Дисертації з теми "Singular functions"
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1
Penso, Valentina <1988>. "Singular Sets of Generalized Convex Functions." Doctoral thesis, Alma Mater Studiorum - Università di Bologna, 2017. http://amsdottorato.unibo.it/7882/1/Penso_Valentina_Tesi.pdf.
Повний текст джерелаАнотація:
In the first part of the dissertation we prove that, under quite general conditions on a cost function $c$ in $\RR^n$, the Hausdorff dimension of the singular set of a $c$-concave function has dimension at most $n-1$. Our result applies for non-semiconcave cost functions and has applications in optimal mass transportation.
The purpose of the second part of the thesis is to extend a result of Alberti and Ambrosio about singularity sets of monotone multivalued maps to the sub-Riemannian setting of Heisenberg groups.
We prove that the $k$-th horizontal singular set of a $H$-monotone multivalued map of the Heisenberg group $\HH^n$, with values in $\RR^{2n}$, has Hausdorff dimension at most $2n+2-k$.
2
Kytmanov, Aleksandr, Simona Myslivets, and Nikolai Tarkhanov. "Removable singularities of CR functions on singular boundaries." Universität Potsdam, 2000. http://opus.kobv.de/ubp/volltexte/2008/2583/.
Повний текст джерелаАнотація:
The problem of analytic representation of integrable CR functions on hypersurfaces with singularities is treated. The nature o singularities does not matter while the set of singularities has surface measure zero. For simple singularities like cuspidal points, edges, corners, etc., also the behaviour of representing analytic functions near singular points is studied.
3
Neuner, Christoph. "Generalized Titchmarsh-Weyl functions and super singular perturbations." Licentiate thesis, Stockholms universitet, Matematiska institutionen, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-113389.
Повний текст джерелаАнотація:
In this thesis we study certain singular Sturm-Liouville differential expressions from an operator theoretic point of view.In particular we are interested in expressions that involve strongly singular potentials as introduced by Gesztesy and Zinchenko.On the ODE side, analyzing these expressions involves the so-called $m$-functions, often generalized Nevanlinna functions, who encapsulate spectral information of the underlying problem.The aim of the two papers in this thesis is to further understanding on the operator theory side.In the first paper, we use a model for super singular perturbations to describe a family of induced self-adjoint realizations of a perturbed Schr\"o\-din\-ger operator, i.e., with a potential of the form $c/x^2 + q$ where $q$ is a perturbation.Following the unperturbed example of Kurasov and Luger, we find that the so-called $Q$-function appearing in this approach is in good agreement with the above named $m$-function.Furthermore, we show that the operator model can be chosen such that $Q \equiv m$.In the second paper, we present a negative result in this area, namely that the supersingular perturbations model cannot be used for all strongly singular potentials.For a potential with a stronger singularity at the origin, namely $1/x^4$, we discuss the asymptotic behaviour of the Weyl solution at zero.It turns out that this function cannot be regularized appropriately and the operator model breaks down.
4
Vutha, Amit C. "Normal Forms and Unfoldings of Singular Strategy Functions." The Ohio State University, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=osu1385461288.
Повний текст джерела
5
Raeisidehkordi, Hengameh. "Finsler Transnormal Functions and Singular Foliations of Codimension 1." Universidade de São Paulo, 2018. http://www.teses.usp.br/teses/disponiveis/45/45131/tde-05042018-210826/.
Повний текст джерелаАнотація:
Transnormal functions are generalization of distance functions and this topic has some applications in Physics and real world problems. In this work, some results are generalized from Riemannian case to the Finsler one. Moreover certain new phenomena that happen only in Finsler spaces are discussed. To have a better understanding, certain examples based on the mentioned results in Randers spaces are provided. Moreover, some applications on propagation of waves of fire and water are introducedAs funções transnormais são a generalização da função de distância e este tópico tem algumas aplicações em Física e no mundo real. Neste trabalho, alguns resultados do caso riemanniana para o Finsler são generalizados. Alem disso, alguns fenômenos novos que ocorrem apenas nos espaços de Finsler são discutidos. Para ter uma melhor compreensão, são fornecidos certos exemplos com base nos resultados mencionados nos espaços de Randers. Além disso, algumas aplicações sobre propagação de ondas de fogo e água são introduzidas.
6
Coiculescu, Ion. "Dynamics, Thermodynamic formalism and Perturbations of Transcendental Entire Functions of Finite Singular Type." Thesis, University of North Texas, 2005. https://digital.library.unt.edu/ark:/67531/metadc4783/.
Повний текст джерелаАнотація:
In this dissertation, we study the dynamics, fractal geometry and the topology of the Julia set of functions in the family H which is a set in the class S, the Speiser class of entire transcendental functions which have only finitely many singular values. One can think of a function from H as a generalized expanding function from the cosh family. We shall build a version of thermodynamic formalism for functions in H and we shall show among others, the existence and uniqueness of a conformal measure. Then we prove a Bowen's type formula, i.e. we show that the Hausdorff dimension of the set of returning points, is the unique zero of the pressure function. We shall also study conjugacies in the family H, perturbation of functions in the family and related dynamical properties. We define Perron-Frobenius operators for some functions naturally associated with functions in the family H and then, using fundamental properties of these operators, we shall prove the important result that the Hausdorff dimension of the subset of returning points depends analytically on the parameter taken from a small open subset of the n-dimensional parameter space.
7
Nguyen, Van Luong. "On regular and singular points of the minimum time function." Doctoral thesis, Università degli studi di Padova, 2014. http://hdl.handle.net/11577/3424058.
Повний текст джерелаАнотація:
In this thesis, we study the regularity of the minimum time function Τ for both linear and nonlinear control systems in Euclidean space.
We first consider nonlinear problems satisfying Petrov condition. In this case, Τ is locally Lipschitz and then is differentiable almost everywhere. In general, Τ fails to be differentiable at points where there are multiple time optimal trajectories and its differentiability at a point does not guarantee continuous differentiability around this point. We show that, under some regularity assumptions, the non-emptiness of proximal subdifferential of the minimum time function at a point x implies its continuous differentiability on a neighborhood of Υ. The technique consists of deriving sensitivity relations for the proximal subdifferential of the minimum time function and excluding the presence of conjugate points when the proximal subdifferential is nonempty.
We then study the regularity the minimum time function Τ to reach the origin under controllability conditions which do not imply the Lipschitz continuity of Τ. Basing on the analysis of zeros of the switching function, we find out singular sets (e.g., non - Lipschitz set, non - differentiable set) and establish rectifiability properties for them. The results imply further regularity properties of Τ such as the SBV regularity, the differentiability and the analyticity. The results are mainly for linear control problems.La presente tesi è dedicata allo studio della regolarità della funzione tempo minimo Τ per sistemi di controllo sia lineari che non lineari in dimensione finita. Si considerano dapprima problemi non lineari in cui la condizione di controllabilità detta di Petrov è soddisfatta. Come è ben noto, in questo caso Τ è localmente Lipschitziana e quindi è differenziabile quasi ovunque. In generale, Τ non è differenziabile nei punti dai quali escono diverse traiettorie ottimali e inoltre il fatto che Τ è differenziabile in un punto non garantisce che lo sia in un intorno (l'insieme dei punti di differenziabilità non è aperto). Imponendo alcune condizioni di regolarità sulla dinamica, si dimostra che se il sottodifferenziale prossimale di Τ è non vuoto in un punto x, allora Τ è differenziabile in tutto un intorno di x. La tecnica usata consiste nel derivare relazioni di sensitività per il sottodifferenziale prossimale di Τ e nell'escludere la presenza di punti coniugati dove tale sottodifferenziale è non vuoto. In secondo luogo si studia la regolarità di Τ sotto condizioni di controllabilità più generali, tali da non imporre la Lipschitzianità. In questo caso il bersaglio è l'origine e la dinamica è -- principalmente -- lineare a coefficienti costanti. Si identificano alcuni insiemi singolari (cioè dove Τ non è differenziabile), ad esempio l'insieme dove Τ non è Lipschitz e l'insieme dei punti dove l'insieme raggiungibile presenta più di un versore normale, e si dimostrano risultati di rettificabilità, in questo modo mostrando che sono ``molto piccoli''. Come conseguenza si ricavano ulteriori risultati di regolarità per Τ, fra i quali la regolarità SBV e la differenziabilità e l'analiticità in aperti il cui complementare ha dimensione inferiore a quella dello spazio degli stati. La tecnica usata è basata principalmente su un'analisi accurata degli zeri della cosiddetta funzione di switching.
8
Schürmann, Jörg. "Topology of singular spaces and constructible sheaves /." Basel [u.a.] : Birkhäuser, 2003. http://www.loc.gov/catdir/toc/fy0803/2003062963.html.
Повний текст джерела
9
Pham, Hoang. "A perturbation solution for forced response of systems displaying eigenvalue veering and mode localization." Diss., Georgia Institute of Technology, 1995. http://hdl.handle.net/1853/19120.
Повний текст джерела
10
Du, Zhe. "A description of discrete spectrum of (spin(10,2) x SL(2, R)) and singular theta correspondence /." View abstract or full-text, 2009. http://library.ust.hk/cgi/db/thesis.pl?MATH%202009%20DU.
Повний текст джерела
11
Luther, Uwe. "Approximation Spaces in the Numerical Analysis of Cauchy Singular Integral Equations." Doctoral thesis, Universitätsbibliothek Chemnitz, 2005. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200500895.
Повний текст джерелаАнотація:
The paper is devoted to the foundation of
approximation methods for integral equations of
the form (aI+SbI+K)f=g,
where S is the Cauchy singular
integral operator on (-1,1) and K is a weakly
singular integral operator.
