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

Author: Grafiati

Published: 4 June 2021

Last updated: 18 February 2022

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1

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

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2

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

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3

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

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4

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

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5

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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6

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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7

Ortel, M., and W. Schneider. "A Parametric Gauss-Green Theorem in Several Variables." Canadian Mathematical Bulletin 32, no. 2 (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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8

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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9

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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10

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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11

LUO, Weiyu, and Jinyuan DU. "The gauss–green theorem in clifford analysis and its applications." Acta Mathematica Scientia 35, no. 1 (2015): 235–54. http://dx.doi.org/10.1016/s0252-9602(14)60154-5.

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12

Romanowski, Z., та S. Krukowski. "Derivation of von Weizsäcker Equation Based οn Green-Gauss Theorem". Acta Physica Polonica A 115, № 3 (2009): 653–55. http://dx.doi.org/10.12693/aphyspola.115.653.

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13

PFEFFER, WASHEK F. "THE GAUSS–GREEN THEOREM IN THE CONTEXT OF LEBESGUE INTEGRATION." Bulletin of the London Mathematical Society 37, no. 01 (2005): 81–94. http://dx.doi.org/10.1112/s0024609304003777.

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14

Nonnenmacher, Dirk Jens F. "Sets of Finite Perimeter and the Gauss-Green Theorem with Singularities." Journal of the London Mathematical Society 52, no. 2 (1995): 335–44. http://dx.doi.org/10.1112/jlms/52.2.335.

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15

Pauw, Thierry De, and Washek F. Pfeffer. "The Gauss–Green theorem and removable sets for PDEs in divergence form." Advances in Mathematics 183, no. 1 (2004): 155–82. http://dx.doi.org/10.1016/s0001-8708(03)00085-9.

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16

Lyons, Terry J., and Phillip S. C. Yam. "On Gauss–Green theorem and boundaries of a class of Hölder domains." Journal de Mathématiques Pures et Appliquées 85, no. 1 (2006): 38–53. http://dx.doi.org/10.1016/j.matpur.2005.10.005.

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17

Chen, Gui-Qiang, William P. Ziemer, and Monica Torres. "Gauss-Green theorem for weakly differentiable vector fields, sets of finite perimeter, and balance laws." Communications on Pure and Applied Mathematics 62, no. 2 (2009): 242–304. http://dx.doi.org/10.1002/cpa.20262.

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18

Guseynov, Yevgeniy. "Summability on non-rectifiable Jordan curves." Georgian Mathematical Journal 25, no. 2 (2018): 249–58. http://dx.doi.org/10.1515/gmj-2018-0031.

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Abstract For a given parameterization of a Jordan curve, we define the notion of summability or classes of measurable functions on a contour where a new integral is introduced. It is shown that natural functional spaces defining summability for non-rectifiable Jordan curves are the Lebesgue spaces with the weighted norm. For non-rectifiable Jordan curves where an integral was previously defined for continuous (Hölder) functions [Y. Guseynov, Integrable boundaries and fractals for Hölder classes; the Gauss–Green theorem, Calc. Var. Partial Differential Equations 55 2016, 4, Article ID 103], a w

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19

Solecki, R., and F. Forouhar. "Vibration of a Cracked Cylindrical Shell of Rectangular Planform." Journal of Applied Mechanics 52, no. 4 (1985): 927–32. http://dx.doi.org/10.1115/1.3169170.

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Harmonic vibrations of a circular, cylindrical shell of rectangular planform and with an arbitrarily located crack, are investigated. The problem is described by Donnell’s equations and solved using triple finite Fourier transformation of discontinuous functions. The unknowns of the problem are the discontinuities of the slope and of three displacement components across the crack. These last quantities are replaced, using constitutive equations, by curvatures and strain in order to improve convergence and to represent explicitly the singularities at the tips. The formulas for differentiation o

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20

Karaiev, Artem, and Elena Strelnikova. "Singular integrals in axisymmetric problems of elastostatics." International Journal of Modeling, Simulation, and Scientific Computing 11, no. 01 (2020): 2050003. http://dx.doi.org/10.1142/s1793962320500038.

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Singular integral equations arisen in axisymmetric problems of elastostatics are under consideration in this paper. These equations are received after applying the integral transformation and Gauss–Ostrogradsky’s theorem to the Green tensor for equilibrium equations of the infinite isotropic medium. Initially, three-dimensional problems expressed in Cartesian coordinates are transformed to cylindrical ones and integrated with respect to the circumference coordinate. So, the three-dimensional axisymmetric problems are reduced to systems of one-dimensional singular integral equations requiring t

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21

Harrison, J. "Flux across nonsmooth boundaries and fractal Gauss/Green/Stokes' theorems." Journal of Physics A: Mathematical and General 32, no. 28 (1999): 5317–27. http://dx.doi.org/10.1088/0305-4470/32/28/310.

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22

HARRISON, JENNY. "Geometric Hodge star operator with applications to the theorems of Gauss and Green." Mathematical Proceedings of the Cambridge Philosophical Society 140, no. 01 (2006): 135. http://dx.doi.org/10.1017/s0305004105008716.

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23

Xu, Lei, Wu Zhang, Zhengzheng Yan, Zheng Du, and Rongliang Chen. "A novel median dual finite volume lattice Boltzmann method for incompressible flows on unstructured grids." International Journal of Modern Physics C 31, no. 12 (2020): 2050173. http://dx.doi.org/10.1142/s0129183120501739.

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A novel median dual finite volume lattice Boltzmann method (FV-LBM) for the accurate simulation of incompressible flows on unstructured grids is presented in this paper. The finite volume method is adopted to discretize the discrete velocity Boltzmann equation (DVBE) on median dual control volumes (CVs). In the previous studies on median dual FV-LBMs, the fluxes for each partial face have to be computed separately. In the present second-order scheme, we assume the particle distribution functions (PDFs) to be constant for all faces grouped around a particular edge. The fluxes are then evaluated

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24

Guseynov, Yevgeniy. "Integrable boundaries and fractals for Hölder classes; the Gauss–Green theorem." Calculus of Variations and Partial Differential Equations 55, no. 4 (2016). http://dx.doi.org/10.1007/s00526-016-1031-6.

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25

Wang, Nianhua, Ming Li, Rong Ma, and Laiping Zhang. "Accuracy analysis of gradient reconstruction on isotropic unstructured meshes and its effects on inviscid flow simulation." Advances in Aerodynamics 1, no. 1 (2019). http://dx.doi.org/10.1186/s42774-019-0020-9.

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Abstract The accuracy of gradient reconstruction methods on unstructured meshes is analyzed both mathematically and numerically. Mathematical derivations reveal that, for gradient reconstruction based on the Green-Gauss theorem (the GG methods), if the summation of first-and-lower-order terms does not counterbalance in the discretized integral process, which rarely occurs, second-order accurate approximation of face midpoint value is necessary to produce at least first-order accurate gradient. However, gradient reconstruction based on the least-squares approach (the LSQ methods) is at least fi

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