Dissertationen zum Thema „Mathematical analysis - functional analysis“
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1
Izquierdo, Ángel Cabrera. „A functional analysis of categorization“. Diss., Georgia Institute of Technology, 1995. http://hdl.handle.net/1853/30522.
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2
Reumerman, Richard A. „Functional and mathematical analysis of the glyoxylate shunt in Streptomyces coelicolor“. Thesis, University of Strathclyde, 2015. http://oleg.lib.strath.ac.uk:80/R/?func=dbin-jump-full&object_id=26435.
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Streptomyces coelicolor is the model organism for the genus Streptomyces, which produces many bioactive secondary metabolites with clinical applications. Based on work done in Escherichia coli, the glyoxylate shunt was thought to be the main anapleurotic pathway in S. coelicolor during growth on fatty acids and therefore an important pathway in providing precursors for secondary metabolism. The S. coelicolor genome contains genes for a second anapleurotic pathway, the ethylmalonyl-CoA pathway. The relative importance of both to anapleurosis in streptomycete metabolism was unclear. The function of the glyoxylate shunt was investigated in this thesis using sequence analysis, genetic manipulation, transcriptomics and mathematical modelling. Analysis of orthologues of aceA, ccr and genes encoding tricarboxylic acid (TCA) cycle genes revealed that all are subject to a similar level of purifying selection pressure. The operons of the glyoxylate shunt and the ethylmalonyl-CoA pathway share a 15 bp palindromic motif in their upstream sequences, which was also found upstream of other genes. This suggests an overlap in regulation and thus an overlap in function. The sequence analysis is contradicted by results of experiments with an aceA⁻ aceB1⁻ mutant, which did not display a phenotype during growth on Tween 40, a model carbon source for fatty acids. Results obtained by total RNA sequencing indicate that the ethylmalonyl-CoA pathway is the main anapleurotic pathway during growth of S. coelicolor on fatty acids whereas expression of the glyoxylate shunt is minimal. This apparent contradiction is resolved by hypothesising that the ethylmalonyl-CoA pathway is the main anapleurotic pathway, but that the glyoxylate shunt provides a backup when acyl-CoA thioesters are withdrawn from the ethylmalonyl-CoA pathway for secondary metabolite biosynthesis. Enzymes of the isocitrate branchpoint were isolated following heterologous expression and analysed. The resulting kinetic parameters, as well as their specific activities measured during growth on Tween 40 and additional data from literature, were used to set up a mathematical model of the TCA cycle and the glyoxylate shunt. Simulations of this model predicted that, as growth proceeds from early to mid and late exponential phase, the relative concentrations of TCA cycle intermediates changed from promoting gluconeogenesis to accomodating secondary metabolism. Further model refinement is needed using data on the flux through the ethylmalonyl- CoA pathway as these were unavailable at the time of writing.
3
Li, Ben. „Müller Density-Matrix-Functional Theory: Existence of Solutions and their Properties“. Thesis, Uppsala universitet, Analys och tillämpad matematik, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-190518.
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4
Awunganyi, John. „A study of optimization in Hilbert Space“. CSUSB ScholarWorks, 1998. https://scholarworks.lib.csusb.edu/etd-project/1459.
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5
Zhang, Bairu. „Functional data analysis in orthogonal designs with applications to gait patterns“. Thesis, Queen Mary, University of London, 2018. http://qmro.qmul.ac.uk/xmlui/handle/123456789/44698.
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This thesis presents a contribution to the active research area of functional data analysis (FDA) and is concerned with the analysis of data from complex experimental designs in which the responses are curves. High resolution, closely correlated data sets are encountered in many research fields, but current statistical methodologies often analyse simplistic summary measures and therefore limit the completeness and accuracy of conclusions drawn. Specifically the nature of the curves and experimental design are not taken into account. Mathematically, such curves can be modelled either as sample paths of a stochastic process or as random elements in a Hilbert space. Despite this more complex type of response, the structure of experiments which yield functional data is often the same as in classical experimentation. Thus, classical experimental design principles and results can be adapted to the FDA setting. More specifically, we are interested in the functional analysis of variance (ANOVA) of experiments which use orthogonal designs. Most of the existing functional ANOVA approaches consider only completely randomised designs. However, we are interested in more complex experimental arrangements such as, for example, split-plot and row-column designs. Similar to univariate responses, such complex designs imply that the response curves for different observational units are correlated. We use the design to derive a functional mixed-effects model and adapt the classical projection approach in order to derive the functional ANOVA. As a main result, we derive new functional F tests for hypotheses about treatment effects in the appropriate strata of the design. The approximate null distribution of these tests is derived by applying the Karhunen- Lo`eve expansion to the covariance functions in the relevant strata. These results extend existing work on functional F tests for completely randomised designs. The methodology developed in the thesis has wide applicability. In particular, we consider novel applications of functional F tests to gait analysis. Results are presented for two empirical studies. In the first study, gait data of patients with cerebral palsy were collected during barefoot walking and walking with ankle-foot orthoses. The effects of ankle-foot orthoses are assessed by functional F tests and compared with pointwise F tests and the traditional univariate repeated-measurements ANOVA. The second study is a designed experiment in which a split-plot design was used to collect gait data from healthy subjects. This is commonly done in gait research in order to better understand, for example, the effects of orthoses while avoiding confounded analysis from the high variability observed in abnormal gait. Moreover, from a technical point of view the study may be regarded as a real-world alternative to simulation studies. By using healthy individuals it is possible to collect data which are in better agreement with the underlying model assumptions. The penultimate chapter of the thesis presents a qualitative study with clinical experts to investigate the utility of gait analysis for the management of cerebral palsy. We explore potential pathways by which the statistical analyses in the thesis might influence patient outcomes. The thesis has six chapters. After describing motivation and introduction in Chapter 1, mathematical representations of functional data are presented in Chapter 2. Chapter 3 considers orthogonal designs in the context of functional data analysis. New functional F tests for complex designs are derived in Chapter 4 and applied in two gait studies. Chapter 5 is devoted to a qualitative study. The thesis concludes with a discussion which details the extent to which the research question has been addressed, the limitations of the work and the degree to which it has been answered.
