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1
Azamov, Nurulla, and azam0001@infoeng flinders edu au. "Spectral shift function in von Neumann algebras." Flinders University. Informatics and Engineering, 2008. http://catalogue.flinders.edu.au./local/adt/public/adt-SFU20080129.121422.
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The main subsect of this thesis is the theory of Lifshits-Krein spectral shift function in semifinite von Neumann algebras and its connection with the theory of spectral flow.
Main results are an analogue of the Krein trace formula for semifinite von Neumann algebras, the semifinite analogue of the Birman-Solomyak spectral averaging formula, a connection between the spectral shift function and the spectral flow and a Lidskii type formula for Dixmier traces. In particular, it is established that in the case of operators with compact resolvent, the spectral shift function and the spectral flow are identical notions.
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fr, vbruneau@math u.-bordeaux. "Meromorphic Continuation of the Spectral Shift Function." ESI preprints, 2001. ftp://ftp.esi.ac.at/pub/Preprints/esi1073.ps.
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Czapla-Myers, Jeffrey S. "Spectral response function characterization methodologies for imaging spectrometers." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2000. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp03/MQ56168.pdf.
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Megaides, Rodrigo. "Spectral and wave function statistics in quantum digraphs." Thesis, Brunel University, 2012. http://bura.brunel.ac.uk/handle/2438/7252.
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Spectral and wave function statistics of the quantum directed graph, QdG, are studied. The crucial feature of this model is that the direction of a bond (arc) corresponds to the direction of the waves propagating along it. We pay special attention to the full Neumann digraph, FNdG, which consists of pairs of antiparallel arcs between every node, and differs from the full Neumann graph, FNG, in that the two arcs have two incommensurate lengths. The spectral statistics of the FNG (with incommensurate bond lengths) is believed to be universal, i.e. to agree with that of the random matrix theory, RMT, in the limit of large graph size. However, the standard perturbative treatment of the field theoretical representation of the 2-point correlation function [1, 2] for a FNG, does not account for this behaviour. The nearest-neighbor spacing distribution of the closely related FNdG is studied numerically. An original, efficient algorithm for the generation of the spectrum of large graphs allows for the observation that the distribution approaches indeed universality at increasing graph size (although the convergence cannot be ascertained), in particular "level repulsion" is confirmed. The numerical technique employs a new secular equation which generalizes the analogous object known for undirected graphs [3, 4], and is based on an adaptation to digraphs of the idea of wave function continuity. In view of the contradiction between the field theory [2] and the strong indications of universality, a non-perturbative approach to analysing the universal limit is presented. The substitution of the FNG by the FNdG results in a field theory with fewer degrees of freedom. Despite this simplification, the attempt is inconclusive. Possible applications of this approach are suggested. Regarding the wave function statistics, a field theoretical representation for the spectral average of the wave intensity on an fixed arc is derived and studied in the universal limit. The procedure originates from the study of wave function statistics on disordered metallic grains [5] and is used in conjunction with the field theory approach pioneered in [2].
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Townsend, Whitney Jeanne. "Discrete function representations utilizing decision diagrams and spectral techniques." Thesis, Mississippi State : Mississippi State University, 2002. http://library.msstate.edu/etd/show.asp?etd=etd-07012002-160303.
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Artiles, Oswaldo. "Multinucleon Short-range Correlation Model for Nuclear Spectral Functions." FIU Digital Commons, 2017. http://digitalcommons.fiu.edu/etd/3384.
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The main goal of the research presented in my dissertation was to develop a theoretical model for relativistic nuclear spectral functions at high missing momenta and removal energies based on the multi-nucleon short-range correlation (SRC) model. The nuclear spectral functions are necessary for the description of high energy nuclear processes currently being studied at different labs such as JLAB, LHC and FNAL.
The model followed the effective Feynman diagrammatic approach in order to ac-count for the relativistic effects important in the SRC domain. In addition to the two-nucleon (2N) SRC with center of mass motion contribution, the contribution of the three-nucleon SRCs to the spectral functions was also derived. The latter was modeled based on the assumption that the 3N SRCs are a product of two sequential short range nucleon-nucleon (NN) interactions.
The nuclear spectral functions models were derived from two theoretical frameworks for evaluating covariant Feynman diagrams: In the first, referred to as the virtual nucleon approximation, the Feynman diagrams were reduced to the time ordered non-covariant diagrams by evaluating the nucleon spectators in the SRC at their positive energy poles, neglecting explicitly the contribution from vacuum diagrams. In the second approach, referred to as the light-front approximation, the boost invariant nuclear spectral function was formulated in the light-front reference frame in which case the vacuum diagrams are kinematically suppressed and the bound nucleon is described by its light-front variables such as momentum fraction, transverse momentum and invariant mass.
On the basis of the derived nuclear spectral functions, the corresponding computational models were developed from which the numerical estimates of the SRC spectral functions, the SRC momentum distributions, and the SRC density matrices were obtained.
7
Watson, Simon P. "On the asymptotics of the Dirichlet Laplacian : cones, corners and conduction." Thesis, University of Bristol, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.246266.
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Alsaedy, Ammar, and Nikolai Tarkhanov. "Spectral projection for the dbar-Neumann problem." Universität Potsdam, 2012. http://opus.kobv.de/ubp/volltexte/2012/5861/.
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Hendricks, Jeffrey James. "Spectral Stability of Weak Detonations in the Majda Model." BYU ScholarsArchive, 2013. https://scholarsarchive.byu.edu/etd/3626.
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Using analytical and numerical Evans-function techniques, we examine the spectral stability of weak-detonation-wave solutions of Majda's scalar model for a reacting gas mixture. We provide a proof of monotonicity of solutions. Using monotonicity we obtain a bound on possible unstable eigenvalues for weak-detonation-wave solutions that improves on the more general bound given by Humpherys, Lyng, and Zumbrun. We use a numerical approximation of the Evans function to search for possible unstable eigenvalues in the bounded region obtained by the energy estimate. For the parameter values tested, our results combined with the result of Lyng, Raoofi, Texier, and Zumbrun demonstrate that these waves are nonlinearly phase-asymptotically orbitally stable throughout the parameter space for which solutions were obtainable.
10
Yoo, Hyungsuk. "Quality of the Volterra transfer function estimation /." Digital version accessible at:, 1998. http://wwwlib.umi.com/cr/utexas/main.
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Dargel, Piet. "Spectral functions of low-dimensional quantum systems." Doctoral thesis, Niedersächsische Staats- und Universitätsbibliothek Göttingen, 2012. http://hdl.handle.net/11858/00-1735-0000-000D-F1A3-6.
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Busche, Tom. "Renormalization group approach to the spectral function of the Tomonaga-Luttinger model." [S.l. : s.n.], 2003. http://deposit.ddb.de/cgi-bin/dokserv?idn=968930050.
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Ulm, German [Verfasser], and Alexander [Akademischer Betreuer] Lichtenstein. "Spectral Function Calculation for Strongly Correlating Systems / German Ulm. Betreuer: Alexander Lichtenstein." Hamburg : Staats- und Universitätsbibliothek Hamburg, 2011. http://d-nb.info/1020384646/34.
