Dissertations / Theses on the topic 'Singular integral'
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Chunaev, Petr. "Singular integral operators and rectifiability." Doctoral thesis, Universitat Autònoma de Barcelona, 2018. http://hdl.handle.net/10803/663827.
Full textThe problems that we study in this thesis lie in the area of Harmonic Analysis and Geometric Measure Theory. Namely, we consider the connection between the analytic properties of singular integral operators defined in $L^2(\mu)$ and associated with some Calderón-Zygmund kernels and the geometric properties of the measure $\mu$. Let us be more precise. Let $E$ be a Borel set in the complex plane with non-vanishing and finite linear Hausdorff measure $H^1$, i.e. such that $0
Bosch, Camós Anna. "Controlant la integral singular maximal." Doctoral thesis, Universitat Autònoma de Barcelona, 2015. http://hdl.handle.net/10803/314177.
Full textThe main objects of study of this dissertation are the singular integrals. We find an special motivation in three papers originated from the idea of bounding the norm of maximal operator of a singular integral by the norm of the singular integral itself. In the first one, of J. Mateu and J. Verdera from 2006, [MV], they prove pointwise inequalities for the particular cases of the j-th Riesz transform and the Beurling transform. For the first time, one notice that we obtain different bounds depending on the parity of the kernel of each operator. A posteriori, in the papers of J. Mateu, J. Orobitg and J. Verdera from 2011, [MOV], and in [MOPV] from 2010 from same authors plus C. Pérez, they prove pointwise inequalities as the aforementioned for higher order Riesz transforms. In the first work they treat the case of operators with even kernel, and in the second one, they do the same but for odd kernels. Here is when Cotlar inequality takes shows of, because we can notice that the inequality for the even case is an improvement of this one In [MOV] they prove that, for even Calderón-Zygmund singular integrals with smooth kernel, the pointwise inequality of the maximal operator bounded by the operator itself is equivalent to the L^2 estimate and also to an algebraic condition on the kernel of the singular integral. For the odd operators, in [MOPV], it's proved the same result, but in the pointwise inequality we need the second iteration of the Hardy-Littlewood maximal operator. It was proved before, in [MV], that one cannot bound without this iteration in the case of the Riesz trasnform. From here on, in this dissertation we have been working on this kind of estimates. In the first chapter we give a positive answer to one open question in [MOV]. We prove that the L^p estimate (and the weighted L^p) is also equivalent to the pointwise inequality, not only with p=2. This results are reflected in [BMO1]. In the second chapter we work on another open question from the same paper. We deal with the same estimates but relaxing the regularity of the kernel. When we are in the plane, we give a good answer, setting an initial differenciability for the kernel. For higher dimensions, with n bigger than 2, we have a partial answer, in the sense that the initial regularity depends on the degree of a polynomial depending on the kernel. This means that we may should ask for a very big differentiability, but a finite one. In the third chapter, we give an example for which we can't bound de weak L^1 norm of the maximal function in terms of the L^1 norm of the operator. We give the case of a harmonic polynomial of degree 3 in the plane and we explain how we can generalize to all polynomials with odd degree in the plane. However, because of the difficult caracterization of the harmonic polynomials en higher dimensions, the problem in R^n, for n>2, is open. In the last chapter, we consider the same problem of pointwise estimating the maximal operator of a singular integral by the same operator, but in this case we define a new maximal where we truncate by cubes instead of balls. We work with the Beurling transform and we prove that we need the second iteration of the Hardy-Littlewood maximal operator, and that we can't replace it for the first iteration. This results are reflected in [BMO2]. Bibliography [BMO1] A. Bosch-Camós, J. Mateu, J. Orobitg, «L^p estimates for the maximal singular integral in terms of the singular integral», J. Analyse Math. 126 (2015), 287-306. [BMO2] A. Bosch-Camós, J. Mateu, J. Orobitg, «The maximal Beurling transform associated with squares», Ann. Acad. Sci. Fenn. 40 (2015), 215-226. [MOPV] J. Mateu, J. Orobitg, C. Perez, J. Verdera, «New estimates for the maximal singular integral», Int. Math. Res. Not. 19 (2010), 3658-3722. [MOV] J. Mateu, J. Orobitg, J. Verdera, «Estimates for the maximal singular integral in terms of the singular integral: the case of even kernels», Ann. of Math. 174 (2011), 1429-1483. [MV] J. Mateu, J. Verdera, «L^p and weak L^1 estimates for the maximal Riesz transform and the maximal Beurling transform, Math. Res. Lett. 13 (2006), 957-966.
Vaktnäs, Marcus. "On Singular Integral Operators." Thesis, Uppsala universitet, Analys och sannolikhetsteori, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-355872.
Full textHerdman, Darwin T. "Approximations for Singular Integral Equations." Thesis, Virginia Tech, 1999. http://hdl.handle.net/10919/43206.
Full textMaster of Science
Reguera, Rodriguez Maria del Carmen. "Sharp weighted estimates for singular integral operators." Diss., Georgia Institute of Technology, 2011. http://hdl.handle.net/1853/39522.
Full textSantana, Edixon Manuel Rojas. "A study of singular integral operators with shift." Doctoral thesis, Universidade de Aveiro, 2010. http://hdl.handle.net/10773/3882.
