantique. On établit les inégalités maximales pour diverses moyennes de sommation des séries de Fourier définies sur le tore quantique et obtient les théorèmes de convergence ponctuelle correspondant. En particulier, on obtient un analogue non commutative du théorème classique de Stein sur les moyennes de Bochner-Riesz. Ensuite, on démontre que les multiplicateurs de Fourier complètement bornés sur le tore quantique coïncident à ceux définis sur le tore classique. Finalement, on présente la théorie des espaces de Hardy et montre que ces espaces possèdent les propriétés des espaces de Hardy usuels. En particulier, on établit la dualité entre H1 et BMO.

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The regional climatic conditions in the State of Goias Brazil are favorable for herbaceous cotton (Gossypium hirsutum L. r. latifolium hutch) cultivation. However, for achieving the best productivities, it is important that both the planting date and the fruiting period be matched with the adequate soil-water availability as well as that the period from open bull to harvesting be coincident with the dry period. Thus, the knowledge of cotton cycle as function of planting location is very important for choosing the optimum planting date. In this context, the air temperature is one of the climatic variables that mostly influence the cotton growth. Nevertheless, the low density of meteorological stations with capability for measuring temperature has restricted the modeling studies for estimating cotton cycle. This work was carried out with the objective of developing and validating mathematical models to estimate average daily air temperature and based on the degreesday theory, the cycle of herbaceous cotton in the State of Goias, considering altogether its variations in space and time. Both models were based on a linear combination of elevation, latitude, longitude, and the daily time variation, represented by an incomplete Fourier series. The parameter models were adjusted to the data from 21 meteorological stations available in the State of Goiás and Federal District of Brazil, using multiple linear regressions with observations varying from eight to twenty four years. In the case of modeling degrees-day, the maximum and minimum temperature data were limited between 15°C and 40°C, which were taken as the lower and upper threshold temperatures, respectively. The air-temperature model was validated against the measured data from three meteorological stations from different elevations: high (1100 m), medium (554 m) and low (431 m). The coefficients of determination obtained from fitting the models for both daily air-temperature and daily degrees-day were 0.82 and 0.84, respectively, resulting in a medium performance for both low and high altitudes and very good for intermediate altitudes. The validation of the degrees-day model was conducted by comparing the period duration running from crop emergence to 90% open bulls observed from cotton cultivars, cropped in commercial fields. The results showed an overall performance index of 0.85, which was considered as very good. The models developed in this study adequately estimated the average daily air temperature and the cycle of herbaceous cotton cultivars in the State of Goias
As condições climáticas regionais do Estado de Goiás são favoráveis ao cultivo do algodoeiro herbáceo (Gossypium hirsutum L. r. latifolium hutch), contudo, para alcançar as melhores produtividades, é imprescindível que a semeadura e o período de frutificação coincidam com o período de maior disponibilidade de água no solo e os períodos de abertura dos capulhos e da colheita coincidam com o período seco. Assim, o conhecimento acerca do ciclo da cultura em função do local de cultivo, é muito importante na definição da melhor época de plantio. Nesse contexto, é a temperatura do ar, uma das variáveis climáticas, que mais influencia o desenvolvimento do algodoeiro. No entanto, a baixa densidade de estações meteorológicas com capacidade de medição da temperatura tem limitado os estudos de modelagem de estimativa do ciclo deste cultivo. Este trabalho foi conduzido com o objetivo de desenvolver e validar modelos matemáticos para estimar a temperatura média diária do ar e, com base na teoria de graus-dia, o ciclo do algodoeiro herbáceo no Estado de Goiás, considerando, simultaneamente, suas variações no espaço e no tempo. Ambos os modelos basearam-se em uma combinação linear da altitude, latitude, longitude e da variação temporal diária, representada pela série trigonométrica incompleta de Fourier. Os parâmetros dos modelos foram ajustados aos dados de 21 estações meteorológicas disponíveis no Estado de Goiás e Distrito Federal, por meio de regressão linear múltipla, com observações variando de 8 a 24 anos. No caso da modelagem de graus-dia, os dados de temperatura máxima e mínima ficaram restritos ao intervalo de 15°C a 40°C, cujos limites foram adotados como os valores de temperatura de base inferior e superior, respectivamente. O modelo de temperatura foi validado, considerando os dados observados de temperatura em estações localizadas em condições de altitudes diferentes: elevada (1100 m), média (554 m) e baixa (431 m). Os coeficientes de determinação resultantes do ajuste dos modelos aos dados de temperatura média diária ou aos de grausdia foram 0,82 e 0,84, respectivamente. O desempenho do modelo foi mediano nas altitudes baixas e elevadas e muito bom nas altitudes médias. A validação do modelo de graus-dia foi feita comparando-se a duração observada do período entre a emergência e 90% de capulhos abertos de cultivares de algodoeiro, plantados em lavouras comerciais, resultando em um índice de desempenho de 0,85, classificado como muito bom. Os modelos desenvolvidos estimaram adequadamente a temperatura média diária do ar e a duração do ciclo dos cultivares de algodoeiro herbáceo no Estado de Goiás