Here a,b,g are given functions on (-1,1) and
the unknown function f on (-1,1) is looked for.
It is assumed that a and b are real-valued and
Hölder continuous functions on [-1,1] without
common zeros and that g belongs to some
weighted space of Hölder continuous functions.
In particular, g may have a finite number of
singularities.
Based on known spectral properties of Cauchy
singular integral operators approximation methods
for the numerical solution of the above equation
are constructed, where both aspects the
theoretical convergence and the numerical
practicability are taken into account.
The weighted uniform convergence of these methods
is studied using a general
approach based on the theory of approximation
spaces. With the help of this approach it is
possible to prove simultaneously the stability,
the convergence and results on the order of
convergence of the approximation methods under
consideration.
12
Grudsky, Serguey, and Nikolai Tarkhanov. "Conformal reduction of boundary problems for harmonic functions in a plane domain with strong singularities on the boundary." Universität Potsdam, 2012. http://opus.kobv.de/ubp/volltexte/2012/5774/.
Повний текст джерелаАнотація:
We consider the Dirichlet, Neumann and Zaremba problems for harmonic functions in a bounded plane domain with nonsmooth boundary. The boundary curve belongs to one of the following three classes: sectorial curves, logarithmic spirals and spirals of power type. To study the problem we apply a familiar method of Vekua-Muskhelishvili which consists in using a conformal mapping of the unit disk onto the domain to pull back the problem to a boundary problem for harmonic functions in the disk. This latter is reduced in turn to a Toeplitz operator equation on the unit circle with symbol bearing discontinuities of second kind. We develop a constructive invertibility theory for Toeplitz operators and thus derive solvability conditions as well as explicit formulas for solutions.
13
Hirose, Toru. "The reduction of quantum many-body systems with symmetry and the boundary behavior of wave functions at singular configurations." 京都大学 (Kyoto University), 2003. http://hdl.handle.net/2433/148782.
Повний текст джерела
14
Hanine, Abdelouahab. "Cyclic vectors in some spaces of analytic functions." Thesis, Aix-Marseille, 2013. http://www.theses.fr/2013AIXM4725.
Повний текст джерелаАнотація:
Cette thèse est consacrée à l'étude du problème de la cyclicité dans certains espaces de fonctions analytiques sur le disque unité. Nous nous intéressons aux espaces de type Bergman et aux espaces de type Korenblum. Dans la première partie, nous étudions les fonctions cycliques dans les espaces de type Korenblum en utilisant la notion des prémesures. Cette notion a été introduite et développée par B. Korenblum au début des années 1970s. En particulier, nous donnons une réponse positive à une conjecture énoncée par C. Deninger. Dans la deuxième partie, nous utilisons la méthode de la résolvante pour étudier la cyclicité des fonctions intérieures singulières associées aux mesures de Dirac dans les espaces de type Bergman à poidsIn this thesis, we study the cyclicity problem in some spaces of analytic functions on the open unit disc. We focus our attention on Korenblum type spaces and on weighted Bergman type spaces. First, we use the technique of premeasures, introduced and developed by Korenblum in the 1970-s and the 1980-s, to give a characterization of cyclic functions in the Korenblum type spaces. In particular, we give a positive answer to a conjecture by Deninger. Second, we use the so called resolvent transform method to study the cyclicity of the one point mass singular inner function in weighted Bergman type spaces, especially with weights depending on the distance to a subset of the unit circle
15
Sendov, Hristo. "Variational Spectral Analysis." Thesis, University of Waterloo, 2000. http://hdl.handle.net/10012/1089.
Повний текст джерелаАнотація:
We present results on smooth and nonsmooth variational properties of {it symmetric} functions of the eigenvalues of a real symmetric matrix argument, as well as {it absolutely symmetric} functions of the singular values of a real rectangular matrix. Such results underpin the theory of optimization problems involving such functions. We answer the question of when a symmetric function of the eigenvalues allows a quadratic expansion around a matrix, and then the stronger question of when it is twice differentiable. We develop simple formulae for the most important nonsmooth subdifferentials of functions depending on the singular values of a real rectangular matrix argument and give several examples. The analysis of the above two classes of functions may be generalized in various larger abstract frameworks. In particular, we investigate how functions depending on the eigenvalues or the singular values of a matrix argument may be viewed as the composition of symmetric functions with the roots of {it hyperbolic polynomials}. We extend the relationship between hyperbolic polynomials and {it self-concordant barriers} (an extremely important class of functions in contemporary interior point methods for convex optimization) by exhibiting a new class of self-concordant barriers obtainable from hyperbolic polynomials.
16
Gokay, Kemal. "Contact Mechanics Of Graded Materials With Two Dimensional Material Property Variations." Master's thesis, METU, 2005. http://etd.lib.metu.edu.tr/upload/12606527/index.pdf.
Повний текст джерелаАнотація:
ABSTRACT
CONTACT MECHANICS OF GRADED MATERIALS WITH TWODIMENSIONAL
MATERIAL PROPERTY VARIATIONS
Gökay, Kemal M.S., Department of Mechanical Engineering Supervisor: Asst. Prof. Dr. Serkan Dag September 2005, 62 pages Ceramic layers used as protective coatings in tribological applications are known to be prone to cracking and debonding due to their brittle nature. Recent experiments with functionally graded ceramics however show that these material systems are particularly useful in enhancing the resistance of a surface to tribological damage. This improved behavior is attributed to the influence of the material property gradation on the stress distribution that develops at the contacting surfaces. The main interest in the present study is in the contact mechanics of a functionally graded surface with a two &ndash
dimensional spatial variation in the modulus of elasticity. Poisson&rsquo
s ratio is assumed to be constant due to its insignificant effect on the contact stress distribution [30]. In the formulation of the problem it is assumed that the functionally graded surface is in frictional sliding contact with a rigid flat stamp. Using elasticity theory and semi-infinite plane approximation for the graded medium, the problem is reduced to a singular integral equation of the second kind. Integral equation is solved numerically by expanding the unknown contact stress distribution into a series of Jacobi polynomials and using suitable collocation points. The developed method is validated by providing comparisons to a closed form solution derived for homogeneous materials. Main numerical results consist of the effects of the material nonhomogeneity parameters, coefficient of friction and stamp size and location on the contact stress distribution.
17
Quellmalz, Michael. "Reconstructing Functions on the Sphere from Circular Means." Universitätsverlag Chemnitz, 2019. https://monarch.qucosa.de/id/qucosa%3A38406.
Повний текст джерелаАнотація:
The present thesis considers the problem of reconstructing a function f that is defined on the d-dimensional unit sphere from its mean values along hyperplane sections. In case of the two-dimensional sphere, these plane sections are circles. In many tomographic applications, however, only limited data is available. Therefore, one is interested in the reconstruction of the function f from its mean values with respect to only some subfamily of all hyperplane sections of the sphere. Compared with the full data case, the limited data problem is more challenging and raises several questions. The first one is the injectivity, i.e., can any function be uniquely reconstructed from the available data? Further issues are the stability of the reconstruction, which is closely connected with a description of the range, as well as the demand for actual inversion methods or algorithms.
We provide a detailed coverage and answers of these questions for different families of hyperplane sections of the sphere such as vertical slices, sections with hyperplanes through a common point and also incomplete great circles. Such reconstruction problems arise in various practical applications like Compton camera imaging, magnetic resonance imaging, photoacoustic tomography, Radar imaging or seismic imaging. Furthermore, we apply our findings about spherical means to the cone-beam transform and prove its singular value decomposition.Die vorliegende Arbeit beschäftigt sich mit dem Problem der Rekonstruktion einer Funktion f, die auf der d-dimensionalen Einheitssphäre definiert ist, anhand ihrer Mittelwerte entlang von Schnitten mit Hyperebenen. Im Fall d=2 sind diese Schnitte genau die Kreise auf der Sphäre. In vielen tomografischen Anwendungen sind aber nur eingeschränkte Daten verfügbar. Deshalb besteht das Interesse an der Rekonstruktion der Funktion f nur anhand der Mittelwerte bestimmter Familien von Hyperebenen-Schnitten der Sphäre. Verglichen mit dem Fall vollständiger Daten birgt dieses Problem mehrere Herausforderungen und Fragen. Die erste ist die Injektivität, also können alle Funktionen anhand der gegebenen Daten eindeutig rekonstruiert werden? Weitere Punkte sind die die Frage nach der Stabilität der Rekonstruktion, welche eng mit einer Beschreibung der Bildmenge verbunden ist, sowie der praktische Bedarf an Rekonstruktionsmethoden und -algorithmen. Diese Arbeit gibt einen detaillierten Überblick und Antworten auf diese Fragen für verschiedene Familien von Hyperebenen-Schnitten, angefangen von vertikalen Schnitten über Schnitte mit Hyperebenen durch einen festen Punkt sowie Kreisbögen. Solche Rekonstruktionsprobleme treten in diversen Anwendungen auf wie der Bildgebung mittels Compton-Kamera, Magnetresonanztomografie, fotoakustischen Tomografie, Radar-Bildgebung sowie der Tomografie seismischer Wellen. Weiterhin nutzen wir unsere Ergebnisse über sphärische Mittelwerte, um eine Singulärwertzerlegung für die Kegelstrahltomografie zu zeigen.
18
Filip, Tomić. "A new type of regularity with applications to the wave front sets." Phd thesis, Univerzitet u Novom Sadu, Prirodno-matematički fakultet u Novom Sadu, 2016. https://www.cris.uns.ac.rs/record.jsf?recordId=101444&source=NDLTD&language=en.