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Miranda, Navarro Maria. „Comparative Study of Several Bases in Functional Analysis“. Thesis, Linköpings universitet, Matematik och tillämpad matematik, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-150462.
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From the beginning of the study of spaces in functional analysis, bases have been an indispensable tool for operating with vectors and functions over a concrete space. Bases can be organized by types, depending on their properties. This thesis is intended to give an overview of some bases and their relations. We study Hamel basis, Schauder basis and Orthonormal basis; we give some properties and compare them in different spaces, explaining the results. For example, an infinite dimensional Hilbert space will never have a basis which is a Schauder basis and a Hamel basis at the same time, but if this space is separable it has an orthonormal basis, which is also a Schauder basis. The project deals mainly with Banach spaces, but we also talk about the case when the space is a pre Hilbert space.
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Hadjipantelis, Pantelis-Zenon. „Functional data analysis in phonetics“. Thesis, University of Warwick, 2013. http://wrap.warwick.ac.uk/62527/.
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The study of speech sounds has established itself as a distinct area of research, namely Phonetics. This is because speech production is a complex phenomenon mediated by the interaction of multiple components of a linguistic and non-linguistic nature. To investigate such phenomena, this thesis employs a Functional Data Analysis framework where speech segments are viewed as functions. FDA treats functions as its fundamental unit of analysis; the thesis takes advantage of this, both in conceptual as well as practical terms, achieving theoretical coherence as well as statistical robustness in its insights. The main techniques employed in this work are: Functional principal components analysis, Functional mixed-effects regression models and phylogenetic Gaussian process regression for functional data. As it will be shown, these techniques allow for complementary analyses of linguistic data. The thesis presents a series of novel applications of functional data analysis in Phonetics. Firstly, it investigates the influence linguistic information carries on the speech intonation patterns. It provides these insights through an analysis combining FPCA with a series of mixed effect models, through which meaningful categorical prototypes are built. Secondly, the interplay of phase and amplitude variation in functional phonetic data is investigated. A multivariate mixed effects framework is developed for jointly analysing phase and amplitude information contained in phonetic data. Lastly, the phylogenetic associations between languages within a multi-language phonetic corpus are analysed. Utilizing a small subset of related Romance languages, a phylogenetic investigation of the words' spectrograms (functional objects defined over two continua simultaneously) is conducted to showcase a proof-of-concept experiment allowing the interconnection between FDA and Evolutionary Linguistics.
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Patti, S. „Mathematical Modelling, Simulation and Statistical Analysis of Crystallization processes“. Doctoral thesis, Università degli Studi di Milano, 2008. http://hdl.handle.net/2434/152008.
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In this thesis a specific birth and growth process is analyzed; namely a mass crystallization process, where growth is driven by supersaturation only.
Based on purely physical grounds, a multifronts moving boundary model is derived and a non-linear condition for the concentration arises on the boundary. The deterministic growth model is completed by considering stochastic nucleations in space and time. A new formulation of the deterministic process based on the Schwartz distributions is proposed. This formulation is well adapted for a numerical solution in a multi-fronts framework and a fixed grid, since it gives a global description of the evolution of all the crystals in a single equation. Simulations are performed for different sets of values of the physical parameters, also for extreme cases where real experiments would be unfeasible.
The coupling of the growth dynamics with the evolution of the underlying field of the concentration of matter finally causes the stochastic geometry of the crystals. By collecting observations from independent simulations, the relationship between the physical parameters of the model and the final morphology of the system is analyzed. Finally, the inverse problem of estimation
of the initial concentration, given a target final distribution of sizes, is solved
by applying functional data analysis techniques.
The rigorous mathematical description of the crystallization phenomena and the morphological analysis give the possibility to experimentalists to design optimal experiments and to foresee the behaviour of the system.
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Blower, G. „A topic in functional analysis“. Thesis, University of Oxford, 1989. http://ora.ox.ac.uk/objects/uuid:0724199d-41fd-48f1-882c-19602576a2a0.
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We introduce the class AUMD of Banach spaces X for which X-valued analytic martingales converge unconditionally. We shew that various possible definitions of this class are equivalent by methods of martingale decomposition. We shew that such X have finite cotype and are q-complex uniformly convex in the sense of Garling. Using multipliers we shew that analytic martingales valued in L1 converge unconditionally and that AUMD spaces have the analytic Radon-Nikodym property. We shew that X has the AUMD property if and only if strong Hbrmander-Mihlin multipliers are bounded on the Hardy space H1x(T). We achieve this by representing multipliers as martingale transforms. It is shewn that if X is in AUMD and is of cotype two then X has the Paley Theorem property. Using an isomorphism result we shew that if A is an injective operator system on a separable Hilbert space and P a completely bounded projection on A, then either PA or (I-P)A is completely boundedly isomorphic to A. The finite-dimensional version of this result is deduced from Ramsey's Theorem. It is shewn that B(e2 is primary. It is shewn that weakly compact homomorphisms T from the 2 disc algebra into B(e2 are necessarily compact. An explicit form for such T is obtained using spectral projections and it is deduced that such T are absolutely summing.
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Sharikov, Evgenii. „Conditions for global minimum through abstract convexity“. Thesis, University of Ballarat, 2008. http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/45930.
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The theory of abstract convexity generalizes ideas of convex analysis by using the notion of global supports and the global definition of subdifferential. In order to apply this theory to optimization, we need to extend subdifferential calculus and separation properties into the area of abstract convexity.Doctor of Philosophy
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Zoglat, Abdelhak. „Analysis of variance for functional data“. Thesis, University of Ottawa (Canada), 1994. http://hdl.handle.net/10393/10136.
