"Holota, Petr" . "Reproducing kernel and Neumann\u2019s function for the exterior of an oblate ellipsoid of revolution: Application in gravity field studies"@en . . . "Nesvadba, Otakar" . . . "Earth\u2019s gravity field; geodetic boundary value problems; Green\u2019s functions; variational methods; reproducing kernels; spherical and ellipsoidal harmonics"@en . "RIV/00025615:_____/12:#0001840" . "Reproduk\u010Dn\u00ED j\u00E1dro a Neumannova funkce pro zplo\u0161t\u011Bl\u00FD rota\u010Dn\u00ED elipsoid: aplikace p\u0159i studiu t\u00EDhov\u00E9ho pole Zem\u011B"@cs . . "Integr\u00E1ln\u00ED j\u00E1dra hraj\u00ED d\u016Fle\u017Eitou roli p\u0159i \u0159e\u0161en\u00ED \u00FAloh matematick\u00E9 fyziky a tedy i \u0159e\u0161en\u00ED \u00FAloh teorie potenci\u00E1lu ve fyzik\u00E1ln\u00ED geod\u00E9zii a studiu t\u00EDhov\u00E9ho pole Zem\u011B. Reproduk\u010Dn\u00ED j\u00E1dro m\u016F\u017Ee b\u00FDti vyu\u017Eito jako \u00FA\u010Dinn\u00FD n\u00E1stroj pro tvorbu funk\u010Dn\u00EDch b\u00E1z\u00ED p\u0159i aproximaci hledan\u00E9ho poruchov\u00E9ho potenci\u00E1lu. V\u00FDhodn\u011B se uplatn\u00ED i jeho reproduk\u010Dn\u00ED vlastnost p\u0159i v\u00FDpo\u010Dtu element\u016F Galerkinovy matice line\u00E1rn\u00EDho syst\u00E9mu pro nezn\u00E1m\u00E9 koeficienty v jejich kombinac\u00EDch s b\u00E1zick\u00FDmi funkcemi, kter\u00FDmi je hledan\u00FD potenci\u00E1l aproximov\u00E1n. Konstrukce j\u00E1dra je relativn\u011B snadn\u00E1 v p\u0159\u00EDpad\u011B, kdy oblast \u0159e\u0161en\u00ED dan\u00E9 \u00FAlohy m\u00E1 jednoduchou geometrickou podobu. To je p\u0159\u00EDpad zejm\u00E9na matematick\u00E9ho apar\u00E1tu vybudovan\u00E9ho pro vn\u011Bj\u0161ek koule. Nicm\u00E9n\u011B na\u0161im c\u00EDle je diskutovat apar\u00E1t, kter\u00FD bude schopn\u00FD poslou\u017Eit jako \u00FA\u010Dinn\u00FD n\u00E1stroj pro \u0159e\u0161en\u00ED geodetick\u00FDch \u00FAloh teorie potenci\u00E1lu vn\u011B zplo\u0161t\u011Bl\u00E9ho rota\u010Dn\u00EDho elipsoidu. P\u0159i konstrukci j\u00E1dra hraj\u00ED kl\u00ED\u010Dovou roli elipsoid\u00E1ln\u00ED harmonick\u00E9 funkce. Uk\u00E1\u017Eeme, jak lze zm\u00EDn\u011Bn\u00E9 j\u00E1dro \u0159adami t\u011Bchto funkc\u00ED vyj\u00E1d\u0159it. Z\u00E1kladn\u00EDm probl\u00E9mem se zna\u010Dn\u00FDm dopadem je v\u0161ak mo\u017Enost praktick\u00E9 sumace pou\u017Eit\u00FDch \u0159ad. Alternativn\u00ED cesta op\u0159en\u00E1 jen o numerick\u00E9 p\u0159\u00EDstupy nesk\u00FDt\u00E1 uspokojiv\u00E9 \u0159e\u0161en\u00ED, a to i p\u0159i pou\u017Eit\u00ED velmi v\u00FDkonn\u00FDch v\u00FDpo\u010Detn\u00EDch prost\u0159edk\u016F. J\u00E1dro je proto analyzov\u00E1no a vhodn\u011B rozd\u011Blena na \u010D\u00E1sti. Pro reprezentaci struktury j\u00E1dra jsou vedle hypergeometrick\u00FDch funkc\u00ED a \u0159ad pou\u017Eity r\u016Fzn\u00E9 obraty, postupy a tak\u00E9 n\u00E1stroje diferenci\u00E1ln\u00EDho a integr\u00E1ln\u00EDho po\u010Dtu. V\u00FDsledn\u00E9 analytick\u00E9 vyj\u00E1d\u0159en\u00ED reproduk\u010Dn\u00EDho j\u00E1dra spolu s \u00FA\u010Dinn\u00FDmi numerick\u00FDmi postupy a v\u00FDkonn\u00FDmi v\u00FDpo\u010Detn\u00EDmi prost\u0159edky je pak cestou k re\u00E1ln\u00E9 a \u00FAsp\u011B\u0161n\u00E9 aplikaci. V z\u00E1v\u011Bru je diskutov\u00E1n vztah k Neumannov\u011B funkci."