Повний текст джерелаАнотація:
We introduce a family of smooth functions which are "less regu-lar" than the Gevrey functions, and study its basic properties. In particular we prove the standard results concerning algebra property and stability under finite order derivation. Moreover, we construct infnite order operators which leads us to the definition of class with ultradifferentiable property. We also prove that our classes are inverse-closed, and this result is the essential part in the proof of our main result presented in the final Chapter. Moreover, using the techniques of microlocal analysis, we introduce and investigate thecorresponding wave front sets, and the prove the results related to singular support of a distribution. Our main results shows how the singularities of solutions to partial differential equations (PDE's in short) propagate in the framework of our regularity.U ovoj tezi definišemo novu klasu glatkih funkcija i izučavamo njihove osnovne osobine. Pokazujemo da naše klase imaju svojsto algebre kao i da su zatvorene u odnosu na delovanje operatora izvoda konačnog reda.Sta više, konstruišemo diferencijalne operatore beskonačnog reda i to nas dovodi do definicije ultradiferencijabilnih klasa funkcija. Takode dokazujemo osobinu zatvorenosti u odnosu na inverze, i taj rezultat je najvažniji deo u dokazu glavne teoreme koja je formulisana u poslednjoj glavi. Koristeći tehnike mikrolokalne analize, uvodimo i izučavamo odgovarajuće talasne frontove, i pokazujemo odgovarajuća tvrdjenja vezana za singularni nosač distribucije. Naš glavni rezultat pokazuje kako se prostiru singulariteti rešenja linearnih parcijalnih diferencijalnih jednačina u okviru naše regularnosti.
19
Pukhtaievych, Roman. "Periodic and hypercomplex potentials. Properties and applications." Doctoral thesis, Università degli studi di Padova, 2018. http://hdl.handle.net/11577/3425759.
Повний текст джерелаАнотація:
This Dissertation is devoted to the study of boundary value problems and concerns two research areas. The first one is related to the perturbation analysis of boundary value problems in perforated domains and its application to the investigation of effective properties of composite materials. We investigate the dependence of the solutions of transmission boundary value problems upon some parameters and their behavior when the parameter corresponding to the size of the inclusions tends to zero, and the other parameters tend to some fixed values. Then we apply our results to study the effective conductivity of periodic composites. We also investigate the behavior of the solution of the Dirichlet problem for the Poisson equation in the domain in R3 which consists of a periodic array of cylinders upon perturbation of the shape of the cross-section of the cylinders and the periodic structure. Moreover, we apply our results to study the behavior of the longitudinal permeability of a periodic array of cylinders upon such perturbation. The second part of the Dissertation is related to the development of tools for solving boundary value problems for functions taking values in commutative Banach algebras. In particular, we investigate the properties of logarithmic residues of monogenic (continuous and differentiable in the sense of Gateau) functions and the behavior of the certain Cauchy type integral on the boundary of its definition.
The Dissertation consists of two parts and is organized as follows.
Part I consists of three chapters. In Chapter 1 we investigate the asymptotic behavior of the solutions of singularly perturbed (ideal and nonideal nonlinear) transmission problems in a periodically perforated domain. In Chapter 2 we apply the results of Chapter 1 to study the asymptotic behavior of the effective thermal conductivity of a periodic two-phase dilute composite. Chapter 3 is devoted to the study of the behavior of the longitudinal permeability of a periodic array of cylinders upon perturbation of the shape of the cross section of the cylinders and of the periodic structure.
Part II consists of two chapters. In Chapter 4 we introduce a three-dimensional commutative algebra over C with a one-dimensional radical and study the logarithmic residues of monogenic functions in this algebra. Chapter 5 is devoted to the investigation of a certain analog of Cauchy type integral taking values in the mentioned algebra and its limiting values on the boundary of the domain of definition. At the end of the Dissertation, we have enclosed three appendices with some results which we have exploited in the Dissertation.Questa Tesi si occupa dello studio di problemi al contorno e analizza due linee di ricerca. La prima riguarda lo studio di perturbazioni di problemi al contorno in domini perforati e la sua applicazione all'analisi delle proprieta efficaci dei materiali compositi. Studiamo la dipendenza delle soluzioni di problemi di trasmissione da alcuni parametri e il loro comportamento quando il parametro corrispondente alla dimensione delle inclusioni tende a zero e gli altri parametri tendono ad alcuni valori fissati. In seguito, applichiamo i nostri risultati allo studio della conduttivita efficace di composti periodici. Analizziamo anche il comportamento della soluzione del problema di Dirichlet per l'equazione di Poisson nell'insieme di R3 che consiste in una serie periodica di cilindri in caso di perturbazione della forma della sezione trasversale dei cilindri e la struttura periodica. Inoltre, applichiamo i nostri risultati per studiare il comportamento della permeabilita longitudinale di una serie periodica di cilindri rispetto a tale perturbazione. La seconda parte della Tesi riguarda lo sviluppo di strumenti per risolvere problemi al contorno per funzioni che assumono valore in algebre di Banach commutative. In particolare, studiamo le proprieta dei residui logaritmici delle funzioni monogeniche (continue e differenziabili nel senso di Gateaux) e il comportamento di certi integrali di tipo Cauchy sulla frontiera dell'insieme di definizione. La Tesi si suddivide in due parti ed è organizzata come segue. La parte I è composta da tre capitoli. Nel capitolo 1 studiamo il comportamento asintotico delle soluzioni di problemi di trasmissione (ideale e nonideale) singolarmente perturbati in un dominio periodicamente perforato. Nel capitolo 2 applichiamo i risultati del capitolo 1 per studiare il comportamento asintotico della conduttivita termica efficace di un composto periodico a due fasi diluito. Il capitolo 3 è dedicato allo studio del comportamento della permeabilita longitudinale di una serie periodica di cilindri quando perturbiamo la forma della sezione trasversale dei cilindri e la struttura periodica. La parte II è composta da due capitoli. Nel capitolo 4 introduciamo un'algebra commutativa tridimensionale su C con un radicale unidimensionale e studiamo i residui logaritmici delle funzioni monogeniche in questa algebra. Il capitolo 5 è dedicato allo studio di un analogo dell'integrale di Cauchy che assume valore nell'algebra menzionata e dei suoi valori limite sulla frontiera del dominio di definizione. Alla fine della Tesi, abbiamo inserito tre appendici con alcuni risultati che abbiamo utilizzato nella Tesi.
20
Tang, Hongzhen. "Efficient analysis for nonlinear effects and power handling capability in high power HTSC thin film microwave circuits." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2000. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape4/PQDD_0015/NQ56679.pdf.
Повний текст джерела
21
Salles, Nicolas. "Calcul des singularités dans les méthodes d’équations intégrales variationnelles." Thesis, Paris 11, 2013. http://www.theses.fr/2013PA112164/document.
Повний текст джерелаАнотація:
La mise en œuvre de la méthode des éléments finis de frontière nécessite l'évaluation d'intégrales comportant un intégrand singulier. Un calcul fiable et précis de ces intégrales peut dans certains cas se révéler à la fois crucial et difficile. La méthode que nous proposons consiste en une réduction récursive de la dimension du domaine d'intégration et aboutit à une représentation de l'intégrale sous la forme d'une combinaison linéaire d'intégrales mono-dimensionnelles dont l'intégrand est régulier et qui peuvent s'évaluer numériquement mais aussi explicitement. L'équation de Helmholtz 3-D sert d'équation modèle mais ces résultats peuvent être utilisés pour les équations de Laplace et de Maxwell 3-D. L'intégrand est décomposé en une partie homogène et une partie régulière ; cette dernière peut être traitée par les méthodes usuelles d'intégration numérique. Pour la discrétisation du domaine, des triangles plans sont utilisés ; par conséquent, nous évaluons des intégrales sur le produit de deux triangles. La technique que nous avons développée nécessite de distinguer entre diverses configurations géométriques ; c'est pourquoi nous traitons séparément le cas de triangles coplanaires, dans des plans sécants ou parallèles. Divers prolongements significatifs de la méthode sont présentés : son extension à l'électromagnétisme, l'évaluation de l'intégrale du noyau de Green complet pour les coefficients d'auto-influence, et le calcul de la partie finie d'intégrales hypersingulièresThe implementation of the boundary element method requires the evaluation of integrals with a singular integrand. A reliable and accurate calculation of these integrals can in some cases be crucial and difficult. The proposed method is a recursive reduction of the dimension of the integration domain and leads to a representation of the integral as a linear combination of one-dimensional integrals whose integrand is regular and that can be evaluated numerically and even explicitly. The 3-D Helmholtz equation is used as a model equation, but these results can be used for the Laplace and the Maxwell equations in 3-D. The integrand is decomposed into a homogeneous part and a regular part, the latter can be treated by conventional numerical integration methods. For the discretization of the domain we use planar triangles, so we evaluate integrals over the product of two triangles. The technique we have developped requires to distinguish between several geometric configurations, that's why we treat separately the case of triangles in the same plane, in secant planes and in parallel planes
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Tu, Xuemin. "Enhanced Singular Function Mortar Finite Element Methods." Digital WPI, 2002. https://digitalcommons.wpi.edu/etd-theses/947.