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In this dissertation we present an extension to the well known theory of multivariate analysis of variance. In various situations data are continuous stochastic functions of time or space. The speed of pollutants diffusing through a river, the real amplitude of a signal received from a broadcasting satellite, or the hydraulic conductivity rates at a given region are examples of such processes. After the mathematical background we develop tools for analyzing such data. Namely, we develop estimators, tests, and confidence sets for the parameters of interest. We extend these results, obtained under the normality assumption, and show that they are still valid if this assumption is relaxed. Some examples of applications of our techniques are given. We also outline how the latter can apply to random and mixed models for continuous data. In the appendix, we give some programs which we use to compute the distributions of some of our tests statistics.
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CHESSA, MICHELA. „A MATHEMATICAL ANALYSIS OF CONFLICTS IN VOTING SYSTEMS“. Doctoral thesis, Università degli Studi di Milano, 2013. http://hdl.handle.net/2434/217565.
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Game Theory applied to voting gives rise to the study of many different topics. In this thesis we present some results in order to evaluate the power share inside a Parliament, to analyze the criteria for the assessment of the voters’ preferences and to provide more efficient ways to compute the existing instruments.
The first part of the thesis deals with the issue of power in a voting system. In order to better analyze it, we investigate the way of combining a communication structure with the already existing indices of power. Moreover, we present the possibility of assuming some coalitions as less probable, but not infeasible, as the political scenario is complex enough to admit the possibility of very unlikely coalitions to form. Then, we add another important aspect to the problem; the alliances inside a decisional situation are not stable, but may evolve with time, mainly due to the fact that each agent aims at getting a higher power. We refer to an already existing instrument which, theoretically, may perfectly describe this situation. Unfortunately, the current computational complexity does not permit to adopt it in many real cases. Another important topic is the evaluation of the power to block instead of the power to win. We provide an index which evaluates the veto power and which can be extended in order to catch other characteristics of the game; for example, the probability that a party takes a particular decision, or that not every member of a party is present at the vote.
The second part of this thesis considers a previous step of the formation of a democracy: the evaluation of how much the resulting Parliament reflects the preferences expressed by the electors. We think that the goodness of a Parliament mainly depends on the power share between the parties and not only on the number of seats.
Finally, the last part shows a new exact method to improve the efficiency of the evaluation of one of the existing indices of power, the Public Good index.
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Essomba, Rene Franck. „An investigation into Functional Linear Regression Modeling“. Master's thesis, University of Cape Town, 2015. http://hdl.handle.net/11427/15591.
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Functional data analysis, commonly known as FDA", refers to the analysis of information on curves of functions. Key aspects of FDA include the choice of smoothing techniques, data reduction, model evaluation, functional linear modeling and forecasting methods. FDA is applicable in numerous applications such as Bioscience, Geology, Psychology, Sports Science, Econometrics, Meteorology, etc. This dissertation main objective is to focus more specifically on Functional Linear Regression Modelling (FLRM), which is an extension of Multivariate Linear Regression Modeling. The problem of constructing a Functional Linear Regression modelling with functional predictors and functional response variable is considered in great details. Discretely observed data for each variable involved in the modelling are expressed as smooth functions using: Fourier Basis, B-Splines Basis and Gaussian Basis. The Functional Linear Regression Model is estimated by the Least Square method, Maximum Likelihood method and more thoroughly by Penalized Maximum Likelihood method. A central issue when modelling Functional Regression models is the choice of a suitable model criterion as well as the number of basis functions and an appropriate smoothing parameter. Four different types of model criteria are reviewed: the Generalized Cross-Validation, the Generalized Information Criterion, the modified Akaike Information Criterion and Generalized Bayesian Information Criterion. Each of these aforementioned methods are applied to a dataset and contrasted based on their respective results.
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Griesenauer, Erin. „Algebras of cross sections“. Diss., University of Iowa, 2016. https://ir.uiowa.edu/etd/2086.
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My research studies algebras of holomorphic functions from $d$-tuples of $n\times n$- matrices, $M_n(\bC)^d$, to $M_n(\bC)$. In particular, I study the holomorphic functions that can be approximated by \emph{polynomial matrix concomitants}, that is polynomial maps from $M_n(\bC)^d$ to $M_n(\bC)$ that satisfy the relationship
\[
f(g^{-1}\fz g) = g^{-1}f(\fz)g
\]
for every $\fz \in M_n(\bC)^d$ and $g\in GL_n(\bC)$. In a sense, these are the polynomial maps that “remember” the structure of the $d$-tuple $\fz$.
My first result is that these holomorphic matrix concomitants can be identified with holomorphic cross sections of certain matrix bundles. A holomorphic matrix bundle is a fibred space in which every fibre is $M_n(\bC)$ and the fibres are glued together in such a way that the total space has a holomorphic structure.
Once the identification between holomorphic cross sections and holomorphic concomitants is established, the structure of the matrix bundle is used to endow the algebra of continuous cross sections with a $C^*$-algebra structure. Then we study the subalgebra of cross sections that can be approximated by polynomial concomitants. By identifying the matrix concomitants with cross sections, we are able to prove interesting results about these algebras.
15
Chadman, Corey S. „Functional Limits in Topology“. Youngstown State University / OhioLINK, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=ysu1371035042.
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Satyal, Neeraj Raj. „An Analysis of Fifth-Grade Teachers’ Mathematical Inputs on Eighth-Grade Students’ Mathematical Outputs“. Digital Commons at Loyola Marymount University and Loyola Law School, 2015. https://digitalcommons.lmu.edu/etd/183.
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The purpose of this study was to explore and analyze which fifth-grade teacher inputs were the most important predictors of future outcomes of eighth-grade math students. This quantitative study looked at mathematical achievement through the lens of an education production function. The three inputs that were analyzed were fifth-grade teachers’ background; perception of professional development; and instructional practices and the relationship of those practices to achievement in eighth-grade math. In order to find the relationship between the above variables and student achievement, descriptive statistics, multiple correlations, and multi-variable regression analysis were conducted to examine which predictors had a stronger relationship between eighth-grade math outcomes than others. Taken as a whole, fifth-grade teacher math inputs in this study seemed to explain a small part of the variance regarding eighth-grade math achievement. As a whole, the more frequently students wrote and spoke about math in fifth grade as well as used math tools effectively, the better the outcome in eighth grade.