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Oliver, Christopher William. "Development of surface electromyographic spectral analysis techniques for assessing paraspinal muscle function." Thesis, University College London (University of London), 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.307581.
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Overmoyer, Kate. "Applications of Entire Function Theory to the Spectral Synthesis of Diagonal Operators." Bowling Green State University / OhioLINK, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1305826657.
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Janczak, Julia. "Theory of Spectral Function and Optical Conductivity for Half-Metallic Double Perovskites." The Ohio State University, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=osu1354713689.
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Mroz, Kamil. "Bounds on eigenfunctions and spectral functions on manifolds of negative curvature." Thesis, Loughborough University, 2014. https://dspace.lboro.ac.uk/2134/15038.
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In this dissertation we study the Laplace operator acting on functions on a smooth, compact Riemannian manifold. Our approach is based on the study of the spectrum of the aforementioned operator. The main objects of our interest are the counting function of the Laplacian and its Riesz means. We discuss the asymptotics of aforementioned functions when the argument approaches infinity.
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Schmidt-Grund, Rüdiger, Krauß Hannes, Christian Kranert, Michael Bonholzer, and Marius Grundmann. "Temperature dependence of the dielectric function in the spectral range (0.5–8.5) eV of an In2O3 thin film." AIP Publishing, 2014. https://ul.qucosa.de/id/qucosa%3A31382.
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We present the dielectric function of a bcc-In2O3 thin film in the wide spectral range from nearinfrared to vacuum-ultraviolet and for temperatures 10 K–300K, determined by spectroscopic ellipsometry. From the temperature dependence of electronic transition energies, we derive electron-phonon coupling properties and found hints that the direct parabolic band-band transitions involve In-d states. Further we discuss possible excitonic contributions to the dielectric function.
19
Pradhan, Pushkar Shrikant. "Measuring the effects of soil parameters on bidirectional reflectance distribution function." Master's thesis, Mississippi State : Mississippi State University, 2001. http://library.msstate.edu/etd/show.asp?etd=etd-11132001-113251.
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Deborah, Hilda. "Towards spectral mathematical morphology." Thesis, Poitiers, 2016. http://www.theses.fr/2016POIT2328/document.
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En fournissant en plus de l'information spatiale une mesure spectrale en fonction des longueurs d'ondes, l'imagerie hyperspectrale s'enorgueillie d'atteindre une précision bien plus importante que l'imagerie couleur. Grâce à cela, elle a été utilisée en contrôle qualité, inspection de matériaux,… Cependant, pour exploiter pleinement ce potentiel, il est important de traiter la donnée spectrale comme une mesure, d'où la nécessité de la métrologie, pour laquelle exactitude, incertitude et biais doivent être maitrisés à tous les niveaux de traitement.Face à cet objectif, nous avons choisi de développer une approche non-linéaire, basée sur la morphologie mathématique et de l'étendre au domaine spectral par le biais d'une relation d'ordre spectral basée sur les fonctions de distance. Une nouvelle fonction de distance spectrale et une nouvelle relation d'ordonnancement sont ainsi proposées. De plus, un nouvel outil d'analyse du basé sur les histogrammes de différences spectrales a été développé.Afin d'assurer la validité des opérateurs, une validation théorique rigoureuse et une évaluation métrologique ont été mises en œuvre à chaque étage de développement. Des protocoles d'évaluation de la qualité des traitements morphologiques sont proposés, exploitant des jeux de données artificielles pour la validation théorique, des ensembles de données dont certaines caractéristiques sont connues pour évaluer la robustesse et la stabilité et des jeux de données de cas réel pour prouver l'intérêt des approches en contexte applicatif. Les applications sont développées dans le contexte du patrimoine culturel pour l'analyse de peintures et pigmentsProviding not only spatial information but also spectral measure as a function of wavelength, hyperspectral imaging boasts a much greater gain in accuracy than the traditional color imaging. And for this capability, hyperspectral imaging has been employed for quality control, inspection of materials in various fields. However, to fully exploit this potential, it is important to process the spectral data as a measure. This induces the need of metrology where accuracy, uncertainty, and bias are managed at every level of processing.Aiming at developing a metrological image processing framework for spectral data, we select to develop a nonlinear approach using the mathematical morphology framework and extended it to the spectral domain by means of a distance-based ordering relation. A novel spectral distance function and spectral ordering relation are proposed, in addition of a new analysis tools based on spectral differences. To ensure the validity of the spectral mathematical morphology framework, rigorous theoretical validation and metrological assessment are carried out at each development stages. So, protocols for quality assessment of spectral image processing tools are developed. These protocols consist of artificial datasets to validate completely the theoretical requirements, datasets with known characteristics to assess the robustness and stability, and datasets from real cases to proof the usefulness of the framework on applicative context. The application tasks themselves are within the cultural heritage domain, where the target images come from pigments and paintings
Hyperspektral avbildning muliggjør mye mer nøyaktige målinger enn tradisjonelle gråskala og fargebilder, gjennom både høy romlig og spektral oppløsning (funksjon av bølgelengde). På grunn av dette har hyperspektral avbildning blitt anvendt i økende grad ulike applikasjoner som kvalitetskontroll og inspeksjon av materialer. Men for å fullt ut utnytte sitt potensiale, er det viktig å være i stand til å behandle spektrale bildedata som målinger på en gyldig måte. Dette induserer behovet for metrologi, der nøyaktighet, usikkerhet og skjevhet blir adressert og kontrollert på alle nivå av bildebehandlingen.Med sikte på å utvikle et metrologisk rammeverk for spektral bildebehandling valgte vi en ikke-lineær metodikk basert på det etablerte matematisk morfologi-rammeverket. Vi har utvidet dette rammeverket til det spektrale domenet ved hjelp av en avstandsbasert sorteringsrelasjon. En ny spektral avstandsfunksjon og nye spektrale sorteringsrelasjoner ble foreslått, samt nye verktøy for spektral bildeanalyse basert på histogrammer av spektrale forskjeller.For å sikre gyldigheten av det nye spektrale rammeverket for matematisk morfologi, har vi utført en grundig teoretisk validering og metrologisk vurde-ring på hvert trinn i utviklingen. Dermed er og-så nye protokoller for kvalitetsvurdering av spektrale bildebehandlingsverktøy utviklet. Disse protokollene består av kunstige datasett for å validere de teoretiske måletekniske kravene, bildedatasett med kjente egenskaper for å vurdere robustheten og stabiliteten, og datasett fra reelle anvendelser for å bevise nytten av rammeverket i en anvendt sammenheng. De valgte anvendelsene er innenfor kulturminnefeltet, hvor de analyserte bildene er av pigmenter og malerier
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at, Andreas Cap@esi ac. "Smoothness and High Energy Asymptotics of the Spectral Shift Function in Many--Body Scattering." ESI preprints, 2001. ftp://ftp.esi.ac.at/pub/Preprints/esi1048.ps.