Повний текст джерелаАнотація:
"It is well known that singularities occur when solving elliptic value problems with non-convex domains or when some part of the data or the coefficients of the PDE are not smooth. Such problems and correspondent singularities often arise in practice, for instance, in fracture mechanics, in the material science with heterogeneities, or when dealing with mixed boundary conditions. A great deal is known about the nature of the singularities, which arise in some of these problems. In this thesis, we consider the scalar transmission problems with straight interfaces and with cross points across coefficients and possibly on a non-convex region ($L$-shaped domain). It is known that only $H^{1+au}$ ($0 < au< 1$) regularity on the solution is obtained and therefore the use of finite element method with the piecewise linear continuous function space does not give optimal accuracy. In this thesis, we introduce a new algorithm which are second order accurate on the (weighted) $L_2$, first order accurate on the (weighted) $H_1$ norm and second order accurate for the Stress Intensive Factor (SIF). The new methods take advantage of Mortar techniques. The main feature of the proposed algorithms is that we use primal singular functions {it without} cutting-off functions. The old algorithms use cutting-off functions as a tool of satisfying boundary conditions. In algorithms proposed in this thesis, use instead Mortar finite element technique to match the boundary and interfaces conditions. In this thesis, we also consider non-matching meshes sizes for different coefficients. We note that a new Mortar Lagrange multiplier is required in order to obtain optimal consistence errors for transmission problems. The proposed algorithms are very appealing over other methods because they are very accurate, do not require complicated numerical quadratures or interpolations, it is simple to design PCGs, and it can be generalized to other PDEs and to higher order methods."
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Zhang, Lingsong Marron James Stephen Zhu Zhengyuan Shen Haipeng. "Functional singular value decomposition and multi-resolution anomaly detection." Chapel Hill, N.C. : University of North Carolina at Chapel Hill, 2007. http://dc.lib.unc.edu/u?/etd,1166.
Повний текст джерелаАнотація:
Thesis (Ph. D.)--University of North Carolina at Chapel Hill, 2007.Title from electronic title page (viewed Mar. 27, 2008). "... in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Department of Statistics and Operations Research." Discipline: Statistics and Operations Research; Department/School: Statistics and Operations Research.
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Cerezo, Graciela M. "Solution Representation and Indentification for Singular neutral Functional Differential Equations." Diss., Virginia Tech, 1996. http://hdl.handle.net/10919/30365.
Повний текст джерелаАнотація:
The solutions for a class of Neutral Functional Di erential Equations (NFDE) with weakly singular kernels are studied. Using singular expansion techniques, a representation of the solution of the NFDE is obtained by studing an associated Volterra Integral Equation. We study the Collocation Method as a projection method for the approximation of solutions for Volterra Integral Equations. Particulary, the possibility of achieving higher order ap- proximations is discussed. Special attention is given to the choice of the projection space and its relation to the smoothness of the approximated solution. Finally, we study the identification problem for a parameter appearing in the weakly singular operator of the NFDE.Ph. D.
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AGOSTI, ABRAMO. "MODELS OF TURBULENCE. APPLICATIONS TO PARTICULATE MIXING INDUCED BY TRAFFIC FLOW IN URBAN AREAS." Doctoral thesis, Università degli Studi di Milano, 2013. http://hdl.handle.net/2434/217169.
Повний текст джерелаАнотація:
In this work we address our attention to the estimation of the contribution of non-exhaust sources, like brake abrasion, tire and road wear and resuspension of particles, to the final PM air concentration; particularly we focus our investigation on the resuspension of PM deposited on road pavement surfaces and raised by the air turbulence produced by the vehicles flux, under urban and extra-urban traffic conditions.
Our approach to the problem is based on modeling techniques. We refer to measurement data from literature to determine the selected empirical parameters contained in our models.
Analytical models based on algebraic eddy diffusivity hypothesis are applied to describe the mean statistical component of flow generated by air recirculation inside a canyon and by the far-wake structure besides moving vehicles of simplified geometrical shapes.
The analysis of the far wake solutions is suitable to the description of vehicle wakes interaction, which permits to apply our analysis to different driving cycles conditions.
Numerical simulations based on finite element discretization of suitable two-equation turbulence models are employed to describe near-wake structures, which cause the strongest mixing of atmospheric pollutants and resuspension of road dust.
These different components of turbulence fields at different scales of the street geometry are composed to define a set of operational and numerical models for the dispersion dynamics at the canyon scale of two classes of PM10 pollutants, corresponding to a Soot and a road dust components.
The deposition and the resuspension of pollutants are described by resistance and filtration models on porous asphalts, inserting the corresponding terms in the dispersion equations as
suitable boundary conditions on the ground.
We estimate the resuspension fraction of traffic-related PM10 emissions at the tailpipe, through a simplified linear-emission model, considering representative data describing traffic statistics coming from empirical data.
Profile laws of resuspension factors are drawn, for different vehicles geometries and velocities, and how resuspension changes with different asphalt characteristics.
The results are applied to typical traffic situations in the city of Milan, studying the effect of implementations of different reduction scenarios to the total amount of traffic-related PM10 emissions.
The results point at a new approach to the local PM10 reduction policies, based on more effective asphalt design and maintenance.
Finally, we apply one of the dispersion operational models to the case of a congested urban traffic configuration in a canyon street, in order to obtain the pollutant spatial distribution.
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Cerezo, Graciela M. "Numerical approximation and identification problems for singular neutral equations." Thesis, This resource online, 1994. http://scholar.lib.vt.edu/theses/available/etd-09052009-040632/.
Повний текст джерела
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Sensi, Mattia. "A Geometric Singular Perturbation approach to epidemic compartmental models." Doctoral thesis, Università degli studi di Trento, 2021. http://hdl.handle.net/11572/286191.
Повний текст джерелаАнотація:
We study fast-slow versions of the SIR, SIRS and SIRWS epidemiological models, and of the SIRS epidemiological model on homogeneous graphs, obtained through the application of the moment closure method. The multiple time scale behavior is introduced to account for large differences between some of the rates of the epidemiological pathways. Our main purpose is to show that the fast-slow models, even though in nonstandard form, can be studied by means of Geometric Singular Perturbation Theory (GSPT). In particular, without using Lyapunov's method, we are able to not only analyze the stability of the endemic equilibria of the SIR and SIRS models, but also to show that in the remaining models limit cycles arise. We show that the proposed approach is particularly useful in more complicated (higher dimensional) models such as the SIRWS model and the SIRS on homogeneous graphs, for which we provide a detailed description of their dynamics by combining analytic and numerical techniques. In particular, for the latter we show that the model can give rise to periodic solutions, differently from the corresponding model based on homogeneous mixing.
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Sensi, Mattia. "A Geometric Singular Perturbation approach to epidemic compartmental models." Doctoral thesis, Università degli studi di Trento, 2021. http://hdl.handle.net/11572/286191.
Повний текст джерелаАнотація:
We study fast-slow versions of the SIR, SIRS and SIRWS epidemiological models, and of the SIRS epidemiological model on homogeneous graphs, obtained through the application of the moment closure method. The multiple time scale behavior is introduced to account for large differences between some of the rates of the epidemiological pathways. Our main purpose is to show that the fast-slow models, even though in nonstandard form, can be studied by means of Geometric Singular Perturbation Theory (GSPT). In particular, without using Lyapunov's method, we are able to not only analyze the stability of the endemic equilibria of the SIR and SIRS models, but also to show that in the remaining models limit cycles arise. We show that the proposed approach is particularly useful in more complicated (higher dimensional) models such as the SIRWS model and the SIRS on homogeneous graphs, for which we provide a detailed description of their dynamics by combining analytic and numerical techniques. In particular, for the latter we show that the model can give rise to periodic solutions, differently from the corresponding model based on homogeneous mixing.
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Avila, Leonardo. "Sobre singularidades analíticas de soluções de uma classe de campos vetoriais no Toro." Universidade de São Paulo, 2009. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-30032010-104911/.
Повний текст джерелаАнотація:
O objetivo principal deste trabalho é o estudo da regularidade anallítica global de certos operadores diferenciais definidos no toro. Uma ferramenta fundamental utilizada neste estudo são as séries parciais de Fourier, que nos permitem caracterizar tanto as distribuições periódicas quanto as funções anallíticas reais periódicas através do comportamento assintótico de seus coeficientes parciais de Fourier. Neste sentido, apresentamos também um estudo detalhado das relações destes objetos com seus coeficientes parciais de FourierThe main goal of this work is to study global analytic regularity properties of certain differential operators acting in the torus. A main tool that will be used to achieve our goals are the partial Fourier series, which allow us to characterize objects such as periodic distributions or periodic real analytic functions in terms of the growth of their partial Fourier coefficients
30
Workalemahu, Tsegaselassie. "Singular Value Decomposition in Image Noise Filtering and Reconstruction." Digital Archive @ GSU, 2008. http://digitalarchive.gsu.edu/math_theses/52.
Повний текст джерелаАнотація:
The Singular Value Decomposition (SVD) has many applications in image processing. The SVD can be used to restore a corrupted image by separating significant information from the noise in the image data set. This thesis outlines broad applications that address current problems in digital image processing. In conjunction with SVD filtering, image compression using the SVD is discussed, including the process of reconstructing or estimating a rank reduced matrix representing the compressed image. Numerical plots and error measurement calculations are used to compare results of the two SVD image restoration techniques, as well as SVD image compression. The filtering methods assume that the images have been degraded by the application of a blurring function and the addition of noise. Finally, we present numerical experiments for the SVD restoration and compression to evaluate our computation.
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Bank, Peter. "Singular control of optional random measures." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, 2000. http://dx.doi.org/10.18452/14556.