Full textNesta tese, consideram-se operadores integrais singulares com a acção extra de um operador de deslocacamento de Carleman e com coeficientes em diferentes classes de funções essencialmente limitadas. Nomeadamente, funções contínuas por troços, funções quase-periódicas e funções possuíndo factorização generalizada. Nos casos dos operadores integrais singulares com deslocamento dado pelo operador de reflexão ou pelo operador de salto no círculo unitário complexo, obtêm-se critérios para a propriedade de Fredholm. Para os coeficientes contínuos, uma fórmula do índice de Fredholm é apresentada. Estes resultados são consequência das relações de equivalência explícitas entre aqueles operadores e alguns operadores adicionais, tais como o operador integral singular, operadores de Toeplitz e operadores de Toeplitz mais Hankel. Além disso, as relações de equivalência permitem-nos obter um critério de invertibilidade e fórmulas para os inversos laterais dos operadores iniciais com coeficientes factorizáveis. Adicionalmente, aplicamos técnicas de análise numérica, tais como métodos de colocação de polinómios, para o estudo da dimensão do núcleo dos dois tipos de operadores integrais singulares com coeficientes contínuos por troços. Esta abordagem permite também a computação do inverso no sentido Moore-Penrose dos operadores principais. Para operadores integrais singulares com operadores de deslocamento do tipo Carleman preservando a orientação e com funções contínuas como coeficientes, são obtidos limites superiores da dimensão do núcleo. Tal é implementado utilizando algumas estimativas e com a ajuda de relações (explícitas) de equivalência entre operadores. Focamos ainda a nossa atenção na resolução e nas soluções de uma classe de equações integrais singulares com deslocamento que não pode ser reduzida a um problema de valor de fronteira binomial. De forma a atingir os objectivos propostos, foram utilizadas projecções complementares e identidades entre operadores. Desta forma, as equações em estudo são associadas a sistemas de equações integrais singulares. Estes sistemas são depois analisados utilizando um problema de valor de fronteira de Riemann. Este procedimento tem como consequência a construção das soluções das equações iniciais a partir das soluções de problemas de valor de fronteira de Riemann. Motivados por uma grande diversidade de aplicações, estendemos a definição de operador integral de Cauchy para espaços de Lebesgue sobre grupos topológicos. Assim, são investigadas as condições de invertibilidade dos operadores integrais neste contexto.
In this thesis we consider singular integral operators with the extra action of a Carleman shift operator and having coefficients on different classes of essentially bounded functions. Namely, continuous, piecewise continuous, semi-almost periodic and generalized factorable functions. In the cases of the singular integral with shift action given by the reflection or the flip operator on the complex unit circle, we obtain a Fredholm criteria and, for the continuous coefficients case, an index formula is also provided. These results are consequence of explicit equivalence operator relations between those operators and some extra operators such as pure singular integral, Toeplitz and Toeplitz plus Hankel operators. Furthermore, the equivalence relations allow us to give an invertibility criterion and formulas for the left-sided and right-sided inverses of the initial operators with generalized factorable coefficients. In addition, we apply numerical analysis techniques, as polynomial collocation methods, for the study of the kernel dimension of these two kinds of singular integral operators with piecewise continuous coefficients. This approach also permits us to compute the Moore-Penrose inverse of the main operators. For singular integral operators with generic preserving-orientation Carleman shift operators and continuous functions as coefficients, upper bounds for the kernel dimensions are obtained. This is implemented by using some estimations which are derived with the help of certain explicit operator relations. We also focus our attention to the solvability, and the solutions, of a class of singular integral equations with shift which cannot be reduced to a binomial boundary value problem. To attain our goals, some complementary projections and operator identities are used. In this way, the equations under study are associated with systems of pure singular integral equations. These systems will be then analyzed by means of a corresponding Riemann boundary value problem. As a consequence of such a procedure, the solutions of the initial equations are constructed from the solutions of Riemann boundary value problems. Motivated by a large diversity of applications, we extend the definition of Cauchy integral operator to the framework of Lebesgue spaces on topological groups. Thus, invertibility conditions for paired operators in this setting are investigated.
FCT - SFRH/BD/30679/2006
Vähäkangas, Antti V. "Boundedness of weakly singular integral operators on domains /." Helsinki : Suomalainen Tiedeakatemia, 2009. http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&doc_number=018603140&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA.
Full textRogozhin, Alexander. "Approximation methods for two classes of singular integral equations." Doctoral thesis, [S.l. : s.n.], 2002. http://deposit.ddb.de/cgi-bin/dokserv?idn=968783279.
Full textRogozhin, Alexander. "Approximation Methods for Two Classes of Singular Integral Equations." Doctoral thesis, Universitätsbibliothek Chemnitz, 2003. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200300091.
Full textDie Dissertation beschäftigt sich insgesamt mit der numerischen Analysis singulärer Integralgleichungen, besteht aber aus zwei voneinander unabhängigen Teilen. Der este Teil behandelt Diskretisierungsverfahren für mehrdimensionale schwach singuläre Integralgleichungen mit operatorwertigen Kernen. Darüber hinaus wird hier die Anwendung dieser allgemeinen Resultate auf ein Strahlungstransportproblem diskutiert, und numerische Ergebnisse werden präsentiert. Im zweiten Teil betrachten wir ein Kollokationsverfahren zur numerischen Lösung Cauchyscher singulärer Integralgleichungen auf Intervallen. Der Operator der Integralgleichung hat die Form \ $aI + b \mu^{-1} S \mu I $\ mit dem Cauchyschen singulären Integraloperator \ $S,$\ mit stückweise stetigen Koeffizienten \ $a$\ und \ $b,$\ und mit einem klassischen Jacobigewicht \ $\mu.$\ Als Kollokationspunkte dienen die Nullstellen des n-ten Tschebyscheff-Polynoms erster Art und Ansatzfunktionen sind ein in einem geeigneten Hilbertraum orthonormales System gewichteter Tschebyscheff-Polynome zweiter Art. Wir erhalten notwendige und hinreichende Bedingungen für die Stabilität und Konvergenz dieses Kollokationsverfahrens. Außerdem wird das Stabilitätskriterium auf alle Folgen aus der durch die Folgen des Kollokationsverfahrens erzeugten Algebra erweitert. Diese Resultate liefern uns Aussagen über das asymptotische Verhalten der Singulärwerte der Folge der diskreten Operatoren
Chapman, Geoffrey John Douglas. "A weakly singular integral equation approach for water wave problems." Thesis, University of Bristol, 2005. http://hdl.handle.net/1983/54f56a00-8496-4990-8410-d2c677839095.
