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Journal articles on the topic 'Cauchy integral'

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Published: 4 June 2021

Last updated: 10 March 2023

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1

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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2

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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3

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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4

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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5

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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6

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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7

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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8

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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9

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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10

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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11

Abdulkawi, M. "Bounded solution of Cauchy type singular integral equation of the first kind using differential transform method." JOURNAL OF ADVANCES IN MATHEMATICS 14, no. 1 (April 30, 2018): 7580–95. http://dx.doi.org/10.24297/jam.v14i1.7049.

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In this paper, an efficient approximate solution for solving the Cauchy type singular integral equation of the first kind is presented. Bounded solution of the Cauchy type singular Integral equation is discussed. Two type of kernel, separable and convolution, are considered. The differential transform method is used in the solution. New theorems for transformation of Cauchy singular integrals are given with proofs. Approximate results areshown to illustrate the efficiency and accuracy of the approximate solution.

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12

Choe, Boo Rim. "Cauchy integral equalities and applications." Transactions of the American Mathematical Society 315, no. 1 (January 1, 1989): 337. http://dx.doi.org/10.1090/s0002-9947-1989-0935531-9.

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13

Feng, Bao Qi, and Andrew Tonge. "A Cauchy–Khinchin integral inequality." Linear Algebra and its Applications 433, no. 5 (October 2010): 1024–30. http://dx.doi.org/10.1016/j.laa.2010.04.037.

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14

Kats, Boris A., and David B. Katz. "Cauchy–Hadamard integral with applications." Monatshefte für Mathematik 189, no. 4 (January 28, 2019): 683–89. http://dx.doi.org/10.1007/s00605-019-01263-z.

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15

Plaksa, S. A., and R. P. Pukhtaievych. "Monogenic Functions in a Finite-Dimensional Semi-Simple Commutative Algebra." Analele Universitatii "Ovidius" Constanta - Seria Matematica 22, no. 1 (December 10, 2014): 221–35. http://dx.doi.org/10.2478/auom-2014-0018.

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AbstractWe obtain a constructive description of monogenic functions taking values in a finite-dimensional semi-simple commutative algebra by means of holomorphic functions of the complex variable. We prove that the mentioned monogenic functions have the Gateaux derivatives of all orders. For monogenic functions we prove also analogues of classical integral theorems of the holomorphic function theory: the Cauchy integral theorems for surface and curvilinear integrals, the Morera theorem and the Cauchy integral formula.

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16

Lin, Feng. "On error for Cauchy principal integrals and Cauchy-type integrals under perturbation of integral curve and their applications." Complex Variables and Elliptic Equations 60, no. 11 (March 26, 2015): 1457–74. http://dx.doi.org/10.1080/17476933.2015.1022167.

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17

Sun, Xing Rong. "The Research on the Relationship between Cauchy Integral Theorem and Complex Function Integral in Mechanics of Materials." Advanced Materials Research 502 (April 2012): 120–23. http://dx.doi.org/10.4028/www.scientific.net/amr.502.120.

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This paper is the Cauchy integral theorem and integral of complex function carried out a comparative analysis, summarized in the Cauchy integral theorem and Cauchy integral formula, higher-order derivative formula, residue theorem and the relationship between the derivations to be proved, the formula can be used in these areas, such as mechanics of materials.

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18

Hajjari, Arwa. "Some Results about Cauchy Improper Integral." Galoitica: Journal of Mathematical Structures and Applications 1, no. 2 (2022): 08–10. http://dx.doi.org/10.54216/gjmsa.010201.

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19

De Bie, H., and F. Sommen. "A Cauchy integral formula in superspace." Bulletin of the London Mathematical Society 41, no. 4 (May 22, 2009): 709–22. http://dx.doi.org/10.1112/blms/bdp045.

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20

Brennan, James E. "The Cauchy integral and analytic continuation." Mathematical Proceedings of the Cambridge Philosophical Society 97, no. 3 (May 1985): 491–98. http://dx.doi.org/10.1017/s0305004100063076.