@cs . "Reproducing kernel and Neumann\u2019s function for the exterior of an oblate ellipsoid of revolution: Application in gravity field studies"@en . . . . . "Odd\u011Blen\u00ED geomatiky Z\u00E1pado\u010Desk\u00E9 univerzity a N\u00E1rodn\u00ED pam\u00E1tkov\u00FD \u00FAstav" . "165087" . "I" . "Integr\u00E1ln\u00ED j\u00E1dra hraj\u00ED d\u016Fle\u017Eitou roli p\u0159i \u0159e\u0161en\u00ED \u00FAloh matematick\u00E9 fyziky a tedy i \u0159e\u0161en\u00ED \u00FAloh teorie potenci\u00E1lu ve fyzik\u00E1ln\u00ED geod\u00E9zii a studiu t\u00EDhov\u00E9ho pole Zem\u011B. Reproduk\u010Dn\u00ED j\u00E1dro m\u016F\u017Ee b\u00FDti vyu\u017Eito jako \u00FA\u010Dinn\u00FD n\u00E1stroj pro tvorbu funk\u010Dn\u00EDch b\u00E1z\u00ED p\u0159i aproximaci hledan\u00E9ho poruchov\u00E9ho potenci\u00E1lu. V\u00FDhodn\u011B se uplatn\u00ED i jeho reproduk\u010Dn\u00ED vlastnost p\u0159i v\u00FDpo\u010Dtu element\u016F Galerkinovy matice line\u00E1rn\u00EDho syst\u00E9mu pro nezn\u00E1m\u00E9 koeficienty v jejich kombinac\u00EDch s b\u00E1zick\u00FDmi funkcemi, kter\u00FDmi je hledan\u00FD potenci\u00E1l aproximov\u00E1n. Konstrukce j\u00E1dra je relativn\u011B snadn\u00E1 v p\u0159\u00EDpad\u011B, kdy oblast \u0159e\u0161en\u00ED dan\u00E9 \u00FAlohy m\u00E1 jednoduchou geometrickou podobu. To je p\u0159\u00EDpad zejm\u00E9na matematick\u00E9ho apar\u00E1tu vybudovan\u00E9ho pro vn\u011Bj\u0161ek koule. Nicm\u00E9n\u011B na\u0161im c\u00EDle je diskutovat apar\u00E1t, kter\u00FD bude schopn\u00FD poslou\u017Eit jako \u00FA\u010Dinn\u00FD n\u00E1stroj pro \u0159e\u0161en\u00ED geodetick\u00FDch \u00FAloh teorie potenci\u00E1lu vn\u011B zplo\u0161t\u011Bl\u00E9ho rota\u010Dn\u00EDho elipsoidu. P\u0159i konstrukci j\u00E1dra hraj\u00ED kl\u00ED\u010Dovou roli elipsoid\u00E1ln\u00ED harmonick\u00E9 funkce. Uk\u00E1\u017Eeme, jak lze zm\u00EDn\u011Bn\u00E9 j\u00E1dro \u0159adami t\u011Bchto funkc\u00ED vyj\u00E1d\u0159it. Z\u00E1kladn\u00EDm probl\u00E9mem se zna\u010Dn\u00FDm dopadem je v\u0161ak mo\u017Enost praktick\u00E9 sumace pou\u017Eit\u00FDch \u0159ad. Alternativn\u00ED cesta op\u0159en\u00E1 jen o numerick\u00E9 p\u0159\u00EDstupy nesk\u00FDt\u00E1 uspokojiv\u00E9 \u0159e\u0161en\u00ED, a to i p\u0159i pou\u017Eit\u00ED velmi v\u00FDkonn\u00FDch v\u00FDpo\u010Detn\u00EDch prost\u0159edk\u016F. J\u00E1dro je proto analyzov\u00E1no a vhodn\u011B rozd\u011Blena na \u010D\u00E1sti. Pro reprezentaci struktury j\u00E1dra jsou vedle hypergeometrick\u00FDch funkc\u00ED a \u0159ad pou\u017Eity r\u016Fzn\u00E9 obraty, postupy a tak\u00E9 n\u00E1stroje