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Academic literature on the topic 'Singular integral'

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Published: 4 June 2021
Last updated: 7 September 2023

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Journal articles on the topic "Singular integral"

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Jefferies, Brian, and Susumu Okada. "Pettis integrals and singular integral operators." Illinois Journal of Mathematics 38, no. 2 (June 1994): 250–72. http://dx.doi.org/10.1215/ijm/1255986799.

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Du, Jinyuan. "SINGULAR INTEGRAL OPERATORS AND SINGULAR QUADRATURE OPERATORS ASSOCIATED WITH SINGULAR INTEGRAL EQUATIONS." Acta Mathematica Scientia 18, no. 2 (April 1998): 227–40. http://dx.doi.org/10.1016/s0252-9602(17)30757-9.

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Estrada, Ricardo, and Ram P. Kanwal. "Singular Integral Equations." Mathematical Gazette 84, no. 500 (July 2000): 379. http://dx.doi.org/10.2307/3621739.

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Carbery, A. "SINGULAR INTEGRAL OPERATORS." Bulletin of the London Mathematical Society 20, no. 4 (July 1988): 373–75. http://dx.doi.org/10.1112/blms/20.4.373.

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Namazi, Javad. "A singular integral." Proceedings of the American Mathematical Society 96, no. 3 (March 1, 1986): 421. http://dx.doi.org/10.1090/s0002-9939-1986-0822432-2.

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Shi, Yanlong, Li Li, and Zhonghua Shen. "Boundedness of p -Adic Singular Integrals and Multilinear Commutator on Morrey-Herz Spaces." Journal of Function Spaces 2023 (April 18, 2023): 1–11. http://dx.doi.org/10.1155/2023/9965919.

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In this paper, we establish the boundedness of classical p -adic singular integrals on Morrey-Herz spaces, as well as the boundedness of multilinear commutator generated by p -adic singular integral operators and Lipschitz functions or by p -adic singular integral operators and λ -central BMO functions.
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Banerjea, Sudeshna, Barnali Dutta, and A. Chakrabarti. "Solution of Singular Integral Equations Involving Logarithmically Singular Kernel with an Application in a Water Wave Problem." ISRN Applied Mathematics 2011 (May 12, 2011): 1–16. http://dx.doi.org/10.5402/2011/341564.

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A direct function theoretic method is employed to solve certain weakly singular integral equations arising in the study of scattering of surface water waves by vertical barriers with gaps. Such integral equations possess logarithmically singular kernel, and a direct function theoretic method is shown to produce their solutions involving singular integrals of similar types instead of the stronger Cauchy-type singular integrals used by previous workers. Two specific ranges of integration are examined in detail, which involve the following: Case(i) two disjoint finite intervals (0,a)∪(b,c) and (a,b,c being finite ) and Case(ii) a finite union of n disjoint intervals. The connection of such integral equations for Case(i), with a particular water wave scattering problem, is explained clearly, and the important quantities of practical interest (the reflection and transmission coefficients) are determined numerically by using the solution of the associated weakly singular integral equation.
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Xu, Yong Jia. "On Weighted Hadamard-Type Singular Integrals and Their Applications." Abstract and Applied Analysis 2007 (2007): 1–17. http://dx.doi.org/10.1155/2007/62852.

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By means of an expression with a kind of integral operators, some properties of the weighted Hadamard-type singular integrals are revealed. As applications, the solution for certain strongly singular integral equations is discussed and illustrated.
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Zozulya, V. V. "Divergent Integrals in Elastostatics: General Considerations." ISRN Applied Mathematics 2011 (August 2, 2011): 1–25. http://dx.doi.org/10.5402/2011/726402.

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This article considers weakly singular, singular, and hypersingular integrals, which arise when the boundary integral equation methods are used to solve problems in elastostatics. The main equations related to formulation of the boundary integral equation and the boundary element methods in 2D and 3D elastostatics are discussed in details. For their regularization, an approach based on the theory of distribution and the application of the Green theorem has been used. The expressions, which allow an easy calculation of the weakly singular, singular, and hypersingular integrals, have been constructed.
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SATO, SHUICHI. "ESTIMATES FOR SINGULAR INTEGRALS ALONG SURFACES OF REVOLUTION." Journal of the Australian Mathematical Society 86, no. 3 (June 2009): 413–30. http://dx.doi.org/10.1017/s1446788708000773.