Full textHakk, Kristiina. "Approximation methods for weakly singular integral equations with discontinuous coefficients /." Online version, 2004. http://dspace.utlib.ee/dspace/bitstream/10062/588/5/Hakk.pdf.
Full textMonguzzi, A. "ON THE REGULARITY OF SINGULAR INTEGRAL OPERATORS ON COMPLEX DOMAINS." Doctoral thesis, Università degli Studi di Milano, 2015. http://hdl.handle.net/2434/269875.
Full textLuther, 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.
Full textPrats, Soler Martí. "Singular integral operators on sobolev spaces on domains and quasiconformal mappings." Doctoral thesis, Universitat Autònoma de Barcelona, 2015. http://hdl.handle.net/10803/314193.
Full textIn this dissertation some new results on the boundedness of Calderón-Zygmund operators on Sobolev spaces on domains in Rd. First a T(P)-theorem is obtained which is valid for Wn,p (U), where U is a bounded uniform domain of Rd, n is a given natural number and p>d. Essentially, the result obtained states that a convolution Calderón-Zygmund operator is bounded on this function space if and only if T(P) belongs to Wn,p (U) for every polynomial P of degree smaller than n restricted to the domain. For indices p less or equal than d, a sufficient condition for the boundedness in terms of Carleson measures is obtained. In the particular case of n=1 and p<=d, this Carleson condition is shown to be necessary in fact. The case where n is not integer and 0
Cai, Yulin. "Integral Points on Modular Curves, Singular Moduli and Conductor-Discriminant Inequality." Thesis, Bordeaux, 2020. http://www.theses.fr/2020BORD0098.
Full textThis thesis discusses three topics, so it includes three parts. In the first part, we study S-integral points on the modular curve X0(p). Bilushowed that, using Baker’s method, they can be effectively bounded in terms of p, the base field and the set of places S. Sha made this result explicit, but the bound he obtained is double exponential in p. We drastically improve upon the result of Sha, obtaining a simple exponential bound. This is done using a very explicit version of the Chevalley-Weil principle based on the work of Liu and Lorenzini. Our bound is not only sharper than that of Sha, but is also explicit in all parameters. In the second part, we consider singular moduli. For a fixed singular modulus a, we give an effective upper bound of norm of x - a for another singular modulus x with large discriminant. In the third part, we give a relation between Artin conductors of a Weierstrass model Y and the ones of two given Weierstrass models Y1,Y2. With this relation, we know that the conductor-discriminant inequality holds for Y if it holds for Y1 and Y2
Gama, Rômulo Lima da. "Interação de ondas aquáticas com obstáculos quase circulares finos e submersos." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2015. http://hdl.handle.net/10183/118639.
Full textThe hydrodynamic force, in terms of the added mass and damping coefficients, for thin and submerged nearly circular obstacles below a water free surface is computed by a spectral method. Firstly, a mathematical model for surface water waves is presented. Next, the diffraction problem of waves due to the presence of an obstacle is described. When the body is thin and submerged, the problem can be formulated in terms of a hypersingular integral equation. Using a conformal mapping over a circular disc, it is shown that the solution can be obtained by means of a spectral method where the hipersingularity is analytically evaluated in terms of orthogonal polynomials. The hydrodynamics coefficients, in function of the wavenumber, are computed and shown for nearly circular obstacles. The occurrence of resonant frequencies is observed for sufficiently small submergences and subpeaks of resonances appear for moderate values of the submergence, in comparison with the case of a circular disc.
Ehrhardt, Torsten. "Factorization theory for Toeplitz plus Hankel operators and singular integral operators with flip." Doctoral thesis, [S.l. : s.n.], 2004. http://deposit.ddb.de/cgi-bin/dokserv?idn=972573305.
Full textJunghanns, P., and U. Weber. "Local theory of projection methods for Cauchy singular integral equations on an interval." Universitätsbibliothek Chemnitz, 1998. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-199801281.
Full textAwala, Hussein. "SINGULAR INTEGRAL OPERATORS ASSOCIATED WITH ELLIPTIC BOUNDARY VALUE PROBLEMS IN NON-SMOOTH DOMAINS." Diss., Temple University Libraries, 2017. http://cdm16002.contentdm.oclc.org/cdm/ref/collection/p245801coll10/id/453799.
Full textPh.D.
