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1
Wright, P. S. "The accurate analysis of smoothly fluctuating harmonics applied to the calibration of harmonic analysers." Thesis, University of Surrey, 2002. http://epubs.surrey.ac.uk/843265/.
Повний текст джерелаАнотація:
The aim of this research is to develop an accurate method for the analysis of signals composed of fluctuating harmonics. The results obtained of analysis are applied to the calibration of harmonic analysis instruments. A new method is presented suitable for the accurate analysis of smoothly fluctuating harmonic signals. The method is based on a model of signals with a known period, in which the harmonics are individually modulated by polynomial functions normalised over a sampled signal sequence time. Using this model, a decomposition method is developed such that the modulating polynomials can be recovered from a signal. The polynomial decomposition method leads to a piece-wise analysis of the waveform. Two methods based on least squares and splines respectively, are developed with the aim of giving continuity to the piece-wise analysis. Comparisons of the new method with the short time Fourier transform are given. Having defined a test signal and obtained and accurate analysis of it properties, it can be used to calibrate harmonic analysers. For a given applied signal, analysis with these devices can give rise to variation in results as a function of the phase between the signal and the STFT windows. This result distribution due to variable phase (RDVP) is discussed and examples are given for various signals. The RDVP complicates the calibration process due to the spread of results that occur when testing the device. A method is developed to find the RDVP for an applied signal that uses the polynomial decomposition method to find the modulation functions of each harmonic in the applied calibration signal. Having found the RDVP for an applied signal, it is necessary to fit the results of the analyser under test, to the distribution. The random nature of the phase makes the systematic comparison of the theoretical and measured distributions difficult to achieve. A novel method that uses multiple phase shifted modulated harmonics is presented. By comparing the results of the analyser under test to the distributions of each of the phase-shifted harmonics, a best-fit phase shift can be determined and the required calibration comparison made. Key words: time-frequency analysis, demodulation, harmonic analysis, fluctuating harmonics, waveform metrology, calibration of harmonic analysers.
2
Scurry, James. "One and two weight theory in harmonic analysis." Diss., Georgia Institute of Technology, 2013. http://hdl.handle.net/1853/47565.
Повний текст джерелаАнотація:
This thesis studies several problems dealing with weighted inequalities and vector-valued operators. A weight is a nonnegative locally integrable function, and weighted inequalities refers to studying a given operator's continuity from one weighted Lebesgue space to another. The case where the underlying measure of both Lebesgue spaces is given by the same weight is known as a one weight inequality and the case where the weights are different is called a two weight inequality. These types of inequalities appear naturally in harmonic analysis from attempts to extend classical results to function spaces where the underlying measure is not necessarily Lebesgue measure. For most operators from harmonic analysis, Muckenhoupt weights represent the class of weights for which a one weight inequality holds. Chapters II and III study questions involving these weights. In particular, Chapter II focuses on determining the sharp dependence of a vector-valued singular integral operator's norm on a Muckenhoupt weight's characteristic; we determine that the vector-valued operator recovers the scalar dependence. Chapter III presents material from a joint work with M. Lacey. Specifically, in this chapter we estimate the weak-type norms of a simple class of vector-valued operators, but are unable to obtain a sharp result. The final two chapters consider two weight inequalities. Chapter IV characterizes the two weight inequality for a subset of the vector-valued operators considered in Chapter III. The final chapter presents examples to argue there is no relationship between the Hilbert transform and the Hardy-Littlewood maximal operator in the two weight setting; the material is taken from a joint work with M. Reguera.
3
Lak, Rashad Rashid Haji. "Harmonic analysis using methods of nonstandard analysis." Thesis, University of Birmingham, 2015. http://etheses.bham.ac.uk//id/eprint/5754/.
Повний текст джерелаАнотація:
Throughout this research we use techniques of nonstandard analysis to derive and interpret results in classical harmonic analysis particularly in topological (metric) groups and theory of Fourier series. We define monotonically definable subset \(N\) of a nonstandard *finite group \(F\), which is the monad of the neutral element of \(F\) for some invariant *metric \(d\) on \(F\). We prove some nice properties of \(N\) and the nonstandard metrisation version of first-countable Hausdorff topological groups. We define locally embeddable in finite metric groups (LEFM). We show that every abelian group with an invariant metric is LEFM. We give a number of LEFM group examples using methods of nonstandard analysis. We present a nonstandard version of the main results of the classical space \(L\)\(^1\)(T) of Lebesgue integrable complex-valued functions defined on the topological circle group T, to study Fourier series throughout: the inner product space; the DFT of piecewise continuous functions; some useful properties of Dirichlet and Fejér functions; convolution; and convergence in norm. Also we show the relationship between \(L\)\(^1\)(T) and the nonstandard \(L\)\(^1\)(\(F\)) via Loeb measure. Furthermore, we model functionals defined on the test space of exponential polynomial functions on T by functionals in NSA.
4
Van, der Merwe Marius. "Harmonic mixer analysis and design." Thesis, Stellenbosch : Stellenbosch University, 2002. http://hdl.handle.net/10019.1/52872.
Повний текст джерелаАнотація:
Thesis (MScEng) -- Stellenbosch University, 2002.Some digitised pages may appear illegible due to the condition of the original hard copy.
ENGLISH ABSTRACT: Harmonic mixers are capable of extended frequency operation by mixing with a harmonic of the LO (local oscillator) signal, eliminating the need for a high frequency, high power LO. Their output spectra also have certain characteristics that make them ideal for a variety of applications. The operation of the harmonic mixer is investigated, and the mixer is analyzed using an extension of the classic mixer theory. The synthesis of harmonic mixers is also investigated, and a design procedure is proposed for the design and realization of a variety of harmonic mixers. This design procedure is evaluated with the design and realization of two harmonic mixers, one in X-band and the other in S-band. Measurements suggest that the procedure is successful for the specific applications.