WiFi can provide network coverage for users on land at anytime and anywhere, but on the sea, the wireless communication scenes change dramatically due to the signals are non-existence. Although some techniques (e.g. satellite, undersea fiber, microwave communication) have been used in marine communication, they are either too expensive with very small bandwidth, or too limited in its coverage range. We propose to develop a marine wireless mesh network which is formed by low cost buoyed wireless base stations to provide broadband connectivity for users on the sea. Ocean wave simulation and prediction are key technologies in developing marine mesh network, because marine environments are dramatically different from terrestrial environment. The ocean waves have characteristics of rhythmic oscillations and the line of sight between two communication nodes is often blocked by them. Therefore, we have to develop a new wave-state-aware networking protocol which is suitable for marine environments. Ocean wave simulation technology can simulate this kind of dynamic environments and provide a test platform for the development of marine mesh network. Ocean wave prediction technology can improve the throughput of marine wireless network. Thus, they are indispensable technologies in developing marine mesh network. In this thesis, we designed an ocean wave measurement method, two ocean wave prediction methods, and an ocean wave simulation method. Firstly, we designed an accelerometer-based ocean wave measurement method. It can measure the real time wave height accurately. Secondly, we designed an Elman-neural-network-based ocean wave prediction method for nonlinear waves. It has a higher prediction accuracy than other neural network methods in nonlinear wave prediction. Thirdly, we designed a multiple-linear-regression-based ocean wave prediction method for linear waves. It has a higher prediction accuracy and less time consumption than other methods in linear wave prediction. Finally, we implemented and improved a spectrum-based ocean wave simulation method which is originally proposed by Tessendorf. It can present the movement of ocean waves realistically and in real time. To sum up, above four methods provide an effective test platform and technical support for the development of our marine mesh network.
Master of Science

Cette thèse a pour but d'étudier l'analyse sur les groupes quantiques compacts. Elle se compose de deux parties. La première présente la classification des semi-groupes de Markov invariants sur ces espaces homogènes quantiques. Les générateurs de ces semi-groupes sont considérés comme des opérateurs de Laplace sur ces espaces.La sphère classique , la sphère libre et la sphère semi-libérée sont considérées comme des exemples et les générateurs de semi-groupes de Markov sur ces sphères sont classés. Nous calculons aussi les dimensions spectrales des trois familles de sphères en fonction du comportement asymptotique des valeurs propres de leur opérateur de Laplace.Dans la deuxième partie, nous étudions la convergence des séries de Fourier pour les groupes non abéliens et les groupes quantiques. Il est bien connu qu'un certain nombre de propriétés d'approximation de groupes peuvent être interprétées comme des méthodes de sommation et de convergence moyenne de séries de Fourier non commutatives associées. Nous établissons un critère général d'inégalités maximales pour les identités approximatives de multiplicateurs non commutatifs de Fourier. En conséquence, nous prouvons que pour tout groupe dénombrable discret moyennable, il existe une suite de fonctions définies positives à support fini, telle que les multiplicateurs de Fourier associés sur les espaces Lp non commutatifs satisfassent à la convergence ponctuelle. Nos résultats s'appliquent également à la convergence presque partout des séries de Fourier de fonctions Lp sur des groupes compacts non-abéliens. D'autre part, nous obtenons des bornes indépendantes de la dimension pour les inégalités maximales de Hardy-Littlewood non commutatives dans l'espace à valeurs opérateurs associées à des corps convexes
This thesis is devoted to studying the analysis on compact quantum groups. It consists of two parts. First part presents the classification of invariant quantum Markov semigroups on these quantum homogeneous spaces. The generators of these semigroups are viewed as Laplace operators on these spaces.The classical sphere, the free sphere, and the half-liberated sphere are considered as examples and the generators of Markov semigroups on these spheres are classified. We compute spectral dimensions for the three families of spheres based on the asymptotic behavior of the eigenvalues of their Laplace operator.In the second part, we study of convergence of Fourier series for non-abelian groups and quantum groups. It is well-known that a number of approximation properties of groups can be interpreted as some summation methods and mean convergence of associated noncommutative Fourier series. We establish a general criterion of maximal inequalities for approximative identities of noncommutative Fourier multipliers. As a result, we prove that for any countable discrete amenable group, there exists a sequence of finitely supported positive definite functions, so that the associated Fourier multipliers on noncommutative Lp-spaces satisfy the pointwise convergence. Our results also apply to the almost everywhere convergence of Fourier series of Lp-functions on non-abelian compact groups. On the other hand, we obtain the dimension free bounds of noncommutative Hardy-Littlewood maximal inequalities in the operator-valued Lp space associated with convex bodies

