Results 21 to 30 of about 12,887 (176)
Extending valuations to the field of rational functions using pseudo-monotone sequences [PDF]
, 2021 Let $V$ be a valuation domain with quotient field $K$. We show how to describe all extensions of $V$ to $K(X)$ when the $V$-adic completion $\widehat{K}$ is algebraically closed, generalizing a similar result obtained by Ostrowski in the case of one ...
Peruginelli, Giulio, Spirito, Dario
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Cauchy Theorem and Cauchy Residue Theorem
Highlights in Science, Engineering and Technology, 2023 Cauchy theorem is widely used in solving analytic function problems in complex variables. It is an important theorem on path integrals of holomorphic functions in the complex plane. In this paper, the main work is about the application of the Cauchy theorem on the integrals which have singularities.
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Cauchy Residue Theorem and K-residue Theorem
Highlights in Science, Engineering and Technology, 2023 Due to negative numbers do not have square roots, scientists introduced complex numbers, which are more abstract compared with real numbers. Residue Theorem has a very significant status in complex analysis – it can be used to simplify difficult integrals. In this article, Cauchy’s Residue Theorem is first introduced with definition and proof. Then the
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Cauchy Residue Theorem’s Application in Improper integrals
Highlights in Science, Engineering and Technology, 2023 Definite integrals are an essential tool for understanding and calculating many aspects of the natural world. An improper integral, one type of definite integral, has either an infinite interval or an integrand that is not defined at one or more points within the interval of integration.
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Ax-Schanuel condition in arbitrary characteristic [PDF]
, 2017 We prove a positive characteristic version of Ax's theorem on the intersection of an algebraic subvariety and an analytic subgroup of an algebraic group.
Kowalski, Piotr
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Notes on extremal and tame valued fields [PDF]
, 2016 We extend the characterization of extremal valued fields given in [2] to the missing case of valued fields of mixed characteristic with perfect residue field. This leads to a complete characterization of the tame valued fields that are extremal.
Engler, Eršov, Fried, JIZHAN HONG
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Proof and Application of Cauchy’s Residue Theorem
Highlights in Science, Engineering and Technology, 2023 Complex analysis is a major subfield of mathematics that is concerned with investigating complex functions and their behaviors. The Cauchy’s residue theorem plays an important role in complex analysis. It is also the main focus for this paper. The residue theorem connects complex integrals of functions with their residues at singular points.
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Cauchy’s residue theorem for a class of real valued functions [PDF]
Czechoslovak Mathematical Journal, 2010 6 ...
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Application of Cauchy’s Residue Theorem in Several Improper Integrals
Highlights in Science, Engineering and Technology, 2023 Calculating definite integrals in complex functions requires the Cauchy's residue theorem, which is a key concept in the complex variables. It is based on several ideas, including the isolated singular points theory, the Laurent theorem, and the Cauchy integral theorem.
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Applications of Cauchy’s Residue Theorem in Computing Improper Integral
Highlights in Science, Engineering and Technology, 2023 An improper integral is a definite integral that either has an infinite interval or has the integrand that is not defined on some points in the interval. Many improper integrals are difficult to compute by using real analysis methods, especially those containing infinity.
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