Many boundary value problems of mathematical physics are modelled by elliptic differential operators L in a given domain Ω . An effective method for treating such problems is the method of layer potentials, whose essence resides in reducing matters to solving a boundary integral equation. This, in turn, requires inverting a singular integral operator, naturally associated with L and Ω, on appropriate function spaces on ƌΩ. When the operator L is of second order and the domain Ω is Lipschitz (i.e., Ω is locally the upper-graph of a Lipschitz function) the fundamental work of B. Dahlberg, C. Kenig, D. Jerison, E. Fabes, N. Rivière, G. Verchota, R. Brown, and many others, has opened the door for the development of a far-reaching theory in this setting, even though several very difficult questions still remain unanswered. In this dissertation, the goal is to solve a number of open questions regarding spectral properties of singular integral operators associated with second and higher-order elliptic boundary value problems in non-smooth domains. Among other spectral results, we establish symmetry properties of harmonic classical double layer potentials associated with the Laplacian in the class of Lipschitz domains in R2. An array of useful tools and techniques from Harmonic Analysis, Partial Differential Equations play a key role in our approach, and these are discussed as preliminary material in the thesis: --Mellin Transforms and Fourier Analysis; --Calderón-Zygmund Theory in Uniformly Rectifiable Domains; -- Boundary Integral Methods. Chapter four deals with proving invertibility properties of singular integral operators naturally associated with the mixed (Zaremba) problem for the Laplacian and the Lamé system in infinite sectors in two dimensions, when considering their action on the Lebesgue scale of p integrable functions, for 1 < p < ∞. Concretely, we consider the case in which a Dirichlet boundary condition is imposed on one ray of the sector, and a Neumann boundary condition is imposed on the other ray. In this geometric context, using Mellin transform techniques, we identify the set of critical integrability indexes p for which the invertibility of these operators fails. Furthermore, for the case of the Laplacian we establish an explicit characterization of the Lp spectrum of these operators for each p є (1,∞), as well as well-posedness results for the mixed problem. In chapter five, we study spectral properties of layer potentials associated with the biharmonic equation in infinite quadrants in two dimensions. A number of difficulties have to be dealt with, the most significant being the more complex nature of the singular integrals arising in this 4-th order setting (manifesting itself on the Mellin side by integral kernels exhibiting Mellin symbols involving hyper-geometric functions). Finally, chapter six, deals with spectral issues in Lipschitz domains in two dimensions. Here we are able to prove the symmetry of the spectra of the double layer potentials associated with the Laplacian. This is in essence a two-dimensional phenomenon, as known examples show the failure of symmetry in higher dimensions.
Temple University--Theses
Kaye, Adelina E. "Singular integration with applications to boundary value problems." Kansas State University, 2016. http://hdl.handle.net/2097/32717.
Full textMathematics
Nathan Albin
Pietro Poggi-Corradini
This report explores singular integration, both real and complex, focusing on the the Cauchy type integral, culminating in the proof of generalized Sokhotski-Plemelj formulae and the applications of such to a Riemann-Hilbert problem.
Hibbs, T. T. "C'('1') continuous representations and advanced singular kernal integrations in the three dimensional boundary integral method." Thesis, Teesside University, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.384606.
Full textLi, Xiaochun. "Uniform bounds for the bilinear Hilbert transforms /." free to MU campus, to others for purchase, 2001. http://wwwlib.umi.com/cr/mo/fullcit?p3025634.
Full textCerezo, Graciela M. "Solution Representation and Indentification for Singular neutral Functional Differential Equations." Diss., Virginia Tech, 1996. http://hdl.handle.net/10919/30365.
Full textPh. D.
Junghanns, P., and U. Weber. "Local theory of a collocation method for Cauchy singular integral equations on an interval." Universitätsbibliothek Chemnitz, 1998. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-199801203.
Full textGomez, Daniel. "A non-singular integral equation formulation of permeable semi-infinite hydraulic fractures driven by shear-thinning fluids." Thesis, University of British Columbia, 2016. http://hdl.handle.net/2429/58976.
Full textScience, Faculty of
Mathematics, Department of
Graduate
Nagamine, Andre. "Solução numérica de equações integro-diferenciais singulares." Universidade de São Paulo, 2009. http://www.teses.usp.br/teses/disponiveis/55/55134/tde-27052009-102500/.
Full textThe theory of the integral equations, since the second half of the 20th century, has been assuming an ever more important role in the modelling of applied problems. Consequently, the development of new numerical methods for integral equations is called for and a larger range of problems has been possible to be solved by these new techniques. In this sense, many types of integral equations have been derived from applications and been the object of studies, among them the so called singular integro-differential equation. The present work has, as its main objective, the study of singular integrodifferential equations, both linear and non-linear. More specifically, in the linear case, we present our main results regarding the derivation of a numerical method and its uniform convergence properties. The non-linear case is introduced through the mathematical model of boiler tubes in a specific type of nuclear reactor (LMFBR) from which the integro-differential equation originates. For this integro-differential equation a numerical method is proposed based on the physical conditions of the problem
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/.
Full textSilva, Livia Gouveia da. "Projeto terapêutico singular: uma revisão integrativa da literatura." Universidade de São Paulo, 2015. http://www.teses.usp.br/teses/disponiveis/7/7141/tde-31082016-121126/.
Full textIntroduction: The Singular Therapeutic Project (known as PTS in Brazil) is an arrangement of therapeuct actions that is due to guide the work process directed towards a singular person or a collective subjects, that results in an interdisciplinary collective discussion of employees of health services and has its bases in a historical setting and Public Policies, oriented at the national level by the National Health System. Objective: Identify if the development of the PTS in the psychosocial field meets its theoretical and conceptual assumptions, as well as propose the rearrangement of the work processes, aiming the shared development of the PTS with the user of the health services, in the psychosocial field, through the regulations and guidelines of the Ministry of Health, in the presence of the governement program Attention Networks to Psychosocial Health (known as RAPS). Method: Its an Integrative Literature Review. Were combined in this review two index-terms: Comprehensive Health Care and Mental Health Services. The keyword Therapeutic Project was used in same databases in order to refine searches that were very broad. Data were collected at the Bank of Theses and Dissertations of CAPES and USP, Virtual Health Library and, in the databases, Cinahl, Pubmed and Web of Science. The period of publication of localized references was not limited. Results: A total of fourteen (14) studies, producted from 1997 to 2014. Thirteen (13) of them were performed at the national level and only one of them was produced internationally. For analysis of the studies, we sought to categorize the findings into five groups: 1) concepts and theoretical bases of the psychosocial field and the rehabilitation as citizenship; 2) structure, shape and the how-to of the PTS; 3) advantages of using the PTS in the health care practices; 4) the challenges, obstacles and difficulties that the PTS faces; 5) proposals for overcoming the challenges related to PTS. Conclusion: This Integrative Review drew on the combination of the index-terms and keyword, which allowed the recovery of the greatest number of relevant studies to the proposed goal. The PTS is a powerful tool care, but it faces many challenges to its development which may restrict its potentialities. It is recommended that future studies could propose a registration that guides actions, which corresponds to the theoretical and conceptual knowledge of the psychosocial field and the rehabilitation as citizenship, in order to contribute to the development of the PTS. This guide for the actions should point the possibility of guiding the collective construction of the PTS to achieve effectively the psychosocial rehabilitation, the quality of life, the dignity, the social exchanges, the labor, the social and family support and the right of belonging, in other words, the true right to citizenship and life.