AFRIKAANSE OPSOMMING: Harmoniese mengers kan by hoer frekwensies gebruik word as gewone mengers deurdat hulle gebruik maak van ‘n harmoniek van die LO. ‘n Hoe-frekwensie, hoe-drywing LO word dus nie benodig nie. Die mengers se uittreespektra het ook ‘n aantal karakteristieke wat hulle goeie kandidate maak vir ‘n verskeidenheid van toepassings. Die werking van die harmoniese menger word ondersoek deur uit te brei op die klassieke menger-teorie. Die ontwerp van die harmoniese menger word vervolgens ondersoek, waama ‘n ontwerpsprosedure voorgestel word vir die ontwerp van ‘n verskeidenheid van harmoniese mengers. Hierdie prosedure word getoets met die ontwerp en realisering van twee harmoniese mengers, een in X-band en die ander in S-band. Vanuit die metings is dit duidelik dat die ontwerpsprosedure geslaagd is vir die spesifieke geval.
5
Li, Jialun. "Harmonic analysis of stationary measures." Thesis, Bordeaux, 2018. http://www.theses.fr/2018BORD0311/document.
Повний текст джерелаАнотація:
Soit μ une mesure de probabilité borélienne sur SL m+1 (R) tel que le sous-groupe engendré par le support de μ est Zariski dense. Soit V une représentation irréductible de dimension finie de SL m+1 (R). D’après un théorème de Furstenberg, il existe une unique mesure μ-stationnaire sur PV et nous nous somme intéressés à la décroissance de Fourier de cette mesure. Le résultat principal de cette thèse est que la transformée de Fourier de la mesure stationnaire a une décroissance polynomiale. À partir de ce résultat, nous obtenons un trou spectral de l’opérateur de transfert, dont les propriétés nous permettent d’établir un terme d’erreur exponentiel pour le théorème de renouvellement dans le cadre des produits de matrices aléatoires. L’ingrédient essentiel est une propriété de décroissance de Fourier des convolutions multiplicatives de mesures sur R n , qui est une généralisation d’un théorème de Bourgain en dimension 1. Nous établissons cet ingrédient en utilisant un estimée somme produit de He et de Saxcé.Dans la dernière partie, nous généralisons un résultat de Lax et Phillips et un résultat de Hamenstädt sur la finitude des petites valeurs propres de l’opérateur de Laplace sur les variétés hyperboliques géométriquement finiesLet μ be a Borel probability measure on SL m+1 (R), whose support generates a Zariski dense subgroup. Let V be a finite dimensional irreducible linear representation of SL m+1 (R). A theorem of Furstenberg says that there exists a unique μ-stationary probability measure on PV and we are interested in the Fourier decay of the stationary measure. The main result of the thesis is that the Fourier transform of the stationary measure has a power decay. From this result, we obtain a spectral gap of the transfer operator, whose properties allow us to establish an exponential error term for the renewal theorem in the context of products of random matrices. A key technical ingredient for the proof is a Fourier decay of multiplicative convolutions of measures on R n , which is a generalisation of Bourgain’s theorem on dimension 1. We establish this result by using a sum-product estimate due to He-de Saxcé. In the last part, we generalize a result of Lax-Phillips and a result of Hamenstädt on the finiteness of small eigenvalues of the Laplace operator on geometrically finite hyperbolic manifolds
6
Thunberg, Erik. "On the Benefit of Harmonic Measurements in Power Systems." Doctoral thesis, Stockholm, 2001. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-3219.
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7
Smith, Zachary J. "The Bochner Identity in Harmonic Analysis." Fogler Library, University of Maine, 2007. http://www.library.umaine.edu/theses/pdf/SmithZJ2007.pdf.
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8
Chung, Kin Hoong School of Mathematics UNSW. "Compact Group Actions and Harmonic Analysis." Awarded by:University of New South Wales. School of Mathematics, 2000. http://handle.unsw.edu.au/1959.4/17639.
Повний текст джерелаАнотація:
A large part of the structure of the objects in the theory of Dooley and Wildberger [Funktsional. Anal. I Prilozhen. 27 (1993), no. 1, 25-32] and that of Rouviere [Compositio Math. 73 (1990), no. 3, 241-270] can be described by considering a connected, finite-dimentional symmetric space G/H (as defined by Rouviere), with ???exponential map???, Exp, from L G/L H to G/H, an action, ???: K ??? Aut??(G) (where Aut?? (G) is the projection onto G/H of all the automorphisms of G which leave H invariant), of a Lie group, K, on G/H and the corresponding action, ???# , of K on L G/L H defined by g ??? L (???g), along with a quadruple (s, E, j, E#), where s is a ???# - invariant, open neighbourhood of 0 in L G/L H, E is a test-function subspace of C??? (Exp s), j ?? C??? (s), and E# is a test-function subspace of C??? (s) which contains { j.f Exp: f ?? E }. Of interest is the question: Is the function ???: ?? ??? ????, where ??: f ??? j.f Exp, a local associative algebra homomorphism from F# with multiplication defined via convolution with respect to a function e: s x s ??? C, to F, with the usual convolution for its multiplication (where F is the space of all ??? - invariant distributions of E and F# is the space of all ???# - invariant distributions of E#)? For this system of objects, we can show that, to some extent, the choice of the function j is not critical, for it can be ???absorbed??? into the function e. Also, when K is compact, we can show that ??? ker ?? = { f ?? E : ???k f (???g) dg = 0}. These results turn out to be very useful for calculations on s2 ??? G/H, where G = SO(3) and H??? SO(3) with H ??? SO(2) with ??? : h ??? Lh, as we can use these results to show that there is no quadruple (s, E, j, E#) for SO(3)/H with j analytic in some neighbourhood of 0 such that ??? is a local homomorphism from F# to F. Moreover, we can show that there is more than one solution for the case where s, E and E# are as chosen by Rouviere, if e is does not have to satisfy e(??,??) = e(??,??).
9
Digby, G. "Harmonic analysis of A.C. traction schemes." Thesis, Swansea University, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.233938.
Повний текст джерела
10
Xu, Zengfu. "Harmonic analysis on Chébli-Trimèche hypergroups." Thesis, Xu, Zengfu (1994) Harmonic analysis on Chébli-Trimèche hypergroups. PhD thesis, Murdoch University, 1994. https://researchrepository.murdoch.edu.au/id/eprint/51538/.
