Relevant bibliographies by topics / The Gauss-Green theorem

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  2. Dissertations / Theses
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Academic literature on the topic 'The Gauss-Green theorem'

Author: Grafiati
Published: 4 June 2021
Last updated: 18 February 2022

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Journal articles on the topic "The Gauss-Green theorem"

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Pfeffer. "THE GAUSS-GREEN THEOREM." Real Analysis Exchange 14, no. 2 (1988): 523. http://dx.doi.org/10.2307/44151972.

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Pfeffer, Washek F. "The Gauss-Green theorem." Advances in Mathematics 87, no. 1 (May 1991): 93–147. http://dx.doi.org/10.1016/0001-8708(91)90063-d.

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Ortel, M., and W. Schneider. "The parametric Gauss-Green theorem." Proceedings of the American Mathematical Society 98, no. 4 (April 1, 1986): 615. http://dx.doi.org/10.1090/s0002-9939-1986-0861762-5.

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Harrison, Jenny, and Alec Norton. "The Gauss-Green theorem for fractal boundaries." Duke Mathematical Journal 67, no. 3 (September 1992): 575–88. http://dx.doi.org/10.1215/s0012-7094-92-06724-x.

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Comi, Giovanni E., and Valentino Magnani. "The Gauss–Green theorem in stratified groups." Advances in Mathematics 360 (January 2020): 106916. http://dx.doi.org/10.1016/j.aim.2019.106916.

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Pfeffer. "GAUSS-GREEN THEOREM FOR VECTOR FIELDS WITH SINGULARITIES." Real Analysis Exchange 14, no. 1 (1988): 60. http://dx.doi.org/10.2307/44153622.

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Ortel, M., and W. Schneider. "A Parametric Gauss-Green Theorem in Several Variables." Canadian Mathematical Bulletin 32, no. 2 (June 1, 1989): 156–65. http://dx.doi.org/10.4153/cmb-1989-023-x.

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AbstractWe present a short, computational proof of the parametric Gauss-Green theorem for a broad class of closed chains. The proof involves only measure theory and the basic theory of differential forms: in particular, no constructions from topology are used. For completeness, the standard properties of winding numbers are also established by methods from analysis.
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Crasta, Graziano, and Virginia De Cicco. "Anzellotti's pairing theory and the Gauss–Green theorem." Advances in Mathematics 343 (February 2019): 935–70. http://dx.doi.org/10.1016/j.aim.2018.12.007.

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Yang, Xiao-Jun. "The vector calculus with respect to monotone functions applied to heat conduction problems." Thermal Science 24, no. 6 Part B (2020): 3949–59. http://dx.doi.org/10.2298/tsci2006949y.

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This paper addresses the theory of the vector calculus with respect to monotone functions for the first time. The Green-like theorem, Stokes-like theorem, Gauss-like theorem, and Green-like identities are obtained with the aid of the notation of Gibbs. The results are used to model the heat-conduction problems arising in the complex phenomenon.
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Nonnenmacher. "NEW INTEGRALS AND THE GAUSS–GREEN THEOREM WITH SINGULARITIES." Real Analysis Exchange 20, no. 1 (1994): 51. http://dx.doi.org/10.2307/44152459.

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Dissertations / Theses on the topic "The Gauss-Green theorem"

1

Kuncová, Kristýna. "Nonabsolutely convergent integrals." Master's thesis, 2011. http://www.nusl.cz/ntk/nusl-313882.

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Title: Nonabsolutely convergent integrals Author: Kristýna Kuncová Department: Department of Mathematical Analysis Supervisor: Prof. RNDr. Jan Malý, DrSc., Department of Mathematical Analysis Abstract: Our aim is to introduce an integral on a measure metric space, which will be nonabsolutely convergent but including the Lebesgue integral. We start with spaces of continuous and Lipschitz functions, spaces of Radon measures and their dual and predual spaces. We build up the so-called uniformly controlled integral (UC-integral) of a function with respect to a distribution. Then we investigate the relationship between the UC-integral with respect to a measure and the Lebesgue integral. Then we introduce another kind of integral, called UCN-integral, based on neglecting of small sets with respect to a Hausdorff measure. Hereafter, we focus on the concept of n-dimensional metric currents. We build the UC-integral with respect to a current and then we proceed to a very general version of Gauss-Green Theorem, which includes the Stokes Theorem on manifolds as a special case. Keywords: Nonabsolutely convergent integrals, Multidimensional integrals, Gauss-Green Theorem 1
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Book chapters on the topic "The Gauss-Green theorem"

1

Ziemer, William. "The Gauss-Green theorem for weakly differentiable vector fields." In CRM Proceedings and Lecture Notes, 233–67. Providence, Rhode Island: American Mathematical Society, 2008. http://dx.doi.org/10.1090/crmp/044/16.

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Shapiro, Ilya L. "Theorems of Green, Stokes, and Gauss." In Undergraduate Lecture Notes in Physics, 101–8. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-26895-4_9.

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"Green-Gauss Theorem." In The Finite Element Method in Engineering, 657–58. Elsevier, 2005. http://dx.doi.org/10.1016/b978-075067828-5/50024-x.

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"Green-Gauss Theorem (Integration by Parts in Two and Three Dimensions)." In The Finite Element Method in Engineering, 705–6. Elsevier, 2011. http://dx.doi.org/10.1016/b978-1-85617-661-3.00034-9.

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"Green–Gauss Theorem (Integration by Parts in Two and Three Dimensions)." In The Finite Element Method in Engineering, 757–58. Elsevier, 2018. http://dx.doi.org/10.1016/b978-0-12-811768-2.15002-3.

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A. Alexeyeva, Lyudmila, and Gulmira K. Zakiryanova. "Singular Boundary Integral Equations of Boundary Value Problems for Hyperbolic Equations of Mathematical Physics." In Mathematical Theorems - Boundary Value Problems and Approximations. IntechOpen, 2020. http://dx.doi.org/10.5772/intechopen.92449.

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The method of boundary integral equations is developed for solving the nonstationary boundary value problems (BVP) for strictly hyperbolic systems of second-order equations, which are characteristic for description of anisotropic media dynamics. The generalized functions method is used for the construction of their solutions in spaces of generalized vector functions of different dimensions. The Green tensors of these systems and new fundamental tensors, based on it, are obtained to construct the dynamic analogues of Gauss, Kirchhoff, and Green formulas. The generalized solution of BVP has been constructed, including shock waves. Using the properties of integrals kernels, the singular boundary integral equations are constructed which resolve BVP. The uniqueness of BVP solution has been proved.
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