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Schmidt-Grund, Rüdiger, Christian Kranert, Tammo Böntgen, Wenckstern Holger von, Hannes Krauß, and Marius Grundmann. "Dielectric function in the NIR-VUV spectral range of (InxGa1-x)2O3 thin films." American Institute of Physics, 2014. https://ul.qucosa.de/id/qucosa%3A31191.
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We determined the dielectric function of the alloy system (InxGa1−x)2O3 by spectroscopic
ellipsometry in the wide spectral range from 0.5 eV to 8.5 eV and for In contents ranging from
x = 0.02 to x = 0.61. The predicted optical transitions for binary, monoclinic β-Ga2O3, and cubic
bcc-In2O3 are well reflected by the change of the dielectric functions’ lineshape as a function of the
In content. In an intermediate composition range with phase-separated material (x ≈ 0.3…0.4), the
lineshape differs considerably, which we assign to the presence of the high-pressure rhombohedral
InGaO3-II phase, which we also observe in Raman experiments in this range. By model analysis of
the dielectric function, we derived spectra of the refractive index and the absorption coefficient and
energy parameters of electronic band-band transitions. We discuss the sub-band gap absorption tail
in relation to the influence of the In 4d orbitals on the valence bands. The data presented here provide
a basis for a deeper understanding of the electronic properties of this technologically important
material system and may be useful for device engineering.
23
Wilking, B. A., C. J. Lada, and E. R. Young. "IRAS Observations of the Rho Ophiuchi Infrared Cluster: Spectral Energy Distributions and Luminosity Function." Steward Observatory, The University of Arizona (Tucson, Arizona), 1988. http://hdl.handle.net/10150/623919.
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Hardegree-Ullman, Kevin Karlyle. "Kepler Planet Occurrence Rates for Mid-Type M Dwarfs as a Function of Spectral Type." University of Toledo / OhioLINK, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=toledo1533214839813619.
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Munir, Nazia Binte. "Manufacturing and Characterization of Gold-Black and Prediction and Measurement of its Directional Spectral Absorptivity." Diss., Virginia Tech, 2021. http://hdl.handle.net/10919/102097.
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Gold-black has emerged as a popular absorptive coating for thermal radiation detectors in aerospace applications. The performance and accuracy of thermal radiation detectors largely depends on the surface optical properties of the absorptive coating. If the absorptivity of the layer is directional or wavelength dependent, then so will be the detector gain itself. This motivates our interest in the manufacture, physical characterization, and study of the wavelength and polarization sensitivity of the directional spectral absorptivity of gold-black. A first-principle model based on lossy antenna theory is presented to predict the polarization dependent directional spectral absorptivity of gold-black in the visible and near infrared. Results for normal spectral absorptivity are in good agreement with measurements reported in the literature. However, suitable experimental data were not available to validate the theory for directional spectral absorptivity. Therefore, an experimental campaign to fabricate and measure the directional spectral behavior of gold-black had to be undertaken to validate the first-principle model. New in-plane bidirectional reflectance distribution function (BRDF) measurements for two thicknesses (~4 μm and ~8 μm) of gold-black laid down on a gold mirror substrate are reported in the visible (532 nm) and near-infrared (800 and 850 nm) for p- and s-polarizations. The investigation is then extended to a three-layer sample, which is shown to exhibit off-specular reflectivity. Described are processes for laying down gold-black coatings and for measuring their in-plane BRDF as a function of thickness, wavelength, and polarization state. A novel method for retrieving the directional absorptivity from in-plane BRDF measurements is presented. The influence of polarization on directional absorptivity is shown to follow our earlier theory except at large incident zenith angles, where an unanticipated mirage effect is observed.Doctor of Philosophy
Instruments called thermal radiation detectors play an important role in monitoring the global climate from space. Gold-black is often used as an absorptive coating to enhance the performance of these instruments. Users need to know how gold-black coatings influence instrument performance. In general, coating properties depend on the wavelength and direction of incident radiation, as well as on an optical phenomenon called polarization. This dissertation investigates the relationship between the creation of gold-black coatings and their performance. A physical model is postulated for predicting the optical behavior of gold-black in the visible and near infrared. The model produces results that are in good agreement with measurements reported in the literature. However, suitable directional measurements were not available to validate the theory. Therefore, an experimental campaign was mounted to fabricate gold-black coatings and measure their optical behavior in order to validate the mathematical model. We observed the optical behavior of several of our gold-black samples of various thickness and over a range of wavelengths. We also studied a three-layer sample which was found to exhibit an unexpected behavior called off-specular reflectivity. Described are processes for creating gold-black coatings and for measuring and explaining their optical performance. During the course of this investigation an unanticipated mirage effect was observed for the first time.
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Omenyi, Louis Okechukwu. "On the second variation of the spectral zeta function of the Laplacian on homogeneous Riemanniann manifolds." Thesis, Loughborough University, 2014. https://dspace.lboro.ac.uk/2134/16167.
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The spectral zeta function, introduced by Minakshisundaram and Pleijel in [36] and denoted by ζg(s), encodes important spectral information for the Laplacian on Riemannian manifolds. For instance, the important notions of the determinant of the Laplacian and Casimir energy are defined via the spectral zeta function. On homogeneous manifolds, it is known that the spectral zeta function is critical with respect to conformal metric perturbations, (see e.g Richardson ([47]) and Okikiolu ([41])). In this thesis, we compute a second variation formula of ζg(s) on closed homogeneous Riemannian manifolds under conformal metric perturbations. It is well known that the quadratic form corresponding to this second variation is given by a certain pseudodifferential operator that depends meromorphically on s. The symbol of this operator was analysed by Okikiolu in ([42]). We analyse it in more detail on homogeneous spaces, in particular on the spheres Sn. The case n = 3 is treated in great detail. In order to describe the second variation we introduce a certain distributional integral kernel, analyse its meromorphic properties and the pole structure. The Casimir energy defined as the finite part of ζg(-½) on the n-sphere and other points of ζg(s) are used to illustrate our results. The techniques employed are heat kernel asymptotics on Riemannian manifolds, the associated meromorphic continuation of the zeta function, harmonic analysis on spheres, and asymptotic analysis.
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Munir, Riffat. "Effect of Wavelength Dependent Point Spread Function on Shear Measurements." Ohio University / OhioLINK, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1462532342.
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Williams, Nicholas Owen. "The relationship between partition function zeros, the spectral properties of transfer matrices and finite size scaling." Thesis, King's College London (University of London), 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.265977.
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Selander, Keith N. "A function space approach to the generalized nonlinear model with applications to frequency domain spectral estimation." Diss., This resource online, 1992. http://scholar.lib.vt.edu/theses/available/etd-06062008-172034/.
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Leon, Ralph Daniel. "Module structure of a Hilbert space." CSUSB ScholarWorks, 2003. https://scholarworks.lib.csusb.edu/etd-project/2469.
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This paper demonstrates the properties of a Hilbert structure. In order to have a Hilbert structure it is necessary to satisfy certain properties or axioms. The main body of the paper is centered on six questions that develop these ideas.