Повний текст джерелаАнотація:
In this thesis we develop the theory on Chebli-Trimeche hypergroups of such topics as maximal functions, the convergence and boundedness of certain convolution operator families in Lp spaces and Hardy spaces as well as Fourier multipliers. As the basis of the theory we first investigate the Schwartz classes, Plancherel measure and hypergroup characters on these hypergroups, and establish basic facts about approximations to the identity and the important results concerning Fourier transforms and the estimates for the Plancherel measure and characters. These lead to estimates for the translation operator as well as the heat and Poisson kernels, all of which play a significant role in our study of various maximal operators. The latter include the Hardy-Littlewood maximal operator, the heat and Poisson maximal operators, a class of radial maximal operators, and the grand maximal operator. The behaviour of these maximal convolution operators on Lp and Hardy spaces is investigated, and some classical results are extended to Chebli-Trimeche hypergroups. We also develop local Hardy space theory, and give some results concerning Fourier multipliers and Riesz potentials.
11
Lai, Tsz-ming Terence. "Harmonic simulation of traction system /." Hong Kong : University of Hong Kong, 2000. http://sunzi.lib.hku.hk/hkuto/record.jsp?B21929543.
Повний текст джерела
12
Lidberg, Petter. "Barycentric and harmonic coordinates." Thesis, Uppsala universitet, Algebra och geometri, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-179487.
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13
Renz, Adrian Daniel. "A Comparison Of Harmonic And Holomorphic Functions." Thesis, Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:mdh:diva-48865.
Повний текст джерелаАнотація:
Many results in real and complex analysis are the consequence of mean value properties and theorems. This is the case for harmonic and holomorphic functions as well. The mean value property builds the foundation for several properties of each set of functions. Using this property one can derive more properties like the maximum principle for harmonic functions and the maximum modulus principle for holomorphic functions. These results are then used to show other properties. The goal is to compare the theorems and proofs for harmonic and holomorphic functions and to understand why the results seem to be similar.
14
Hickman, Jonathan Edward. "Topics in affine and discrete harmonic analysis." Thesis, University of Edinburgh, 2015. http://hdl.handle.net/1842/10559.
Повний текст джерелаАнотація:
In this thesis a number of problems in harmonic analysis of a geometric flavour are discussed and, in particular, the Lebesgue space mapping properties of certain averaging and Fourier restriction operators are studied. The first three chapters focus on the perspective afforded by affine-geometrical considerations whilst the remaining chapter considers some discrete variants of these problems. In Chapter 1 there is an overview of the basic affine theory of the aforementioned operators and, in particular, the affine arc-length and surface measures are introduced. Chapter 2 presents work of the author, submitted for publication, concerning an operator which takes averages of functions on Euclidean space over both translates and dilates of a fixed polynomial curve. Moreover, the averages are taken with respect to the affine arc-length; this allows one to prove Lebesgue space estimates with a substantial degree of uniformity in the constants. The sharp range of uniform estimates is obtained in all dimensions except for an endpoint. Chapter 3 presents some work of the author, published in Mathematika, concerning a family of Fourier restriction operators closely related to the averaging operators discussed in Chapter 2. Specifically, a Fourier restriction estimate is obtained for a broad class of conic surfaces by introducing a certain measure which exhibits a special kind of affine invariance. Again, the sharp range of estimates is obtained, but the results are limited to the case of 2-dimensional cones. Finally, Chapter 4 discusses some recent joint work of the author and Jim Wright considering the restriction problem over rings of integers modulo a prime power. The sharp range of estimates is obtained for Fourier restriction to the moment curve in finitely-generated free modules over such rings. This is achieved by lifting the problem to the p-adics and applying a classical argument of Drury in this setting. This work aims to demonstrate that rings of integers offer a simplified model for the Euclidean restriction problem.
15
Salahifar, Raydin. "Analysis of Pipeline Systems Under Harmonic Forces." Thesis, Université d'Ottawa / University of Ottawa, 2011. http://hdl.handle.net/10393/19820.
Повний текст джерелаАнотація:
Starting with tensor calculus and the variational form of the Hamiltonian functional, a generalized theory is formulated for doubly curved thin shells. The formulation avoids geometric approximations commonly adopted in other formulations. The theory is then specialized for cylindrical and toroidal shells as special cases, both of interest in the modeling of straight and elbow segments of pipeline systems. Since the treatment avoids geometric approximations, the cylindrical shell theory is believed to be more accurate than others reported in the literature. By adopting a set of consistent geometric approximations, the present theory is shown to revert to the well known Flugge shell theory. Another set of consistent geometric approximations is shown to lead to the Donnell-Mushtari-Vlasov (DMV) theory. A general closed form solution of the theory is developed for cylinders under general harmonic loads. The solution is then used to formulate a family of exact shape functions which are subsequently used to formulate a super-convergent finite element. The formulation efficiently and accurately captures ovalization, warping, radial expansion, and other shell behavioural modes under general static or harmonic forces either in-phase or out-of-phase. Comparisons with shell solutions available in Abaqus demonstrate the validity of the formulation and the accuracy of its predictions. The generalized thin shell theory is then specialized for toroidal shells. Consistent sets of approximations lead to three simplified theories for toroidal shells. The first set of approximations has lead to a theory comparable to that of Sanders while the second set of approximation has lead to a theory nearly identical to the DMV theory for toroidal shells. A closed form solution is then obtained for the governing equation. Exact shape functions are then developed and subsequently used to formulate a finite element. Comparisons with Abaqus solutions show the validity of the formulation for short elbow segments under a variety of loading conditions. Because of their efficiency, the finite elements developed are particularly suited for the analysis of long pipeline systems.
16
Bayan, Nima. "Harmonic flow analysis in power distribution networks." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1999. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape8/PQDD_0011/MQ52509.pdf.
Повний текст джерела
17
Uppalapati, Sunitha. "Development of Application Program for Harmonic Analysis." MSSTATE, 2002. http://sun.library.msstate.edu/ETD-db/theses/available/etd-11072002-153105/.