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AbstractWe prove certain Lp estimates (1<p<∞) for nonisotropic singular integrals along surfaces of revolution. The singular integrals are defined by rough kernels. As an application we obtain Lp boundedness of the singular integrals under a sharp size condition on their kernels. We also prove a certain estimate for a trigonometric integral, which is useful in studying nonisotropic singular integrals.
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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.

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Los problemas que estudiamos en esta tesis se encuentran en el área de Análisis Armónico y Teoría de la Medida Geométrica. En particular, consideramos la conexión entre las propiedades analíticas de operadores integrales singulares definidos en $L^2(\mu)$ y asociados con algunos núcleos de Calderón-Zygmund y las propiedades geométricas de la medida $\mu$. Seamos más precisos. Sea $E$ un conjunto de Borel en el plano complejo con la medida lineal de Hausdorff $H^1$ finita y distinta de cero, es decir, $00$ es una pequeña constante absoluta. Es importante que, para algunos de los $t$ que acabamos de mencionar, el llamado método de curvatura comúnmente utilizado para relacionar $L^2$-acotación y rectificabilidad no está disponible, pero todavía es posible establecer la propiedad mencionada. Hasta donde sabemos, es el primer ejemplo de este tipo en el plano complejo. También vale la pena mencionar que ampliamos nuestros resultados a una clase aún más general de núcleos y, además, consideramos problemas análogos para conjuntos $E$ Ahlfors-David-regulares.
The 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 $00$ is a small absolute constant. It is important that for some of the $t$ just mentioned the so called curvature method commonly used to relate $L^2$-boundedness and rectifiability is not available but it is still possible to establish the above-mentioned property. To the best of our knowledge, it is the first example of this type in the plane. It is also worth mentioning that we extend our results to even more general class of kernels and additionally consider analogous problems for Ahlfors-David regular sets $E$.
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Bosch, Camós Anna. "Controlant la integral singular maximal." Doctoral thesis, Universitat Autònoma de Barcelona, 2015. http://hdl.handle.net/10803/314177.

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Els principals objectes d'estudi d'aquesta memòria són les integrals singulars. Per l'elaboració d'aquesta memòria, trobem una especial motivació en tres articles originats a partir de la idea d'acotar la norma de l'operador maximal d'una integral singular per la norma de la integral singular. En el primer article, de J. Mateu i J. Verdera del 2006, [MV], s'hi proven desigualtats puntuals pels casos particulars de la j-èssima transformada de Riesz i de la transformada de Beurling. Es fa notar per primer cop que les acotacions són diferents degut a la paritat del nucli de les respectives transformades. A posteriori, en els articles de J. Mateu, J. Orobitg i J. Verdera de 2011, [MOV], i en [MOPV] de 2010 dels mateixos autors més C. Pérez, s'han provat acotacions puntuals com les esmentades per transformades de Riesz d'ordre superior. En el primer treball es tracta el cas d'operadors amb el nucli parell i en el segon es fa el mateix pels de nucli senar. Aquí, la desigualtat de Cotlar pren protagonisme, ja que es fa notar que la desigualtat puntual pel cas parell és una millora d'aquesta. En [MOV] es demostra que, per les integrals singulars de Calderón-Zygmund de grau parell i amb nucli prou regular, l'acotació puntual de l'operador maximal pel mateix operador és equivalent a l'acotació en L^2 i al mateix temps a una condició algebraica sobre el nucli de la integral singular. En el cas de les integrals de grau senar, en [MOPV], es veu que succeeix el mateix però en la desigualtat puntual necessitem la segona iterada de l'operador maximal de Hardy-Littlewood. Ja s'havia vist en [MV] que l'acotació sense iteració no funcionava en el cas de la transformada de Riesz. A partir d'aquí, en el treball que ens ocupa, ens hem dedicat a estendre aquestes acotacions. En el primer capítol es resol una pregunta oberta que es planteja a [MOV]. Es demostra que l'acotació en L^p (i en L^p amb pesos) és també equivalent a la desigualtat puntual, no només amb p=2. Aquests resultats estan reflectits en [BMO1]. En el segon capítol es treballa una altra pregunta plantejada al mateix article. Es tracta de veure si es pot relaxar la regularitat del nucli i que segueixi passant el mateix. Quan ens trobem al pla, donem una bona resposta fixant una diferenciabilitat inicial que ha de tenir el nucli. En el cas de que la dimensió és més gran que 2, tenim una resposta parcial, en el sentit de que aquesta regularitat inicial depèn del grau d'un cert polinomi que depèn del nucli. Això podria fer que s'hagués de demanar una diferenciabilitat molt gran. Però, això sí, finita. En el tercer capítol donem un exemple pel qual no tenim acotació de la norma L^1 feble de la funció maximal en termes de la norma L^1 de l'operador. Presentem el cas d'un polinomi harmònic de grau 3 en el pla i expliquem com es pot generalitzar al cas d'operadors de qualsevol grau senar en el pla. Tot i això, degut a la difícil caracterització dels polinomis harmònics en dimensions superiors, ens ha quedat obert el problema a R^n, per n>2. En l'últim capítol considerem el mateix problema d'acotar puntualment l'operador maximal d'una integral singular pel mateix operador, però en aquest cas definim una nova maximal on trunquem amb cubs en lloc de boles. Treballem el cas de la transformada de Beurling i veiem que per poder acotar ho hem de fer utilitzant la segona iterada del maximal de Hardy-Littlewood, i que no ho podem reemplaçar per la primera iteració. Aquests resultats estan reflectits en [BMO2]. Bibliografia [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.
The 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.
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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.