Повний текст джерелаАнотація:
In dieser Arbeit untersuchen wir das Problem der Maximierung bestimmter konkaver Funktionale auf dem Raum der optionalen, zufälligen Maße. Deartige Funktionale treten in der mikroökonomischen Literatur auf, wo ihre Maximierung auf die Bestimmung des optimalen Konsumplans eines ökomischen Agenten hinausläuft. Als Alternative zu den wohlbekannten Methoden der dynamischen Programmierung wird ein neuer Zugang vorgestellt, der es erlaubt, die Struktur der maximierenden Maße in einem über den üblicherweise angenommenen Markovschen Rahmen hinausgehenden, allgemeinen Semimartingalrahmen zu klären. Unser Zugang basiert auf einer unendlichdimensionalen Version des Kuhn-Tucker-Theorems. Die implizierten Bedingungen erster Ordnung erlauben es uns, das Maximierungsproblem auf ein neuartiges Darstellungsproblem für optionale Prozesse zu reduzieren, das damit als ein nicht-Markovsches Substitut für die Hamilton-Jacobi-Bellman Gleichung der dynamischen Programmierung dient. Um dieses Darstellungsproblem im deterministischen Fall zu lösen, führen wir eine zeitinhomogene Verallgemeinerung des Konvexitätsbegriffs ein. Die Lösung im allgemeinen stochastischen Fall ergibt sich über eine enge Beziehung zur Theorie des Gittins-Index der optimalen dynamischen Planung. Unter geeigneten Annahmen gelingt ihre Darstellung in geschlossener Form. Es zeigt sich dabei, daß die maximierenden Maße absolutstetig, diskret und auch singulär sein können, je nach Struktur der dem Problem zugrundeliegenden Stochastik. Im mikroökonomischen Kontext ist es natürlich, daß Problem in einen Gleichgewichtsrahmen einzubetten. Der letzte Teil der Arbeit liefert hierzu ein allgemeines Existenzresultat für ein solches Gleichgewicht.In this thesis, we study the problem of maximizing certain concave functionals on the space of optional random measures. Such functionals arise in microeconomic theory where their maximization corresponds to finding the optimal consumption plan of some economic agent. As an alternative to the well-known methods of Dynamic Programming, we develop a new approach which allows us to clarify the structure of maximizing measures in a general stochastic setting extending beyond the usually required Markovian framework. Our approach is based on an infinite-dimensional version of the Kuhn-Tucker Theorem. The implied first-order conditions allow us to reduce the maximization problem to a new type of representation problem for optional processes which serves as a non-Markovian substitute for the Hamilton-Jacobi-Bellman equation of Dynamic Programming. In order to solve this representation problem in the deterministic case, we introduce a time-inhomogeneous generalization of convexity. The stochastic case is solved by using an intimate relation to the theory of Gittins-indices in optimal dynamic scheduling. Closed-form solutions are derived under appropriate conditions. Depending on the underlying stochastics, maximizing random measures can be absolutely continuous, discrete, and also singular. In the microeconomic context, it is natural to embed the above maximization problem in an equilibrium framework. In the last part of this thesis, we give a general existence result for such an equilibrium.
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Hassanpour, Hamid. "Time-frequency based detection of newborn EEG seizure." Thesis, Queensland University of Technology, 2004. https://eprints.qut.edu.au/15853/1/Hamid_Hassanpour_Thesis.pdf.
Повний текст джерелаАнотація:
Neurological diseases in newborns are usually first revealed by seizures, which are characterised by a synchronous discharge of a large number of neurons. Failure to control seizures may lead to brain damage or even death.
The importance of this problem prompted many researchers to look for accurate automatic methods for seizure detection. Nonstationarity and multicomponent behaviour of newborn EEG signals made this task very challenging. The significant overlap in the characteristic of background and seizure activities in newborn EEG signals added to the difficulty of seizure detection.
This research uses time-frequency based methods for automatic seizure detection. Since time-frequency signal analysis methods use joint representation in both time and frequency domains, they proved to be very suitable for analysis and processing of nonstationary and multicomponent signals such as newborn EEG.
Before using any seizure detector, the EEG data is pre-processed in order to reduce the noise effects using a time-frequency based technique. The proposed method is based on the singular value decomposition (SVD) technique applied to the matrix representing the time-frequency distribution (TFD) of the EEG signal. It has been shown that by appropriately filtering the singular vectors associated with the TFD, one can effectively enhance the desired information embedded in the signal.
Neonatal EEG seizures can have signatures in both low frequency (lower than 10 Hz) and high frequency (higher than 70 Hz) areas. The seizure detection techniques proposed in the literature concentrated on using either low frequency or high frequency signatures but not both simultaneously. These methods tend to miss the seizures that reveal themselves only in one of the two frequency areas. In this research, we propose a detection method that uses seizure features in both low and high frequency areas.
To detect EEG seizures using the low frequency signatures, an SVD-based technique is employed. The technique uses the estimated distribution function of the singular vectors associated with the time-frequency distribution of EEG epochs to discriminate between seizure and nonseizure patterns.
The high frequency signatures of seizures are mostly the result of spike events in the EEG signals. To detect these spike events, the signal is mapped into the TF domain. The high instantaneous energy of spikes is reflected as a localised energy in the high frequency area of the TF domain. Consequently, a spike can be seen as a ridge in this area of the TF domain. It has been shown that during seizure activity there is regularity in the distribution of the interspike intervals. This feature has been used as the basis for discriminating between seizure and nonseizure patterns.
The performance results obtained by applying the proposed methods on EEG signals extracted from a number of newborns show the superiority of these methods over the existing ones.
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Hassanpour, Hamid. "Time-Frequency Based Detection of Newborn EEG Seizure." Queensland University of Technology, 2004. http://eprints.qut.edu.au/15853/.
Повний текст джерелаАнотація:
Neurological diseases in newborns are usually first revealed by seizures, which are characterised by a synchronous discharge of a large number of neurons. Failure to control seizures may lead to brain damage or even death. The importance of this problem prompted many researchers to look for accurate automatic methods for seizure detection. Nonstationarity and multicomponent behaviour of newborn EEG signals made this task very challenging. The significant overlap in the characteristic of background and seizure activities in newborn EEG signals added to the difficulty of seizure detection. This research uses time-frequency based methods for automatic seizure detection. Since time-frequency signal analysis methods use joint representation in both time and frequency domains, they proved to be very suitable for analysis and processing of nonstationary and multicomponent signals such as newborn EEG. Before using any seizure detector, the EEG data is pre-processed in order to reduce the noise effects using a time-frequency based technique. The proposed method is based on the singular value decomposition (SVD) technique applied to the matrix representing the time-frequency distribution (TFD) of the EEG signal. It has been shown that by appropriately filtering the singular vectors associated with the TFD, one can effectively enhance the desired information embedded in the signal. Neonatal EEG seizures can have signatures in both low frequency (lower than 10 Hz) and high frequency (higher than 70 Hz) areas. The seizure detection techniques proposed in the literature concentrated on using either low frequency or high frequency signatures but not both simultaneously. These methods tend to miss the seizures that reveal themselves only in one of the two frequency areas. In this research, we propose a detection method that uses seizure features in both low and high frequency areas. To detect EEG seizures using the low frequency signatures, an SVD-based technique is employed. The technique uses the estimated distribution function of the singular vectors associated with the time-frequency distribution of EEG epochs to discriminate between seizure and nonseizure patterns. The high frequency signatures of seizures are mostly the result of spike events in the EEG signals. To detect these spike events, the signal is mapped into the TF domain. The high instantaneous energy of spikes is reflected as a localised energy in the high frequency area of the TF domain. Consequently, a spike can be seen as a ridge in this area of the TF domain. It has been shown that during seizure activity there is regularity in the distribution of the interspike intervals. This feature has been used as the basis for discriminating between seizure and nonseizure patterns. The performance results obtained by applying the proposed methods on EEG signals extracted from a number of newborns show the superiority of these methods over the existing ones.
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Prescott, Thomas Paul. "Large-scale layered systems and synthetic biology : model reduction and decomposition." Thesis, University of Oxford, 2014. http://ora.ox.ac.uk/objects/uuid:205a18fb-b21f-4148-ba7d-3238f4b1f25b.
Повний текст джерелаАнотація:
This thesis is concerned with large-scale systems of Ordinary Differential Equations that model Biomolecular Reaction Networks (BRNs) in Systems and Synthetic Biology. It addresses the strategies of model reduction and decomposition used to overcome the challenges posed by the high dimension and stiffness typical of these models. A number of developments of these strategies are identified, and their implementation on various BRN models is demonstrated. The goal of model reduction is to construct a simplified ODE system to closely approximate a large-scale system. The error estimation problem seeks to quantify the approximation error; this is an example of the trajectory comparison problem. The first part of this thesis applies semi-definite programming (SDP) and dissipativity theory to this problem, producing a single a priori upper bound on the difference between two models in the presence of parameter uncertainty and for a range of initial conditions, for which exhaustive simulation is impractical. The second part of this thesis is concerned with the BRN decomposition problem of expressing a network as an interconnection of subnetworks. A novel framework, called layered decomposition, is introduced and compared with established modular techniques. Fundamental properties of layered decompositions are investigated, providing basic criteria for choosing an appropriate layered decomposition. Further aspects of the layering framework are considered: we illustrate the relationship between decomposition and scale separation by constructing singularly perturbed BRN models using layered decomposition; and we reveal the inter-layer signal propagation structure by decomposing the steady state response to parametric perturbations. Finally, we consider the large-scale SDP problem, where large scale SDP techniques fail to certify a system’s dissipativity. We describe the framework of Structured Storage Functions (SSF), defined where systems admit a cascaded decomposition, and demonstrate a significant resulting speed-up of large-scale dissipativity problems, with applications to the trajectory comparison technique discussed above.
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Musolino, Paolo. "Singular perturbation and homogenization problems in a periodically perforated domain. A functional analytic approach." Doctoral thesis, Università degli studi di Padova, 2012. http://hdl.handle.net/11577/3422452.
Повний текст джерелаАнотація:
This Dissertation is devoted to the singular perturbation and homogenization analysis
of boundary value problems in the periodically perforated Euclidean space. We investigate the behaviour of the solutions of boundary value problems for the Laplace, the Poisson, and the Helmholtz equations, as parameters related to diameter of the holes or the size of the periodicity cells tend to 0.