Cette thèse de doctorat est consacrée à l'étude de quelques problèmes en analyse non commutative. Elle comprend quatre parties, allant des groupes quantiques et de l'analyse harmonique non commutative à l'information quantique. Tout d'abord, nous déterminons les états idempotents sur les groupes quantiques de Sekine, ce qui est obtenu en résolvant un système d'équations à l'aide de l'algèbre linéaire et de la théorie des nombres élémentaire. Ceci répond à une question de Franz et Skalski énoncée en 2009. Deuxièmement, nous étudions les états infiniment divisibles sur des groupes quantiques finis, c'est-à-dire, les états qui admettent une racine n-ième pour tout nge 1. Nous montrons que tout état infiniment divisible sur un groupe quantique fini est de type Poisson, c'est-à-dire qu'il peut être représenté sous la forme d'une exponentielle par rapport à un état idempotent. Troisièmement, nous donnons deux conditions suffisantes pour que les multiplicateurs de Fourier de L_p sur les algèbres de von Neumann de groupes discrets soient bornés. Très peu de résultats de ce type étaient connus auparavant. Notre idée est l'observation que, dans le cas discret, il suffit de considérer les multiplicateurs de Fourier de L_p-L_q. Enfin, dans le domaine de l'information quantique, nous confirmons une conjecture de Carlen, Frank et Lieb (puis une conjecture plus faible d'Audenaert et Datta). En conséquence, nous identifions toutes les paires (alpha, z) telles que l'alpha-z entropie relative de Rényi soit monotone sous l'action des applications complètement positives préservant la trace, ou satisfait à l'inégalité de traitement des données. La clé de la preuve est une modification d'une méthode variationnelle largement utilisée, qui permet d'obtenir des preuves simples de nombreux résultats connus
This PhD thesis is devoted to the study of some problems in noncommutative analysis. It consists of four parts, ranging from quantum groups and noncommutative harmonic analysis to quantum information. Firstly, we decide all the idempotent states on Sekine quantum groups, which is achieved by solving a system of equations using linear algebras and elementary number theory. This answers a question of Franz and Skalski stated in 2009. Secondly, we study the infinitely divisible states on finite quantum groups, i.e., states that admit n-th root for all nge 1. We show that every infinitely divisible state on a finite quantum group is of Poisson type, that is, it can be represented as an exponential relative to some idempotent state. Thirdly, we give two sufficient conditions for boundedness of L_p-Fourier multipliers on discrete group von Neumann algebras. Very few of such results were known before. Our idea is the observation that in the discrete case it suffices to consider L_p-L_q Fourier multipliers. Finally, in the area of quantum information, we confirm a conjecture of Carlen, Frank and Lieb (and then a weaker conjecture of Audenaert and Datta). As a consequence, we identify all the pairs (alpha,z) such that the alpha-z Rényi relative entropy is monotone under completely positive trace preserving maps, or satisfies Data Processing Inequality. The key part of the proof is a modification of a widely-used variational method. Its power yields simple proofs of many known results

Cette thèse a pour but d’étudier quelques problèmes dans l'analyse harmonique sur les produits croisés tordus qui sont définis par des actions tordues d'un groupe localement compact G sur une algèbre de von Neumann M. Elle se compose de deux parties. La première porte sur les produits croisés tordus et leurs multiplicateurs de Fourier et de Schur. Nous démontrons que la propriété d’être QWEP pour l’algèbre de von Neumann tordue d’un groupe G est indépendante du 2-cocycle sous-ajacent et que les Lp-multiplicateurs de Fourier complètement bornés sur cette algèbre tordue sont aussi indépendants du 2-cocycle. Sous l’hypothèse d’une action moyennable, nous établissons plusieurs résultats de transfert entre les multiplicateurs de Fourier et de Schur sur les espaces Lp non-commutatifs du produit croisé tordu.Dans la deuxième partie, nous étudions les commutateurs de multiplicateurs de Fourier sur le produit croisé tordu d’un espace euclidien. Nous caractérisons leur appartenance à la p-classes de Schatten par celle de leurs symboles à un espace de Besov associé. Cette partie contient aussi une formule sur la trace de Dixmier qui nous donne également une caractérisation de l’appartenance de ces commutateurs à une p-classe de Schatten faible par un espace de Sobolev. En particulier, nos résultats s'appliquent au cas d’un espace euclidien quantique
This thesis is devoted to the study of some problems in the harmonic analysis on twisted crossed products defined by twisted actions of a locally compact group G on a von Neumann algebra M. It consists of two parts. The first concerns twisted crossed products and their Fourier and Schur multipliers. We prove that the property of being QWEP for the twisted von Neumann algebra of a group G is independent of the underlying 2-cocycle and that the completely bounded Lp-Fourier multipliers on this twisted algebra are also independent of the 2-cocycle. Under the hypothesis of an amenable action, we establish several transference results between the Fourier and Schur multipliers on the noncommutative Lp spaces of the twisted crossed product.In the second part, we study Fourier multiplier commutators on the twisted crossed product of an Euclidean space. We characterize their Schatten p-class membership by that of their symbols in the associated Besov space. In addition, this part contains a formula on the Dixmier trace, which also gives us a characterization of the weak Schatten p-class membership of these commutators by a Sobolev space. In particular, our results apply to the case of quantum Euclidean spaces