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Harper, John-Paul. „The class number one problem in function fields“. Thesis, Stellenbosch : Stellenbosch University, 2003. http://hdl.handle.net/10019.1/53619.
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Thesis (MComm)--Stellenbosch University, 2003.ENGLISH ABSTRACT: In this dissertation I investigate the class number one problem in function fields. More precisely I give a survey of the current state of research into extensions of a rational function field over a finite field with principal ring of integers. I focus particularly on the quadratic case and throughout draw analogies and motivations from the classical number field situation. It was the "Prince of Mathematicians" C.F. Gauss who first undertook an in depth study of quadratic extensions of the rational numbers and the corresponding rings of integers. More recently however work has been done in the situation of function fields in which the arithmetic is very similar. I begin with an introduction into the arithmetic in function fields over a finite field and prove the analogies of many of the classical results. I then proceed to demonstrate how the algebra and arithmetic in function fields can be interpreted geometrically in terms of curves and introduce the associated geometric language. After presenting some conjectures, I proceed to give a survey of known results in the situation of quadratic function fields. I present also a few results of my own in this section. Lastly I state some recent results regarding arbitrary extensions of a rational function field with principal ring of integers and give some heuristic results regarding class groups in function fields.
AFRIKAANSE OPSOMMING: In hierdie tesis ondersoek ek die klasgetal een probleem in funksieliggame. Meer spesifiek ondersoek ek die huidige staat van navorsing aangaande uitbreidings van 'n rasionale funksieliggaam oor 'n eindige liggaam sodat die ring van heelgetalle 'n hoofidealgebied is. Ek kyk in besonder na die kwadratiese geval, en deurgaans verwys ek na die analoog in die klassieke getalleliggaam situasie. Dit was die beroemde wiskundige C.F. Gauss wat eerste kwadratiese uitbreidings van die rasionale getalle en die ooreenstemende ring van heelgetalle in diepte ondersoek het. Onlangs het wiskundiges hierdie probleme ook ondersoek in die situasie van funksieliggame oor 'n eindige liggaam waar die algebraïese struktuur baie soortgelyk is. Ek begin met 'n inleiding tot die rekenkunde in funksieliggame oor 'n eindige liggaam en bewys die analogie van baie van die klassieke resultate. Dan verduidelik ek hoe die algebra in funksieliggame geometries beskou kan word in terme van kurwes en gee 'n kort inleiding tot die geometriese taal. Nadat ek 'n paar vermoedes bespreek, gee ek 'n oorsig van wat alreeds vir quadratiese funksieliggame bewys is. In hierdie afdeling word 'n paar resultate van my eie ook bewys. Dan vermeld ek 'n paar resultate aangaande algemene uitbreidings van 'n rasionale funksieliggaam oor 'n eindige liggaam waar die van ring heelgetalle 'n hoofidealgebied is. Laastens verwys ek na 'n paar heurisitiese resultate aangaande klasgroepe in funksieliggame.
18
Sadykov, Timour. „Hypergeometric functions in several complex variables“. Doctoral thesis, Stockholm : Univ, 2002. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-198.
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Petersson, Albin. „Characterizations of Gelfand-Shilov Spaces“. Thesis, Linnéuniversitetet, Institutionen för matematik (MA), 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-105127.
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In this thesis we examine properties of Gelfand-Shilov spaces Ssσ and Pilipović spaces Σsσ. These are spaces of smooth functions which, along with their Fourier transforms, decay sub-exponentially. Results for the two types of spaces relating to Fourier transforms, analyticity of functions, triviality of the spaces and short-time Fourier transforms are explored. It is determined that Σsσ is nontrivial if and only if s+σ>1, and that results for Ssσ when s+σ≥1 can generally be found to have corresponding counterparts for Σsσ when s+σ>1.
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Roysdon, Michael A. „ON SOME GEOMETRIC AND FUNCTIONAL INEQUALITIES INASYMPTOTIC GEOMETRIC ANALYSIS“. Kent State University / OhioLINK, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=kent1599821442510494.
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Lindström, Jens. „On the origin and early history of functional analysis“. Thesis, Uppsala University, Department of Mathematics, 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-120527.
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Rice, Gregory. „Invariance principles in functional time series analysis with applications“. Thesis, The University of Utah, 2016. http://pqdtopen.proquest.com/#viewpdf?dispub=3746458.
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This dissertation aims to develop the theory and applications of functional time series analysis. Functional data analysis came into prominence in the 1990s when more sophisticated data collection and storage systems became prevalent, and many of the early developments focused on simple random samples of curves. However, a common source of functional data is when long, continuous records are broken into segments of smaller curves. An example of this is geologic and economic data that are presented as hourly or daily curves. In these instances, successive curves may exhibit dependencies which invalidate statistical procedures that assume a simple random sample.
The theory of functional time series analysis has grown tremendously in the last decade to provide methodology for such data, and researchers have focused primarily on adapting methods available in finite dimensional time series analysis to the function space setting. As a first problem, we consider an invariance principle for the partial sum process of stationary random functions. This theory is then applied to the problems of testing for stationarity of a functional time series and the one-way functional analysis of variance problem under dependence.
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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.
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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.
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Velasquez, Rafael. „The Implicit Function Theorem“. Thesis, Umeå universitet, Institutionen för matematik och matematisk statistik, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-151933.
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In this essay we present an introduction to real analysis, with the purpose of proving the Implicit Function Theorem. Our proof relies on other well-known theorems in set theory and real analysis as the Heine-Borel Covering Theorem and the Inverse Function Theorem.I denna uppsats ger vi en introduktion till reel analys, med syftet att bevisa den implicita funktionssatsen. Vårt bevis bygger på andra välkända satser i mängdteori och reel analys som Heine-Borels övertäckningssats och inversa funktionssatsen.