The Dissertation is organized as follows.
In Chapter 1, we present two known constructions of a periodic analogue of the fundamental solution of the Laplace equation and we introduce the periodic layer and volume potentials for the Laplace equation and some basic results of periodic potential theory. Chapter 2 is devoted to singular perturbation and homogenization problems for the Laplace and the Poisson equations with Dirichlet and Neumann boundary conditions. In Chapter 3 we consider the case of (linear and nonlinear) Robin boundary value problems for the Laplace equation, while in Chapter 4 we analyze (linear and nonlinear) transmission problems. In Chapter 5 we apply the results of Chapter 4 in order to prove the real analyticity of the effective conductivity of a periodic dilute composite. Chapter 6 is dedicated to the construction of a periodic analogue of the fundamental solution of the Helmholtz equation and of the corresponding periodic layer potentials. In Chapter 7 we collect some results of spectral theory for the Laplace operator in periodically perforated domains. In Chapter 8 we investigate singular perturbation and homogenization problems for the Helmholtz equation with Neumann boundary conditions. In Chapter 9 we consider singular perturbation and homogenization problems with Dirichlet boundary conditions for the Helmholtz equation, while in Chapter 10 we study (linear and nonlinear) Robin boundary value problems. Chapter 11 is devoted to the study of periodic layer potentials for general second order differential operators with constant coefficients. At the end of the Dissertation we have enclosed some Appendices with some results that we have exploited.Questa Tesi è dedicata all'analisi di problemi di perturbazione singolare e omogeneizzazione nello spazio Euclideo periodicamente perforato. Studiamo il comportamento delle soluzioni di problemi al contorno per le equazioni di Laplace, di Poisson e di Helmholtz al tendere a 0 di parametri legati al diametro dei buchi o alla dimensione delle celle di periodicità. La Tesi è organizzata come segue. Nel Capitolo 1, presentiamo due costruzioni note di un analogo periodico della soluzione fondamentale dell'equazione di Laplace, e introduciamo potenziali di strato e di volume periodici per l'equazione di Laplace e alcuni risultati basilari di teoria del potenziale periodica. Il Capitolo 2 è dedicato a problemi di perturbazione singolare e omogeneizzazione per le equazioni di Laplace e Poisson con condizioni al bordo di Dirichlet e Neumann. Nel Capitolo 3 consideriamo il caso di problemi al contorno di Robin (lineari e nonlineari) per l'equazione di Laplace, mentre nel Capitolo 4 analizziamo problemi di trasmissione (lineari e nonlineari). Nel Capitolo 5 applichiamo i risultati del Capitolo 4 al fine di provare l'analiticità della conduttività effettiva di un composto periodico. Il Capitolo 6 è dedicato alla costruzione di un analogo periodico della soluzione fondamentale dell'equazione di Helmholtz e dei corrispondenti potenziali di strato. Nel Capitolo 7 raccogliamo alcuni risultati di teoria spettrale per l'operatore di Laplace in domini periodicamente perforati. Nel Capitolo 8 studiamo problemi di perturbazione singolare e di omogeneizzazione per l'equazione di Helmholtz con condizioni al contorno di Neumann. Nel Capitolo 9 consideriamo problemi di perturbazione singolare e di omogeneizzazione con condizioni al contorno di Dirichlet per l'equazione di Helmholtz, mentre nel Capitolo 10 studiamo problemi al contorno di Robin (lineari e nonlineari). Il Capitolo 11 è dedicato allo studio di potenziali di strato periodici per operatori differenziali generali del secondo ordine a coefficienti costanti. Alla fine della Tesi abbiamo incluso delle Appendici con alcuni risultati utilizzati.
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Oikonomopoulos, Dimitrios [Verfasser]. "Functional Inequalities and Heat Kernel Asymptotics on Some Classes of Singular Riemannian Manifolds / Dimitrios Oikonomopoulos." Bonn : Universitäts- und Landesbibliothek Bonn, 2019. http://d-nb.info/1200019814/34.
Повний текст джерела
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Tanja, Krunić. "Numeričke procedure u definisanju pravilnih rešenja zakona održanja." Phd thesis, Univerzitet u Novom Sadu, Prirodno-matematički fakultet u Novom Sadu, 2016. https://www.cris.uns.ac.rs/record.jsf?recordId=101094&source=NDLTD&language=en.
Повний текст джерелаАнотація:
U okviru ove doktorske disertacije posmatrani su zakoni održanja sa funkcijom fluksa koja ima prekid u x = 0, pri čemu delovi fluksa levo i desno od x = 0 imaju smo po jedan ekstrem. U prvoj glavi se može naći pregled osnovnih pojmova, definicija i teorema. U drugoj glavi su opisani hiperbolični sistemi zakona održanja, slaba rešenja, kao i numerički postupci za njihovo rešavanje. U trećoj glavi su predstavljeni diskretni profili darnih talasa. U četvrtoj glavi su opisani zakoni održanja sa prekidnom funkcijom fluksa i ukratko su predstvaljeni rezultati drugih autora iz ove oblasti. U petoj glavi je najpre analizirana tzv. jednačina sa dva fluksa u slučaju kada oba dela fluksa levo i desno od x = 0 imaju minimum, a pri tome se seku u najviše jednoj tačci unutar intervala. Primenom regularizacije na intervalu [−ε, ε], za ε > 0 dovoljno malo, dokazano je postojanje diskretnih udarnih profila za postupak Godunova za zakone održanja sa promenljivom funkcijom fluksa. Definisan je i odgovarajući diskretan uslov entropije, a postojanje entropijskog diskretnog udarnog profila je postavljen kao kriterijum za dopustivost udarnih talasa. Potom je analizirana ista jednačina u slucaju kada deo fluksa levo od x = 0 ima maksimum, a deo fluksa desno od x = 0 minimum, dok se oba dela fluksa seku na krajevima posmatranog intervala. U ovom slučaju, uopšten je uslov entropije. U okviru ove glave je prikazano nekoliko numeričkih primera za oba opisana slučaja. Numerički rezultati su dobijeni korišcenjem softvera razvijenog za potrebe ove teze u programskom paketu Mathematica.We consider conservation laws with a flux discontinuity at x = 0, where the flux parts from both left and right hand side of x = 0 have at most one extreme on the observed domain. The first chapter provides elementary definitions and theorems..The second chapter refers to hyperbolic systems of conservation laws, their solutions, and numerical procedures. The third chapter is devoted to discrete shock profiles. The fourth chapter describes conservation laws with discontinuous flux functions and provides basic information upon known results in this field. In the fifth chapter, we first analyse the two-flux equation when both flux parts have a minimum and cross at most at one point in the interior of the domain. Using a flux regularization on the interval [−ε, ε], for ε > 0 small enough, we show the existence of discrete shock profiles for Godunov’s scheme for conservation laws with discontinuous flux functions. We also define a discrete entropy condition accordingly, and use the existence of an entropy discrete shock profile as an entropy criterion for shocks. Then we analyse the same problem in the case when the flux part on the left of x = 0 has a maximum and the part on the right of x = 0 has a minimum, whereas the fluxes cross at the edges of the interval. We derive a more general discrete entropy condition in this case. We provide several numerical examples in both of the above mentioned flux cases. All the presented numerical results are obtained using a program written in Mathematica. Finally, in chapter six, we prove the existence of singular shock waves in the case when the graph of one of the flux parts is above the graph of the other one on the entire domain. For that purpose, we use the shadow wave technique. At the end of this chapter, we provide a numerical verification of the obtained singular solution.
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Ouoba, Mahamadi. "Asymptotic expansion of the expected discounted penalty function in a two-scalestochastic volatility risk model." Thesis, Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:mdh:diva-26100.
Повний текст джерелаАнотація:
In this Master thesis, we use a singular and regular perturbation theory to derive an analytic approximation formula for the expected discounted penalty function. Our model is an extension of Cramer–Lundberg extended classical model because we consider a more general insurance risk model in which the compound Poisson risk process is perturbed by a Brownian motion multiplied by a stochastic volatility driven by two factors- which have mean reversion models. Moreover, unlike the classical model, our model allows a ruin to be caused either by claims or by surplus’ fluctuation. We compute explicitly the first terms of the asymptotic expansion and we show that they satisfy either an integro-differential equation or a Poisson equation. In addition, we derive the existence and uniqueness conditions of the risk model with two stochastic volatilities factors.
39
Kerker, Mohamed Amine. "Sur le problème de Cauchy singulier." Thesis, Reims, 2013. http://www.theses.fr/2013REIMS005.
Повний текст джерелаАнотація:
L'objet de cette thèse porte sur le problème de Cauchy singulier dans le domaine complexe. Il s'agit d'étudier les singularités de la solution du problème pour trois classes d'équations aux dérivées partielles. Cette thèse s'inscrit dans la continuité des travaux initiés par Jean Leray et son école. Pour décrire les singularités de la solution, on cherche la solution sous la forme d'un développement asymptotique de fonctions hypergéométriques de Gauss. Comme les singularités sont portées par les fonctions hypergéométriques, l'étude de la ramification de la solution se ramène à celle de ces fonctionsThis thesis deals with the singular Cauchy problem in the complex domain. We study the singularities of the solution of the problem for three classes of partial differential equations. This thesis is a continuation of the work initiated by Jean Leray and his school. To describe the singularities of the solution, we seek the solution in the form of asymptotic an expansion of Gauss hypergeometric functions. As the singularities are carried by the hypergeometric functions, the study of the ramification of the solution reduces to that of these functions
40
Pugliese, Alessandro. "Theoretical and numerical aspects of coalescing of eigenvalues and singular values of parameter dependent matrices." Diss., Atlanta, Ga. : Georgia Institute of Technology, 2008. http://hdl.handle.net/1853/24730.