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Samavat, Reza. "Mean Eigenvalue Counting Function Bound for Laplacians on Random Networks." Doctoral thesis, Universitätsbibliothek Chemnitz, 2015. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-159578.
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Spectral graph theory widely increases the interests in not only discovering new properties of well known graphs but also proving the well known properties for the new type of graphs. In fact all spectral properties of proverbial graphs are not acknowledged to us and in other hand due to the structure of nature, new classes of graphs are required to explain the phenomena around us and the spectral properties of these graphs can tell us more about the structure of them. These both themes are the body of our work here. We introduce here three models of random graphs and show that the eigenvalue counting function of Laplacians on these graphs has exponential decay bound. Since our methods heavily depend on the first nonzero eigenvalue of Laplacian, we study also this eigenvalue for the graph in both random and nonrandom cases.
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Parks, Robert E., and Michael T. Tuell. "The structure function as a metric for roughness and figure." SPIE-INT SOC OPTICAL ENGINEERING, 2016. http://hdl.handle.net/10150/622535.
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As optical designs become more sophisticated and incorporate aspheric and free form surfaces, the need to specify limits on mid-spatial frequency manufacturing errors becomes more critical, particularly as we better understand the effects of these errors on image quality. While there already exist methods based on Fourier analysis to specify these errors in most commercial interferometry software, the method of calculation and the power spectral density (PSD) results remain obscure to many in the optical design and manufacturing field. We suggest that the structure functions (SF) contains the same information as in the Fourier based PSD but in a way that is much more transparent to analysis, interpretation and application as a specification. The units of measure are more familiar and the concept behind the analysis is simpler to understand. Further, the information contained in the structure function (or PSD) allows a complete specification of an optical surface from the finest measurable detail of roughness to the overall figure. We discuss the origin of the structure function in the field of astronomy to describe the effects of air turbulence on image quality, the simple mathematical definition of the structure function and its easy means of calculation and how its results should be scaled depending on the location of the optical surface in a system from pupil to image plane. Finally, we give an example of how to write a specification of an optical surface using the structure function.
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Schmidt-Grund, Rüdiger, Hannes Krauß, Christian Kranert, Michael Bonholzer, and Marius Grundmann. "Temperature dependence of the dielectric function in the spectral range (0.5–8.5) eV of an In2O3 thin film." American Institute of Physics, 2014. https://ul.qucosa.de/id/qucosa%3A31187.
Full textAbstract:
We present the dielectric function of a bcc-In2O3 thin film in the wide spectral range from nearinfrared
to vacuum-ultraviolet and for temperatures 10 K–300K, determined by spectroscopic
ellipsometry. From the temperature dependence of electronic transition energies, we derive
electron-phonon coupling properties and found hints that the direct parabolic band-band transitions
involve In-d states. Further we discuss possible excitonic contributions to the dielectric
function.
34
Tzovanis, Maria. "Power spectral components of heart rate variability at rest and exercise after surgical repair of tetralogy of fallot." Thesis, McGill University, 1998. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=21274.
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An abnormal chronotropic response to exercise is a common finding following surgical repair of tetralogy of Fallot (TOF) which has generally been attributed to a putative sympathetic dysfunction. There exists little information on sympathetic function in patients operated for a congenital heart defect to support such a claim. This study used spectral analysis of heart rate (HRV) and blood pressure (BPV) variability to examine sympathovagal influences on the sinus node in 9 adolescents operated for TOF 13.0 +/- 1.12 years previously and in 8 healthy age and sex-matched control (CTRL) subjects. Continuous ECG and BP recordings were obtained under supine or seated resting positions, with or without controlled respiration at 0.20 Hz (CR); after passive 85° head-up tilt (HUT); during cycling at steady-state heart rates of 100 and 120 bpm (Ex 100, Ex 120), and after 10 and 20 minutes of passive seated recovery. (Abstract shortened by UMI.)
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Akkouche, Sofiane. "Sur la theorie spectrale des opérateurs de Schrödinger discrets." Thesis, Bordeaux 1, 2010. http://www.theses.fr/2010BOR14098/document.
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Cette thèse traite de la théorie spectrale des opérateurs de Schrödinger discrets H(λ) := - Δ + b sur Zd et plus généralement sur des graphes pondérés infinis. Plus précisément, nous étudions le comportement des fonctions spectrales qui représentent les bornes du spectre de ces opérateurs. Un des principaux résultats est l'obtention d'une condition nécessaire et suffisante sur le potentiel b pour que le bas du spectre soit strictement positif. L'étude du haut du spectre est également considérée.Nous étudions tout d'abord ces questions pour les opérateurs de Schrödinger discrets sur Zd. La régularité de cet espace permet alors d'obtenir des résultats spécifiques dans ce cas particulier. Nous généralisons ensuite nos travaux au cas des graphes infinis pondérés. Les techniques développées dans ce cadre nous permettent également d'étudier le comportement asymptotique du bas du spectre pour les grandes valeurs de λThis thesis deals with the spectral theory of discrete Schrödinger operators H(λ) := - Δ + b on Zd and more generally on in#nite weighted graphs. Precisely, we study the behavior of the spectral functions which represent the spectral bounds of these operators. One of the main results is the obtention of a necessary and sufficient condition on the potential b such that the bottom of the spectrum is stricly positive.The study of the top of the spectrum is also treated.We first study these questions for discrete Schrödinger operators on Zd. The regularity of this space provides specific results in this particular case. Then we extend our work to the case of infinite weighted graphs. Moreover, the technics developed in this framework allow us to study the asymptotic behavior of the bottom of the spectrum for large values of λ
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Prasert, Sunyaruk. "Multi angle imaging with spectral remote sensing for scene classification." Thesis, Monterey, Calif. : Springfield, Va. : Naval Postgraduate School ; Available from National Technical Information Service, 2005. http://library.nps.navy.mil/uhtbin/hyperion/05Mar%5FPrasert.pdf.
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Thesis (M.S. in Information Technology Management)--Naval Postgraduate School, March 2005.Thesis Advisor(s): Richard C. Olsen. Includes bibliographical references (p. 95-97). Also available online.
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Berntsson, Linn. "Evaluation of cognitive workload using EEG : Investigation of how sensory feedback improves function of osseo-neuromuscular upper limb prostheses." Thesis, Linköpings universitet, Institutionen för medicinsk teknik, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-160183.
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The e-OPRA Implant System (Integrum AB, Sweden) is a system which employs permanently accessible implantable neuromuscular electrodes in combination with osseointegrated attachment of the prosthesis to the skeleton, in order to create a more natural control of advanced robotic upper-limb prostheses. The system enables the possibility of sensory feedback, via a cuff electrode to the ulnar nerve which allows for direct neurostimulation of the nerve. This work proposes a method using electroencephalography (EEG) to quantitatively evaluate the cognitive workload of a person controlling a prosthesis, and how said workload changes when sensory feedback is enabled. Based on previous studies on EEG and cognitive workload, the proposed methods include collecting EEG data from subjects who are performing a grasping task while listening to a selection of sounds and counting the number of times a specific tone is presented. The data is analysed using both event related potentials (ERPs) as well as spectral analysis. The method was used in a trial run consisting of two healthy subjects, and one transhumeral amputee implanted with the e-OPRA system. Although the subject group was not large enough to draw any statistical conclusions, the trial run and the results from it suggest that the methods could be used in a larger study to evaluate the cognitive workload of amputees implanted with the e-OPRA system.