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Graneland, Elsa. „Orthogonal polynomials and special functions“. Thesis, Uppsala universitet, Analys och sannolikhetsteori, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-418820.
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Lee, Robert. „Teaching Algebra through Functional Programming:An Analysis of the Bootstrap Curriculum“. BYU ScholarsArchive, 2013. https://scholarsarchive.byu.edu/etd/3519.
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Bootstrap is a computer-programming curriculum that teaches students to program video games using Racket, a functional programming language based on algebraic syntax. This study investigated the relationship between learning to program video games from a Bootstrap course and the resulting effect on students' understanding of algebra. Courses in three different schools, lasting about six weeks each, were studied. Control and treatment groups were given a pre and post algebra assessment. A qualitative component consisting of observations and interviews was also used to further triangulate findings. Statistical analysis revealed that students who completed the Bootstrap course gained a significantly better understanding of variables and a suggestive improvement in understanding functions. In the assessments, students failed to demonstrate a transfer of the advanced concepts of function composition and piecewise functions from programming to algebraic notation. Interviews with students demonstrated that with coaching, students were able to relate functions written in Racket to functions written in algebraic notation, but were not yet able to transfer their experience of function composition from programming to algebra.
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Ashraf, Pouya. „Pathological functions and the Baire category theorem“. Thesis, Uppsala universitet, Analys och sannolikhetsteori, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-322944.
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Petersson, Albin. „On the Properties of Wiener-Lévy Functions“. Thesis, Linnéuniversitetet, Institutionen för matematik (MA), 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-84606.
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This thesis concerns the Wiener algebra of periodic functions with absolutely convergent Fourier series, and the "Wiener-Lévy functions", meaning functions that preserve absolute convergence of Fourier series under composition. Results regarding the properties of functions in the Wiener algebra are established, as well as properties of Wiener-Lévy functions. By the Wiener-Lévy Theorem, analyticity is a sufficient condition for a function to be a Wiener-Lévy function, and in this paper, we find the necessary condition of being real analytic in the real and imaginary variable, separately.
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Bouya, Ismaël. „Instabilités en magnétohydrodynamique“. Phd thesis, Université Paris-Diderot - Paris VII, 2013. http://tel.archives-ouvertes.fr/tel-00867318.
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La magnétohydrodynamique, ou effet dynamo, consiste en la génération d'énergie électrique à partir d'énergie mécanique. Plus précisément, on étudie l'évolution d'un champ magnétique généré par un fluide conducteur. Ce phénomène se retrouve dans les planètes, les étoiles, ou même les galaxies, où le champ magnétique provient du mouvement interne. Dans cette thèse, nous nous intéressons plus précisément aux instabilités en magnétohydrodynamique : partant d'un fluide conducteur sans champs magnétique, est-ce qu'une perturbation légère de l'écoulement et du champ magnétique (par exemple, un résidu de champs magnétique arrivant d'un autre système) peut engendrer une amplification de ce champ magnétique, créant ainsi une dynamo ? La deuxième interrogation consiste en le temps nécessaire pour obtenir une telle amplification du champ magnétique. Cette thèse consiste donc en l'étude de ces deux questions, et donne deux résultats d'ordre théorique et deux résultats d'ordre numérique.
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麥可瑩 und Ho-ying Mak. „Functional magnetic resonance image registration using fourier phase and residue error detection“. Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2002. http://hub.hku.hk/bib/B30163304.
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Kou, Kit Ian. „Paley-Wiener theorem and Shannon sampling with the Clifford analysis setting“. Thesis, University of Macau, 2005. http://umaclib3.umac.mo/record=b2492153.
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Waara, Einar. „Gauss and Jacobi Sums and the Congruence Zeta Function“. Thesis, Uppsala universitet, Analys och sannolikhetsteori, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-354760.
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Burtseva, Evgeniya. „Operators and Inequalities in various Function Spaces and their Applications“. Licentiate thesis, Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:ltu:diva-59666.
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This Licentiate thesis is devoted to the study of mapping properties of different operators (Hardy type, singular and potential) between various function spaces. The main body of the thesis consists of five papers and an introduction, which puts these papers into a more general frame. In paper A we prove the boundedness of the Riesz Fractional Integration Operator from a Generalized Morrey Space to a certain Orlicz-Morrey Space, which covers the Adams resultfor Morrey Spaces. We also give a generalization to the case of Weighted Riesz Fractional Integration Operators for a class of weights. In paper B we study the boundedness of the Cauchy Singular Integral Operator on curves in complex plane in Generalized Morrey Spaces. We also consider the weighted case with radial weights. We apply these results to the study of Fredholm properties of Singular Integral Operators in Weighted Generalized Morrey Spaces. In paper C we prove the boundedness of the Potential Operator in Weighted Generalized Morrey Spaces in terms of Matuszewska-Orlicz indices of weights and apply this result to the Hemholtz equation with a free term in such a space. We also give a short overview of some typical situations when Potential type Operators arise when solving PDEs. In paper D some new inequalities of Hardy type are proved. More exactly, the boundedness of multidimensional Weighted Hardy Operators in Hölder Spaces are proved in cases with and without compactification. In paper E the mapping properties are studied for Hardy type and Generalized Potential type Operators in Weighted Morrey type Spaces.
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Zagar, Susanna Maria. „Convex functions“. CSUSB ScholarWorks, 1996. https://scholarworks.lib.csusb.edu/etd-project/986.
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Escobar, Alvaro E. „The multidimensional 0-1 knapsack problem an empirical analysis /“. Instructions for remote access. Click here to access this electronic resource. Access available to Kutztown University faculty, staff, and students only, 1990. http://www.kutztown.edu/library/services/remote_access.asp.