Повний текст джерелаАнотація:
Thesis (Ph.D.)--Mathematics, Georgia Institute of Technology, 2008.Committee Chair: Dieci, Luca; Committee Member: Chow, Shui-Nee; Committee Member: Liu, Yingjie; Committee Member: Loss, Michael; Committee Member: Verriest, Erik.
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Hamedani, Ladan. "The Function of Number in Persian." Thesis, Université d'Ottawa / University of Ottawa, 2011. http://hdl.handle.net/10393/20167.
Повний текст джерелаАнотація:
This thesis investigates the function of number marking in Persian, within the framework of principles and parameters (P&P), and its relationship to inflectional and derivational number marking. Following the assumption in Distributed Morphology that inflectional and derivational morphology are not distinct, the distribution and properties of number marking in Persian provide evidence for both inflectional and derivational number marking.
Assuming the two parameters of number marking (Wiltschko, 2007, 2008), number marking as a functional head and number marking as a modifier, I propose that number marking in Persian is mainly inflectional while number functions as a functional head; moreover, I propose that number marking in Persian can be derivational while number functions as a modifier. This explains that number morphology in Persian is not split to either inflectional or derivational. Rather, following Booij’s (1993, 1995) claim that inflectional morphology can be used contextually as well as inherently, I propose that number morphology in Persian is inflectional while number is a functional head; however, it has inherent residues as a modifier.
Considering the functions of inflectional plural morphology in Persian, I argue that the functional category Number Phrase (NumP) is projected in Persian, and number is generated in the head of this functional category. Besides, Persian is a classifier language in which classifiers are in complementary distribution with plural marking. Following Borer’s (2005) discussion of the complementary distribution of plural marking and classifiers in Armenian, I argue that the head of NumP in Persian is either occupied by the plural maker or by full/empty classifiers.
Moreover, I show that the presence of bare singulars/plurals in certain syntactic positions in Persian is related to the projection/non-projection of NumP.
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Junior, Raimundo Alves LeitÃo. "Regularidade e estimativas geomÃtricas para mÃnimos de funcionais descontÃnuos e singulares." Universidade Federal do CearÃ, 2012. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=11135.
Повний текст джерелаАнотація:
CoordenaÃÃo de AperfeiÃoamento de Pessoal de NÃvel SuperiorConselho Nacional de Desenvolvimento CientÃfico e TecnolÃgico
Este trabalho à constituÃdo de duas partes. Na primeira parte estudamos mÃnimos nÃo negativos de funcionais elÃpticos degenerados, ∫ F (X, u, ∇u)dX → min, para nÃcleos variacionais F que sÃo descontÃnuos em u com descontinuidade de ordem ~ X{u>0}. A equaÃÃo de Euler-Lagrange à governada por uma equaÃÃo elÃptica degenerada e nÃo-homogÃnea, com fronteira livre entre as fases positiva e zero do mÃnimo. Mostraremos estimativa gradiente Ãtima e nÃo-degenerescÃncia do mÃnimo. TambÃm trataremos de propriedades de regularidade fracas e fortes de fronteira livre. Provaremos que o conjunto {u>0} tem localmente perÃmetro finito e que a fronteira livre reduzida ∂ red {u>0} tem medida Hn-1-total. Para problemas mais especÃficos que aparecem em Jet flows, provaremos que a fronteira livre reduzida à localmente o grÃfico de uma funÃÃo C1,y. Na segunda parte do trabalho forneceremos uma descriÃÃo bastante completa da teoria de regularidade Ãtima para uma famÃlia de problemas de fronteira livre de duas fases, heterogÃneos, y→ min, governados por operadores elÃpticos degenerados e nÃo-lineares. IncluÃdos em tal famÃlia estÃo os problemas de Jet flows heterogÃneos e os problemas de cavidades do tipo Prandtl-Batchelor, y = 0; equaÃÃes elÃpticas degeneradas singulares e sistemas do tipo obstÃculo y =1.VersÃes lineares destes problemas tÃm sido objeto de intensa pesquisa nas Ãltimas quatro dÃcadas ou mais. As contrapartidas nÃo-lineares tratadas neste trabalho introduzem novas e considerÃveis dificuldades, pois a maioria das teorias desenvolvidas anteriormente, tais como fÃrmulas de monotonicidade e de quase monotonicidade nÃo estÃo disponÃveis. Contudo, as soluÃÃes inovadoras desenvolvidas neste trabalho fornecem novas respostas mesmo no contexto clÃssico de equaÃÃes lineares e nÃo-degeneradas.
This work consists of two parts. In the first part we study nonnegative minimizers of general degenerate elliptic functionals, ∫ F (X, u, ∇u)dX → min, for variational kernels F that are discontinuous in ụ with discontinuity of order ~ X{u>0}. The Euler-Lagrange equation is therefore governed by a non-homogeneous, degenerate elliptic equation with free boundary between the positive and the zero phases of the minimizer. We show optimal gradient estimate and nondegeneracy of minima. We also address weak and strong regularity properties of free boundary, ∂ red {u>0}, has H n-1- total measure. For more specific problems that arise in jet flows, we show the reduced free boundary is locally the graph of a C1,y function. In the second part of work we provide a rather complete description of the sharp regularity theory for a family of heterogeneous, two-phase variational free boundary problems, y→ min, ruled by nonlinear, degenerate elliptic operators. Included in such family are heterogeneous jets and cavities problems of Prandtl-Batchelor type, y = 0; singular degenerate elliptic equations and obstacle type systems, y = 1. Linear versions of these problems have been subjects of intense research for the past four decades or so. The nonlinear counterparts treated in this present work introduce substantial new difficulties since the most of the classical theories developed earlier, such that as monotonicity and almost monotonicity formulae, are no longer available. Nonetheless, the innovative solutions designed in this work provide new answers even in the classical context of linear, nondegenerate equations.
43
Patiño, Diego. "Pilotage des cycles limites dans les systèmes dynamiques hybrides : application aux alimentations électriques statiques." Electronic Thesis or Diss., Vandoeuvre-les-Nancy, INPL, 2009. http://www.theses.fr/2009INPL013N.
Повний текст джерелаАнотація:
Cette thèse s'intéresse au pilotage des cycles limites pour une classe particulière de systèmes hybrides (SDH): les systèmes commutés cycliques. La thématique des SDH est née du constat d'insuffisance des modèles dynamiques classiques pour décrire les comportements lorsque des aspects évènementiels interviennent. Une classe particulièrement importante de SDH est formée par celle qui présente un régime permanent cyclique. Ces systèmes ont des points de fonctionnement non auto-maintenables: il n'existe pas de commande qui maintienne le système sur ce point. Le maintien n'est assuré qu'en valeur moyenne, en effectuant un cycle dans un voisinage du point par commutation des sous systèmes. L'établissement d'une loi de commutation pour cette classe de systèmes doit répondre aux objectifs de stabilité et de performance dynamique, mais doit également garantir la satisfaction de critères liés à la forme d'onde. A l'heure actuelle, peu de méthodes de commande prennent en compte le caractère cyclique du système. Les travaux de cette thèse ont pour objectif de développer des méthodes génériques et robustes pour piloter cette classe de systèmes. Les algorithmes proposés doivent également pouvoir être implémenté en temps réels. On modélise le système comme un système non - linéaire affine en la commande dont la loi de commande apparait dans le modèle. Ce type de modélisation permet d'envisager deux types de synthèse: l'une à base de commande prédictive et l'autre à base de commande optimale. Ce travail est validé par une partie applicative sur des manipulations dans le CRAN et dans des laboratoires du réseau d'excellence européenne HYCON dans le cadre duquel s'est déroulé cette étudeThis work deals with limit cycle control for one particular class of hybrid dynamical systems (HDS): The cyclic switched systems. The HDS were born because the traditional dynamical models were not able to describe complex behaviors and most of all, behaviors with discontinuities. From an application point of view, one important class of HDS depicts a cyclic behavior in steady state. The main characteristic of these systems is that the operation point cannot be maintained: It does not exist a control that maintains the system on a desired operation point. However, this point can be obtained in average by turning into its neighborhood. Thus, a cycle is produced by switching among the system modes. A switched control law must satisfy stability and dynamic performance. Moreover, criteria related to the waveform must be verified. Nowadays, few methods take into account the cyclic behavior of the system. In this research, some generic methods are studied. They show good performance for controlling the cyclic switched systems. The proposed algorithms can be implemented in real-time. The approaches are based on an affine non-linear model of the system whose control explicitly appears. Two control methods are considered: i) A predictive control, ii) An optimal control. Since the predictive control is a good choice for tracking, it will be able to maintain the system in a cycle. The optimal control yields solutions that can be applied to the transients. Some experiments with both control methods applied to the power converters are shown. These tests were carried out not only in our laboratory (CRAN), but also in other laboratories as part of the HYCON excellence network
44
Franz, Sebastian. "Uniform Error Estimation for Convection-Diffusion Problems." Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2014. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-133017.
Повний текст джерелаАнотація:
Let us consider the singularly perturbed model problem
Lu := -epsilon laplace u-bu_x+cu = f
with homogeneous Dirichlet boundary conditions on the unit-square (0,1)^2. Assuming that b > 0 is of order one, the small perturbation parameter 0 < epsilon << 1 causes boundary layers in the solution.
In order to solve above problem numerically, it is beneficial to resolve these layers. On properly layer-adapted meshes we can apply finite element methods and observe convergence.
We will consider standard Galerkin and stabilised FEM applied to above problem. Therein the polynomial order p will be usually greater then two, i.e. we will consider higher-order methods.