Moussai, Madani. "Continuite de certains operateurs integraux singuliers sur les espaces de besov." Paris 7, 1987. http://www.theses.fr/1987PA077016.
Full textMeszmer, Peter. "Hierarchische Integration und der Strahlungstransport in streuenden Medien." Doctoral thesis, Universitätsbibliothek Leipzig, 2012. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-98584.
Full textPuliatti, Carmelo. "Singular integrals, rectifiability and elliptic measure." Doctoral thesis, Universitat Autònoma de Barcelona, 2019. http://hdl.handle.net/10803/670127.
Full textLa tesis investiga la relación entre las propiedades geométricas de las medidas en espacios euclídeos y el comportamiento de ciertos operadores integrales singulares asociados. También mostramos alguna aplicación al estudio de EDPs elípticas. Primero, caracterizamos la regularidad de las curvas planas de Jordan cuerda-arco cuya transformada maximal de Cauchy puede ser dominada puntualmente por la iteración de segundo orden de la función maximal de Hardy-Littlewood en la curva, suponiendo una condición natural de conformidad asintótica de fondo. En particular, resulta que estas curvas no necesariamente tienen tangentes en cada punto, pero son diferenciables en casi todas partes con derivadas en VMO. Las condiciones que determinan si la transformada de Cauchy asociada a una medida define un operador compacto en L ^ 2 se estudian en el segundo capítulo; determinamos que la compacidad puede caracterizarse por una convergencia uniforme a cero de la densidad superior de la medida. Luego, investigamos un equivalente en el contexto de ecuaciones elípticas de dos importantes resultados recientes sobre la transformada de Riesz y la rectificabilidad uniforme. Bajo una suposición de continuidad de Hölder para la matriz que define el operador uniformemente elíptico en forma de divergencia demostramos, en colaboración con Laura Prat y Xavier Tolsa, que el gradiente del potencial de capa única asociado a una medida n-Alhfors-David regular con soporte compacto en R ^ (n + 1) está acotado en L ^ 2 si y sólo si la medida es uniformemente n-rectificable. Este resultado amplía el importante artículo de F. Nazarov, X. Tolsa y A. Volberg sobre la solución del problema de David y Semmes en co-dimensión 1, y lo aplicamos a un problema de una fase para la medida elíptica. Bajo la misma hipótesis para la ecuación elíptica, establecemos un criterio local de rectificabilidad para las medidas de Radon que no son necesariamente regulares. El teorema se formula en términos de un control de la oscilación media del gradiente del potencial de una sola capa. Esto generaliza un resultado reciente de D. Girela-Sarriòn y X. Tolsa. Este estudio constituye un paso importante para lograr un resultado de rectificabilidad para un problema de dos-fases para la medida elíptica.
The thesis investigates the relation between the geometric properties of measures in Euclidean spaces and the behavior of certain associated singular integral operators. We also show some application to the study of elliptic PDEs. First, we characterize the regularity of the planar chord-arc Jordan curves whose associated maximal Cauchy transform can be pointwise dominated by the second-order iteration of the Hardy-Littlewood maximal function on the curve, assuming a natural background asymptotic conformality condition. In particular, it turns out that this curves do not necessarily have tangents at each point but they are differentiable almost everywhere with derivatives in VMO. The conditions on a measure that determine whether its associated Cauchy transform defines a compact operator on L^2 are studied in the second chapter; we determine that the compactness can be characterized by a uniform convergence to zero of the upper density of the measure. Then, we investigate an equivalent in the context of elliptic equations of two important recent results on Riesz transform and uniform rectifiabilty. Under a Hölder continuity assumption for the matrix defining the uniformly elliptic operator in divergence form we prove, in collaboration with Laura Prat and Xavier Tolsa, that the gradient of the single layer potential associated with a compactly supported n-Alhfors-David regular mesaure in R^(n+1) is bounded on L^2 if and only if the measure is uniformly n-rectifiable. This result extends the important article by F. Nazarov, X. Tolsa and A. Volberg on the solution of the so-called co-dimension 1 David and Semmes’ problem and we apply it to a one-phase problem for the elliptic measure. Under the same hypothesis for the elliptic equation we establish a local rectifiability criterion for Radon measures which are not necessarily regular. The theorem is formulated in terms of a control of the mean oscillation of the gradient of the single layer potential. This generalizes a recent result by D. Girela-Sarriòn and X. Tolsa. This study constitutes an important step to achieve a rectifiability result for a two-phase problem for the elliptic measure.
Hidalgo, Delgado Francisco. "Investigación integral de las unidades constructivas-arquitectónicas que definen el Mercado Central de Valencia como ejemplo singular de la arquitectura modernista valenciana." Doctoral thesis, Universitat Politècnica de València, 2010. http://hdl.handle.net/10251/8474.
Full textHidalgo Delgado, F. (2010). Investigación integral de las unidades constructivas-arquitectónicas que definen el Mercado Central de Valencia como ejemplo singular de la arquitectura modernista valenciana [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/8474
Palancia
Castro, Mario Henrique de. "Decaimento dos autovalores de operadores integrais positivos gerados por núcleos Laplace-Beltrami diferenciáveis." Universidade de São Paulo, 2011. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-14092011-094712/.