My thesis deals with the study of elliptic PDE. It is divided into two parts, the first one concerning a nonlinear equation involving the p-Laplacian, and the second one focused on a nonlocal problem. In the first part, we study the regularity of stable solutions to a nonlinear equation involving the p-Laplacian in a bounded domain. This is the nonlinear version of the widely studied semilinear equation involving the classical Laplacian. Stable solutions to semilinear equations have been very recently proved to be bounded, and therefore smooth, up to dimension n=9 by Cabré, Figalli, Ros-Oton, and Serra. This result is known to be optimal by counterexamples in higher dimensions. In the case of the p-Laplacian, the boundedness of stable solutions is conjectured to hold up to a critical dimension depending on p. Examples of unbounded stable solutions are known if the dimension exceeds the critical one. Moreover, in the radial case or under strong assumptions on the nonlinearity, stable solutions are proved to be bounded in the optimal dimension range. We prove the boundedness of stable solutions under a new condition on n and p, which is optimal in the radial case, and more restrictive in the general one. It improves the known results in the field, and it is the first example, concerning the p-Laplacian, of a technique providing both a result in the nonradial case and the optimal result in the radial case. In the first part, we also investigate Hardy-Sobolev inequalities on hypersurfaces of Euclidean space, all containing a mean curvature term. Our motivation comes from several applications of these inequalities to the study of a priori estimates for stable solutions. Specifically, we give a simplified proof of the celebrated Michael-Simon and Allard inequality, we obtain two new forms of the Hardy inequality on hypersurfaces, and an improved Hardy inequality in the Poincaré sense. In the second part of this thesis, we deal with a Dirichlet to Neumann problem arising in a model for water waves. The system is described by a diffusion equation in a slab of fixed height, containing a weight that depends on a parameter a belonging to (-1,1). The top of the slab is endowed with a 0-Neumann condition, while on the bottom we have a Dirichlet datum and an equation involving a smooth nonlinearity. The system can also be reformulated as a nonlocal problem on the component endowed with the Dirichlet datum, by defining a suitable Dirichlet to Neumann operator. First, we prove a Liouville theorem that establishes the one dimensional symmetry of stable solutions, provided that a control on the growth of the energy associated with the problem is satisfied. As a consequence, we obtain the 1D symmetry of stable solutions to our problem in dimension 2. For n=3, we establish sharp energy estimates for both the energy minimizers and the monotone solutions, deducing the 1D symmetry of these classes of solutions, by an application of our Liouville theorem. Concerning this problem, we also investigate the nature of the associated Dirichlet to Neumann operator. First, we deduce its expression as a Fourier operator, which was known only in the case a=0. This result highlights the mixed nature of the operator, which is nonlocal, but not purely fractional. To better understand the dual behaviour of the operator, we provide a G-convergence result for an energy functional associated with the operator. Specifically, as a G-limit of our energy functional we find a mere interaction energy when a is greater than 0, and the classical perimeter when a is smaller or equal than 0. We point out that the threshold a=0 that we obtain here, as well as the G-limit behaviour for nonpositive values of a, is common to other nonlocal problems treated in the literature. On the contrary, the limit functional that we obtain in the other case appears to be new and structurally different from other nonlocal energy functionals that have been investigated in the literature.
Mi tesis se encaja en el estudio de las EDPs elípticas. Está dividida en dos partes: la primera trata una ecuación no-lineal con el p-Laplaciano, la segunda de un problema no-local. En la primera parte, estudiamos la regularidad de las soluciones estables de una ecuación no lineal con el p-Laplaciano en un dominio acotado. Esta ecuacion es la versión no-lineal de la ámpliamente estudiada ecuacion semilineal con el Laplaciano. Cabré, Figalli, Ros-Oton, y Serra han demostrado recientemente que las soluciones estables de las ecuaciones semilineales son acotadas, y por tanto regulares, hasta la dimensión 9. Este resultado es optimal. En el caso del p-Laplaciano, la regularidad de las soluciones estables se conjetura de ser cierta hasta una dimension critica y, de hecho, se conocen ejemplos de soluciones no acotadas cuando la dimension llega al valor critico. Además, se ha demostrado que en el caso radial o assumiendo hipótesis fuertes sobre la no-linealidad las soluciones estables son acotadas hasta la dimension critica. En el primer capítulo, demostramos que las soluciones estables son acotadas, bajo una nueva condición en n y p, que es optimal en el caso radial, y más restrictiva en el caso general. Esta investigación mejora conocidos resultados del tema y es el primer ejemplo, para el p-Laplaciano, de un método que produce un resultado para el caso general y un resultado optimal en el caso radial. En la primera parte, nos