Relevant bibliographies by topics / Cauchy integral

Academic literature on the topic 'Cauchy integral'

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Published: 4 June 2021
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Journal articles on the topic "Cauchy integral"

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Fomin, V. I. "Cauchy Integral Theorem and Cauchy Integral Formula." Vestnik Tambovskogo gosudarstvennogo tehnicheskogo universiteta 21, no. 2 (2015): 330–34. http://dx.doi.org/10.17277/vestnik.2015.02.pp.330-334.

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Azram, M., and F. A. M. Elfaki. "Cauchy Integral Formula." IOP Conference Series: Materials Science and Engineering 53 (December 20, 2013): 012003. http://dx.doi.org/10.1088/1757-899x/53/1/012003.

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OBAIYS, SUZAN J., Z. K. ESKHUVATOV, and N. M. A. NIK LONG. "AUTOMATIC QUADRATURE SCHEME FOR EVALUATING HYPERSINGULAR INTEGRALS." International Journal of Modern Physics: Conference Series 09 (January 2012): 581–85. http://dx.doi.org/10.1142/s2010194512005697.

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Hasegawa constructed the automatic quadrature scheme (AQS), of Cauchy principle value integrals for smooth functions. There is a close connection between Hadamard and Cauchy principle value integral. In this paper, we modify AQS for hypersingular integrals with second-order singularities, using hasegawa's formula and based on the relations between Hadamard finite part integral and Cauchy principle value integral. Numerical experiments are also given, to validate the modified AQS.
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Du, Jun, Sicen Lu, and Tianyi Yang. "Cauchy Integral Theorem and its Applications." Journal of Physics: Conference Series 2386, no. 1 (December 1, 2022): 012017. http://dx.doi.org/10.1088/1742-6596/2386/1/012017.

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Abstract Italian mathematicians Girolamo Cardano and Raphael Bombelli made the initial dis covery of complex numbers somewhere in the 16th century while attempting to solve a algebra icquestion. The relevance of complex analysis in mathematics, physics, and engineering is incre asing now after hundreds of years of growth, particularly in the areas of algebraic geometry, flu id dynamics, quantum mechanics, and other relatedtopics. This paper discusses three aspects of integration of complex functions, properties and valuation of complex line integral, and Cauchy’s Theorem and its applications. It mainly gives a detailed definition of complex integrals, clarifies the properties of operations such as indefinite integrals and integral paths, and briefly lists several applications of Cauchy’s theorem and proves them. Several theorems are proved from Cauchy’s theorem, Local existence of primitives and Cauchy’s theorem in a disc, and Cauchy’s integral formulas.
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Kraines, David P., Vivian Y. Kraines, and David A. Smith. "The Cauchy Integral Formula." College Mathematics Journal 21, no. 4 (September 1990): 327. http://dx.doi.org/10.2307/2686371.

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Lax, Peter D. "The Cauchy Integral Theorem." American Mathematical Monthly 114, no. 8 (October 2007): 725–27. http://dx.doi.org/10.1080/00029890.2007.11920463.

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Ghiloni, Riccardo, Alessandro Perotti, and Vincenzo Recupero. "Noncommutative Cauchy Integral Formula." Complex Analysis and Operator Theory 11, no. 2 (February 23, 2016): 289–306. http://dx.doi.org/10.1007/s11785-016-0543-6.

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Shpakivskyi, V. S., and T. S. Kuzmenko. "Integral theorems for the quaternionic G-monogenic mappings." Analele Universitatii "Ovidius" Constanta - Seria Matematica 24, no. 2 (June 1, 2016): 271–81. http://dx.doi.org/10.1515/auom-2016-0042.

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Abstract In the paper [1] considered a new class of quaternionic mappings, so- called G-monogenic mappings. In this paper we prove analogues of classical integral theorems of the holomorphic function theory: the Cauchy integral theorems for surface and curvilinear integrals, and the Cauchy integral formula for G-monogenic mappings.
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Kai, Hiroshi, and Matu-Tarow Noda. "Cauchy principal value integral using hybrid integral." ACM SIGSAM Bulletin 31, no. 3 (September 1997): 37–38. http://dx.doi.org/10.1145/271130.271192.

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Bavrin, I. I. "Inverse problems for the Cauchy integral formula and the Cauchy integral derivative formulas." Doklady Mathematics 78, no. 2 (October 2008): 679–80. http://dx.doi.org/10.1134/s1064562408050098.

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Dissertations / Theses on the topic "Cauchy integral"

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Oliveira, Saulo Henrique de. "Integral complexa: teorema de Cauchy, fórmula integral de Cauchy e aplicações." Universidade Federal de Goiás, 2015. http://repositorio.bc.ufg.br/tede/handle/tede/4981.