Full textIn this work we obtain decay rates for singular values and eigenvalues of integral operators generated by square integrable kernels on the unit sphere in \'R m+1\', m 2, under assumptions on both, certain derivatives of the kernel and the integral operators generated by such derivatives. This type of problem is common in the literature but the assumptions are usually defined via standard differentiation in \'R POT. m+1\'. Here, the assumptions are all defined via the Laplace-Beltrami derivative, a concept first investigated by W. Rudin in the early fifties and genuinely spherical in nature. The rates we present are optimal and depend on both, the differentiability order used to define the smoothness conditions and the dimension m
Ozatas, Cihan A. "Contact Mechanics Of A Graded Surface With Elastic Gradation In Lateral Direction." Master's thesis, METU, 2003. http://etd.lib.metu.edu.tr/upload/1225119/index.pdf.
Full textAtay, Mehmet Tarik. "Fracture Of A Three Layer Elastic Panel." Phd thesis, METU, 2005. http://etd.lib.metu.edu.tr/upload/3/12606360/index.pdf.
Full textFerreira, Marcos Rondiney dos Santos. "Comportamento assintótico de soluções da equação do aerofólio em intervalos disjuntos." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2015. http://hdl.handle.net/10183/128043.
Full textIn this work we investigate, of the analytical and numerical points of views, the asymptotic behavior of the airfoil equation solution with a singularity of the Cauchy type, de ned over a interval with a small opening. We display a mathematical model with a f" solution to the disjoint interval G" = (−1,−ε)∪(ε, 1) and a f0 solution corresponding to limit of f" when (ε → 0), linking the latter with the solution of the airfoil equation f in the interval (−1, 1). Furthermore, we demonstrate particular cases of functions ψ = Tm and ψ = Un (where Tm and Un are the Chebyshev polynomials of the rst and second type respectively) where we have equality f = f0 and then f" ≈ f. We present and compare numerically the solutions f", f0 and f for di erent functions ψ and values of ε in G". We also show almost polynomial analytical solutions for the airfoil equation, and we propose a spectral method for the generalized airfoil equation. Finally, we obtain analytical solutions of the airfoil equations to the interval G", (−1, 1)\ {0} and (−1, 1) for various functions ψ(t) by expanding in series the density of the Cauchy singular integral.
Girela, Sarrión Daniel. "Singular integrals and rectifiability." Doctoral thesis, Universitat Autònoma de Barcelona, 2016. http://hdl.handle.net/10803/392746.
Full textDesiderio, Luca. "H-matrix based Solver for 3D Elastodynamics Boundary Integral Equations." Thesis, Université Paris-Saclay (ComUE), 2017. http://www.theses.fr/2017SACLY002/document.
Full textThis thesis focuses on the theoretical and numerical study of fast methods to solve the equations of 3D elastodynamics in frequency-domain. We use the Boundary Element Method (BEM) as discretization technique, in association with the hierarchical matrices (H-matrices) technique for the fast solution of the resulting linear system. The BEM is based on a boundary integral formulation which requires the discretization of the only domain boundaries. Thus, this method is well suited to treat seismic wave propagation problems. A major drawback of classical BEM is that it results in dense matrices, which leads to high memory requirement (O (N 2 ), if N is the number of degrees of freedom) and computational costs.Therefore, the simulation of realistic problems is limited by the number of degrees of freedom. Several fast BEMs have been developed to improve the computational efficiency. We propose a fast H-matrix based direct BEM solver
VOLPI, SARA MARIA. "Bochner-riesz means of eigenfunction expansions and local hardy spaces on manifolds with bounded geometry." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2012. http://hdl.handle.net/10281/29105.
Full textAksoy, Umit. "Schwarz Problem For Complex Partial Differential Equations." Phd thesis, METU, 2006. http://etd.lib.metu.edu.tr/upload/3/12607977/index.pdf.
Full textФильштинський, Леонід Аншелович, Леонид Аншелович Фильштинский, Leonid Anshelovych Fylshtynskyi, and И. Ю. Дудык. "Характеристики разрушения пьезомагнитной пластины с трещиной." Thesis, Сумский государственный университет, 2015. http://essuir.sumdu.edu.ua/handle/123456789/41237.
Full textTamayo, Palau José María. "Multilevel adaptive cross approximation and direct evaluation method for fast and accurate discretization of electromagnetic integral equations." Doctoral thesis, Universitat Politècnica de Catalunya, 2011. http://hdl.handle.net/10803/6952.
Full textLas formulaciones MFIE y CFIE son válidas únicamente para objetos cerrados y necesitan tratar la integración de núcleos con singularidades de orden superior al de la EFIE. La falta de técnicas eficientes y precisas para el cálculo de dichas integrales singulares a llevado a imprecisiones en los resultados. Consecuentemente, su uso se ha visto restringido a propósitos puramente académicos, incluso cuando tienen una velocidad de convergencia muy superior cuando son resuelto iterativamente, debido a su excelente número de condicionamiento.
En general, la principal desventaja del MoM es el alto coste de su construcción, almacenamiento y solución teniendo en cuenta que es inevitablemente un sistema denso, que crece con el tamaño eléctrico del objeto a analizar. Por tanto, un gran número de métodos han sido desarrollados para su compresión y solución. Sin embargo, muchos de ellos son absolutamente dependientes del núcleo de la ecuación integral, necesitando de una reformulación completa para cada núcleo, en caso de que sea posible.
Esta tesis presenta nuevos enfoques o métodos para acelerar y incrementar la precisión de ecuaciones integrales discretizadas con el Método de los Momentos (MoM) en electromagnetismo computacional.