diferenci\u00E1ln\u00EDho a integr\u00E1ln\u00EDho po\u010Dtu. V\u00FDsledn\u00E9 analytick\u00E9 vyj\u00E1d\u0159en\u00ED reproduk\u010Dn\u00EDho j\u00E1dra spolu s \u00FA\u010Dinn\u00FDmi numerick\u00FDmi postupy a v\u00FDkonn\u00FDmi v\u00FDpo\u010Detn\u00EDmi prost\u0159edky je pak cestou k re\u00E1ln\u00E9 a \u00FAsp\u011B\u0161n\u00E9 aplikaci. V z\u00E1v\u011Bru je diskutov\u00E1n vztah k Neumannov\u011B funkci." . . "Reproduk\u010Dn\u00ED j\u00E1dro a Neumannova funkce pro zplo\u0161t\u011Bl\u00FD rota\u010Dn\u00ED elipsoid: aplikace p\u0159i studiu t\u00EDhov\u00E9ho pole Zem\u011B" . . "Reproduk\u010Dn\u00ED j\u00E1dro a Neumannova funkce pro zplo\u0161t\u011Bl\u00FD rota\u010Dn\u00ED elipsoid: aplikace p\u0159i studiu t\u00EDhov\u00E9ho pole Zem\u011B" . . "[8425C184B510]" . "2"^^ . "Reproduk\u010Dn\u00ED j\u00E1dro a Neumannova funkce pro zplo\u0161t\u011Bl\u00FD rota\u010Dn\u00ED elipsoid: aplikace p\u0159i studiu t\u00EDhov\u00E9ho pole Zem\u011B"@cs . "In gravity field studies linear combinations of basis functions are often used to approximate the gravitational potential of the Earth or its disturbing part. The problem is interpreted for the exterior of a sphere or an oblate ellipsoid of revolution. As a rule, spherical or ellipsoidal harmonics are used as basis functions within this concept. The second case is less frequent, but is stimulated by a number of driving impulses. In general its investigation and possibilities for routine implementation are given a considerable attention. As known basis functions like spherical or ellipsoidal harmonics are frequency localized. Alternatively, our aim is to study the use of space localize basis functions. We focus on basis functions generated by means of the reproducing kernel in the respective Hilbert space. The use of the reproducing kernel offers a straightforward way leading to entries in Galekin\u2019s matrix of the linear system for unknown scalar coefficients. In spherical case the problem may be solved relatively easily. Nevertheless our effort aims to approximations in the exterior of the oblate ellipsoid of revolution. We show how the reproducing kernel can be obtained and give its series representation. The fundamental problem, however, is the possibility of practical summation of the series that represents the kernel. This makes the computation of the kernel and especially the set of the entries in Galerkin\u2019s matrix, even by means of high performance facilities, rather demanding. In this paper the reproducing kernel is analyzed, split into parts and various methods and tools, including hypergeometric functions and series, differential and integral calculus are used to represent its structure, so as to enable an effective numerical treatment. In the end the relation to Neumann\u2019s function is discusses."@en . . "RIV/00025615:_____/12:#0001840!RIV13-MSM-00025615" . "Z\u00E1mek Kozel" . . . . . "2"^^ . . . .