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Relevant bibliographies by topics / Cauchy's theorem

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Academic literature on the topic 'Cauchy's theorem'

Author: Grafiati

Published: 4 June 2021

Last updated: 8 February 2022

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Journal articles on the topic "Cauchy's theorem"

1

W. M. Greenlee. "On Green's Theorem and Cauchy's Theorem." Real Analysis Exchange 30, no. 2 (2005): 703. http://dx.doi.org/10.14321/realanalexch.30.2.0703.

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Rodríguez Cano, José Juan, and Enrique de Amo. "Taylor's Expansion Revisited: A General Formula for the Remainder." International Journal of Mathematics and Mathematical Sciences 2012 (2012): 1–5. http://dx.doi.org/10.1155/2012/645736.

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We give a new approach to Taylor's remainder formula, via a generalization of Cauchy's generalized mean value theorem, which allows us to include the well-known Schölomilch, Lebesgue, Cauchy, and the Euler classic types, as particular cases.

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Egahi, M., I. O. Ogwuche, and J. Ode. "Deriving Cauchy's Integral Formula Using Division Method." NIGERIAN ANNALS OF PURE AND APPLIED SCIENCES 1 (March 14, 2019): 259–64. http://dx.doi.org/10.46912/napas.32.

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Cauchy's integral theorem and formula which holds for analytic functions is proved in most standard complex analysis texts. The nth derivative form is also proved. Here we derive the nth derivative form of Cauchy's integral formula using division method and showed its link with Taylor's theorem and demonstrate the result with some polynomials.

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Ikebe, Yasuhiko, Toshiyuki Inagaki, and Sadaaki Miyamoto. "The Monotonicity Theorem, Cauchy's Interlace Theorem, and the Courant- Fischer Theorem." American Mathematical Monthly 94, no. 4 (1987): 352. http://dx.doi.org/10.2307/2323096.

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Ikebe, Yasuhiko, Toshiyuki Inagaki, and Sadaaki Miyamoto. "The Monotonicity Theorem, Cauchy's Interlace Theorem, and the Courant-Fischer Theorem." American Mathematical Monthly 94, no. 4 (1987): 352–54. http://dx.doi.org/10.1080/00029890.1987.12000645.

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Kim, Hwajoon. "The variant of Cauchy's integral theorem, and Morera's theorem." Applied Mathematical Sciences 9 (2015): 5325–29. http://dx.doi.org/10.12988/ams.2015.56461.

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Zhang, Zifang, Daoyi Xu, and Jianren Niu. "On the refinement of Cauchy's theorem and Pellet's theorem." Journal of Mathematical Analysis and Applications 291, no. 1 (2004): 262–69. http://dx.doi.org/10.1016/j.jmaa.2003.11.001.

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Dvurečenskij, Anatolij. "Gleason's theorem and Cauchy's functional equation." International Journal of Theoretical Physics 35, no. 12 (1996): 2687–95. http://dx.doi.org/10.1007/bf02085773.

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Tong, Jingcheng. "Cauchy's Mean Value Theorem Involving n Functions." College Mathematics Journal 35, no. 1 (2004): 50. http://dx.doi.org/10.2307/4146885.

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Kupka, Ivan. "Topological generalization of Cauchy's mean value theorem." Annales Academiae Scientiarum Fennicae Mathematica 41 (February 2016): 315–20. http://dx.doi.org/10.5186/aasfm.2016.4120.

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Dissertations / Theses on the topic "Cauchy's theorem"

1

Chung, Kwok-Chiu. "Computing oscillatory integrals by complex methods." Thesis, Loughborough University, 1998. https://dspace.lboro.ac.uk/2134/33239.

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The research is concerned with the proposal and the development of a general method for computing rapidly oscillatory integrals with sine and cosine weight integrands of the form f(x) exp(iωq(x)). In this method the interval (finite or infinite) of integration is transformed to an equivalent contour in the complex plane and consequently the problem of evaluating the original oscillatory integral reduces to the evaluation of one or more contour integrals. Special contours, called the optimal contours, are devised and used so that the resulting real integrals are non-oscillatory and have rapidly decreasing integrands towards one end of the integration range. The resulting real integrals are then easily computed using any general-purpose quadrature rule.

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Judd, Kristin N. "An extension of green's theorem with application." Diss., Columbia, Mo. : University of Missouri-Columbia, 2008. http://hdl.handle.net/10355/5638.

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Thesis (M.S.)--University of Missouri-Columbia, 2008.<br>The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file (viewed on September 5, 2008) Includes bibliographical references.