Повний текст джерелаАнотація:
Increased power quality problems due to intensive usage of power electronic devices resulted in development of software applications to perform quick harmonic analysis. However, the present harmonic analysis applications have special software or computer locks requirements and occupy huge memory and cost high. An application program (using Microsoft Visual C++) that is simple yet accurate in calculations; with no special software or high memory requirements is developed in this thesis work. The program uses the automatic acceptance criteria (AAC) and the harmonic penetration techniques in calculating the system voltages. Several user-friendly features and tools that aid in better understanding of system harmonics are included in the program. Comparison of case study results with Superharm simulation results proves the program?s accuracy. This thesis work resulted in an informative and time saving program with which the user can document the study results and analyze them with minimum effort.
18
Datta, Somantika. "Wiener's generalized harmonic analysis and waveform design." College Park, Md. : University of Maryland, 2007. http://hdl.handle.net/1903/6701.
Повний текст джерелаАнотація:
Thesis (Ph. D.) -- University of Maryland, College Park, 2007.Thesis research directed by: Mathematics. Title from t.p. of PDF. Includes bibliographical references. Published by UMI Dissertation Services, Ann Arbor, Mich. Also available in paper.
19
Li, Qifan. "Two results in Harmonic analysis and PDEs." Doctoral thesis, Norges teknisk-naturvitenskapelige universitet, Institutt for matematiske fag, 2014. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-24801.
Повний текст джерела
20
Stones, Brendan. "Aspects of harmonic analysis over finite fields." Thesis, University of Edinburgh, 2005. http://hdl.handle.net/1842/14492.
Повний текст джерелаАнотація:
In this thesis we study three topics in Harmonic Analysis in the finite field setting. The methods used are purely combinatorial in nature. We prove a sharp result for the maximal operator associated to dilations of quadric surfaces. We use Christ’s method ([Christ, Convolution, Curvature and Combinatorics. A case study, International Math. Research Notices 19 (1998)]), for Lp→ Lq estimates for convolution with the twisted n-bic curve in the European setting, to give Lp → Lq estimates for convolution with k-dimensional surfaces in the finite field setting. We give solution to the k-plane Radon transform problem and embark on a study of a generalisation of this problem.
21
Bell, James Joseph. "Input harmonic and mixing behavioural model analysis." Thesis, Cardiff University, 2014. http://orca.cf.ac.uk/64151/.
Повний текст джерелаАнотація:
This thesis details the necessary evolutions to Cardiff University's HF measurement system and current CAD model implementation to allow for input second harmonic and mixing models to be measured, generated, and simulated. A coherent carrier distribution system was built to allow four Agilent PSGs to be trigger linked, thus enabling for the first time three harmonic active source- and load-pull measurements at X-band. Outdated CAD implementations of the Cardiff Model were made dynamic with the use of ADS' AEL. The move to a program controlled schematic population for the model allows for any type of model to be generated and input into ADS for simulation. The investigations into isolated input second harmonic models have yielded an optimal formulation augmentation that describes a quadratic magnitude and phase dependency. Furthermore, augmentations to the model formulation have to comprise of a model coefficient and its complex conjugate in order to maintain real port DC components. Any additional terms that describe higher than a cubic phase dependency are not recommended as average model accuracy plateaus, at 0.89%, from the quartic terms onwards. Further model investigations into input and output harmonic mixing of coefficients has been detailed and shows that model coefficient mixing achieves better model accuracy, however, coefficient filtering is suggested to minimize model file sizes. Finally, exercising the modelling process from measurement to design, a generated source- and load-pull mixing model was used to simulate an extrinsic input second harmonic short circuit, an intrinsic input second harmonic short circuit, and input second harmonic impedance that half-rectified the input voltage waveform with Class-B output impedances. The tests were set up to see the impact of input second harmonic tuning on drain efficiency. Efficiencies of 77.31%, 78.72%, and 73.35% were observed for the respective cases, which are approximately a 10% efficiency improvement from measurements with no input second harmonic tuning. These results indicate that to obtain performances at X-band close to theory or comparable to performance at lower frequencies input waveform engineering is required.
22
Oliver, Douglas L. "Analysis of a Pseudo-Harmonic Tubular Bell." University of Toledo / OhioLINK, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=toledo149980725594691.
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23
Gidelew, Getnet Abebe. "Topics in Harmonic Analysis on Combinatorial Graphs." Diss., Temple University Libraries, 2014. http://cdm16002.contentdm.oclc.org/cdm/ref/collection/p245801coll10/id/262601.
Повний текст джерелаАнотація:
MathematicsPh.D.
In recent years harmonic analysis on combinatorial graphs has attracted considerable attention. The interest is stimulated in part by multiple existing and potential applications of analysis on graphs to information theory, signal analysis, image processing, computer sciences, learning theory, and astronomy. My thesis is devoted to sampling, interpolation, approximation, and multi-resolution on graphs. The results in the existing literature concern mainly with these theories on unweighted graphs. My main objective is to extend existing theories and obtain new results about sampling, interpolation, approximation, and multi-resolution on general combinatorial graphs such as directed, undirected and weighted.
Temple University--Theses
24
Harris, Stephen Elliott Ian. "Restriction and isoperimetric inequalities in harmonic analysis." Thesis, University of Edinburgh, 2015. http://hdl.handle.net/1842/14168.
Повний текст джерелаАнотація:
We study two related inequalities that arise in Harmonic Analysis: restriction type inequalities and isoperimetric inequalities. The (Lp, Lq) Restriction type inequalities have been the subject of much interest since they were first conceived in the 1960s. The classical restriction type inequality involving surfaces of non-vanishing curvature is only fully resolved in two dimensions and there have been a lot of recent developments to establish the conjectured (p,q) range in higher dimensions. However, it also interesting to consider what can be said for curves where the curvature does vanish. In particular we build upon a restriction result for homogeneous polynomial surfaces, using what is considered the natural weight - the one induced by the affine curvature of the surface. This is known to hold with a non-universal constant which depends in some way on the coefficients of the polynomial. In this dissertation we shall quantify that relationship. Restriction estimates (for curves or surfaces) using the affine curvature weight can be shown to lead to an affine isoperimetric inequality for such curves or surfaces. We first prove, directly, this inequality for polynomial curves, where the constant depends only on the degree of the underlying polynomials. We then adapt this method, to prove an isoperimetric inequality for a wide class of curves, which includes curves for which a restriction estimate is not yet known. Next we state and prove an analogous result of the relative affine isoperimetric inequality, which applies to unbounded convex sets. Lastly we demonstrate that this relative affine isoperimetric inequality for unbounded sets is in fact equivalent to the classical affine isoperimetric inequality.