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One of the most important concepts in the theory of approximation by analytic functions is that of analytic continuation. In a typical problem, for example, there is generally a region Ω, a Banach space B of functions analytic in Ω and a subfamily ℱ ⊂ B, each member of which is analytic in some larger open set, and one might be asked to decide whether or not ℱ is dense in B. It often happens, however, that either ℱ is dense or the only functions which can be so approximated have a natural analytic continuation across ∂Ω. A similar phenomenon is also known to occur even for approximation on sets without interior. In this article we shall describe a method for proving such theorems which can be applied in a variety of settings and, in particular, to: (1) the Bernštein problem for weighted polynomial approximation on the real line; (2) the completeness problem for weighted polynomial approximation on bounded simply connected regions; (3) the Shapiro overconvergence problem for sequences of rational functions with sparse poles; (4) the Akutowicz-Carleson minimum problem for interpolating functions. Although we shall present no new results, the method of proof, which is based on an argument of the author [6], seems sufficiently versatile to warrant exposition.

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21

Porter, D. "On some Cauchy-separable integral equations." Mathematical Proceedings of the Cambridge Philosophical Society 99, no. 3 (May 1986): 547–64. http://dx.doi.org/10.1017/s0305004100064495.

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In a recent paper, Porter [9] devised two generalized Volterra operators which convert integral equations with the Hankel function kernel into Cauchy singular equations. The transformations were exploited in [9], and in a subsequent paper (Porter and Chu [10]), in relation to certain wave diffraction problems.

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22

Junghanns, Peter, and Robert Kaiser. "Collocation for Cauchy singular integral equations." Linear Algebra and its Applications 439, no. 3 (August 2013): 729–70. http://dx.doi.org/10.1016/j.laa.2012.09.010.

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23

Dyn’kin, Evsey. "Cauchy integral decomposition for harmonic forms." Journal d'Analyse Mathématique 73, no. 1 (December 1997): 165–86. http://dx.doi.org/10.1007/bf02788142.

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24

司, 红颖. "A Note on Cauchy Integral Formula." Pure Mathematics 09, no. 03 (2019): 282–86. http://dx.doi.org/10.12677/pm.2019.93037.

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25

Tvrdá, Katarína, and Mária Minárová. "Computation of Definite Integral Over Repeated Integral." Tatra Mountains Mathematical Publications 72, no. 1 (December 1, 2018): 141–54. http://dx.doi.org/10.2478/tmmp-2018-0026.

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Abstract The tasks involving repeated integral occur from time to time in technical practice. This paper introduces the research of authors in the field of repeated integrals within the required class of functions. Authors focus on the definite integral over repeated integral and they develop a tool for its computation. It involves two principal steps, analytical and numerical step. In the analytical step, the definite integral over a repeated integral is decomposed into n integrals and then the Cauchy form is used for further rearrangement. Numerical step involves Gauss type integration slightly modified by the authors. Several examples illustrating the operation of both analytical and numerical steps of the method are provided in the paper.

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26

Okamura, Kazuki. "Characterizations of the Cauchy distribution associated with integral transforms." Studia Scientiarum Mathematicarum Hungarica 57, no. 3 (October 20, 2020): 385–96. http://dx.doi.org/10.1556/012.2020.57.3.1469.

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AbstractWe give two new simple characterizations of the Cauchy distribution by using the Möbius and Mellin transforms. They also yield characterizations of the circular Cauchy distribution and the mixture Cauchy model.

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27

Rotkevich, Aleksandr. "External Area Integral Inequality for the Cauchy-Leray-Fantappiè Integral." Complex Analysis and Operator Theory 13, no. 6 (November 27, 2018): 2687–706. http://dx.doi.org/10.1007/s11785-018-0872-8.

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28

Blaya, Ricardo Abreu, Juan Bory Reyes, and Boris Kats. "Cauchy integral and singular integral operator over closed Jordan curves." Monatshefte für Mathematik 176, no. 1 (June 27, 2014): 1–15. http://dx.doi.org/10.1007/s00605-014-0656-9.

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29

Perfekt, Karl-Mikael, Sandra Pott, and Paco Villarroya. "Endpoint compactness of singular integrals and perturbations of the Cauchy integral." Kyoto Journal of Mathematics 57, no. 2 (June 2017): 365–93. http://dx.doi.org/10.1215/21562261-3821837.