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Este trabalho ...
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Ruppenthal, Jean. "Zur regularität der Cauchy-Riemannschen Differentialgleichungen auf komplexen Räumen." Bonn : Mathematisches Institut der Universität, 2006. http://catalog.hathitrust.org/api/volumes/oclc/173261836.html.

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Cuminato, José Alberto. "Numerical solutions of Cauchy integral equations and applications." Thesis, University of Oxford, 1987. http://ora.ox.ac.uk/objects/uuid:434954bb-bf08-448b-9e02-9948d1287e37.

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This thesis investigates the polynomial collocation method for the numerical solution of Cauchy type integral equations and the use of those equations and the related numerical techniques to solve two practical problem in Acoustics and Aerodynamics. Chapters I and II include the basic background material required for the development of the main body of the thesis. Chapter I discusses a number of practical problems which can be modelled as a singular integral equations. In Chapter II the theory of those equations is given in great detail. In Chapter III the polynomial collocation method for singular integral equations with constant coefficients is presented. A particular set of collocation points, namely the zeros of the first kind Chebyshev polynomials, is shown to give uniform convergence of the numerical approximation for the cases of the index K = 0. 1. The convergence rate for this method is also given. All these results were obtained under slightly stronger assumptions than the minimum required for the existence of an exact solution. Chapter IV contains a generalization of the results in Chapter III to the case of variable coefficients. In Chapter V an example of a practical problem which results in a singular integral equation and which is successfully solved by the collocation method is described in substantial detail. This problem consists of the interaction of a sound wave with an elastic plate freely suspended in a fluid. It can be modelled by a system of two coupled boundary value problems - the Helmholtz equation and the beam equation. The collocation method is then compared with asymptotic results and a quadrature method due to Miller. In Chapter VI an efficient numerical method is developed for solving problems with discontinuous right-hand sides. Numerical comparison with other methods and possible extensions are also discussed.
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Ahmad, Khan Mumtaz, and M. Najmi. "Discrete analogue of Cauchy's integral formula." Pontificia Universidad Católica del Perú, 2014. http://repositorio.pucp.edu.pe/index/handle/123456789/96478.

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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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Luther, Uwe. "Approximation Spaces in the Numerical Analysis of Cauchy Singular Integral Equations." Doctoral thesis, Universitätsbibliothek Chemnitz, 2005. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200500895.

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The paper is devoted to the foundation of approximation methods for integral equations of the form (aI+SbI+K)f=g, where S is the Cauchy singular integral operator on (-1,1) and K is a weakly singular integral operator. Here a,b,g are given functions on (-1,1) and the unknown function f on (-1,1) is looked for. It is assumed that a and b are real-valued and Hölder continuous functions on [-1,1] without common zeros and that g belongs to some weighted space of Hölder continuous functions. In particular, g may have a finite number of singularities. Based on known spectral properties of Cauchy singular integral operators approximation methods for the numerical solution of the above equation are constructed, where both aspects the theoretical convergence and the numerical practicability are taken into account. The weighted uniform convergence of these methods is studied using a general approach based on the theory of approximation spaces. With the help of this approach it is possible to prove simultaneously the stability, the convergence and results on the order of convergence of the approximation methods under consideration.
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Hanson-Hart, Zachary Aaron. "A Cauchy Problem with Singularity Along the Initial Hypersurface." Diss., Temple University Libraries, 2011. http://cdm16002.contentdm.oclc.org/cdm/ref/collection/p245801coll10/id/126171.

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Mathematics
Ph.D.
We solve a one-sided Cauchy problem with zero right hand side modulo smooth errors for the wave operator associated to a smooth symmetric 2-tensor which is Lorentz on the interior and degenerate at the boundary. The degeneracy of the metric at the boundary gives rise to singularities in the wave operator. The initial data prescribed at the boundary must be modified from the classical Cauchy problem to suit the problem at hand. The problem is posed on the interior and the local solution is constructed using microlocal analysis and the techniques of Fourier Integral Operators.
Temple University--Theses
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Camargo, Rubens de Figueiredo. "Do teorema de Cauchy ao metodo de Cagniard." [s.n.], 2005. http://repositorio.unicamp.br/jspui/handle/REPOSIP/307011.