25
Gautam, Sushrut Zubin Sulaksh. "Two geometric obstruction results in harmonic analysis." Diss., Restricted to subscribing institutions, 2009. http://proquest.umi.com/pqdweb?did=1872162601&sid=1&Fmt=2&clientId=1564&RQT=309&VName=PQD.
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26
Goh, K. M. "Harmonic analysis of power systems containing multiple convertors." Thesis, Staffordshire University, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.382488.
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27
Mattsson, Tobias. "Abstract Harmonic Analysis on Locally Compact Abelian Groups." Thesis, Uppsala universitet, Analys och sannolikhetsteori, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-354740.
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28
Cavina, Michelangelo. "Bellman functions and their method in harmonic analysis." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2019. http://amslaurea.unibo.it/19214/.
Повний текст джерелаАнотація:
This work uses the method of the Bellman function to show a new proof of Hardy's inequality for Carleson measures.
Bellman functions come from the theory of stochastic optimal control and there is a method to prove theorems about inequalities over dyadic trees (which have applications in harmonic analysis) that takes inspiration from concepts from the theory of the Bellman functions. The work will display the important concepts of the theory of Bellman functions in stochastic analysis, will show how to use the method of the Bellman function to prove the estimate over dyadic trees for Carleson measures for Hardy spaces (while also showing the connections between the stochastic theory and the harmonic analysis) and will give a new proof of Hardy's inequality for dyadic trees (which is related to the characterization of Carleson measures in Besov spaces) using the Bellman function method.
29
Wang, Simeng. "Some problems in harmonic analysis on quantum groups." Thesis, Besançon, 2016. http://www.theses.fr/2016BESA2062/document.
Повний текст джерелаАнотація:
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 PhysicsThis 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
30
Granroth-Wilding, Mark Thomas. "Harmonic analysis of music using combinatory categorial grammar." Thesis, University of Edinburgh, 2013. http://hdl.handle.net/1842/8019.
Повний текст джерелаАнотація:
Various patterns of the organization of Western tonal music exhibit hierarchical structure, among them the harmonic progressions underlying melodies and the metre underlying rhythmic patterns. Recognizing these structures is an important part of unconscious human cognitive processing of music. Since the prosody and syntax of natural languages are commonly analysed with similar hierarchical structures, it is reasonable to expect that the techniques used to identify these structures automatically in natural language might also be applied to the automatic interpretation of music. In natural language processing (NLP), analysing the syntactic structure of a sentence is prerequisite to semantic interpretation. The analysis is made difficult by the high degree of ambiguity in even moderately long sentences. In music, a similar sort of structural analysis, with a similar degree of ambiguity, is fundamental to tasks such as key identification and score transcription. These and other tasks depend on harmonic and rhythmic analyses. There is a long history of applying linguistic analysis techniques to musical analysis. In recent years, statistical modelling, in particular in the form of probabilistic models, has become ubiquitous in NLP for large-scale practical analysis of language. The focus of the present work is the application of statistical parsing to automatic harmonic analysis of music. This thesis demonstrates that statistical parsing techniques, adapted from NLP with little modification, can be successfully applied to recovering the harmonic structure underlying music. It shows first how a type of formal grammar based on one used for linguistic syntactic processing, Combinatory Categorial Grammar (CCG), can be used to analyse the hierarchical structure of chord sequences. I introduce a formal language similar to first-order predicate logical to express the hierarchical tonal harmonic relationships between chords. The syntactic grammar formalism then serves as a mechanism to map an unstructured chord sequence onto its structured analysis. In NLP, the high degree of ambiguity of the analysis means that a parser must consider a huge number of possible structures. Chart parsing provides an efficient mechanism to explore them. Statistical models allow the parser to use information about structures seen before in a training corpus to eliminate improbable interpretations early on in the process and to rank the final analyses by plausibility. To apply the same techniques to harmonic analysis of chord sequences, a corpus of tonal jazz chord sequences annotated by hand with harmonic analyses is constructed. Two statistical parsing techniques are adapted to the present task and evaluated on their success at recovering the annotated structures. The experiments show that parsing using a statistical model of syntactic derivations is more successful than a Markovian baseline model at recovering harmonic structure. In addition, the practical technique of statistical supertagging serves to speed up parsing without any loss in accuracy. This approach to recovering harmonic structure can be extended to the analysis of performance data symbolically represented as notes. Experiments using some simple proof-of-concept extensions of the above parsing models demonstrate one probabilistic approach to this. The results reported provide a baseline for future work on the task of harmonic analysis of performances.
31
Bärlund, Johnny. "Numerical Investigation on Spherical Harmonic Synthesis and Analysis." Thesis, KTH, Geodesi och satellitpositionering, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-171779.
Повний текст джерелаАнотація:
In this thesis work the accuracy of the spherical harmonic synthesis and analysis are investigated, by simulated numerical studies.The main idea is to investigate the loss of accuracy, in the geopotential coeffcients, by the following testing method. We start with a synthesis calculation, using the coefficients(EGM2008), to calculate geoid heights on a regular grid. Those geoid heights are then used in an analysis calculation to obtain a new set of coeffcients, which are in turn used to derive a new set of geoid heights. The difference between those two sets of geoid heights will be analyzed to assess the accuracy of the synthesis and analysis calculations.The tests will be conducted with both point-values and area-means in the blocks in the grid. The area-means are constructed in some different ways and will also be compared to the mean value from 10000 point values as separate tests. Numerical results from this investigation show there are signifi
cant systematic errors in the geoid heights computed by spherical harmonic synthesis and analysis, sometimes reaching as high as several meters. Those big errors are most common at the polar regions and at the mid-latitude regions.
32
Zhou, Jun. "Harmonic Analysis of Linea Continuous-Time Periodic Systems." 京都大学 (Kyoto University), 2001. http://hdl.handle.net/2433/77905.
