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| rdf:type
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| Description
| - A relation between the description of the physical surface of the Earth and the structure of the Laplace operator seems to be an important moment in the solution of boundary value problems in physical geodesy. Here, similarly as in other branches of engineering and mathematical physics a transformation of coordinates may be used to solve an alternative between the boundary complexity and the complexity of the coefficients of the partial differential equation governing the solution. In a sense, in the theory of the figure of the Earth the problem is of an intrinsic nature. For instance the Laplace operator has a relatively simple structure in terms of spherical coordinates which are frequently used in geodesy. However, the physical surface of the Earth substantially differs from a (geocentric) sphere of (even optimally chosen) radius. The situation may be more convenient in a system of curvilinear coordinates such that the physical surface of the Earth is imbedded in the family of coordinate surfaces. However, the structure of the Laplace operator is more complicated and in a sense it represents the topography of the physical surface of the Earth. In the suggested approach the effects caused by the topography of the physical surface of the Earth are interpreted as perturbations and the boundary value problem considered is solved by means of successive approximations. A spherical mathematical apparatus is used in each iteration step. This also enables an easy construction of the respective Green’s function. The convergence of the iterations is discussed as well as the possibility to use a mathematical apparatus related to an oblate ellipsoid of revolution for the solution of the problem. (en)
- A relation between the description of the physical surface of the Earth and the structure of the Laplace operator seems to be an important moment in the solution of boundary value problems in physical geodesy. Here, similarly as in other branches of engineering and mathematical physics a transformation of coordinates may be used to solve an alternative between the boundary complexity and the complexity of the coefficients of the partial differential equation governing the solution. In a sense, in the theory of the figure of the Earth the problem is of an intrinsic nature. For instance the Laplace operator has a relatively simple structure in terms of spherical coordinates which are frequently used in geodesy. However, the physical surface of the Earth substantially differs from a (geocentric) sphere of (even optimally chosen) radius. The situation may be more convenient in a system of curvilinear coordinates such that the physical surface of the Earth is imbedded in the family of coordinate surfaces. However, the structure of the Laplace operator is more complicated and in a sense it represents the topography of the physical surface of the Earth. In the suggested approach the effects caused by the topography of the physical surface of the Earth are interpreted as perturbations and the boundary value problem considered is solved by means of successive approximations. A spherical mathematical apparatus is used in each iteration step. This also enables an easy construction of the respective Green’s function. The convergence of the iterations is discussed as well as the possibility to use a mathematical apparatus related to an oblate ellipsoid of revolution for the solution of the problem.
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| Title
| - Mathematical Apparatus for Boundary Value Problems in Gravity Field Studies and the Geometry of the Solution Domain
- Mathematical Apparatus for Boundary Value Problems in Gravity Field Studies and the Geometry of the Solution Domain (en)
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| skos:prefLabel
| - Mathematical Apparatus for Boundary Value Problems in Gravity Field Studies and the Geometry of the Solution Domain
- Mathematical Apparatus for Boundary Value Problems in Gravity Field Studies and the Geometry of the Solution Domain (en)
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| skos:notation
| - RIV/00025615:_____/14:#0002084!RIV15-GA0-00025615
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| http://linked.open...avai/riv/aktivita
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| http://linked.open...avai/riv/aktivity
| - P(ED1.1.00/02.0090), P(GA14-34595S)
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| http://linked.open...vai/riv/dodaniDat
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| http://linked.open...aciTvurceVysledku
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| http://linked.open.../riv/druhVysledku
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| http://linked.open...iv/duvernostUdaju
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| http://linked.open...titaPredkladatele
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| http://linked.open...dnocenehoVysledku
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| http://linked.open...ai/riv/idVysledku
| - RIV/00025615:_____/14:#0002084
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| http://linked.open...riv/jazykVysledku
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| http://linked.open.../riv/klicovaSlova
| - linear gravimetric boundary value problem; transformation of coordinates; general structure of the Laplace operator; integral representation of the solution; Neumann’s function; method of successive approximations (en)
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| http://linked.open.../riv/klicoveSlovo
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| http://linked.open...i/riv/kodPristupu
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| http://linked.open...ontrolniKodProRIV
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| http://linked.open...i/riv/mistoVydani
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| http://linked.open...telVyzkumneZpravy
| - European Geosciences Union
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| http://linked.open...in/vavai/riv/obor
| |
| http://linked.open...ichTvurcuVysledku
| |
| http://linked.open...cetTvurcuVysledku
| |
| http://linked.open...vavai/riv/projekt
| |
| http://linked.open...UplatneniVysledku
| |
| http://linked.open...iv/tvurceVysledku
| - Holota, Petr
- Nesvadba, Otakar
|
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