Most of the analysis presented here is done in the standard energy norm. Nevertheless, the question arises: Is this the right norm for this kind of problem, especially if characteristic layers occur? We will address this question by looking into a balanced norm.
Finally, a-posteriori error analysis is an important tool to construct adapted meshes iteratively by solving discrete problems, estimating the error and adjusting the mesh accordingly. We will present estimates on the Green’s function associated with L, that can be used to derive pointwise error estimators.
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Davis, Paige N. "Localised structures in some non-standard, singularly perturbed partial differential equations." Thesis, Queensland University of Technology, 2020. https://eprints.qut.edu.au/201835/1/Paige_Davis_Thesis.pdf.
Повний текст джерелаАнотація:
This thesis addresses the existence and stability of localised solutions in some nonstandard systems of partial differential equations. In particular, it locates the linearised spectrum of a Keller-Segel model for bacterial chemotaxis with logarithmic chemosensitivity, establishes the existence of travelling wave solutions to the Gatenby-Gawlinski model for tumour invasion with the acid-mediation hypothesis using geometric singular perturbation theory, and formulates the Evans function for a trivial defect solution in a general reaction diffusion equation with an added heterogeneous defect. Extending the analysis to these non-standard problems provides a foundation and insight for more general dynamical systems.
46
Tang, Ying. "Stability analysis and Tikhonov approximation for linear singularly perturbed hyperbolic systems." Thesis, Université Grenoble Alpes (ComUE), 2015. http://www.theses.fr/2015GREAT054/document.
Повний текст джерелаАнотація:
Les dynamiques des systèmes modélisés par des équations aux dérivées partielles (EDPs) en dimension infinie sont largement liées aux réseaux physiques. La synthèse de la commande et l'analyse de la stabilité de ces systèmes sont étudiées dans cette thèse. Les systèmes singulièrement perturbés, contenant des échelles de temps multiples sont naturels dans les systèmes physiques avec des petits paramètres parasitaires, généralement de petites constantes de temps, les masses, les inductances, les moments d'inertie. La théorie des perturbations singulières a été introduite pour le contrôle à la fin des années $1960$, son assimilation dans la théorie du contrôle s'est rapidement développée et est devenue un outil majeur pour l'analyse et la synthèse de la commande des systèmes. Les perturbations singulières sont une façon de négliger la transition rapide, en la considérant dans une échelle de temps rapide séparée. Ce travail de thèse se concentre sur les systèmes hyperboliques linéaires avec des échelles de temps multiples modélisées par un petit paramètre de perturbation. Tout d'abord, nous étudions une classe de systèmes hyperboliques linéaires singulièrement perturbés. Comme le système contient deux échelles de temps, en mettant le paramètre de la perturbation à zéro, deux sous-systèmes, le système réduit et la couche limite, sont formellement calculés. La stabilité du système complet de lois de conservation implique la stabilité des deux sous-systèmes. En revanche un contre-exemple est utilisé pour illustrer que la stabilité des deux sous-systèmes ne suffit pas à garantir la stabilité du système complet. Cela montre une grande différence avec ce qui est bien connu pour les systèmes linéaires en dimension finie modélisés par des équations aux dérivées ordinaires (EDO). De plus, sous certaines conditions, l'approximation de Tikhonov est obtenue pour tels systèmes par la méthode de Lyapunov. Plus précisément, la solution de la dynamique lente du système complet est approchée par la solution du système réduit lorsque le paramètre de la perturbation est suffisamment petit. Deuxièmement, le théorème de Tikhonov est établi pour les systèmes hyperboliques linéaires singulièrement perturbés de lois d'équilibre où les vitesses de transport et les termes sources sont à la fois dépendant du paramètre de la perturbation ainsi que les conditions aux bords. Sous des hypothèses sur la continuité de ces termes et sous la condition de la stabilité, l'estimation de l'erreur entre la dynamique lente du système complet et le système réduit est obtenue en fonction de l'ordre du paramètre de la perturbation. Troisièmement, nous considérons des systèmes EDO-EDP couplés singulièrement perturbés. La stabilité des deux sous-systèmes implique la stabilité du système complet où le paramètre de la perturbation est introduit dans la dynamique de l'EDP. D'autre part, cela n'est pas valable pour le système où le paramètre de la perturbation est présent dans l'EDO. Le théorème Tikhonov pour ces systèmes EDO-EDP couplés est prouvé par la technique de Lyapunov. Enfin, la synthèse de la commande aux bords est abordée en exploitant la méthode des perturbations singulières. Le système réduit converge en temps fini. La synthèse du contrôle aux bords est mise en œuvre pour deux applications différentes afin d'illustrer les résultats principaux de ce travailSystems modeled by partial differential equations (PDEs) with infinite dimensional dynamics are relevant for a wide range of physical networks. The control and stability analysis of such systems become a challenge area. Singularly perturbed systems, containing multiple time scales, often occur naturally in physical systems due to the presence of small parasitic parameters, typically small time constants, masses, inductances, moments of inertia. Singular perturbation was introduced in control engineering in late $1960$s, its assimilation in control theory has rapidly developed and has become a tool for analysis and design of control systems. Singular perturbation is a way of neglecting the fast transition and considering them in a separate fast time scale. The present thesis is concerned with a class of linear hyperbolic systems with multiple time scales modeled by a small perturbation parameter. Firstly we study a class of singularly perturbed linear hyperbolic systems of conservation laws. Since the system contains two time scales, by setting the perturbation parameter to zero, the two subsystems, namely the reduced subsystem and the boundary-layer subsystem, are formally computed. The stability of the full system implies the stability of both subsystems. However a counterexample is used to illustrate that the stability of the two subsystems is not enough to guarantee the full system's stability. This shows a major difference with what is well known for linear finite dimensional systems. Moreover, under certain conditions, the Tikhonov approximation for such system is achieved by Lyapunov method. Precisely, the solution of the slow dynamics of the full system is approximated by the solution of the reduced subsystem for sufficiently small perturbation parameter. Secondly the Tikhonov theorem is established for singularly perturbed linear hyperbolic systems of balance laws where the transport velocities and source terms are both dependent on the perturbation parameter as well as the boundary conditions. Under the assumptions on the continuity for such terms and under the stability condition, the estimate of the error between the slow dynamics of the full system and the reduced subsystem is the order of the perturbation parameter. Thirdly, we consider singularly perturbed coupled ordinary differential equation ODE-PDE systems. The stability of both subsystems implies that of the full system where the perturbation parameter is introduced into the dynamics of the PDE system. On the other hand, this is not true for system where the perturbation parameter is presented to the ODE. The Tikhonov theorem for such coupled ODE-PDE systems is proved by Lyapunov technique. Finally, the boundary control synthesis is achieved based on singular perturbation method. The reduced subsystem is convergent in finite time. Boundary control design to different applications are used to illustrate the main results of this work
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Hofmann, Bernd, and Wolfersdorf Lothar von. "New results on the degree of ill-posedness for integration operators with weights." Universitätsbibliothek Chemnitz, 2008. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-200800545.
Повний текст джерелаАнотація:
We extend our results on the degree of ill-posedness for linear integration opera-
tors A with weights mapping in the Hilbert space L^2(0,1), which were published in
the journal 'Inverse Problems' in 2005 ([5]). Now we can prove that the degree one
also holds for a family of exponential weight functions. In this context, we empha-
size that for integration operators with outer weights the use of the operator AA^*
is more appropriate for the analysis of eigenvalue problems and the corresponding
asymptotics of singular values than the former use of A^*A.
48
Jakaitytė, Eglė. "Paprastųjų diferencialinių lygčių su ypatuma modifikuotieji kraštiniai uždaviniai." Master's thesis, Lithuanian Academic Libraries Network (LABT), 2008. http://vddb.library.lt/obj/LT-eLABa-0001:E.02~2008~D_20080924_175412-35930.
Повний текст джерелаАнотація:
Magistro baigiamajame darbe nagrinėjama antrosios eilės tiesinė nehomogeninė diferencialinė lygtis intervale, kurio kairysis kraštas yra nagrinėjamosios lygties koeficientų ireguliarusis ypatingasis taškas. Ištirta sprendinių asimptotika ypatingojo taško aplinkoje ir išnagrinėti trys šios lygties kraštiniai uždaviniai, kurių formulavimas iš esmės priklauso nuo lygties parametro ženklo.The present Master thesis analyses the second order linear differential equation in interval which left side coincides with irregular singular point of this equation. The asymptotics of the solutions in the neighbourhood of singular point is investigated and three boundary value problems, statement of which principally depends on equation parameter sign, have been analyzed.
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Ramos, Anthony Kojo. "Forecasting Mortality Rates using the Weighted Hyndman-Ullah Method." Thesis, Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:mdh:diva-54711.
Повний текст джерелаАнотація:
The performance of three methods of mortality modelling and forecasting are compared. These include the basic Lee–Carter and two functional demographic models; the basic Hyndman–Ullah and the weighted Hyndman–Ullah. Using age-specific data from the Human Mortality Database of two developed countries, France and the UK (England&Wales), these methods are compared; through within-sample forecasting for the years 1999-2018. The weighted Hyndman–Ullah method is adjudged superior among the three methods through a comparison of mean forecast errors and qualitative inspection per the dataset of the selected countries. The weighted HU method is then used to conduct a 32–year ahead forecast to the year 2050.
50
ITAKURA, Fumitada, Kazuya TAKEDA, and Hani C. YEHIA. "An Acoustically Oriented Vocal-Tract Model." Institute of Electronics, Information and Communication Engineers, 1996. http://hdl.handle.net/2237/15049.
Повний текст джерела