ocupamos también de las desigualdades funcionales del tipo Hardy y Sobolev sobre hipersuperfícies del espacio Euclideo, todas conteniendo un término de curvatura media. Nuestra motivación proviene de varias apliaciones que tienen estas desigualdades en el estudio de estimaciones para las soluciones estables. En detalle, damos una demostración simple de la conocida desigualdad de Michael-Simon y Allard, obtenemos dos formas nuevas de la desigualdad de Hardy sobre hipersuperfícies, y otra desigualdad de Hardy-Poincaré. En la segunda parte, nos ocupamos de un problema de Dirichlet-Neumann que emerge de un modelo para las ondas en el agua. El sistema se describe con una ecuación de difusión en una tira de altura fija, que contiene un parámetro a en (-1,1). La parte superior de la tira es dotada de una condicion 0 de Neumann, mientras en la parte inferior tenemos un dato de Dirichlet y una ecuación con una nonlinearidad regular. Este problema puede ser reformulado como una ecuación no-local sobre la componente dotada del dato de Dirichlet, definiendo un operador de Dirichlet-Neumann apropiado. Primero, demostramos un teorema del tipo Liouville, que garantiza la simetría unidimensional de las soluciones monótonas, asumiendo un control sobre el crecimiento de la energía asociada. Como consecuencia, obtenemos la simetría 1D de las soluciones estables en dimension 2. Para n=3, obtenemos estimaciónes optimales de la energía para las soluciones que minimizan la energía y para las soluciones monótonas. Estas estimaciones nos conducen a la simetría 1D de estas clases de soluciones, aplicando nuestro teorema del tipo Liouville. Relativo a este problema, estudiamos también la naturaleza del operador de Dirichlet-Neumann. Primero, deducimos su expresión como operador de Fourier, que anteriormente solo se conocía para a=0. Este resultado evidencia la naturaleza del operador, que es no-local pero no puramente fraccionaria. Estudiamos en profundidad este comportamiento mixto del operador a través del estudio de la G-convergencia de un funcional energía asociado al operador. Demostramos la G-convergencia de nuestro funcional a un límite que corresponde a una energía de interacción pura cuando a en (0,1) y al perímetro clásico cuando a en (-1,0]. El límite a=0, así como el G-límite para el régimen a en (-1,0], es común a otros problemas no-locales tratados en la literatura. Al contrario, el funcional límite en el régimen puramente no-local es nuevo y diferente a otros funciona
Questa tesi si occupa di equazioni differenziali alle derivate parziali di tipo ellittico. È divisa in due parti: la prima riguarda un’equazione nonlineare per il p-Laplaciano, mentre la seconda è incentrata su un problema nonlocale, che può essere formulato per mezzo di un operatore di Dirichlet-Neumann collegato con il Laplaciano frazionario. Nella prima parte, studiamo la regolarità delle soluzioni stabili dell’equazione nonlineare per il p-Laplaciano dove W è un dominio limitato, p 2 (1,+¥) e f è una nonlinearità C1. Questa equazione è la versione nonlineare dell’equazione semilineare 􀀀������������Du = f (u) in un dominio limitato W Rn, che è stata ampiamente studiata in letteratura. Molto recentemente, Cabré, Figalli, Ros-Oton, e Serra [38] hanno dimostrato che le soluzioni stabili delle equazioni semilineari sono limitate, e quindi regolari, in dimensione n 9. Questo risultato è ottimale, dato che esempi di soluzioni illimitate e stabili sono noti in dimensione n 10. Inoltre, i risultati in [38] forniscono una risposta completa ad un annoso problema aperto, proposto da Brezis e Vázquez [25], sulla regolarità delle soluzioni estremali dell’equazione 􀀀������������Du = l f (u). Queste ultime sono infatti esempi non banali di soluzioni stabili di equazioni semilineari, che possono essere limitate o illimitate in dipendenza della dimensione n, del dominio W, e della nonlinearità f . In questa tesi studiamo la limitatezza delle soluzioni stabili di (0.4), che si congettura essere vera fino alla dimensione n < p + 4p/(p 􀀀������������ 1). Sono infatti noti esempi di soluzioni stabili e illimitate quando n p + 4p/(p 􀀀������������ 1), anche quando il dominio è la palla unitaria. Inoltre, nel caso radiale o assumendo ipotesi forti sulla nonlinearità, è stato dimostrato che le soluzioni stabili di (0.4) sono limitate quando n < p + 4p/(p 􀀀������������ 1). Nel Capitolo 1 della tesi dimostriamo una nuova stima L¥ a priori per le soluzioni stabili di (0.4), assumendo una nuova condizione su n e p, che è ottimale nel caso radiale e più restrittiva nel caso generale. Il nostro risultato migliora ciò che è noto in letteratura e ed è il primo esempio di tecnica che produce sia un risultato nel caso non radiale sia il risultato ottimale nel caso radiale. Per ottenere questo risultato estendiamo al caso del p-Laplaciano una tecnica sviluppata da Cabré [30] per il caso classico del problema, con p = 2. La strategia si basa su una disuguaglianza di Hardy sugli insiemi di livello della soluzione, combinata con una disuguaglianza di tipo geometrico per le soluzioni stabili di (0.4). Nella prima parte della tesi ci occupiamo anche di disuguaglianze funzionali di tipo Hardy e Sobolev, su ipersuperfici dello spazio euclideo. Nel fare ciò siamo motivati dalle varie applicazioni di questo tipo di risultati allo studio di stime a priori per le soluzioni stabili, sia nel caso semilineare che nel caso nonlineare ...