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Herdman, Darwin T. "Approximations for Singular Integral Equations." Thesis, Virginia Tech, 1999. http://hdl.handle.net/10919/43206.

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This work is a numerical study of a class of weakly singular neutral equations. The motivation for this study is an aeroelastic system. Numerical techniques are developed to approximate the singular integral equation component appearing in the complete dynamical model for the elastic motions of a three degree of freedom structure, an airfoil with trailing edge flap, in a two dimensional unsteady flow. The flap can be viewed as an active control surface to dampen vibrations that contribute to flutter. The goal of this work is to provide accurate approximations for weakly singular neutral equations using finite elements as basis functions for the initial function space. Several examples are presented in order to validate the numerical scheme.
Master of Science
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Reguera, Rodriguez Maria del Carmen. "Sharp weighted estimates for singular integral operators." Diss., Georgia Institute of Technology, 2011. http://hdl.handle.net/1853/39522.

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The thesis provides answers, in one case partial and in the other final, to two conjectures in the area of weighted inequalities for Singular Integral Operators. We study the mapping properties of these operators in weighted Lebesgue spaces with weight w. The novelty of this thesis resides in proving sharp dependence of the operator norm on the Muckenhoupt constant associated to the weigth w for a rich class of Singular Integral operators. The thesis also addresses the end point case p=1, providing counterexamples for the dyadic and continuous settings.
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Santana, Edixon Manuel Rojas. "A study of singular integral operators with shift." Doctoral thesis, Universidade de Aveiro, 2010. http://hdl.handle.net/10773/3882.

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Doutoramento em Matemática
Nesta 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
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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.

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Rogozhin, 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.

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Rogozhin, 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.

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The dissertation consists of two parts. In the first part approximate methods for multidimensional weakly singular integral operators with operator-valued kernels are investigated. Convergence results and error estimates are given. There is considered an application of these methods to solving radiation transfer problems. Numerical results are presented, too. In the second part we consider a polynomial collocation method for the numerical solution of a singular integral equation over the interval. More precisely, the operator of our integral equation is supposed to be of the form \ $aI + b \mu^{-1} S \mu I $\ with \ $S$\ the Cauchy singular integral operator, with piecewise continuous coefficients \ $a$\ and \ $b,$\ and with a Jacobi weight \ $\mu.$\ To the equation we apply a collocation method, where the collocation points are the Chebyshev nodes of the first kind and where the trial space is the space of polynomials multiplied by another Jacobi weight. For the stability and convergence of this collocation method in weighted \ $L^2$\ spaces, we derive necessary and sufficient conditions. Moreover, the extension of these results to an algebra generated by the sequences of the collocation method applied to the mentioned singular integral operators is discussed and the behaviour of the singular values of the discretized operators is investigated
Die 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
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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.

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Books on the topic "Singular integral"

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Estrada, Ricardo, and Ram P. Kanwal. Singular Integral Equations. Boston, MA: Birkhäuser Boston, 2000. http://dx.doi.org/10.1007/978-1-4612-1382-6.

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Ladopoulos, E. G. Singular Integral Equations. Berlin, Heidelberg: Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/978-3-662-04291-5.

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Mikhlin, Solomon G., and Siegfried Prössdorf. Singular Integral Operators. Berlin, Heidelberg: Springer Berlin Heidelberg, 1986. http://dx.doi.org/10.1007/978-3-642-61631-0.

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Mikhlin, S. G. Singular integral operators. Berlin: Akademie-Verlag, 1986.