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30

Vinogradov, S. A. "Continuity of perturbations of integral operators, Cauchy-type integrals, maximal operators." Journal of Soviet Mathematics 34, no. 6 (September 1986): 2033–39. http://dx.doi.org/10.1007/bf01741577.

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31

Muscalu, Camil. "Calderón commutators and the Cauchy integral on Lipschitz curves revisited II. The Cauchy integral and its generalizations." Revista Matemática Iberoamericana 30, no. 3 (2014): 1089–122. http://dx.doi.org/10.4171/rmi/808.

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32

Sohn, Byung Keun. "Cauchy and Poisson Integral of the Convolutor in Beurling Ultradistributions ofLp-Growth." International Journal of Mathematics and Mathematical Sciences 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/926790.

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LetCbe a regular cone inℝand letTC=ℝ+iC⊂ℂbe a tubular radial domain. LetUbe the convolutor in Beurling ultradistributions ofLp-growth corresponding toTC. We define the Cauchy and Poisson integral ofUand show that the Cauchy integral of Uis analytic inTCand satisfies a growth property. We represent Uas the boundary value of a finite sum of suitable analytic functions in tubes by means of the Cauchy integral representation ofU. Also we show that the Poisson integral ofUcorresponding toTCattainsUas boundary value in the distributional sense.

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33

Sulym, Heorhiy, Iaroslav Pasternak, Mariia Smal, and Andrii Vasylyshyn. "Mixed Boundary Value Problem for an Anisotropic Thermoelastic Half-Space Containing Thin Inhomogeneities." Acta Mechanica et Automatica 13, no. 4 (December 1, 2019): 238–44. http://dx.doi.org/10.2478/ama-2019-0032.

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Abstract The paper presents a rigorous and straightforward approach for obtaining the 2D boundary integral equations for a thermoelastic half-space containing holes, cracks and thin foreign inclusions. It starts from the Cauchy integral formula and the extended Stroh formalism which allows writing the general solution of thermoelastic problems in terms of certain analytic functions. In addition, with the help of it, it is possible to convert the volume integrals included in the equation into contour integrals, which, in turn, will allow the use of the method of boundary elements. For modelling of solids with thin inhomogeneities, a coupling principle for continua of different dimensions is used. Applying the theory of complex variable functions, in particular, Cauchy integral formula and Sokhotski–Plemelj formula, the Somigliana type boundary integral equations are constructed for thermoelastic anisotropic half-space. The obtained integral equations are introduced into the modified boundary element method. A numerical analysis of the influence of boundary conditions on the half-space boundary and relative rigidity of the thin inhomogeneity on the intensity of stresses at the inclusions is carried out.

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34

Cai, Hongzhu, and Michael Zhdanov. "Application of Cauchy-type integrals in developing effective methods for depth-to-basement inversion of gravity and gravity gradiometry data." GEOPHYSICS 80, no. 2 (March 1, 2015): G81—G94. http://dx.doi.org/10.1190/geo2014-0332.1.

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One of the most important applications of gravity surveys in regional geophysical studies is determining the depth to basement. Conventional methods of solving this problem are based on the spectrum and/or Euler deconvolution analysis of the gravity field and on parameterization of the earth’s subsurface into prismatic cells. We have developed a new method of solving this problem based on 3D Cauchy-type integral representation of the potential fields. Traditionally, potential fields have been calculated using volume integrals over the domains occupied by anomalous masses subdivided into prismatic cells. This discretization can be computationally expensive, especially in a 3D case. The technique of Cauchy-type integrals made it possible to represent the gravity field and its gradients as surface integrals. In this approach, only the density contrast surface between sediment and basement needed to be discretized for the calculation of gravity field. This was especially significant in the modeling and inversion of gravity data for determining the depth to the basement. Another important result was developing a novel method of inversion of gravity data to recover the depth to basement, based on the 3D Cauchy-type integral representation. Our numerical studies determined that the new method is much faster than conventional volume discretization method to compute the gravity response. Our synthetic model studies also showed that the developed inversion algorithm based on Cauchy-type integral is capable of recovering the geometry and depth of the sedimentary basin effectively with a complex density profile in the vertical direction.