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Orsi, Maia. "Population synthesis models for IMF studies." Thesis, Liverpool John Moores University, 2014. http://researchonline.ljmu.ac.uk/4525/.
Full textAbstract:
Population synthesis models (PSMs) are fundamental tools to study the star formation history and IMF of unresolved stellar populations using spectral features. This work presents a new set of PSMs constructed using theoretical isochrones and two state-ofthe- art synthetic spectral libraries. The BT-Settl and Munari libraries were chosen for their ability to predict the observed values of Lick-type and IMF-sensitive indices in individual stars of the solar neighbourhood. The BT-Settl library was used to sample the cool main sequence stars and the Munari library for the rest of the evolutionary phases. The PSMs cover a range of metallicities with [Fe/H]= 0, -1.31 and -1.81 for scaled-solar and α-enhanced metal mixtures. The models were used to study the behaviour of the IMF indices defined in the literature and the results are in good agreement with what other PSMs have determined. The PSMs in this work predict a strong degeneracy between age, metallicity and IMF. I used the models to study which are the main evolutionary phases contributing to each IMF-sensitive index and found that most indices reach their final integrated values before the turn off. The post-main sequence stars contribute mainly to the continuum of these bands. Uncertainties in the the effective temperature of the isochrones can affect IMF estimates. The PSMs were applied to extragalactic globular clusters (GCs) and early-type galaxies (ETGs) using data from the literature. I determined the ages, metallicities and IMFs of these systems using index combinations in the optical and infrared. I explored how the morphology of the Horizontal Branch (HB) and dynamical evolution (which are key uncertainties in the modelling of GCs) can affect the IMF predictions. In a population with a Milky Way IMF, dynamical evolution can make the IMF indices mimic a bottom-light IMF. HB morphology has no impact on the IMF estimates at low [Fe/H]. In the IMF index-index diagrams for GCs, the results are significantly affected by the unknown sodium abundances of these systems. Using the PSMs in this work the best index combination to determine the IMF is CaH1 and TiO2. The ETGs and the [Fe/H]=0 GCs appear to have a bottom-heavy IMF with x ~ 3:0. These results are discussed in the work.
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Gruber, Michael E. [Verfasser]. "Spectral Domain and FFT Accelerated Cavity Green's Function Boundary Element Methods for Numerical Modeling of Reverberation Chambers / Michael E. Gruber." München : Verlag Dr. Hut, 2016. http://d-nb.info/1106593758/34.
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Wu, Dongsheng. "Eigenvalues of Differential Operators and Nontrivial Zeros of L-functions." BYU ScholarsArchive, 2020. https://scholarsarchive.byu.edu/etd/8729.
Full textAbstract:
The Hilbert-P\'olya conjecture asserts that the non-trivial zeros of the Riemann zeta function $\zeta(s)$ correspond (in a certain canonical way) to the eigenvalues of some positive operator. R. Meyer constructed a differential operator $D_-$ acting on a function space $\H$ and showed that the eigenvalues of the adjoint of $D_-$ are exactly the nontrivial zeros of $\zeta(s)$ with multiplicity correspondence. We follow Meyer's construction with a slight modification. Specifically, we define two function spaces $\H_\cap$ and $\H_-$ on $(0,\infty)$ and characterize them via the Mellin transform. This allows us to show that $Z\H_\cap\subseteq\H_-$ where $Zf(x)=\sum_{n=1}^\infty f(nx)$. Also, the differential operator $D$ given by $Df(x)=-xf'(x)$ induces an operator $D_-$ on the quotient space $\H=\H_-/Z\H_\cap$. We show that the eigenvalues of $D_-$ on $\H$ are exactly the nontrivial zeros of $\zeta(s)$. Moreover, the geometric multiplicity of each eigenvalue is one and the algebraic multiplicity of each eigenvalue is its vanishing order as a nontrivial zero of $\zeta(s)$. We generalize our construction on the Riemann zeta function to some $L$-functions, including the Dirichlet $L$-functions and $L$-functions associated with newforms in $\mathcal S_k(\Gamma_0(M))$ with $M\ge1$ and $k$ being a positive even integer. We give spectral interpretations for these $L$-functions in a similar fashion.
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Kouakou, Kouadio Simplice. "Echantillonnage aléatoire et estimation spectrale de processus et de champs stationnaires." Thesis, Rennes 2, 2012. http://www.theses.fr/2012REN20019.
Full textAbstract:
Dans ce travail nous nous intéressons à l'estimation de la densité spectrale par la méthode du noyau pour des processus à temps continu et des champs aléatoires observés selon des schémas d'échantillonnage (ou plan d'expériences) discrets aléatoires. Deux types d'échantillonnage aléatoire sont ici considérés : schémas aléatoires dilatés, et schémas aléatoires poissonniens. Aucune condition de gaussiannité n'est imposée aux processus et champs étudiés, les hypothèses concerneront leurs cumulants.En premier nous examinons un échantillonnage aléatoire dilaté utilisé par Hall et Patil (1994) et plus récemment par Matsuda et Yajima (2009) pour l'estimation de la densité spectrale d'un champ gaussien. Nous établissons la convergence en moyenne quadratique dans un cadre plus large, ainsi que la vitesse de convergence de l'estimateur.Ensuite nous appliquons l'échantillonnage aléatoire poissonnien dans deux situations différentes : estimation spectrale d'un processus soumis à un changement de temps aléatoire (variation d'horloge ou gigue), et estimation spectrale d'un champ aléatoire sur R2. Le problème de l'estimation de la densité spectrale d'un processus soumis à un changement de temps est résolu par projection sur la base des vecteurs propres d'opérateurs intégraux définis à partir de la fonction caractéristique de l'accroissement du changement de temps aléatoire. Nous établissons la convergence en moyenne quadratique et le normalité asymptotique de deux estimateurs construits l'un à partir d'une observation continue, et l'autre à partir d'un échantillonnage poissonnien du processus résultant du changement de temps.La dernière partie de ce travail est consacrée au cas d'un champ aléatoire sur R2 observé selon un schéma basé sur deux processus de Poissons indépendants, un pour chaque axe de R2. Les résultats de convergence sont illustrés par des simulationsIn this work, we are dealing in the kernel estimation of the spectral density for a continuous time process or random eld observed along random discrete sampling schemes. Here we consider two kind of sampling schemes : random dilated sampling schemes, and Poissonian sampling schemes. There is no gaussian condition for the process or the random eld, the hypotheses apply to their cumulants.First, we consider a dilated sampling scheme introduced by Hall and Patil (1994) and used more recently by Matsuda and Yajima (2009) for the estimation of the spectral density of a Gaussian random eld.We establish the quadratic mean convergence in our more general context, as well as the rate of convergence of the estimator.Next we apply the Poissonian sampling scheme to two different frameworks : to the spectral estimation for a process disturbed by a random clock change (or time jitter), and to the spectral estimation of a random field on R2.The problem of the estimatin of the spectral density of a process disturbed by a clock change is solved with projection on the basis of eigen-vectors of kernel integral operators defined from the characteristic function of the increment of the random clock change. We establish the convergence and the asymptotic normality of two estimators contructed, from a continuous time observation, and the other from a Poissonian sampling scheme observation of the clock changed process.The last part of this work is devoted to random fields on R2 observed along a sampling scheme based on two Poisson processes (one for each axis of R2). The convergence results are illustrated by some simulations
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Vasquez, Vicente. "FIELD SCALE BROMIDE TRANPORT AS A FUNCTION OF PRECIPITATION AMOUNT, INTENSITY AND APPLICATION TIME DELAY." UKnowledge, 2010. http://uknowledge.uky.edu/gradschool_theses/28.