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Mikhlin, S. G. Singular integral operators. Berlin: Springer-Verlag, 1986.

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(Aloknath), Chakrabarti A., ed. Applied singular integral equations. Enfield, NH: Science Publishers, 2011.

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Christ, Francis Michael. Lectures on singular integral operators. Providence, R.I: Published for the Conference Board of the Mathematical Sciences by the American Mathematical Society, 1990.

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I, Gohberg. One-dimensional linear singular integral equations. Basel: Birkhäuser Verlag, 1992.

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Vainikko, Gennadi. Multidimensional Weakly Singular Integral Equations. Berlin, Heidelberg: Springer Berlin Heidelberg, 1993. http://dx.doi.org/10.1007/bfb0088979.

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A, Dzhuraev. Methods of singular integral equations. Harlow, Essex, England: Longman Scientific and Technical, 1992.

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Book chapters on the topic "Singular integral"

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Hackbusch, Wolfgang. "Singular Integral Equations." In Integral Equations, 216–65. Basel: Birkhäuser Basel, 1995. http://dx.doi.org/10.1007/978-3-0348-9215-5_7.

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Santini, P. M. "Integrable Singular Integral Evolution Equations." In Springer Series in Nonlinear Dynamics, 147–77. Berlin, Heidelberg: Springer Berlin Heidelberg, 1993. http://dx.doi.org/10.1007/978-3-642-58045-1_9.

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Kress, Rainer. "Singular Integral Equations." In Linear Integral Equations, 94–124. New York, NY: Springer New York, 1999. http://dx.doi.org/10.1007/978-1-4612-0559-3_7.

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Kanwal, Ram P. "Singular Integral Equations." In Linear Integral Equations, 181–218. Boston, MA: Birkhäuser Boston, 1997. http://dx.doi.org/10.1007/978-1-4612-0765-8_8.

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Kress, Rainer. "Singular Integral Equations." In Linear Integral Equations, 82–107. Berlin, Heidelberg: Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/978-3-642-97146-4_7.

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Kanwal, Ram P. "Singular Integral Equations." In Linear Integral Equations, 181–218. New York, NY: Springer New York, 2012. http://dx.doi.org/10.1007/978-1-4614-6012-1_8.

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Agarwal, Ravi P., and Donal O’Regan. "Singular Integral Equations." In Singular Differential and Integral Equations with Applications, 298–336. Dordrecht: Springer Netherlands, 2003. http://dx.doi.org/10.1007/978-94-017-3004-4_3.

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Zemyan, Stephen M. "Singular Integral Equations." In The Classical Theory of Integral Equations, 243–85. Boston, MA: Birkhäuser Boston, 2012. http://dx.doi.org/10.1007/978-0-8176-8349-8_7.

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Roch, Steffen, Pedro A. Santos, and Bernd Silbermann. "Singular integral operators." In Non-commutative Gelfand Theories, 191–258. London: Springer London, 2011. http://dx.doi.org/10.1007/978-0-85729-183-7_4.

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Nédélec, Jean-Claude. "Singular Integral Operators." In Applied Mathematical Sciences, 150–76. New York, NY: Springer New York, 2001. http://dx.doi.org/10.1007/978-1-4757-4393-7_4.

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Conference papers on the topic "Singular integral"

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Zeng, Guang, Jin Huang, and Hong-yan Jia. "The High Accuracy Algorithm for Cauchy Singular Integral and Cauchy Singular Integral Equation." In 2010 4th International Conference on Bioinformatics and Biomedical Engineering (iCBBE). IEEE, 2010. http://dx.doi.org/10.1109/icbbe.2010.5516242.

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Liao, Wen-I., and Tsung-Jen Teng. "On Evaluation of Lamb’s Integrals for Seismic Waves in a Three-Dimension Elastic Half-Space." In ASME 2005 Pressure Vessels and Piping Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/pvp2005-71448.

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The analytical method such as the boundary integral (element) method or the series expansion method is usually used to solve the wave scattering problem. In these methods, the singular Green’s function should be determined firstly; the main difficulty of the use of the Lamb’s singular solutions in integral form to represent the diffracted fields is the numerical implementation for the evaluation of those improper integrals. The integrands of these integrals are highly irregular and oscillatory. In this paper, a technique is proposed to calculate the integral in wave-number domain based on the method of steepest descent. After replacing the original integration path by steepest decent path, the wave-number integral results in a Gauss-Hermite type quadrature, so the oscillating characteristics of the original integrand can be removed and results a non-oscillating integrand, it is very helpful in computing efficiency.
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Bleszynski, Elizabeth, Marek Bleszynski, and Thomas Jaroszewicz. "Reduction of singular surface integrals to non-singular line integrals in integral equations involving non-parallel surface elements." In 2017 11th European Conference on Antennas and Propagation (EUCAP). IEEE, 2017. http://dx.doi.org/10.23919/eucap.2017.7928100.