En primer lugar, un nuevo método iterativo rápido, el Multilevel Adaptive Cross Approximation (MLACA), ha sido desarrollado para acelerar la solución del sistema lineal del MoM. En la búsqueda por un esquema de propósito general, el MLACA es un método independiente del núcleo de la ecuación integral y es puramente algebraico. Mejora simultáneamente la eficiencia y la compresión con respecto a su versión mono-nivel, el ACA, ya existente. Por tanto, representa una excelente alternativa para la solución del sistema del MoM de problemas electromagnéticos de gran escala.
En segundo lugar, el Direct Evaluation Method, que ha provado ser la referencia principal en términos de eficiencia y precisión, es extendido para superar el cálculo del desafío que suponen las integrales hiper-singulares 4-D que aparecen en la formulación de Ecuación Integral de Campo Magnético (MFIE) así como en la de Ecuación Integral de Campo Combinada (CFIE). La máxima precisión asequible -precisión de máquina se obtiene en un tiempo más que razonable, sobrepasando a cualquier otra técnica existente en la bibliografía.
En tercer lugar, las integrales hiper-singulares mencionadas anteriormente se convierten en casi-singulares cuando los elementos discretizados están muy próximo pero sin llegar a tocarse. Se muestra como las reglas de integración tradicionales tampoco convergen adecuadamente en este caso y se propone una posible solución, basada en reglas de integración más sofisticadas, como la Double Exponential y la Gauss-Laguerre.
Finalmente, un esfuerzo en facilitar el uso de cualquier programa de simulación de antenas basado en el MoM ha llevado al desarrollo de un modelo matemático general de un puerto de excitación en el espacio discretizado. Con este nuevo modelo, ya no es necesaria la adaptación de los lados del mallado al puerto en cuestión.
The Method of Moments (MoM) has been widely used during the last decades for the discretization and the solution of integral equation formulations appearing in several electromagnetic antenna and scattering problems. The most utilized of these formulations are the Electric Field Integral Equation (EFIE), the Magnetic Field Integral Equation (MFIE) and the Combined Field Integral Equation (CFIE), which is a linear combination of the other two.
The MFIE and CFIE formulations are only valid for closed objects and need to deal with the integration of singular kernels with singularities of higher order than the EFIE. The lack of efficient and accurate techniques for the computation of these singular integrals has led to inaccuracies in the results. Consequently, their use has been mainly restricted to academic purposes, even having a much better convergence rate when solved iteratively, due to their excellent conditioning number.
In general, the main drawback of the MoM is the costly construction, storage and solution considering the unavoidable dense linear system, which grows with the electrical size of the object to analyze. Consequently, a wide range of fast methods have been developed for its compression and solution. Most of them, though, are absolutely dependent on the kernel of the integral equation, claiming for a complete re-formulation, if possible, for each new kernel.
This thesis dissertation presents new approaches to accelerate or increase the accuracy of integral equations discretized by the Method of Moments (MoM) in computational electromagnetics.
Firstly, a novel fast iterative solver, the Multilevel Adaptive Cross Approximation (MLACA), has been developed for accelerating the solution of the MoM linear system. In the quest for a general-purpose scheme, the MLACA is a method independent of the kernel of the integral equation and is purely algebraic. It improves both efficiency and compression rate with respect to the previously existing single-level version, the ACA. Therefore, it represents an excellent alternative for the solution of the MoM system of large-scale electromagnetic problems.
Secondly, the direct evaluation method, which has proved to be the main reference in terms of efficiency and accuracy, is extended to overcome the computation of the challenging 4-D hyper-singular integrals arising in the Magnetic Field Integral Equation (MFIE) and Combined Field Integral Equation (CFIE) formulations. The maximum affordable accuracy --machine precision-- is obtained in a more than reasonable computation time, surpassing any other existing technique in the literature.
Thirdly, the aforementioned hyper-singular integrals become near-singular when the discretized elements are very closely placed but not touching. It is shown how traditional integration rules fail to converge also in this case, and a possible solution based on more sophisticated integration rules, like the Double Exponential and the Gauss-Laguerre, is proposed.
Finally, an effort to facilitate the usability of any antenna simulation software based on the MoM has led to the development of a general mathematical model of an excitation port in the discretized space. With this new model, it is no longer necessary to adapt the mesh edges to the port.
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.
Full textkay, 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.
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.
Full textDI, CREDICO GIULIA. "Metodo Energetico agli Elementi di Contorno per problemi di Elastodinamica 2D nel dominio del tempo." Doctoral thesis, Università degli studi di Modena e Reggio Emilia, 2022. http://hdl.handle.net/11380/1265215.