Full textAbstract:
Rapid and deep transport of solutes in soils can potentially pollute groundwater resources. Field estimates of solute leaching depth based on randomized sampling provide extremely variable field average estimates that confound the treatment effects of the leaching study with the high spatial variation of soil hydraulic properties. The purpose of this study was to investigate the spatial scale of variation of solute (Bromide) leaching depth, and apply this scale of variation to study the leaching depth of Bromide as a function of a sinusoidal application of transport causing factors, i.e., rainfall amount, intensity and application time delay. Solute leaching depth varied over different spatial scales. The deepest leaching was observed on plots where the Br center of mass ranged from 19-30 cm depth. Deep leaching occurred with large quantities of low intensity precipitations (5.5 to 6 cm/day) and short time delays (≤ 17 hours), respectively. The hydraulic gradient presented cyclic variation at 8 m wavelength across the 10-30cm depth compartment. Spectral analysis indicated that spatial variation of the leaching depth was mainly affected by precipitation amount and intensity and only a small portion of the leaching depth variation was caused by time delay. Cross-spectral analysis identified common cyclic variation between the Br leaching depth and precipitation amount, intensity and time delay over 32, 32 and 8 m wavelengths, respectively. Simulated Br concentration over depth and horizontal distance and soil water matric potential ψm were in good agreement with experimental observations, the latter revealing a satisfactory Br and water mass balance.
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Call, Daniel M. (Daniel Marcus) 1973. "A spectral analysis method to quantify the relative contribution of different length scales to heterogeneity in PET images of pulmonary function." Thesis, Massachusetts Institute of Technology, 2000. http://hdl.handle.net/1721.1/88846.
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Schmidt-Grund, Rüdiger, Christian Kranert, Wenckstern Holger von, Vitaly Zviagin, Michael Lorenz, and Marius Grundmann. "Dielectric function in the spectral range (0.5–8.5)eV of an (Alx Ga1−x )2O3 thin film with continuous composition spread." American Institute of Physics, 2015. https://ul.qucosa.de/id/qucosa%3A31190.
Full textAbstract:
We determined the dielectric function of the alloy system (AlxGa1−x)2O3 by spectroscopic
ellipsometry in the wide spectral range from 0.5 eV to 8.5 eV and for Al contents ranging from
x = 0.11 to x = 0.55. For the composition range x<0.4, we observe single phase material in the
b-modification and for larger Al content also the occurrence of γ-(Al,Ga)2O3. We derived spectra of
the refractive index and the absorption coefficient as well as energy parameters of electronic bandband
transitions by model analysis of the dielectric function. The dependence of the dielectric functions
lineshape and the energy parameters on x is highly continuous, reflecting theoretical expectations.
The data presented here provide a basis for a deeper understanding of the electronic properties
of this material system and may be useful for device engineering.
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Wing, Lindsey McCall. "Native Mandarin Speakers' Production of English Fricatives as a Function of Linguistic Task Type and Word Position: A Spectral Moment Analysis." BYU ScholarsArchive, 2018. https://scholarsarchive.byu.edu/etd/7313.
Full textAbstract:
The purpose of this study was to analyze the phonetic production of fricatives across differing word positions and task types. Further knowledge about the fricative production of second language learners of English would potentially improve the ability to teach correct pronunciation and improve the productivity of second language programs. All participants in this study were native speakers of Mandarin Chinese with English as their second language. A total of 12 subjects participated, all of whom had English proficiency ratings ranging from novice to advanced. The speakers were between 21-51 years of age, with each speaker having between 2 to 6 years of experience learning English in their country of origin. Using acoustic and spectral moment analyses, the acoustic nature of four types of fricative productions (/f/, /θ/, /s/, and /ʃ/) were analyzed as a function of linguistic task type and word position. Although a number of measures were found to differ significantly as a function of word position and task type, the majority of statistical analyses were not found to be significant. This lack of significance may be due to the specific methodology used, the speakers<'> atypical voicing patterns, and/or decreased length of sound productions. Findings of this study may indicate that second language learners<'> production of fricatives vary minimally across differing word positions and task types.
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Calatayud, Gregori Julia. "Computational methods for random differential equations: probability density function and estimation of the parameters." Doctoral thesis, Universitat Politècnica de València, 2020. http://hdl.handle.net/10251/138396.
Full textAbstract:
[EN] Mathematical models based on deterministic differential equations do not take into account the inherent uncertainty of the physical phenomenon (in a wide sense) under study. In addition, inaccuracies in the collected data often arise due to errors in the measurements. It thus becomes necessary to treat the input parameters of the model as random quantities, in the form of random variables or stochastic processes. This gives rise to the study of random ordinary and partial differential equations.
The computation of the probability density function of the stochastic solution is important for uncertainty quantification of the model output. Although such computation is a difficult objective in general, certain stochastic expansions for the model coefficients allow faithful representations for the stochastic solution, which permits approximating its density function. In this regard, Karhunen-Loève and generalized polynomial chaos expansions become powerful tools for the density approximation. Also, methods based on discretizations from finite difference numerical schemes permit approximating the stochastic solution, therefore its probability density function.
The main part of this dissertation aims at approximating the probability density function of important mathematical models with uncertainties in their formulation. Specifically, in this thesis we study, in the stochastic sense, the following models that arise in different scientific areas: in Physics, the model for the damped pendulum; in Biology and Epidemiology, the models for logistic growth and Bertalanffy, as well as epidemiological models; and in Thermodynamics, the heat partial differential equation. We rely on Karhunen-Loève and generalized polynomial chaos expansions and on finite difference schemes for the density approximation of the solution.
These techniques are only applicable when we have a forward model in which the input parameters have certain probability distributions already set. When the model coefficients are estimated from collected data, we have an inverse problem. The Bayesian inference approach allows estimating the probability distribution of the model parameters from their prior probability distribution and the likelihood of the data. Uncertainty quantification for the model output is then carried out using the posterior predictive distribution.