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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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Submitted by Luciana Ferreira (lucgeral@gmail.com) on 2015-12-03T08:37:01Z No. of bitstreams: 2 Dissertação - Saulo Henrique de Oliveira - 2015.pdf: 1917786 bytes, checksum: 72281ae1c7a550ab53f962bb0da58d07 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5)<br>Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2015-12-03T08:39:30Z (GMT) No. of bitstreams: 2 Dissertação - Saulo Henrique de Oliveira - 2015.pdf: 1917786 bytes, checksum: 72281ae1c7a550ab53f962bb0da58d07 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5)<br>Made available in DSpace on 2015-12-03T08:39:30Z (GMT). No. of bitstreams: 2 Dissertação - Saulo Henrique de Oliveira - 2015.pdf: 1917786 bytes, checksum: 72281ae1c7a550ab53f962bb0da58d07 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Previous issue date: 2015-04-29<br>Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES<br>This work ...<br>Este trabalho ...

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Paneah, Boris. "Dynamic methods in the general theory of cauchy type functional equations." Universität Potsdam, 2002. http://opus.kobv.de/ubp/volltexte/2008/2629/.

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Contents: 1 Introduction. Denfitions and Discussions 2 Solvability of the Cauchy Type Functional Equations 2.1 The Case of a P-configuration 2.2 The Case of a Z-configuration 2.3 Multiplicative Cauchy type functional equations 3 Problems in Analysis Reducing to Cauchy Type Functional Equations 3.1 Some problems in Integral Geometry and Cauchy Functional Equations 3.2 First Boundary Problem for Hyperbolic Differential Equations and Cauchy Type Functional Equations 4 Functional Equations Determining Polynomials

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Wigren, Thomas. "The Cauchy-Schwarz inequality : Proofs and applications in various spaces." Thesis, Karlstads universitet, Avdelningen för matematik, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:kau:diva-38196.

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We give some background information about the Cauchy-Schwarz inequality including its history. We then continue by providing a number of proofs for the inequality in its classical form using various proof techniques, including proofs without words. Next we build up the theory of inner product spaces from metric and normed spaces and show applications of the Cauchy-Schwarz inequality in each content, including the triangle inequality, Minkowski's inequality and Hölder's inequality. In the final part we present a few problems with solutions, some proved by the author and some by others.

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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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Sanomiya, Thais Akemi Tokubo. "Sobre o teorema de Campbell-Magaard e o problema de Cauchy na relatividade." Universidade Federal da Paraíba, 2016. http://tede.biblioteca.ufpb.br:8080/handle/tede/9542.

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Submitted by Vasti Diniz (vastijpa@hotmail.com) on 2017-09-18T11:49:17Z No. of bitstreams: 1 arquivototal.pdf: 2571485 bytes, checksum: 176b4eb5f639864aaef387d41330b286 (MD5)<br>Made available in DSpace on 2017-09-18T11:49:17Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 2571485 bytes, checksum: 176b4eb5f639864aaef387d41330b286 (MD5) Previous issue date: 2016-03-11<br>Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES<br>After the formulation of general relativity differential geometry has become an increasing important tool in theoretical physics. This is even more clear in the investigation of the so-called embedding space-time theories. In this work we focus our attention in the Cauchy problem. These have played a crucial role in our understanding of the mathematical structure of general relativity and embedding theories. We investigate the similarities and differences between the two approaches. We also study an extension of the Campbell-Magaard theorem and give two examples of both formalisms.<br>A geometria diferencial passou a ser uma ferramenta fundamental na fisica com o surgimento da relatividade geral. Em particular, destacamos sua importância na investigado das chamadas teorias de imersdo do espaco-tempo. Neste trabalho analisamos dois grandes formalismos fundamentados de forma direta ou indireta na teoria de imersões: o teorema de Campbell-Magaard e o problema de Cauchy para a relatividade geral. Tendo como principal objetivo tracar um paralelo entre esses dois formalismos, estudamos, nesta dissertacdo, o problema de valor inicial (pvi) para a relatividade geral mostrando que alem de admitir a formulae-do de pvi, a mesma é bem posta. Ademais, aplicamos este formalismo para o caso de uma metrica do tipo Friedmann-Robertson-Walker em (3+1). Estudamos tambem o teorema de Campbell-Magaard e sua extensdo para o espaco-tempo de Einstein e aplicamos este teorema para uma metrica do tipo de Sitter em (2+1).

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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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Paneah, B. "On the general theory of the cauchy type functional equations with applications in analysis." Universität Potsdam, 2005. http://opus.kobv.de/ubp/volltexte/2009/3000/.