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Orientador: Edmundo Capelas de Oliveira
Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica
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Resumo: Este trabalho versa sobre variaveis complexas, em particular sobre o teorema integral de Cauchy, suas consequencias e aplicações. Como consequencia do teorema integral de Cauchy temos o teorema dos residuos, peça chave para o desenvolvimento deste trabalho. Nas aplicações nos concentramos no estudo das transformadas integrais como metodologia na resolução de equações diferenciais parciais, em particular no calculo da inversão das transformadas de Laplace, Fourier e Hankel, bem como na justa posição das transformadas. Para inversão da justa posição das transformadas nos concentramos no metodo de Cagniard e algumas de suas variações
Abstract: This work is about complex variables, in particular about Cauchy¿s integral theorem and its consequences and applications. We have, as consequences of Cauchy¿s integral theorem, Cauchy¿s theorem and the residue theorem, a keynote to the development of this work. As for the applications, our main objective was to study the integral transforms as a method to solve partial differential equations and, specifically, the inversion of the Laplace, Fourier and Hankel transforms, in the same way, the juxtaposition of transforms. In order to invert the juxtaposition of transforms our main concern was to study Cagniard¿s method and some of its variations
Mestrado
Matematica Aplicada
Mestre em Matemática
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Junghanns, 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.

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We consider a finite section (Galerkin) and a collocation method for Cauchy singular integral equations on the interval based on weighted Chebyshev polymoninals, where the coefficients of the operator are piecewise continuous. Stability conditions are derived using Banach algebra techniques, where also the system case is mentioned. With the help of appropriate Sobolev spaces a result on convergence rates is proved. Computational aspects are discussed in order to develop an effective algorithm. Numerical results, also for a class of nonlinear singular integral equations, are presented.
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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.

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We consider a collocation method for Cauchy singular integral equations on the interval based on weighted Chebyshev polynomials , where the coefficients of the operator are piecewise continuous. Stability conditions are derived using Banach algebra methods, and numerical results are given.
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Books on the topic "Cauchy integral"

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Zhdanov, Mikhail Semenovich. Integral transforms in geophysics. Berlin: Springer-Verlag, 1988.

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Kaya, A. C. On the solution of integral equations with a generalized cauchy kernel. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1986.

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Pajot, Hervé. Analytic Capacity, Rectifiability, Menger Curvature and the Cauchy Integral. Berlin, Heidelberg: Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/b84244.

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Analytic capacity, rectifiability, Menger curvature and the Cauchy integral. Berlin: Springer, 2002.

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Zhdanov, M. S. Integral transforms in geophysics. Berlin: Springer-Verlag, 1987.

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Amecke, Jochen. Direkte Berechnung von Wandinterferenzen und Wandadaption bei zweidimensionaler Stromung in Windkanalen mit geschlossenen Wanden. Gottingen: DFVLR, Institut fur Experimentelle Stromungsmechanik, 1985.

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1945-, Leiterer Jürgen, ed. Andreotti-Grauert theory by integral formulas. Boston: Birkhäuser, 1988.

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Henkin, Gennadi. Andreotti-Grauert theory by integral formulas. Berlin: Akademie-Verlag, 1988.

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K, Binienda Wieslaw, and Lewis Research Center, eds. Analysis of an interface crack for a functionally graded strip sandwiched between two homogeneous layers of finite. [Cleveland, Ohio]: National Aeronautics and Space Administration, Lewis Research Center, 1999.

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Kung, Sheng. Integrals of Cauchy type on the ball. Cambridge, MA: International Press, 1993.

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Book chapters on the topic "Cauchy integral"

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Zhdanov, Michael S. "Cauchy-Type Integral." In Integral Transforms in Geophysics, 3–23. Berlin, Heidelberg: Springer Berlin Heidelberg, 1988. http://dx.doi.org/10.1007/978-3-642-72628-6_1.

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Gauthier, Paul M. "Cauchy Integral Formula." In Lectures on Several Complex Variables, 9–14. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-11511-5_3.

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Estrada, Ricardo, and Ram P. Kanwal. "Cauchy Type Integral Equations." In Singular Integral Equations, 71–123. Boston, MA: Birkhäuser Boston, 2000. http://dx.doi.org/10.1007/978-1-4612-1382-6_3.

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Amann, Herbert, and Joachim Escher. "Das Cauchy-Riemannsche Integral." In Analysis II, 17–25. Basel: Birkhäuser Basel, 2006. http://dx.doi.org/10.1007/3-7643-7402-0_3.

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Kythe, Prem K., and Pratap Puri. "Cauchy Singular Equations." In Computational Methods for Linear Integral Equations, 252–85. Boston, MA: Birkhäuser Boston, 2002. http://dx.doi.org/10.1007/978-1-4612-0101-4_9.

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Greene, Robert, and Steven Krantz. "Applications of the Cauchy integral." In Graduate Studies in Mathematics, 69–103. Providence, Rhode Island: American Mathematical Society, 2006. http://dx.doi.org/10.1090/gsm/040/03.