In this regard, the last part of the thesis shows the estimation of the distributions of the model parameters from experimental data on bacteria growth. To do so, a hybrid method that combines Bayesian parameter estimation and generalized polynomial chaos expansions is used.[ES] Los modelos matemáticos basados en ecuaciones diferenciales deterministas no tienen en cuenta la incertidumbre inherente del fenómeno físico (en un sentido amplio) bajo estudio. Además, a menudo se producen inexactitudes en los datos recopilados debido a errores en las mediciones. Por lo tanto, es necesario tratar los parámetros de entrada del modelo como cantidades aleatorias, en forma de variables aleatorias o procesos estocásticos. Esto da lugar al estudio de las ecuaciones diferenciales aleatorias. El cálculo de la función de densidad de probabilidad de la solución estocástica es importante en la cuantificación de la incertidumbre de la respuesta del modelo. Aunque dicho cálculo es un objetivo difícil en general, ciertas expansiones estocásticas para los coeficientes del modelo dan lugar a representaciones fieles de la solución estocástica, lo que permite aproximar su función de densidad. En este sentido, las expansiones de Karhunen-Loève y de caos polinomial generalizado constituyen herramientas para dicha aproximación de la densidad. Además, los métodos basados en discretizaciones de esquemas numéricos de diferencias finitas permiten aproximar la solución estocástica, por lo tanto, su función de densidad de probabilidad. La parte principal de esta disertación tiene como objetivo aproximar la función de densidad de probabilidad de modelos matemáticos importantes con incertidumbre en su formulación. Concretamente, en esta memoria se estudian, en un sentido estocástico, los siguientes modelos que aparecen en diferentes áreas científicas: en Física, el modelo del péndulo amortiguado; en Biología y Epidemiología, los modelos de crecimiento logístico y de Bertalanffy, así como modelos de tipo epidemiológico; y en Termodinámica, la ecuación en derivadas parciales del calor. Utilizamos expansiones de Karhunen-Loève y de caos polinomial generalizado y esquemas de diferencias finitas para la aproximación de la densidad de la solución. Estas técnicas solo son aplicables cuando tenemos un modelo directo en el que los parámetros de entrada ya tienen determinadas distribuciones de probabilidad establecidas. Cuando los coeficientes del modelo se estiman a partir de los datos recopilados, tenemos un problema inverso. El enfoque de inferencia Bayesiana permite estimar la distribución de probabilidad de los parámetros del modelo a partir de su distribución de probabilidad previa y la verosimilitud de los datos. La cuantificación de la incertidumbre para la respuesta del modelo se lleva a cabo utilizando la distribución predictiva a posteriori. En este sentido, la última parte de la tesis muestra la estimación de las distribuciones de los parámetros del modelo a partir de datos experimentales sobre el crecimiento de bacterias. Para hacerlo, se utiliza un método híbrido que combina la estimación de parámetros Bayesianos y los desarrollos de caos polinomial generalizado.
[CAT] Els models matemàtics basats en equacions diferencials deterministes no tenen en compte la incertesa inherent al fenomen físic (en un sentit ampli) sota estudi. A més a més, sovint es produeixen inexactituds en les dades recollides a causa d'errors de mesurament. Es fa així necessari tractar els paràmetres d'entrada del model com a quantitats aleatòries, en forma de variables aleatòries o processos estocàstics. Açò dóna lloc a l'estudi de les equacions diferencials aleatòries. El càlcul de la funció de densitat de probabilitat de la solució estocàstica és important per a quantificar la incertesa de la sortida del model. Tot i que, en general, aquest càlcul és un objectiu difícil d'assolir, certes expansions estocàstiques dels coeficients del model donen lloc a representacions fidels de la solució estocàstica, el que permet aproximar la seua funció de densitat. En aquest sentit, les expansions de Karhunen-Loève i de caos polinomial generalitzat esdevenen eines per a l'esmentada aproximació de la densitat. A més a més, els mètodes basats en discretitzacions mitjançant esquemes numèrics de diferències finites permeten aproximar la solució estocàstica, per tant la seua funció de densitat de probabilitat. La part principal d'aquesta dissertació té com a objectiu aproximar la funció de densitat de probabilitat d'importants models matemàtics amb incerteses en la seua formulació. Concretament, en aquesta memòria s'estudien, en un sentit estocàstic, els següents models que apareixen en diferents àrees científiques: en Física, el model del pèndol amortit; en Biologia i Epidemiologia, els models de creixement logístic i de Bertalanffy, així com models de tipus epidemiològic; i en Termodinàmica, l'equació en derivades parcials de la calor. Per a l'aproximació de la densitat de la solució, ens basem en expansions de Karhunen-Loève i de caos polinomial generalitzat i en esquemes de diferències finites. Aquestes tècniques només són aplicables quan tenim un model cap avant en què els paràmetres d'entrada tenen ja determinades distribucions de probabilitat. Quan els coeficients del model s'estimen a partir de les dades recollides, tenim un problema invers. L'enfocament de la inferència Bayesiana permet estimar la distribució de probabilitat dels paràmetres del model a partir de la seua distribució de probabilitat prèvia i la versemblança de les dades. La quantificació de la incertesa per a la resposta del model es fa mitjançant la distribució predictiva a posteriori. En aquest sentit, l'última part de la tesi mostra l'estimació de les distribucions dels paràmetres del model a partir de dades experimentals sobre el creixement de bacteris. Per a fer-ho, s'utilitza un mètode híbrid que combina l'estimació de paràmetres Bayesiana i els desenvolupaments de caos polinomial generalitzat.
This work has been supported by the Spanish Ministerio de Econom´ıa y Competitividad grant MTM2017–89664–P.
Calatayud Gregori, J. (2020). Computational methods for random differential equations: probability density function and estimation of the parameters [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/138396
TESIS
Premiado
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Assal, Marouane. "Analyse spectrale des systèmes d'opérateurs h-pseudodifférentiels." Thesis, Bordeaux, 2017. http://www.theses.fr/2017BORD0586/document.