Повний текст джерела
33
Russell, Michael L. "The Phenomenology of Harmonic Progression." Thesis, University of North Texas, 2020. https://digital.library.unt.edu/ark:/67531/metadc1703408/.
Повний текст джерелаАнотація:
This dissertation explores a method of music analysis that is designed to reflect the phenomenology of the listening experience, specifically in regards to harmony. It is primarily inspired by the theoretical approaches of the music theorist Moritz Hauptmann and by the writings of philosopher Edmund Husserl.
34
SALOGNI, FRANCESCA. "Harmonic Bergman spaces, Hardy-type spaces and harmonic analysis of a symmetric diffusion semigroup on R^n." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2013. http://hdl.handle.net/10281/41814.
Повний текст джерелаАнотація:
This thesis is divided into two parts, which deal with quite diverse subjects.
The first part is, in turn, divided into two chapters. The first focuses on the development
of new function spaces in $R^n$, called generalized Bergman spaces, and on their application
to the Hardy space $H^1(R^n)$. The second is devoted to the theory of Bergman spaces on
noncompact Riemannian manifolds which possess the doubling property and to its relationships
with spaces of Hardy type. The latter are tailored to produce endpoint estimates for
interesting operators, mainly related to the Laplace-Beltrami operator.
The second part is devoted to the study of some interesting properties of the operator
$A f = -1/2 \Delta f- x \cdot \nabla f \forall f \in C_c^\infty (R^n)$, which is essentially self-adjoint with respect to the measure $d \gamma_{-1}(x) = \pi^{n/2} \e^{|x|^2} d \lambda (x) \forall x \in R^n$, where $\lambda$ denotes the Lebesgue measure, and of the semigroup that $A$ generates.
35
Lai, Tsz-ming Terence, and 黎子明. "Harmonic simulation of traction system." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2000. http://hub.hku.hk/bib/B3122281X.
Повний текст джерела
36
Manna, Utpal. "Harmonic and stochastic analysis aspects of the fluid dynamics equations." Laramie, Wyo. : University of Wyoming, 2007. http://proquest.umi.com/pqdweb?did=1414120661&sid=1&Fmt=2&clientId=18949&RQT=309&VName=PQD.
Повний текст джерела
37
Abat, Diren. "Harmonic Vibration Analysis Of Large Structures With Local Nonlinearity." Master's thesis, METU, 2009. http://etd.lib.metu.edu.tr/upload/2/12610475/index.pdf.
Повний текст джерелаАнотація:
With the rapid development in today&rsquos technology, reliability and performance requirements on components of various mechanical systems, which tend to be much lighter and work under much more severe working conditions, dramatically increased. In general, analysis techniques based on simplified model of structural components with linearity assumption may provide time saving for solutions with reasonable accuracy. However, since most engineering structures are often very complex and intrinsically nonlinear, in some cases they may behave in a different manner which cannot be fully described by linear mathematical models, or linear treatments may not be applicable at all. In fact, some studies revealed that deviations in the modal properties of dynamic structures gathered from measured data are due to nonlinearities in the structure. Hence, in problems where accuracy is the primary concern, taking the nonlinear effects into account becomes inevitable. In this thesis, it is aimed to analyze the harmonic response characteristics of multi degree of freedom nonlinear structures having different type of nonlinearities. The amplitude dependencies of nonlinearities are modelled by using describing function method. To increase the accuracy of the results, effect of the higher order harmonic terms will be considered by using multi harmonic describing function theory. Mathematical formulations are embedded in a computer program developed in MATLAB®
with graphical user interface. The program gets the system matricies from the file which is obtained by using substructuring analysis in ANSYS®
, and nonlinearities in the system can easily be defined through the graphical user interface of the MATLAB®
program.
38
Christoforidis, George P. "Harmonic analysis of power systems connected to converter substations." Diss., Georgia Institute of Technology, 1990. http://hdl.handle.net/1853/14994.
Повний текст джерела
39
Woodington, Simon Philip. "Behavioural model analysis of active harmonic load-pull measurements." Thesis, Cardiff University, 2011. http://orca.cf.ac.uk/13000/.
Повний текст джерелаАнотація:
In this thesis, an investigation of the use of the poly-harmonic distortion model and related techniques is conducted, and applied to model fundamental and harmonic load-pull. Contained within the thesis is a detailed review of the development of the poly-harmonic distortion model and related methods. This thesis shows that although the poly-harmonic distortion model improves on the prediction of fundamental load-pull, over Hot-S-Parameters it still has a limited range of application. To address this observation, higher order models have been investigated along with Fourier methods allowing rapid extraction of the behavioral models. These methods allow conclusions to be drawn on the accuracy of the extracted models, by the direct observation of the magnitudes of the model coefficients. The thesis is concluded with the presentation of the results from third party, using a model extracted using the methods discussed in this thesis. The Model is of a 0.5W GaAs pHEMT at 9 GHz and is used within the design of a Class-J MMIC amplifier.
40
Gu, Xinyi. "Harmonic analysis in power network with renewable power generator." Thesis, University of Strathclyde, 2017. http://digitool.lib.strath.ac.uk:80/R/?func=dbin-jump-full&object_id=28655.