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Kuznetsov, Evgeny. „Maximal theorems and Calderón-Zygmund type decompositions forthe fractional maximal function“. Doctoral thesis, Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, 2005. http://urn.kb.se/resolve?urn=urn:nbn:se:ltu:diva-16836.
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A very significant role in the estimation of different operators in analysis is played by the Hardy-Littlewood maximal function. There are a lot of papers dedicated to the study of properties of it, its variants, and their applications. One of the important variants of the Hardy-Littlewood maximal function is the so-called fractional maximal function, which is deeply connected to the Riesz potential operator. The main goal of the thesis is to establish analogues of some important properties of the Hardy-Littlewood maximal function for the fractional maximal function. In 1930 Hardy and Littlewood proved a remarkable result, known as the Hardy-Littlewood maximal theorem. Therefore its naturally arose a problem: what is an analogue of the Hardy-Littlewood maximal theorem for the fractional maximal function? In the thesis we will give an answer for this problem. Particularly, we will show that the so-called Hausdorff capacity and Morrey spaces, introduced by C. Morrey in 1938 in connection with some problems in elliptic partial differential equations and the theory of variations, naturally appears here. Moreover, recently Morrey spaces found important applications in connection with the Navier-Stokes and Schrödinger equations, elliptic problems with discontinuous coefficients and potential theory. The Hardy-Littlewood maximal theorem is deeply connected with the Stein-Wiener and Riesz-Herz equivalences. Analogues of these equivalences for the fractional maximal function are also given. In 1971 C. Fefferman and E. Stein, by using the Calderón-Zygmund decomposition, obtained the generalization of the maximal theorem of Hardy-Littlewood for a sequence of functions. This result of Fefferman and Stein found many important applications in Harmonic Analysis and its applications, e.g. in Signal Processing. In the thesis we will give an analogue of one part of the Fefferman-Stein maximal theorem for the fractional maximal operator. In 1952 A. Calderón and A. Zygmund published the paper "On Existence of Certain Singular Integrals", which has made a significant influence on the Analysis of the last 50 years. One of the main new tools used by A. Calderón and A. Zygmund was a special family of the decomposition of a given function in its "good" and "bad" parts. This decomposition provides a multidimensional substitution of the famous "sunrise" lemma by F. Riesz and it was used for proving a weak-type estimate for singular integrals. Furthermore, we want to emphasize that Calderón-Zygmund type decompositions have played an important and sometimes crucial role in the proofs of many fundamental results, such as the John-Nirenberg inequality, the theory of Ap-weights, Fefferman-Stein maximal theorem, etc. In the thesis it is showed that it is possible to construct an analogue of the Calderón-Zygmund decomposition for the Morrey spaces.Godkänd; 2005; 20061004 (ysko)
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Ćurić, Vladimir. „Distance Functions and Their Use in Adaptive Mathematical Morphology“. Doctoral thesis, Uppsala universitet, Avdelningen för visuell information och interaktion, 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-221568.
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One of the main problems in image analysis is a comparison of different shapes in images. It is often desirable to determine the extent to which one shape differs from another. This is usually a difficult task because shapes vary in size, length, contrast, texture, orientation, etc. Shapes can be described using sets of points, crisp of fuzzy. Hence, distance functions between sets have been used for comparing different shapes. Mathematical morphology is a non-linear theory related to the shape or morphology of features in the image, and morphological operators are defined by the interaction between an image and a small set called a structuring element. Although morphological operators have been extensively used to differentiate shapes by their size, it is not an easy task to differentiate shapes with respect to other features such as contrast or orientation. One approach for differentiation on these type of features is to use data-dependent structuring elements. In this thesis, we investigate the usefulness of various distance functions for: (i) shape registration and recognition; and (ii) construction of adaptive structuring elements and functions. We examine existing distance functions between sets, and propose a new one, called the Complement weighted sum of minimal distances, where the contribution of each point to the distance function is determined by the position of the point within the set. The usefulness of the new distance function is shown for different image registration and shape recognition problems. Furthermore, we extend the new distance function to fuzzy sets and show its applicability to classification of fuzzy objects. We propose two different types of adaptive structuring elements from the salience map of the edge strength: (i) the shape of a structuring element is predefined, and its size is determined from the salience map; (ii) the shape and size of a structuring element are dependent on the salience map. Using this salience map, we also define adaptive structuring functions. We also present the applicability of adaptive mathematical morphology to image regularization. The connection between adaptive mathematical morphology and Lasry-Lions regularization of non-smooth functions provides an elegant tool for image regularization.
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Edlund, Tomas. „Pluripolar Sets and Pluripolar Hulls“. Doctoral thesis, Uppsala : Matematiska institutionen, Univ. [distributör], 2005. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-5872.
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Strandell, Gustaf. „Linear and Non-linear Deformations of Stochastic Processes“. Doctoral thesis, Uppsala : Matematiska institutionen, Univ. [distributr], 2003. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-3689.
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Reising, Justin. „Function Space Tensor Decomposition and its Application in Sports Analytics“. Digital Commons @ East Tennessee State University, 2019. https://dc.etsu.edu/etd/3676.
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Recent advancements in sports information and technology systems have ushered in a new age of applications of both supervised and unsupervised analytical techniques in the sports domain. These automated systems capture large volumes of data points about competitors during live competition. As a result, multi-relational analyses are gaining popularity in the field of Sports Analytics. We review two case studies of dimensionality reduction with Principal Component Analysis and latent factor analysis with Non-Negative Matrix Factorization applied in sports. Also, we provide a review of a framework for extending these techniques for higher order data structures. The primary scope of this thesis is to further extend the concept of tensor decomposition through the use of function spaces. In doing so, we address the limitations of PCA to vector and matrix representations and the CP-Decomposition to tensor representations. Lastly, we provide an application in the context of professional stock car racing.
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Persson, Leif. „Quasi-radial solutions of the p-harmonic equation in the plane and their stream functions“. Licentiate thesis, Luleå tekniska universitet, 1988. http://urn.kb.se/resolve?urn=urn:nbn:se:ltu:diva-25699.