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Contents: 1 The main notations and definitions. 2 Statement of the problems and main results. 2.1 The case of a Z-configuration. 2.2 The case of a P-configuration. 3 Proofs of Theorems 1-7. 4 Applications. 4.1 Multiplicative Cauchy type functional equation. 4.2 On some integral equations relating to a geometric problem 4.3 On the solvability of boundary problem for hyperbolic differential equations.

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Widman, Linnea. "Från det imaginära till normala familjer : Analytiska konvergenser." Thesis, Umeå universitet, Institutionen för matematik och matematisk statistik, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-59771.

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I komplex analys finns det ett antal olika konvergenser varav vi tittar närmare på några här. Bland annat hur likformig konvergens medför punktvis konvergens men att det omvända ej gäller. Vi tittar också på vad de har för samband med lokal likformig konvergens och normal konvergens dvs. likformig konvergens på kompakta delmängder. Slutligen kommer vi att se på vad som gäller för familjer och kommer då in på lokalt begränsad, ekvikontinuitet, Arzela/Ascoli, Montels och Runges satser. Vi kommer här även se exempel på hur stort fel det egentligen kan bli för punktvisa konvergenta följder. De får normalt inte en gränsfunktion som är analytisk men vi ser både i Exempel 3.19 och Korollarium 3.23 att dessa ger resultat som är analytiska nästan överallt.<br>This report will describe four different types of convergence. The types described are pointwise, local uniformly, uniformly and normal convergence. The different convergences are explored in a way of how they relate to each other. Finally this report will also investigate how this applies to normal families and the theories of Arzela/Ascoli, Montel and Runge. We will here see examples of how wrong it really can go for pointwise convergent sequences. They do usually not have a limit that is analytic but from both Example 3.19 and Corollary 3.23 we will see that they give functions that in fact are analytic almost everywhere.

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Books on the topic "Cauchy's theorem"

1

Watson, G. N. Complex integration and Cauchy's theorem. Dover Publications, Inc., 2012.

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1946-, Matheson Alec L., and Ross William T. 1964-, eds. The Cauchy transform. American Mathematical Society, 2006.

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Glassey, Robert. The Cauchy problem in kinetic theory. Society for Industrial and Applied Mathematics, 1996.

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

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Trèves, François. Homotopy formulas in the tangential Cauchy-Riemann complex. American Mathematical Society, 1990.

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Treves, Francois. Homotopy formulas in the tangential Cauchy-Riemann complex. American Mathematical Society, 1990.

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Bell, Steven Robert. The Cauchy transform, potential theory, and conformal mapping. CRC Press, 1992.

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Jr, Rafael José Iorio. Tópicos na teoria da equação de Schrödinger. Instituto de Matemática Pura e Aplicada, 1987.

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Murai, Takafumi. A real variable method for the Cauchy transform and analytic capacity. Springer-Verlag, 1988.

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1963-, Ruan Shigui, ed. Center manifolds for semilinear equations with non-dense domain and applications to Hopf bifurcation in age structured models. American Mathematical Society, 2009.

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Book chapters on the topic "Cauchy's theorem"

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Cates, Dennis M. "THEOREM OF HOMOGENEOUS FUNCTIONS. MAXIMA AND MINIMA OF FUNCTIONS OF SEVERAL VARIABLES." In Cauchy's Calcul Infinitésimal. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-11036-9_10.

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Alpay, Daniel. "Cauchy’s Theorem." In A Complex Analysis Problem Book. Springer Basel, 2011. http://dx.doi.org/10.1007/978-3-0348-0078-5_5.

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Alpay, Daniel. "Cauchy’s Theorem." In A Complex Analysis Problem Book. Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-42181-0_5.

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Howie, John M. "Cauchy’s Theorem." In Springer Undergraduate Mathematics Series. Springer London, 2003. http://dx.doi.org/10.1007/978-1-4471-0027-0_6.

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Armstrong, M. A. "Cauchy’s Theorem." In Undergraduate Texts in Mathematics. Springer New York, 1988. http://dx.doi.org/10.1007/978-1-4757-4034-9_13.

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Aigner, Martin, and Günter M. Ziegler. "Cauchy’s rigidity theorem." In Proofs from THE BOOK. Springer Berlin Heidelberg, 1998. http://dx.doi.org/10.1007/978-3-662-22343-7_11.

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Aigner, Martin, and Günter M. Ziegler. "Cauchy’s rigidity theorem." In Proofs from THE BOOK. Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-00856-6_13.

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Aigner, Martin, and Günter M. Ziegler. "Cauchy’s rigidity theorem." In Proofs from THE BOOK. Springer Berlin Heidelberg, 2014. http://dx.doi.org/10.1007/978-3-662-44205-0_14.