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Arendt, Wolfgang, Charles J. K. Batty, Matthias Hieber, and Frank Neubrander. "The Laplace Integral." In Vector-valued Laplace Transforms and Cauchy Problems, 5–63. Basel: Springer Basel, 2001. http://dx.doi.org/10.1007/978-3-0348-5075-9_1.

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Arendt, Wolfgang, Charles J. K. Batty, Matthias Hieber, and Frank Neubrander. "The Laplace Integral." In Vector-valued Laplace Transforms and Cauchy Problems, 5–62. Basel: Springer Basel, 2011. http://dx.doi.org/10.1007/978-3-0348-0087-7_1.

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Zhen, Zhao. "Cauchy Formula, Integral of Cauchy Type and Hilbert Problem for Bianalytic Functions." In Partial Differential and Integral Equations, 211–18. Boston, MA: Springer US, 1999. http://dx.doi.org/10.1007/978-1-4613-3276-3_15.

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Davies, B. "Methods Based on Cauchy Integrals." In Integral Transforms and their Applications, 313–41. New York, NY: Springer New York, 1985. http://dx.doi.org/10.1007/978-1-4899-2691-3_19.

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Conference papers on the topic "Cauchy 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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TAO, JICHENG. "FREDHOLM MODULE AND CAUCHY INTEGRAL OPERATOR." In Proceedings of the 13th International Conference on Finite or Infinite Dimensional Complex Analysis and Applications. WORLD SCIENTIFIC, 2006. http://dx.doi.org/10.1142/9789812773159_0026.

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ERIKSSON, SIRKKA-LIISA. "CAUCHY-TYPE INTEGRAL FORMULAS FOR k-HYPERMONOGENIC FUNCTIONS." In Proceedings of the 5th International ISAAC Congress. WORLD SCIENTIFIC, 2009. http://dx.doi.org/10.1142/9789812835635_0101.

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Drin’, Ya M., and I. I. Drin’. "The Cauchy problem for quasilinear pseudodifferential equation with integral coefficients." In 11th International Conference on “Electronics, Communications and Computing". Technical University of Moldova, 2022. http://dx.doi.org/10.52326/ic-ecco.2021/cs.01.

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We consider a quasilinear pseudodifferential evolution equation with the derivative of order one with respect to the time variable t and the pseudodifferential operator this symbol ar (σ), σ € ℝ , homogeneous order 0 < y ≤ 2, by space variable x with integral coefficients. Such equations describe diffusion on inhomogeneous fractals.
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Bolívar, Yanett, Antonio Di Teodoro, and Judith Vanegas. "Generalized Cauchy-Riemann-type operators and some integral representation formulas." In PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2014 (ICNAAM-2014). AIP Publishing LLC, 2015. http://dx.doi.org/10.1063/1.4912659.

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DRAGOMIR, S. S. "APPROXIMATING THE CAUCHY PRINCIPAL VALUE INTEGRAL VIA HERMITE-HADAMARD TYPE INEQUALITIES." In Proceedings of the Wollongong Conference. WORLD SCIENTIFIC, 2002. http://dx.doi.org/10.1142/9789812776372_0009.

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Barbanti, Luciano, and Berenice Camargo Damasceno. "Cauchy-Stieltjes integral on time scales in banach spaces and hysteresis operators." In 9TH INTERNATIONAL CONFERENCE ON MATHEMATICAL PROBLEMS IN ENGINEERING, AEROSPACE AND SCIENCES: ICNPAA 2012. AIP, 2012. http://dx.doi.org/10.1063/1.4765474.

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Setia, Amit, Vaishali Sharma, and Yucheng Liu. "Numerical method to solve Cauchy type singular integral equation with error bounds." In ICNPAA 2016 WORLD CONGRESS: 11th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences. Author(s), 2017. http://dx.doi.org/10.1063/1.4972733.

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MURTHY, A. "An experimental study of wall adaptation and interference assessmentusing Cauchy integral formula." In 29th Aerospace Sciences Meeting. Reston, Virigina: American Institute of Aeronautics and Astronautics, 1991. http://dx.doi.org/10.2514/6.1991-399.

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Li, Hanyan, and Yanduo Zhang. "Calculation on singular integral with Cauchy kernel of anti-Gaussian quadrature formulae." In International Conference on Computer Graphics, Artificial Intelligence, and Data Processing (ICCAID 2021), edited by Feng Wu, Jinping Liu, and Yanping Chen. SPIE, 2022. http://dx.doi.org/10.1117/12.2631133.

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