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Kröger, Viktor. „Classification in Functional Data Analysis : Applications on Motion Data“. Thesis, Umeå universitet, Institutionen för matematik och matematisk statistik, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-184963.
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Anterior cruciate knee ligament injuries are common and well known, especially amongst athletes.These injuries often require surgeries and long rehabilitation programs, and can lead to functionloss and re-injuries (Marshall et al., 1977). This work aims to explore the possibility of applyingsupervised classification on knee functionality, using different types of models, and testing differentdivisions of classes. The data used is gathered through a performance test, where individualsperform one-leg hops with motion sensors attached to their bodies. The obtained data representsthe position over time, and is considered functional data.With functional data analysis (FDA), a process can be analysed as a continuous function of time,instead of being reduced to finite data points. FDA includes many useful tools, but also somechallenges. A functional observation can for example be differentiated, a handy tool not found inthe multivariate tool-box. The speed, and acceleration, can then be calculated from the obtaineddata. How to define "similarity" is, on the other hand, not as obvious as with points. In this work,an FDA-approach is taken on classifying knee kinematic data, from a long-term follow-up studyon knee ligament injuries.This work studies kernel functional classifiers, and k-nearest neighbours models, and performssignificance tests on the model accuracy, using re-sampling methods. Additionally, depending onhow similarity is defined, the models can distinguish different features of the data. Attempts atutilising more information through incorporation of ensemble-methods, does not exceed the singlemodels it is created from. Further, it is shown that classification on optimised sub-domains, canbe superior to classifiers using the full domain, in terms of predictive power.Främre korsbandsskador är vanliga och välkända skador, speciellt bland idrottsutövare. Skadornakräver ofta operationer och långa rehabiliteringsprogram, och kan leda till funktionell nedsättningoch återskador (Marshall et al., 1977). Målet med det här arbetet är att utforska möjligheten attklassificera knän utifrån funktionalitet, där utfallet är känt. Detta genom att använda olika typerav modeller, och genom att testa olika indelningar av grupper. Datat som används är insamlatunder ett prestandatest, där personer hoppat på ett ben med rörelsesensorer på kroppen. Deninsamlade datan representerar position över tid, och betraktas som funktionell data.Med funktionell dataanalys (FDA) kan en process analyseras som en kontinuerlig funktion av tid,istället för att reduceras till ett ändligt antal datapunkter. FDA innehåller många användbaraverktyg, men även utmaningar. En funktionell observation kan till exempel deriveras, ett händigtverktyg som inte återfinns i den multivariata verktygslådan. Hastigheten och accelerationen kandå beräknas utifrån den insamlade datan. Hur "likhet" är definierat, å andra sidan, är inte likauppenbart som med punkt-data. I det här arbetet används FDA för att klassificera knärörelsedatafrån en långtidsuppföljningsstudie av främre korsbandsskador.I detta arbete studeras både funktionella kärnklassificerare och k-närmsta grannar-metoder, och ut-för signifikanstest av modellträffsäkerheten genom omprovtagning. Vidare kan modellerna urskiljaolika egenskaper i datat, beroende på hur närhet definieras. Ensemblemetoder används i ett försökatt nyttja mer av informationen, men lyckas inte överträffa någon av de enskilda modellerna somutgör ensemblen. Vidare så visas också att klassificering på optimerade deldefinitionsmängder kange en högre förklaringskraft än klassificerare som använder hela definitionsmängden.
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Gerhard, Maike Verfasser], Hartmut [Akademischer Betreuer] Führ und Hermann [Akademischer Betreuer] [Wagner. „Mathematical analysis of head-related transfer functions / Maike Gerhard ; Hartmut Führ, Hermann Wagner“. Aachen : Universitätsbibliothek der RWTH Aachen, 2020. http://d-nb.info/1218788216/34.
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Diallo, Ibrahima Castillo. „Analysis of defects in GaN using Hybrid Density Functional Theory“. VCU Scholars Compass, 2013. http://scholarscompass.vcu.edu/etd/3130.
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In this thesis, we first present a brief overview of various theoretical approaches used to examine the electronic structure of defects in GaN. Using the recently developed hybrid density functional theory (HSE06) along with the experimental measurements, we propose a new explanation of the nature of the yellow luminescence band in carbon-doped GaN. We conduct a systematic study of electronic and optical properties of defects (Carbon, Oxygen, Silicon related) that are candidates for the origin of yellow luminescence. We show that the CN-ON complex is significantly more likely to form compared to isolated carbon configurations. In contrast to the properties of the isolated carbon acceptor, calculated defect levels and optical transitions involving deep level of the CN-ON complex agree quite well with our thermal luminescence quenching data as well as with the experimentally measured C-doped GaN luminescence spectra. Hence, the CN-ON complex, rather than isolated C impurity, is more likely to resolve a long-standing problem of the yellow luminescence in GaN.
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Crewe, Paul. „Some problems in abstract stochastic differential equations on Banach spaces“. Thesis, University of Oxford, 2011. http://ora.ox.ac.uk/objects/uuid:195c374f-3181-41b9-92d7-b375701a0b81.
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This thesis studies abstract stochastic differential equations on Banach spaces. The well-posedness of abstract stochastic differential equations on such spaces is a recent result of van Neerven, Veraar and Weis, based on the theory of stochastic integration of Banach space valued processes constructed by the same authors. We study existence and uniqueness for solutions of stochastic differential equations with (possibly infinite) delay in their inputs on UMD Banach spaces. Such problems are also known as functional differential equations or delay differential equations. We show that the methods of van Neerven et al. extend to such problems if the initial history of the system lies in a space of a type introduced by Hale and Kato. The results are essentially of a fixed point type, both autonomous and non-autonomous cases are discussed and an example is given. We also study some long time properties of solutions to these stochastic differential equations on general Banach spaces. We show the existence of solutions to stochastic problems with almost periodicity in a weak or distributional sense. Results are again given for both autonomous and non-autonomous cases and depend heavily on estimates for R-bounds of operator families developed by Veraar. An example is given for a second order differential operator on a domain in ℝd. Finally we consider the existence of invariant measures for such problems. This extends recent work of van Gaans in Hilbert spaces to Banach spaces of type 2.