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35

Rusev, Peter. "Laguerre series and the Cauchy integral representation." Annales Polonici Mathematici 46, no. 1 (1985): 295–97. http://dx.doi.org/10.4064/ap-46-1-295-297.

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36

Li, Ji, Trang T. T. Nguyen, Lesley A. Ward, and Brett D. Wick. "The Cauchy integral, bounded and compact commutators." Studia Mathematica 250, no. 2 (2020): 193–216. http://dx.doi.org/10.4064/sm180715-13-12.

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37

Li, Xingmin, and Lizhong Peng. "The Cauchy integral formulas on the octonions." Bulletin of the Belgian Mathematical Society - Simon Stevin 9, no. 1 (2002): 47–64. http://dx.doi.org/10.36045/bbms/1102715140.

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38

Absalamov, T. "BISINGULAR INTEGRAL OF CAUCHY WITH SUMMABLE DENSITY." Theoretical & Applied Science 103, no. 11 (November 30, 2021): 428–31. http://dx.doi.org/10.15863/tas.2021.11.103.41.

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39

KOMORI, Yasuo. "The Cauchy integral operator on Hardy space." Hokkaido Mathematical Journal 37, no. 2 (May 2008): 389–98. http://dx.doi.org/10.14492/hokmj/1253539561.

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40

Estrada, Ricardo. "The Cauchy integral formula and distributional integration." Complex Variables and Elliptic Equations 64, no. 11 (December 20, 2018): 1854–68. http://dx.doi.org/10.1080/17476933.2018.1557159.

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41

Hu, Chuan-gan, and Ismat Beg. "Cauchy—stieltjes integral in locally convex spaces." Complex Variables, Theory and Application: An International Journal 15, no. 3 (September 1990): 233–39. http://dx.doi.org/10.1080/17476939008814454.

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42

Reyes, Juan Bory, and Dixan Peña Peña. "Some higher order Cauchy–Pompeiu integral representations." Integral Transforms and Special Functions 16, no. 8 (December 2005): 615–24. http://dx.doi.org/10.1080/10652460500110214.

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43

Twomey, J. B. "Tangential Boundary Behaviour of the Cauchy Integral." Journal of the London Mathematical Society s2-37, no. 3 (June 1988): 447–54. http://dx.doi.org/10.1112/jlms/s2-37.3.447.

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44

Kraines, David P., Vivian Y. Kraines, and David A. Smith. "Classroom Computer Capsule: The Cauchy Integral Formula." College Mathematics Journal 21, no. 4 (September 1990): 327–29. http://dx.doi.org/10.1080/07468342.1990.11973329.

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45

Chandler, G. A. "Midpoint collocation for Cauchy singular integral equations." Numerische Mathematik 62, no. 1 (December 1992): 483–509. http://dx.doi.org/10.1007/bf01396240.

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46

Harmse, Jørgen E. "Extensions of the Cauchy–Goursat Integral Theorem." Journal of Mathematical Analysis and Applications 339, no. 1 (March 2008): 429–37. http://dx.doi.org/10.1016/j.jmaa.2007.06.063.

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47

Legua, Matilde, and Luis Sánchez-Ruiz. "Cauchy Principal Value Contour Integral with Applications." Entropy 19, no. 5 (May 10, 2017): 215. http://dx.doi.org/10.3390/e19050215.

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48

Dyn'kin, Evsey. "Cauchy integral decomposition for harmonic vector fields." Complex Variables, Theory and Application: An International Journal 31, no. 2 (October 1996): 165–76. http://dx.doi.org/10.1080/17476939608814956.

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49

Abbasbandy, S., and Du Jin-Yuan. "Numerical implementations of Cauchy-type integral equations." Korean Journal of Computational & Applied Mathematics 9, no. 1 (January 2002): 253–60. http://dx.doi.org/10.1007/bf03012353.

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50

Gera, Amos E. "Singular integral equations with a Cauchy kernel." Journal of Computational and Applied Mathematics 14, no. 3 (March 1986): 311–18. http://dx.doi.org/10.1016/0377-0427(86)90069-5.

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