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Beltiţă, Ingrid. "Multilinear singular integral operators in backscattering." In MATHEMATICAL MODELING OF WAVE PHENOMENA: 2nd Conference on Mathematical Modeling of Wave Phenomena. AIP, 2006. http://dx.doi.org/10.1063/1.2205806.

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Lu, Y. S. "Nonlinear Weakly Singular Iterated Integral Inequality." In 2015 International Conference on Electrical, Automation and Mechanical Engineering. Paris, France: Atlantis Press, 2015. http://dx.doi.org/10.2991/eame-15.2015.89.

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TAIWO, Omotayo A., and Joshua O. OKORO. "Iterative Decomposition Method for solving Singular differential, Singular integral and Singular integro-differential equations." In 2023 International Conference on Science, Engineering and Business for Sustainable Development Goals (SEB-SDG). IEEE, 2023. http://dx.doi.org/10.1109/seb-sdg57117.2023.10124603.

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Sheng, W. T., Z. Y. Zhu, and M. S. Tong. "A novel approach for evaluating singular integrals in electromagnetic integral equations." In 2012 IEEE Antennas and Propagation Society International Symposium and USNC/URSI National Radio Science Meeting. IEEE, 2012. http://dx.doi.org/10.1109/aps.2012.6349051.

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Bleszynski, Elizabeth, Marek Bleszynski, and Thomas Jaroszewicz. "Reduction of singular surface integrals of tensor Green function to non-singular line integrals in integral equations for planar geometries." In 2016 10th European Conference on Antennas and Propagation (EuCAP). IEEE, 2016. http://dx.doi.org/10.1109/eucap.2016.7481173.

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Bleszynski, Elizabeth, Marek Bleszynski, and Thomas Jaroszewicz. "Reduction of singular surface integrals of tensor Green function to non-singular line integrals in integral equations for planar geometries." In 2016 IEEE/ACES International Conference on Wireless Information Technology and Systems (ICWITS) and Applied Computational Electromagnetics (ACES). IEEE, 2016. http://dx.doi.org/10.1109/ropaces.2016.7465368.

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Castro, Luís Filipe Pinheiro de. "ALGEBRAIZATION OF STABILITY FOR SINGULAR INTEGRAL EQUATIONS." In Conferência Brasileira de Dinâmica, Controle e Aplicações. SBMAC, 2011. http://dx.doi.org/10.5540/dincon.2011.001.1.0209.

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Reports on the topic "Singular integral"

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Taylor, Douglas J. Evaluation of Singular Electric Field Integral Equation (EFIE) Matrix Elements. Fort Belvoir, VA: Defense Technical Information Center, June 2001. http://dx.doi.org/10.21236/ada389876.

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Samn, Sherwood. Numerical Analysis of a Singular Integral Equation Arising from Electromagnetic Interior Scattering. Fort Belvoir, VA: Defense Technical Information Center, June 2001. http://dx.doi.org/10.21236/ada388582.

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Samn, Sherwood. Numerical Solution of a Singular Integral Equation Arising from a Sequential Probability Ratio Test. Fort Belvoir, VA: Defense Technical Information Center, March 1995. http://dx.doi.org/10.21236/ada293463.

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Makroglou, A., and E. J. Kansa. Multiquadric collocation methods in the numerical solution of Volterra integral equations with weakly singular kernels. Office of Scientific and Technical Information (OSTI), December 1993. http://dx.doi.org/10.2172/10156921.

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Carasso, Alfred S. Singular integrals, image smoothness, and the recovery of texture in image deblurring. Gaithersburg, MD: National Institute of Standards and Technology, 2003. http://dx.doi.org/10.6028/nist.ir.7005.

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Caraus, Lurie, and Zhilin Li. A Direct Method and Convergence Analysis for Some System of Singular Integro-Differential Equations. Fort Belvoir, VA: Defense Technical Information Center, January 2003. http://dx.doi.org/10.21236/ada451436.