Full textAbstract:
Dans ce travail, nous nous intéressons à l’analyse spectrale des systèmes d’opérateurs pseudodifférentiels semi-classiques. Dans la première partie, nous étudions la généralisation du théorème d’Egorov en temps longs dans le cas où l’Hamiltonien quantique qui génère l’évolution en temps et l’observable quantique initiale sont deux opérateurs pseudodifférentiels semiclassiques associés à des symboles à valeurs matricielles. Sous une condition d’hyperbolicité sur le symbole principal de l’Hamiltonien qui assure l’existence des projecteurs semi-classiques, et pour une classe d’observables "semi-classiquement" diagonales par blocs par rapport à ces projecteurs, nous démontrons un théorème de type Egorov valable pour un temps long d’ordre log(h-1) connu comme le temps d’Ehrenfest. Ici h 0 est le paramètre semi-classique. Dans la deuxième partie, nous nous intéressons à la théorie spectrale et la théorie de la diffusion pour des systèmes d’opérateurs pseudodifférentiels auto-adjoints. Nous développons une approche stationnaire pour l’étude de la fonction de décalage spectral associée à une paire d’opérateurs de Schrödinger semi-classiques à potentiels matriciels. Une asymptotique de type Weyl avec reste optimal sur la fonction de décalage spectral est établie, et sous l’hypothèse d’existence d’une fonction fuite scalaire, un développement asymptotique complet en puissancesde h au sens fort sur sa dérivée est obtenu. Ce dernier résultat est une généralisation au cas matriciel d’un résultat de Robert et Tamura établi dans le cas scalaire près des énergies non-captives. Notre méthode indépendante du temps nous permet de traiter certains potentiels avec des croisements des valeurs propresIn this work, we are interested in the spectral analysis of systems of semiclassical pseudodifferentialoperators. In the first part, we study the extension of the long time semiclassical Egorovtheorem in the case where the quantum Hamiltonian which generates the time evolution andthe initial quantum observable are two semiclassical pseudodifferential operators with matrixvaluedsymbols. Under an hyperbolicity condition on the principal symbol of the Hamiltonianwhich ensures the existence of the semiclassical projections, and for a class of observable thatare "semi-classically" block-diagonal with respect to these projections, we prove an Egorov theoremvalid in a large time interval of order log(h-1) known as the Ehrenfest time. Here h & 0is the semiclassical parameter.In the second part, we are interested in the spectral and scattering theories for self-adjointsystems of pseudodifferential operators. We develop a stationary approach for the study of thespectral shift function (SSF) associated to a pair of self-adjoint semiclassical Schrödinger operatorswith matrix-valued potentials. We prove a Weyl-type asymptotics with sharp remainderestimate on the SSF, and under the existence of a scalar escape function, a pointwise completeasymptotic expansion on its derivative. This last result is a generalisation in the matrix-valuedcase of a result of Robert and Tamura established in the scalar case near non-trapping energies.Our time-independent method allows us to treat certain potentials with energy-level crossings
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Jia, Xiaoyao. "CERTAINS PROBLEMES SPECTRAUX POUR DES OPERATEURS DESCHRODINGER." Phd thesis, Université de Nantes, 2009. http://tel.archives-ouvertes.fr/tel-00403679.
Full textAbstract:
ON ETUDIE DANS CETTE THESE CERTAINS PROBLEMES SPECTRAUX POUR DES OPERATEURS DESCHRODINGER. ON S'INTERESSE D'ABORD A LA LIMITE SEMI-CLASSIQUE POUR LE NOMBRE D'ETATS PROPRESDE L'OPERATEUR DE SCHRODINGER A N CORPS. ON UTILISE ENSUITE LE CROCHET DE DIRICHLET-NEUMANN POUR OBTENIR LA LIMITE SEMI-CLASSIQUE DES MOYENNES DE RIESZ DES VALEURS PROPRES DISCRETES POUR L'OPERATEUR DE SCHR¨ODINGER A N CORPS. ON CONSIDERE EGALEMENT LE POTENTIEL EFFECTIF DE L'OPERATEUR DE SCHRODINGER A N CORPS AVEC POTENTIEL DE COULOMB ET ON OBTIENT QU'IL A UNE DECROISSANCE CRITIQUE A L'INFINI. ON ETUDIE DONC L'OPERATEUR DE SCHRODINGER A POTENTIEL CRITIQUE. ON S'INTERESSE AU SEUIL POUR LA CONSTANTE DE COUPLAGE ET AU DEVELOPPEMENT ASYMPTOTIQUE DE LA RESOLVANTE DE L'OPERATEUR DE SCHRODINGER, PUIS ON UTILISE CE DEVELOPPEMENT POUR ETUDIER LA LIMITE A BASSE ENERGIE DE LA DERIVEE DE LA FONCTION DE DECALAGE SPECTRAL POUR UNE PERTURBATION A DECROISSANCE CRITIQUE. FINALEMENT, ON UTILISE CE RESULTAT AVEC LE RESULTAT CONNU POUR LE DEVELOPPEMENT ASYMPTOTIQUE A HAUTE ENERGIE DE CETTE FONCTION DE DECALAGE SPECTRAL POUR OBTENIR LE THEOREME DE LEVINSON.
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Dorai-Raj, Sundardas Samuel. "First- and Second-Order Properties of Spatiotemporal Point Patterns in the Space-Time and Frequency Domains." Diss., Virginia Tech, 2001. http://hdl.handle.net/10919/28540.
Full textAbstract:
Point processes are common in many physical applications found in engineering and biology.
These processes can be observed in one-dimension as a time series or two-dimensions as a spatial point pattern with extensive amounts of literature devoted to their analyses.
However, if the observed process is a hybrid of spatial and temporal point process, very few practical methods exist.
In such cases, practitioners often remove the temporal component and analyze the spatial dependencies.
This marginal spatial analysis may lead to misleading results if time is an important factor in the process.
In this dissertation we extend the current analysis of spatial point patterns to include a temporal dimension.
First- and second-order intensity measures for analyzing spatiotemporal point patterns are explicitly defined.
Estimation of first-order intensities are examined using 3-dimensional smoothing techniques.
Conditions for weak stationarity are provided so that subsequent second-order analysis can be conducted.
We consider second-order analysis of spatiotemporal point patterns first in the space-time domain through an extension of Ripley's $K$-function.
An alternative analysis is given in the frequency domain though construction of a spatiotemporal periodogram.
The methodology provided is tested through simulation of spatiotemporal point patterns and by analysis of a real data set.
The biological application concerns the estimation of the homerange of groups of the endangered red-cockaded woodpecker in the Fort Bragg area of North Carolina.
Monthly or bimonthly point patterns of the bird distribution are analyzed and integrated over a 23 month period.Ph. D.
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Veenstra, Christian Neil. "Spectral function analysis on the Holstein polaron problem : extraction of the self-energy and coupling strength, and their implications for angle resolved photoemission spectroscopy." Thesis, University of British Columbia, 2007. http://hdl.handle.net/2429/32491.
Full textAbstract:
This thesis first reviews and examines the Angle Resolved Photoemission Spectroscopy (ARPES) experiment. It is shown that the spectral density function, familiar from the Green's function method of studying correlated systems, can be directly measured. A model spectral function with a nontrivial self-energy is then used to test an improvement to a recently arrived method[15,17] to analyze ARPES data. This new method relies on self-consistency between the real and imaginary parts of the self-energy (as measured through the Kramers-Kronig transform) to overcome the requirement of knowing the bare electronic structure. Through this, the method extracts both the complex self-energy and the bare electronic structure from the spectral function. The method described here is an improvement on this idea as previously implemented in that a strict form for the bare band dispersion (previously considered linear or quadratic) is never assumed. Although the method here utilized a polynomial of arbitrary degree, it could be trivially expanded to use any other functional form so long as both the value and first derivative are known analytically as a function of the fitting parameters. Using Mona Berciu's first order momentum average (MA) approximation[2] as implemented by Glen Goodvin[8] the spectral function as well as momentum independent self-energy were calculated for the Holstein polaron for a wide range of parameters. It was found that self-consistent spectral function analysis was highly successful at extracting the self energy and bare electronic dispersion from the spectral function over a consistent subset of these parameters. For studies outside this range of parameters the more traditional ARPES analysis method of measuring renormalization is also examined.Science, Faculty of
Physics and Astronomy, Department of
Graduate