Повний текст джерелаАнотація:
Considering the rapidly rising cost of primary fuel for electricity generation and the extensive concern of the international community for global warning, electricity generation with renewable sources has been actively developed all over the world. A large number of renewable energy generators, more highly sensitive electronic equipment and more electronics or microprocessor controllers are used in the power system. It has brought new challenges to supply quality, and thus the study of Power Quality (PQ) has become obviously important. Harmonic analysis plays an important role in PQ study because harmonic has great influence on the power system equipment as well as on their operation. Harmonics can lead to operation failure of electrical and electronic components, overheating of neutral wires and transformer, failure of power factor correction capacitors, loss in power generation and transmission, and interference with protection, control and communication networks as well as customer loads. Therefore, developing an advanced PQ disturbances classification system and a more accurate harmonic analysis method is the key of this thesis. It is necessary to determine the sources and causes of such disturbances to solve PQ problems. When the type of disturbance has been classified accurately, PQ engineers can define the major effects at the load and analyse the source of the disturbances. Many approaches based on Fourier Transform (FT) and neural network for the classification of PQ disturbance have been developed in the last few years. The key factor of these methods is that the correct rate for the actual event is not high enough and thus there is still space to improve accuracy. In this thesis, a fuzzy-expert system based on Wavelet Transforms (WT) to classify power supply waveforms into different groups or categories for PQ classification is proposed with the aim which is to classify the disturbance type with higher accuracy. A new approach for the evaluation of harmonic contents of power system waveforms is also proposed in [sic] thesis. The conventional harmonic analysis method is Fourier analysis. However, Fourier analysis provides signals which are mainly localised in the frequency domain and it gives limited information of the signals in the time domain. Furthermore, the FT cannot obtain accurate values of amplitude and phases from harmonics with frequencies different from that of the window function frequency. In order to overcome the limitations of Fourier analysis and obtain better results, wavelet analysis has been proposed. A novel harmonic analysis method using Discrete Wavelet Packet Transform (DWPT) filter bank decomposition and Continuous Wavelet Transform (CWT) identification has been proposed. In order to evaluate the performance and result of the proposed analysis method, another two conventional methods, i.e. Fast Fourier Transform (FFT) and the combination method of Discrete Wavelet Transform (DWT) filter bank and CWT calculation, are compared through a large number of identical applications. Based on the harmonic analysis, the harmonic penetration is considered and its effects to power networks with increasing of renewable power generations are investigated. With increasing of renewable generators in power networks, it creates PQ problems caused by harmonic injections with a large frequency range, such as integer-harmonics, inter-harmonics and sub-harmonics. Therefore, the steady state harmonic power flow in power system with discrete frequencies is calculated with Root Mean Square (RMS) values of bus current and voltage magnitudes and Total Harmonic Voltage Distortion (THDv) values. Variable of tests are designed to investigate the effects to the harmonic penetration with multiple types of harmonic sources in power networks.
41
Taylor, Brian John Sidney. "Aspects of anisotropic harmonic analysis beyond Calderón-Zygmund Theory." Thesis, University of Birmingham, 2017. http://etheses.bham.ac.uk//id/eprint/7855/.
Повний текст джерелаАнотація:
We consider three major parts of Fourier analysis and their role in Fefferman-Stein inequalities. The three areas can be considered as three separate topics in their own right, or as three steps to proving certain L^p-L^q inequalities via the Fefferman-Stein inequalities of the form ?R^n|Tf|²w≲?R^n|f|²Mw. The first area discussed is that of maximal functions, specifically obtaining L^p-L^q inequalities on large classes of maximal functions. We then use a simple duality argument to transfer these to operators where we have a Fefferman-Stein inequality via ||T||p→q≲||M||¹/²_(q/2γ→p/2γ). The second area aims to control operators defined via multipliers by the previous section's geometrically defined maximal functions. In particular, we build up to a schema that can be used to prove Fefferman-Stein inequalities via the so called g-functions, originating in work of E.M. Stein but having historic roots that can be easily seen by viewing g-functions as speciality square functions. In the final section we consider some classes of operators with oscillatory kernels and obtain estimates on their multipliers, and by application of the previous two sections obtain some L^p-L^q inequalities.
42
Heyns, Gideon Christiaan. "Analysis of harmonic field effects in reluctance synchronous machines." Thesis, Cape Peninsula University of Technology, 2011. http://hdl.handle.net/20.500.11838/2201.
Повний текст джерелаАнотація:
Thesis (MTech (Electrical Engineering))--Cape Peninsula University of Technology, 2011.The reluctance synchronous machine (RSM) is a type of synchronous machine which has no windings in the rotor and can be referred to as a non-excited synchronous machine. The RSM can be classified as either single or double salient machine. The single salient machine refers to saliency in the rotor only and double saliency refers to saliency in the rotor and stator. The RSM is based on the principle of reluctance, were torque is produced due to different reluctance paths within the rotor of the machine. The term reluctance is referred to the resistance of a material towards the flow of magnetic field. Since the invention of vector controlled drives, RSMs regained the popularity of researchers and are becoming a field of interest. The RSM have numerous advantages, besides being cheap, robust, and reliable, the stator part is exactly the same as an induction machine. This will enable easy and cost efficient upgrades. Furthermore due to the non existing rotor currents heat dissipation will be low. However the RSM has an inherently high torque ripple due to its rotor geometry. The torque ripple is defined as the difference between maximum and minimum deviation of the torque referred to the average torque. The torque ripple creates uneven pull on the rotor which creates deformation of the rotor and consequently uneven run. As a result the torque ripple indicates that the speed of the RSM changes permanently. The machines designers ultimate goal would be to design a machine with the lowest torque ripple combined with a maximum average torque. The aim of this thesis is to provide a detailed analysis on the field quantities and its harmonics of a RSM and to examine the effects which these harmonics have on the torque production. This analysis would give designers a better understanding of the principles of RSMs and help to obtain certain performance results. The research design and methodology will include the harmonic content of the flux density components in the center of the air gap. The flux density components will be analysed in terms of its harmonics and the torque produced by these flux density harmonics will also be investigated.
43
Li, Kuo-tung. "Convergence problems arising from harmonic analysis and ergodic theory /." The Ohio State University, 1994. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487853913100673.
Повний текст джерела
44
Resende, Jose Wilson. "Interaction between controlled reactors and converters : a harmonic analysis." Thesis, University of Aberdeen, 1986. http://digitool.abdn.ac.uk/R?func=search-advanced-go&find_code1=WSN&request1=AAIU367868.