On présente une méthode de calcul pour simuler la propagation d'ondes acoustiques et élastiques générées par une source dans un puits vertical au sein d'un sol multicouche. Ce problème est décomposé en sous-problèmes sur chaque sous-domaine du sol et du fluide. Sur chaque sous-domaine, on doit résoudre une équation d'ondes (Helmholtz ou Navier) et satisfaire des conditions de radiation à l'infini et des conditions aux limites de continuité (interaction sol-fluide). Pour cela, on utilise la méthode des éléments finis de frontière. On suppose que la géométrie du problème est axisymétrique et on décomposé les équations intégrales en séries de Fourier. A basses fréquences, seuls les premiers modes de Fourier interviennent. Les simulations montrent la présence d'une onde de tube, mode propre guide du puits

Questa tesi è incentrata sullo studio di equazioni differenziali alle derivate parziali di tipo ellittico. La prima parte della tesi riguarda la regolarità delle soluzioni stabili per un'equazione nonlineare con il p-Laplaciano, in un dominio limitato dello spazio Euclideo. La tecnica è basata sull'uso di disuguaglianze di tipo Hardy-Sobolev su ipersuperfici, del quale viene approfondito lo studio. Nella seconda parte viene preso in esame un problema nonlocale di tipo Dirichlet-Neumann. Studiamo la simmetria unidimensionale di alcune sottoclassi di soluzioni stabili, ottenendo risultati in dimensione n=2, 3. Inoltre, studiamo il comportamento asintotico dell'operatore associato a questo problema nonlocale, usando tecniche di Γ-convergenza.
This thesis deals with the study of elliptic PDEs. The first part of the thesis is focused on the regularity of stable solutions to a nonlinear equation involving the p-Laplacian, in a bounded domain of the Euclidean space. The technique is based on Hardy-Sobolev inequalities in hypersurfaces involving the mean curvature, which are also investigated in the thesis. The second part concerns, instead, a nonlocal problem of Dirichlet-to-Neumann type. We study the one-dimensional symmetry of some subclasses of stable solutions, obtaining new results in dimensions n=2, 3. In addition, we carry out the study of the asymptotic behaviour of the operator associated with this nonlocal problem, using Γ-convergence techniques.

Wide Area Measurements (WAMs) have been widely used in the energy management system (EMS) of power system for monitoring, operation and control. In recent years, the advent of synchronized Phasor Measurements Unit (PMU) has added another dimension to the field of wide-area measurement. However, the high cost of the PMU, which includes the manufacture and deployment fee, is a hurdle to the wide use of the PMU in power systems. Unlike traditional PMUs, the frequency monitoring network (FNET) developed by the Virginia Tech Power IT lab is an Internetâ based, GPSâ synchronized, wide-area frequency monitoring network deployed at the distribution level, providing a low-cost and easily deployable WAMs solution. In this dissertation, the research work can be categorized into two parts: FNET Design and Situation Awareness Algorithm Development.
Ph. D.

Protein sequencing has produced overwhelming amount of protein sequences, especially in the last decade. Nevertheless, the majority of the proteins' functional and structural classes are still unknown, and experimental methods currently used to determine these properties are very expensive, laborious and time consuming. Therefore, automated computational methods are urgently required to accurately and reliably predict functional and structural classes of the proteins. Several bioinformatics methods have been developed to determine such properties of the proteins directly from their sequence information. Such methods that involve signal processing methods have recently become popular in the bioinformatics area and been investigated for the analysis of DNA and protein sequences and shown to be useful and generally help better characterise the sequences. However, there are various technical issues that need to be addressed in order to overcome problems associated with the signal processing methods for the analysis of the proteins sequences. Amino acid indices that are used to transform the protein sequences into signals have various applications and can represent diverse features of the protein sequences and amino acids. As the majority of indices have similar features, this project proposes a new set of computationally derived indices that better represent the original group of indices. A study is also carried out that resulted in finding a unique and universal set of best discriminating amino acid indices for the characterisation of allergenic proteins. This analysis extracts features directly from the protein sequences by using Discrete Fourier Transform (DFT) to build a classification model based on Support Vector Machines (SVM) for the allergenic proteins. The proposed predictive model yields a higher and more reliable accuracy than those of the existing methods. A new method is proposed for performing a multiple sequence alignment. For this method, DFT-based method is used to construct a new distance matrix in combination with multiple amino acid indices that were used to encode protein sequences into numerical sequences. Additionally, a new type of substitution matrix is proposed where the physicochemical similarities between any given amino acids is calculated. These similarities were calculated based on the 25 amino acids indices selected, where each one represents a unique biological protein feature. The proposed multiple sequence alignment method yields a better and more reliable alignment than the existing methods. In order to evaluate complex information that is generated as a result of DFT, Complex Informational Spectrum Analysis (CISA) is developed and presented. As the results show, when protein classes present similarities or differences according to the Common Frequency Peak (CFP) in specific amino acid indices, then it is probable that these classes are related to the protein feature that the specific amino acid represents. By using only the absolute spectrum in the analysis of protein sequences using the informational spectrum analysis is proven to be insufficient, as biologically related features can appear individually either in the real or the imaginary spectrum. This is successfully demonstrated over the analysis of influenza neuraminidase protein sequences. Upon identification of a new protein, it is important to single out amino acid responsible for the structural and functional classification of the protein, as well as the amino acids contributing to the protein's specific biological characterisation. In this work, a novel approach is presented to identify and quantify the relationship between individual amino acids and the protein. This is successfully demonstrated over the analysis of influenza neuraminidase protein sequences. Characterisation and identification problem of the Influenza A virus protein sequences is tackled through a Subgroup Discovery (SD) algorithm, which can provide ancillary knowledge to the experts. The main objective of the case study was to derive interpretable knowledge for the influenza A virus problem and to consequently better describe the relationships between subtypes of this virus. Finally, by using DFT-based sequence-driven features a Support Vector Machine (SVM)-based classification model was built and tested, that yields higher predictive accuracy than that of SD. The methods developed and presented in this study yield promising results and can be easily applied to proteomic fields.