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Aigner, Martin, and Günter M. Ziegler. "Cauchy’s rigidity theorem." In Proofs from THE BOOK. Springer Berlin Heidelberg, 2018. http://dx.doi.org/10.1007/978-3-662-57265-8_14.

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Aigner, Martin, and Günter M. Ziegler. "Cauchy’s rigidity theorem." In Proofs from THE BOOK. Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/978-3-662-04315-8_11.

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Conference papers on the topic "Cauchy's theorem"

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Sommen, F. "Cauchy-type theorems on surfaces." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2012: International Conference of Numerical Analysis and Applied Mathematics. AIP, 2012. http://dx.doi.org/10.1063/1.4756131.

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Medenica, M. S., and D. Lj Debeljkovic. "A Short Note on Stability of Linear Time Delay Systems." In ASME 8th Biennial Conference on Engineering Systems Design and Analysis. ASMEDC, 2006. http://dx.doi.org/10.1115/esda2006-95055.

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Our research on stability criteria for linear systems with time delay in a frequency domain has brought in a new stability criterion that belongs to the group of graph-analytical stability criteria. Via the theory of functions with a complex variable, this criterion is based upon Cauchy’s theorem of argument and condition that for frequency ω varying from −∞ to +∞ the argument of function f*(jω,ejωτ) has positive change. In solution, as a graphic interpretation in the f* - plane, a spiral curve is obtained, which possesses some characteristics crucial for the stability of a system with time delay. Through given examples, simplicity and facility of criteria application to different cases of systems are shown.

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Sahin, Iskender. "Calculation of Three-Dimensional Flow Field for Moving Pressure Distributions." In ASME 2004 23rd International Conference on Offshore Mechanics and Arctic Engineering. ASMEDC, 2004. http://dx.doi.org/10.1115/omae2004-51127.

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Three-dimensional flow field generated by a moving surface pressure distribution is calculated with an emphasis on estimating the bottom pressure signature of an air cushion vehicle. Analytical studies yield singularities and periodic functions with large oscillations in the integrals. The singularities are removed by the Cauchy’s residue theorem and the resulting integrals are numerically evaluated by the use of adaptive quadrature integrations.

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MIYATAKE, SADAO. "A THEORY OF DIAGONALIZED SYSTEMS OF NONLINEAR EQUATIONS AND APPLICATION TO AN EXTENDED CAUCHY-KOWALEVSKY THEOREM." In Proceedings of the 5th International ISAAC Congress. WORLD SCIENTIFIC, 2009. http://dx.doi.org/10.1142/9789812835635_0056.

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De Ridder, H., H. De Schepper, F. Sommen, Theodore E. Simos, George Psihoyios, and Ch Tsitouras. "The Cauchy-Kovalevskaya Extension Theorem in Discrete Clifford Analysis." In ICNAAM 2010: International Conference of Numerical Analysis and Applied Mathematics 2010. AIP, 2010. http://dx.doi.org/10.1063/1.3498039.

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Jaeger, Benjamin, and Philippe de Forcrand. "Taylor expansion and the Cauchy Residue Theorem for finite-density QCD." In The 36th Annual International Symposium on Lattice Field Theory. Sissa Medialab, 2019. http://dx.doi.org/10.22323/1.334.0178.

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GAUTHIER, P. M. "THE CAUCHY THEOREM FOR DOMAINS OF ARBITRARY CONNECTIVITY ON RIEMANN SURFACES." In Proceedings of a Satellite Conference to the International Congress of Mathematicians in Beijing 2002. WORLD SCIENTIFIC, 2004. http://dx.doi.org/10.1142/9789812702500_0008.

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Fahs, Jihad, and Ibrahim Abou-Faycal. "A cauchy input achieves the capacity of a Cauchy channel under a logarithmic constraint." In 2014 IEEE International Symposium on Information Theory (ISIT). IEEE, 2014. http://dx.doi.org/10.1109/isit.2014.6875400.

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Donghui Li. "On asymptotic properties for the median point of Cauchy Mean-value Theorem." In 2011 International Conference on Multimedia Technology (ICMT). IEEE, 2011. http://dx.doi.org/10.1109/icmt.2011.6002502.

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Shao, Ya-Bin, and Zeng-Tai Gong. "The existence theorems to the Cauchy problems of fuzzy differential equations." In NAFIPS 2011 - 2011 Annual Meeting of the North American Fuzzy Information Processing Society. IEEE, 2011. http://dx.doi.org/10.1109/nafips.2011.5751954.

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