Full textThis thesis deals with the application of the Energetic Boundary Element Method (BEM) for the resolution of elastodynamic problems in bidimensional unbounded domains, outside an open regular obstacle or external to a region with a closed Lipschitz boundary. Starting from the fundamental Green’s tensor, the differential problem is rewritten in terms of different Boundary Integral Equations (BIEs), suitable to solve problems equipped by Dirichlet or Neumann datum at the boundary. These BIEs are then set in a space-time weak form, based on energy arguments, and numerically solved by means of Energetic BEM. All the considered weak BIEs, once discretized, give rise to linear systems with lower triangular Toeplitz matrix, whose entries are quadruple space-time integrals. A consistent part of the thesis discusses the quadrature formulas employed to compute numerically the integrals in space variables on the boundary with high accuracy, and taking into account the characteristic space singularities: O(log(r)) for the single layer integral operator, O(1/r) for the double layer integral operator and O(1/r^2) for the hypersingular integral operator. Moreover, an accurate study of the integration domain in local variables allows to overcome the issues of the integration of peculiar step functions that feature all the integral kernels. A theoretical analysis of the indirect weak form with single layer operator has been executed, in order to prove properties of coercivity and continuity of the associated energetic bilinear operator, and numerous numerical results are presented to confirm the correctness and the effectiveness of the energetic BEM, showing in particular long time stability of the BIE solutions. In alternative to the uniform decomposition of the obstacle, I have taken into account different types of discretization that turn out to be useful, for instance, to catch the asymptotic behaviour of the single layer BIE solution at the endpoints of an open obstacle or at the corners of a polygonal closed arc. In particular, the solution of this BIE for a Dirichlet problem behaves like O(r^-1/2) at the extremes of a crack and like O(r^-w) near a corner, with the exponent w related to the amplitude of the angle. Meshes geometrically or algebraically refined at these critical points improve the convergence towards the solution: therefore, an in dept analysis of the error decay in energy norm is shown with respect to the type of refinement (h-version, p-version and hp-version have been in particular considered). The numerical results verify the theoretical slope of the estimated error for the various discretization method. Similar remarks and numerical experiments are also presented for Neumann problems, solved by indirect weak form depending on the hypersingular operator. Lastly, I take into account the following issue: when standard Lagrangian basis functions are considered, the BEM matrices are made by time-dependent blocks that are generally fully populated. The overall memory cost of the energetic BEM is O(M^2N), M and N being the number of space and time degrees of freedom, respectively. This can prevent the application of BEM to large scale realistic problems. Thus, in this thesis, a fast technique, based on the Adaptive Cross Approximation (ACA), is provided in order to get a low rank approximation of the time blocks, reducing drastically the number of the original entries to be evaluated. This procedure leads to a drop in the computational time, spent for the assembly and the resolution of the linear system, and in the memory storage requirements, which are generally relevant. The effectiveness of this strategy is theoretically proved for the single layer weak formulation and several numerical results are presented and discussed.
Merchan, Rodriguez Tomas. "Singular Integrals and Rectifiability." Kent State University / OhioLINK, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=kent1586774545279842.
Full textOkecha, G. E. "Numerical quadrature involving singular and non-singular integrals." Thesis, University of Bradford, 1985. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.371485.
Full textCossu, Laura. "Factorizations of invertible matrices into products of elementary matrices and of singular matrices into products of idempotent matrices." Doctoral thesis, Università degli studi di Padova, 2017. http://hdl.handle.net/11577/3426221.
Full textIn questa tesi si considerano due problemi classici, originati rispettivamente da un lavoro di P. Cohn del 1966 e da uno di J.A. Erdos del 1967, inerenti la fattorizzazione di matrici quadrate a coefficienti in un arbitrario dominio di integrità: caratterizzare i domini di integrità R che soddisfano la proprietà (GEn), ogni matrice invertibile n x n a valori in R è prodotto di matrici elementari; e quelli che soddisfano la proprietà (IDn), ogni matrice singolare n x n a valori in R è prodotto di matrici idempotenti. Vi è una stretta correlazione tra le proprietà (GEn) e (IDn). Un importante risultato di Ruitenburg (1993) mostra che esse sono equivalenti nei domini di Bézout (cioè domini integrali in cui ogni ideale finitamente generato è principale). Inoltre, se R è un dominio di Bézout, allora R soddisfa (GEn) per ogni n≥2 se e solo se vale la (GE2), se e solo se vale la (ID2), se e solo se verifica la (IDn) per ogni n≥2. In questo caso è quindi sufficiente considerare le matrici di dimensione 2. La trattazione si sviluppa attorno allo studio di due congetture, tanto naturali quanto difficili da dimostrare in generale. La prima, proposta da Salce e Zanardo (2014) e ispirata da importanti risultati sui campi di numeri algebrici, è la seguente: "un dominio a ideali principali R soddisfa la proprieta (GE2) se e solo se è Euclideo". A supporto di tale congettura, nella tesi viene dimostrata la sua validità in due importanti classi di PID non Euclidei: (i) gli anelli delle coordinate di speciali curve algebriche non singolari definite su un campo perfetto k, tra cui l'anello delle coordinate delle coniche prive di punti razionali su k e quello delle curve ellittiche aventi il punto all'infinito come unico punto razionale; (ii) i PID non Euclidei costruiti da D.D. Anderson in un lavoro del 1988. I casi (i) e (ii) richiedono differenti dimostrazioni, basate su delicati lemmi tecnici. Da tali risultati si evince che la congettura sembra essere verificata da tutti i PID non Euclidei apparsi in letteratura. La seconda congettura studiata nella tesi è legata alla fattorizzazione di matrici singolari in idempotenti: "un dominio R avente la proprietà (ID2) deve essere necessariamente un dominio di Bézout". I domini a fattorizzazione unica, quelli projective-free, e i domini PRINC, introdotti da Salce e Zanardo nel 2014, soddisfano la congettura. Nella tesi si è trovato un esempio di dominio PRINC che non è né UFD né projective-free. Si è inoltre provato che se un dominio R soddisfa la proprietà (ID2), allora R è un dominio di Prüfer (i.e. gli ideali finitamente generati sono invertibili); la seconda congettura può essere quindi studiata limitandosi alla classe dei domini di Prüfer. Si è dimostrato che se un qualunque dominino di integrità R verifica la proprietà (ID2), allora verifica anche la (GE2). Utilizzando tale risultato e applicando opportunamente differenti risultati di Cohn (1966), a sostegno della congettura si è trovata una classe di anelli coordinati di curve non singolari che sono domini di Dedekind non PID che non soddisfano la proprietà (ID2); si è inoltre provato che neanche l'anello Int(Z) dei polinomi a valori interi verifica tale proprietà.
Ilhan, Kucuk Ayse. "Mixed-mode Fracture Analysis Of Orthotropic Fgm Coatings Under Mechanical And Thermal Loads." Phd thesis, METU, 2007. http://etd.lib.metu.edu.tr/upload/2/12608743/index.pdf.
Full textChunrungsikul, Sumlearng. "Numerical quadrature methods for singular and nearly singular integrals." Thesis, Brunel University, 2001. http://bura.brunel.ac.uk/handle/2438/7290.
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