Les travaux portent sur les multiplexeurs optiques fonctionnant à mi-IR pour la source à large bande dans l'application de détection de gaz. Deux configurations ont été étudiées: réseau de guides d'onde (AWG) et réseau concave planaire (PCG). Premièrement, le principe du fonctionnement a été compris afin de développer une solution analytique pour le champ de sortie en utilisant une approximation gaussienne du champ et de l'optique de Fourier. Ensuite, un outil de simulation semi-analytique de la réponse spectrale pour les deux configurations de multiplexeur a été développé dans MATLAB. La distribution normale des erreurs de phase a été introduite dans le modèle semi-analytique AWG, ce qui nous a permis d'étudier la corrélation entre l'écart-type des erreurs de phase et le niveau de diaphonie de la réponse spectrale AWG. AWG à 5,65 μm a été fabriqué à partir de la technologie SiGe / Si à l'aide de l'outil MATLAB pour le calcul des paramètres de conception et de l'outil P.Labeye pour le calcul de la géométrie AWG. Les dispositifs avec des paramètres légèrement variables ont été caractérisés: AWG1 avec guides d'ondes de 4,6 μm et MMI de 9 μm; AWG2 avec guides d'ondes de 4,6 μm et MMI de 11 μm; AWG3 avec guides d'ondes de 4,8 μm et MMI de 9 μm. Des mesures des dispositifs sur la puce 36 (centre de la plaquette) et sur la puce 32 (côté de la plaquette) ont été effectuées et analysées. Les mesures de température de AWG2 et AWG3 (puce 32 et puce 36) aux points cinq points de température ont montré une dépendance linéaire du déplacement spectral avec la température qui a une bonne corrélation avec les prédictions de simulation
The work focuses on optical multiplexers operating in mid-IR for broadband source in gas sensing application. Two configurations were studies – arrayed waveguide grating (AWG) and planar concave grating (PCG). First, principle of operation was understood in order to develop analytical solution for output field using Gaussian approximation of the field and Fourier Optics. Then, semi-analytical simulation tool of the spectral response for both multiplexer configurations was developed in MATLAB. Normal distribution of phase errors was introduced to semi-analytical AWG model, which allowed us to study the correlation between standard deviation of phase errors and the level of crosstalk of AWG spectral response. AWG at 5.65 µm was fabricated based on SiGe/Si technology using the MATLAB tool for design parameters calculation and P.Labeye’s tool for AWG geometry calculation. Devices with slightly varying parameters were characterized: AWG1 with 4.6 µm waveguides and 9µm MMI; AWG2 with 4.6 µm waveguides and 11µm MMI; AWG3 with 4.8 µm waveguides and 9µm MMI. Measurements of devices on chip 36 (center of the wafer) and chip 32 (side of the wafer) were performed and analyzed. Temperature measurements of AWG2 and AWG3 (chip 32 and chip 36) at points five temperature points showed linear dependence of spectral shift with the temperature which has a good correlation with simulation predictions

Tato práce popisuje metodu analýzy translačního pohybu užitím křížové korelace. Ukazujeme, jakým způsobem se chová funkce křížové korelace obrazů s navzájem posunutými objekty, a jak nám to umožňuje nacházet jejich vektory posunu. Pro následnou implementaci je nalezena efektivní metoda pro hledání pouze požadovaného počtu lokálních maxim funkce.

In the thesis are introduced and investigated spaces of Burling and of Roumieu type tempered ultradistributions, which are natural generalization of the space of Schwartz’s tempered distributions in Denjoy-Carleman-Komatsu’s theory of ultradistributions.  It has been proved that the introduced spaces preserve all of the good properties Schwartz space has, among others, a remarkable one, that the Fourier transform maps continuposly the spaces into themselves.In the first chapter the necessary notation and notions are given.In the second chapter, the spaces of ultrarapidly decreasing ultradifferentiable functions and their duals, the spaces of Beurling and of Roumieu tempered ultradistributions, are introduced; their topological properties and relations with the known distribution and ultradistribution spaces and structural properties are investigated;  characterization of  the Hermite expansions  and boundary value representation of the elements of the spaces are given.The spaces of multipliers of the spaces of Beurling and of Roumieu type tempered ultradistributions are determined explicitly in the third chapter.The fourth chapter is devoted to the investigation of  Fourier, Wigner, Bargmann and Hilbert transforms on the spaces of Beurling and of Roumieu type tempered ultradistributions and their test spaces.In the fifth chapter the equivalence of classical definitions of the convolution of Beurling type ultradistributions is proved, and the equivalence of, newly introduced definitions, of ultratempered convolutions of Beurling type ultradistributions is proved.In the last chapter is given a necessary and sufficient condition for a convolutor of a space of tempered ultradistributions to be hypoelliptic in a space of integrable ultradistribution, is given, and hypoelliptic convolution equations are studied in the spaces.Bibliograpy has 70 items.
U ovoj tezi su proučavani prostori temperiranih ultradistribucija Beurlingovog  i Roumieovog tipa, koji su prirodna uopštenja prostora Schwarzovih temperiranih distribucija u Denjoy-Carleman-Komatsuovoj teoriji ultradistribucija. Dokazano je ovi prostori imaju sva dobra svojstva, koja ima i Schwarzov prostor, izmedju ostalog, značajno svojstvo da Furijeova transformacija preslikava te prostore neprekidno na same sebe.U prvom poglavlju su uvedene neophodne oznake i pojmovi.U drugom poglavlju su uvedeni prostori ultrabrzo opadajucih ultradiferencijabilnih funkcija i njihovi duali, prostori Beurlingovih i Rumieuovih temperiranih ultradistribucija; proučavana su njihova topološka svojstva i veze sa poznatim prostorima distribucija i ultradistribucija, kao i strukturne osobine; date su i karakterizacije Ermitskih ekspanzija i graničnih reprezentacija elemenata tih prostora.Prostori multiplikatora Beurlingovih i Roumieuovih temperiranih ultradistribucija su okarakterisani u trećem poglavlju.Četvrto poglavlje je posvećeno proučavanju Fourierove, Wignerove, Bargmanove i Hilbertove transformacije na prostorima Beurlingovih i Rouimieovih temperiranih ultradistribucija i njihovim test prostorima.U petoj glavi je dokazana ekvivalentnost klasičnih definicija konvolucije na Beurlingovim prostorima ultradistribucija, kao i ekvivalentnost novouvedenih definicija ultratemperirane konvolucije ultradistribucija Beurlingovog tipa.U poslednjoj glavi je dat potreban i dovoljan uslov da konvolutor prostora temperiranih ultradistribucija bude hipoeliptičan u prostoru integrabilnih ultradistribucija i razmatrane su neke konvolucione jednačine u tom prostoru.Bibliografija ima 70 bibliografskih jedinica.