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Sunehag, Peter. „Interpolation of Subcouples, New Results and Applications“. Doctoral thesis, Uppsala : Matematiska institutionen, Univ. [distributör], 2003. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-3777.
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Balsubramanian, Ravishankar. „Error estimation and grid adaptation for functional outputs using discrete-adjoint sensitivity analysis“. Master's thesis, Mississippi State : Mississippi State University, 2002. http://library.msstate.edu/etd/show.asp?etd=etd-10032002-113749.
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Calzi, Mattia. „Functional Calculus on Homogeneous Groups“. Doctoral thesis, Scuola Normale Superiore, 2019. http://hdl.handle.net/11384/85740.
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In the first part of the thesis, we consider the following problem.
Let G be a homogeneous group, and let (L_1,...,L_n) be a jointly hypoelliptic commutative finite family of formally self-adjoint, homogeneous, left-invariant differential operators without constant terms.
Then, the operators L_j are essentially self-adjoint as operators on L^2(G) with domain C^infty_c(G), and their closures commute emph{as self-adjoint operators}.
Therefore, one may consider the joint functional calculus associated with the family (L_1,...,L_n).
More precisely, for every bounded Borel measurable function $m$ on $R^n$, the corresponding operator m(L_1,...,L_n) commutes with left translations, so that it admits a unique right convolution kernel K(m).
The so-defined kernel transform K then maps S(R^n) continuously into S(G), and L^2(eta) isometrically into L^2(G) for some uniquely determined positive Radon measure eta on R^n; this latter property can be considered as an analogue of the Plancherel isomorphism.
In addition, K maps L^1(eta) continuously into C_0(G), and this property can be considered as an analogue of the Riemann--Lebesgue lemma.
We focus on the following properties of K:
(RL) if K(m)in L^1(G), then m can be taken in C_0(R^n): this is again an analogue of the Riemann--Lebesgue lemma;
(S) if K(m)in S(G), then m can be taken in S(R^n).
We prove that properties (RL) and (S) are compatible with products, and we characterize the Rockland operators which satisfy property (S) when the underlying group G is abelian.
We then consider the case of 2-step stratified groups, and families whose elements are either sub-Laplacians or vector fields of homogeneous degree 2. In this setting, we prove several sufficient conditions, as well as some necessary ones, for properties (RL) and (S); we even characterize them in some more specific settings.
In addition, we study the case of general (that is, not necessarily homogeneous) sub-Laplacians on 2-step stratified groups, and prove that they always satisfy properties (RL) and (S).
We also prove that, under some mild assumptions, a multiplier m can be taken so as to satisfy Mihlin--Hormander conditions of order infinity if and only if the corresponding kernel K(m) satisfies Calderon--Zygmund conditions of order infinity.
In the second part of the thesis, we present some results which are joint work with T. Bruno.
We fix the standard sub-Laplacian on an H-type group, and consider its heat kernel (p_s)_{s>0}. We provide sharp asymptotic estimates at $infty$ for basically all the derivatives of p_1. Because of the homogeneity of the family (p_s), these estimates can also be considered as short-time asymptotics.
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Groves, Adrian R. „Bayesian learning methods for modelling functional MRI“. Thesis, University of Oxford, 2009. http://ora.ox.ac.uk/objects/uuid:fe46e696-a1a6-4a9d-9dfe-861b05b1ed33.
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Bayesian learning methods are the basis of many powerful analysis techniques in neuroimaging, permitting probabilistic inference on hierarchical, generative models of data. This thesis primarily develops Bayesian analysis techniques for magnetic resonance imaging (MRI), which is a noninvasive neuroimaging tool for probing function, perfusion, and structure in the human brain. The first part of this work fits nonlinear biophysical models to multimodal functional MRI data within a variational Bayes framework. Simultaneously-acquired multimodal data contains mixtures of different signals and therefore may have common noise sources, and a method for automatically modelling this correlation is developed. A Gaussian process prior is also used to allow spatial regularization while simultaneously applying informative priors on model parameters, restricting biophysically-interpretable parameters to reasonable values. The second part introduces a novel data fusion framework for multivariate data analysis which finds a joint decomposition of data across several modalities using a shared loading matrix. Each modality has its own generative model, including separate spatial maps, noise models and sparsity priors. This flexible approach can perform supervised learning by using target variables as a modality. By inferring the data decomposition and multivariate decoding simultaneously, the decoding targets indirectly influence the component shapes and help to preserve useful components. The same framework is used for unsupervised learning by placing independent component analysis (ICA) priors on the spatial maps. Linked ICA is a novel approach developed to jointly decompose multimodal data, and is applied to combined structural and diffusion images across groups of subjects. This allows some of the benefits of tensor ICA and spatially-concatenated ICA to be combined, and allows model comparison between different configurations. This joint decomposition framework is particularly flexible because of its separate generative models for each modality and could potentially improve modelling of functional MRI, magnetoencephalography, and other functional neuroimaging modalities.
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Garner, William Howard. „Iteration of the power operation“. Virtual Press, 1995. http://liblink.bsu.edu/uhtbin/catkey/941367.
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This thesis is an investigation of the sequence of functions defined by fl (x) -xand fn+1 (x) -x , where the power is the principal value.In the case where the sequence is restricted to positive real this sequence of functions over thecomplex plane, we attack real numbers, the problem yields to the methods of analysis and we prove the behavior of the sequence.The more general problem of describing the behavior of both analytically and numerically. Though no full rigorous solution is given, the results presented suggest the behavior of the sequence over the complex plane is very interesting.Department of Mathematical Sciences