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Chioro dos Reis, Arthur Ademar, Rosemarie Andreazza, Lumena Almeida Castro Furtado, Eliane Cardoso Araújo, Mariana Arantes Nasser, Ana Lúcia Pereira, Nelma Lourenço de Mattos Cruz, et al. Rede de atenção às urgências e emergências e a produção viva de mapas de cuidado. Universidade Federal de São Paulo, April 2022. http://dx.doi.org/10.34024/1160063754.

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Objetivo: analisar o processo de implementação e conformação dos modos de produção do cuidado da política de Rede de Atenção às Urgências e Emergências (RUE), em duas regiões de saúde: Campinas (SP) e Passo Fundo (RS). Procura, ainda, identificar analisadores da produção micropolítica presentes no processo de pactuação e implementação da RUE nessas regiões; analisar as possíveis mudanças no processo de gestão a partir da implementação das RUE; e caracterizar as transformações ocorridas nos modos de produção do cuidado em saúde a partir da implementação das RUE. Metodologia: a pesquisa tem caráter qualitativo, com abordagem micropolítica, e caracteriza-se como estudo de caso e foi desenvolvida através de revisão de literatura, análise de documentos oficiais, coleta de depoimentos de gestores municipais e estaduais, entrevistas narrativas com usuários, e entrevistas em profundidade com gerentes de serviços. No total, foram entrevistados 61 sujeitos. A análise teve como referência a ‘Abordagem do Ciclo de Políticas’. A pesquisa foi desenvolvida por pesquisadores dos programas de Pós-Graduação em Saúde Coletiva da Escola Paulista de Medicina – Universidade Federal de São Paulo (Unifesp-EPM) e da Imed-Faculdade Meridional de Passo Fundo (RS), com apoio de gestores regionais e municipais de saúde e dos Conselhos de Secretários Municipais de Saúde (COSEMS) dos estados de São Paulo e do Rio Grande do Sul. Resultados: Os principais resultados apontam para uma política pública de caráter plural e multifacetado, formulada a partir de diversas influências sociais, econômicas, políticas e teóricas, que expressa como intencionalidade a ampliação do acesso e o cuidado integral em situações de urgência e emergência em saúde. No contexto da prática, apesar da ênfase aos aspectos organizativos e ao financiamento, é observada a política ‘em cena’ onde podem ser identificadas ações de gestão e de produção de cuidado induzidas pela política, mantidas apesar da política e produzidas para além da política da RUE. A relação entre a política oficial e a ação micropolítica dos gestores, tornou-a uma produção singular no campo da governança regional; a necessidade de autonomia dos usuários e a dimensão do cuidado familiar apontam para caminhos na construção da integralidade; há evidências de produções vivas induzidas pela política que qualificam o cuidado, embora iniquidades sejam mantidas ou produzidas; e, a necessidade de articulação entre os componentes em rede, embora evocada, traduz-se em conexões frágeis e não regulares. Considerações Finais: A compreensão dos complexos processos que envolvem as políticas públicas de saúde, os interesses e poderes que as atravessam, tem potencial para fortalecer os atores implicados com a luta pela promoção da equidade em saúde e pela justiça social.
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Jung, Carina, Karl Indest, Matthew Carr, Richard Lance, Lyndsay Carrigee, and Kayla Clark. Properties and detectability of rogue synthetic biology (SynBio) products in complex matrices. Engineer Research and Development Center (U.S.), September 2022. http://dx.doi.org/10.21079/11681/45345.

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Synthetic biology (SynBio) aims to rationally engineer or modify traits of an organism or integrate the behaviors of multiple organisms into a singular functional organism through advanced genetic engineering techniques. One objective of this research was to determine the environmental persistence of engineered DNA in the environment. To accomplish this goal, the environmental persistence of legacy engineered DNA building blocks were targeted that laid the foundation for SynBio product development and application giving rise to “post-use products.” These building blocks include genetic constructs such as cloning and expression vectors, promoter/terminator elements, selectable markers, reporter genes, and multi-cloning sites. Shotgun sequencing of total DNA from water samples of pristine sites was performed and resultant sequence data mined for frequency of legacy recombinant DNA signatures. Another objective was to understand the fate of a standardized contemporary synthetic genetic construct (SC) in the context of various chassis systems/genetic configurations representing different degrees of “genetic bioavailability” to the environmental landscape. These studies were carried out using microcosms representing different environmental matrices (soils, waters, wastewater treatment plant (WWTP) liquor) and employed a novel genetic reporter system based on volatile organic compounds (VOC) detection to assess proliferation and persistence of the SC in the matrix over time.
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