碩士
國立雲林科技大學
電機工程系碩士班
100
In this thesis, we propose the automatic multiple-signal separation methods especially for the linear-frequency modulation (LFM) signals. In the first part, it is major that it separates two-dimensional LFM (2-D LFM) signals. We determine characteristics that the energy is concentrated in the fractional frequency domain. We determine the distribution based on the dilation, and edge detection to determine the separation block. We separate successfully the 2-D LFM signals based on the method that separate 1-D signals. In the second part, the 1-D signals were separated on different fractional order. In specific the fractional domain, the change rate is more different in the separation block. It subtract the separation signal from the source signal, and first step again, until doesn’t find that the energy is concentrated. In this thesis, we propose the methods using the Fractional Fourier transform, it is automatic to separate signals in the time, frequency, and fractional domain.

Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2008.
Source: Dissertation Abstracts International, Volume: 69-11, Section: B, page: 6848. Adviser: Zhong-Jin Ruan. Includes bibliographical references (leaves 77-80) Available on microfilm from Pro Quest Information and Learning.

碩士
國立高雄應用科技大學
電子工程系
98
Due to the popularity of the communication systems, the Fourier transform is still one of research and development topics of wired and wireless communication. The high-speed computing of the discrete Fourier transform is very important in the real-time signal processing system. So many fast Fourier transform (FFT) algorithm are developed. Because of the regularity of FFT algorithm, it is very suitable for the implementation by using hardware circuits. Most of the developed algorithms reduce the computational complexity. In this thesis, we use radix-22 algorithm which can reduce the computational complexity from to . In this study, we compare various circuit architectures of fast Fourier transform in the view of hardware regularity, needed memory space and the number of computing operation. Finally, we adopt the radix-22 algorithm and the single-path delay feedback (SDF) architecture to implement the high-performance FFT processor. The conventional complex multiplier, multiplier-less canonical signed digit (CSD) complex multiplier and coordinate rotation digital computer (Cordic) architecture are used to realize pipelined fast Fourier transform processors. To reduce the error, we also realize our complex multiplier computing circuits with the double rounding technique. The Xilinx ISE software is used to synthesis the hardware, it shows that the 16-point FFT processor based on the multiplier-less canonical signed digit (CSD) complex multiplier can achieve the advantages of less needed hardware and moderate accuracy.

碩士
國立中正大學
應用地球物理研究所
87
The potential application of the fractional (or angular) Fourier transform (FRFT) is investigated for seismic data processing. The main function of the FRFT is to twist the energy distribution by rotation to an axis where it is easily analyzed. This useful function provides us to reconsider the possibility of solving old problem. In this study, we first introduce the fundamental characteristics of the FRFT, and then use the 2-dimensional FRFT to perform velocity filtering for synthetic data. The traditional velocity filtering encounter a difficulty of unseparable events in the frequency-wavenumber domains, for example, multiple reflections. This study illustrates how implementing the FRFT can lead to a significant improvement in this problem.

In this thesis we deal with two problems in harmonic analysis. In the first problem we discuss weighted norm inequalities for Weyl multipliers satisfying Mauceri’s condition. As an application, we prove certain multiplier theorems on the Heisenberg group and also show in the context of a theorem of Weis on operator valued Fourier multipliers that the R-boundedness of the derivative of the multiplier is not necessary for the boundedness of the multiplier transform. In the second problem we deal with a variation of a theorem of Mauceri concerning the Lp bound-edness of operators Mwhich are known to be bounded on L2 .We obtain sufficient conditions on the kernel of the operaor Mso that it satisfies weighted Lp estimates. As an application we prove Lp boundedness of Hermite pseudo-multipliers.

In this thesis we deal with two problems in harmonic analysis. In the first problem we discuss weighted norm inequalities for Weyl multipliers satisfying Mauceri’s condition. As an application, we prove certain multiplier theorems on the Heisenberg group and also show in the context of a theorem of Weis on operator valued Fourier multipliers that the R-boundedness of the derivative of the multiplier is not necessary for the boundedness of the multiplier transform. In the second problem we deal with a variation of a theorem of Mauceri concerning the Lp bound-edness of operators Mwhich are known to be bounded on L2 .We obtain sufficient conditions on the kernel of the operaor Mso that it satisfies weighted Lp estimates. As an application we prove Lp boundedness of Hermite pseudo-multipliers.