Повний текст джерелаАнотація:
This thesis presents the development of a generalised computer program to calculate harmonic currents and voltages in six and twelve-pulse thyristor controlled reactors under non-ideal conditions. Thyristor controlled reactors are a relatively new source of harmonic distortion in power systems. The steady state characteristic harmonics are well known. Other non-characteristic harmonics can, however, be generated. A detailed representation is therefore necessary. Apart from the most common non-ideal conditions, such as voltage, impedance and firing pulse unbalances, this work allows voltage harmonic distortions, two firing pulse control methods, the effect of the feedback control in the equally spaced firing pulse control and the effect of the step-down transformer saturation. The effect of the a.c. system impedance, filters and capacitor banks is also included. Four different models of filters were implemented. With non-infinite a.c. systems, the harmonic currents generated are not totally absorbed by the filters. The remaining distortion may affect the main busbar voltages. Therefore, an iterative method was adopted in which the distorted voltages calculated at the end of one iteration are used to calculate the new currents and voltages. The process is repeated until convergence is reached. Several cases were then studied using this program which was then joined to an existing steady-state converter harmonic program. For instance, the need for a more complete representation of controlled reactors, converters and a.c. system network is illustrated. This study begins considering an hvdc station under ideal conditions which are then gradually moved towards more real conditions. The influence of the a.c. system representation in harmonic studies is also discussed. This analysis also compares the performance of two filter designs, namely the tuned and the damped filters. A study of harmonic magnification in the presence of a.c. and d.c. resonances is also included. The harmonic calculations program presented in this thesis is able to study so many conditions of operation of converters and/or thyristor controlled reactors that it is impractical to show all the possible cases. For instance, filters and capacitor banks can be installed at the converter busbar or at any controlled reactor busbar. Furthermore, the three-phase calculation approach allows studies in which some abnormal operation, such as the absence of a filter branch or capacitor bank at one phase, can be observed.
45
Maitra, Arindam. "A generic approach to network modeling for harmonic analysis." Diss., Mississippi State : Mississippi State University, 2002. http://library.msstate.edu/etd/show.asp?etd=etd-03272002-133910.
Повний текст джерела
46
Gray, Philippe. "Harmonic Models of Common Converter Topologies for Accurate Harmonic Analysis of Distribution Systems." Thesis, 2013. http://hdl.handle.net/1807/42850.
Повний текст джерелаАнотація:
Harmonic distortion in a power system can excite non-characteristic harmonics from converter interfaced loads and generators which can then propagate back into the system, exciting other harmonics in the system. In this thesis, a harmonic analysis tool is presented that is designed to perform high accuracy, computationally efficient, steady-state harmonic analysis of distribution systems when multiple converter interfaced loads and generators exist in the system. The harmonic analysis tool requires less detail and engineering time than PSCAD/EMTDC while offering reliable assessment of harmonic coupling problems that are not captured by existing frequency-domain harmonic analysis tools. To do this, 5 harmonic models of common power electronic converter topologies were developed and implemented into this tool. The harmonic models are shown to be highly accurate; when tested in an unbalanced system with even and odd harmonic distortion, the harmonic models showed a maximum error of less than 0.4% when compared to PSCAD/EMTDC.
47
LI, RONG-GIAN, and 李榮乾. "Harmonic power flow analysis and the methods of suppressing harmonics." Thesis, 1988. http://ndltd.ncl.edu.tw/handle/16562086664944752849.
Повний текст джерела
48
林士煜. "Power system harmonic analysis." Thesis, 1991. http://ndltd.ncl.edu.tw/handle/80403314004726205987.
Повний текст джерела
49
Shu-Kuang, Chang, and 張曙光. "Harmonic Analysis on Torus." Thesis, 1998. http://ndltd.ncl.edu.tw/handle/80166029721337847613.
Повний текст джерелаАнотація:
碩士東吳大學
數學系研究所
86
The polar coordinate on the plane generalizes to spherical coordinate in 3-dimensional Euclidean space. However, it has many other generalizations other than the spherial. For instance, the cylindrical coordinate is the direct product of it with the z-axis. The name of such coordinate comes from its decomposition of the whole space into cylinders. Just like the spherical into spheres. It is known that the space can be also decomposed into tori of various sizes. So there is the toroidal coordinate corresponding to the tori. In this paper, we introduce the toroidal coordinate in space and attempt to find application in harmonic analysis on the torus. In spherical coordinate, the harmonic homogenous polynomials restrict to spherical harmonics. The same theory doesn't apply successfully in our case. Because the radial doesn't decouple with the angular factors. Still,we can apply such coordinate to estimate the first nonzero eigenvalue of the Laplace operator on the torus.
50
Ghandehari, Mahya. "Harmonic analysis of Rajchman algebras." Thesis, 2010. http://hdl.handle.net/10012/5436.
Повний текст джерелаАнотація:
Abstract harmonic analysis is mainly concerned with the study of locally compact
groups, their unitary representations, and the function spaces associated with them.
The Fourier and Fourier-Stieltjes algebras are two of the most important function
spaces associated with a locally compact group.
The Rajchman algebra associated with a locally compact group is defined to be
the set of all elements of the Fourier-Stieltjes algebra which vanish at infinity. This
is a closed, complemented ideal in the Fourier-Stieltjes algebra that contains the
Fourier algebra. In the Abelian case, the Rajchman algebras can be identified with
the algebra of Rajchman measures on the dual group. Such measures have been
widely studied in the classical harmonic analysis. In contrast, for non-commutative
locally compact groups little is known about these interesting algebras.
In this thesis, we investigate certain Banach algebra properties of Rajchman
algebras associated with locally compact groups. In particular, we study various
amenability properties of Rajchman algebras, and observe their diverse characteristics
for different classes of locally compact groups. We prove that amenability
of the Rajchman algebra of a group is equivalent to the group being compact and
almost Abelian, a property that is shared by the Fourier-Stieltjes algebra. In contrast,
we also present examples of large classes of locally compact groups, such
as non-compact Abelian groups and infinite solvable groups, for which Rajchman
algebras are not even operator weakly amenable. Moreover, we establish various extension
theorems that allow us to generalize the previous result to all non-compact
connected SIN-groups.
Finally, we investigate the spectral behavior of Rajchman algebras associated
with Abelian locally compact groups, and construct point derivations at certain
elements of their spectrum using Varopoulos’ decompositions for Rajchman algebras.
Having constructed similar decompositions, we obtain analytic discs around
certain idempotent characters of Rajchman algebras. These results, and others that
we obtain, illustrate the inherent distinction between the Rajchman algebra and
the Fourier algebra of many locally compact groups.