. "38"^^ . "http://www.isvav.cz/projectDetail.do?rowId=GA201/99/0269"^^ . . . "38"^^ . "2003-04-01+02:00"^^ . . "\u010Casto pou\u017E\u00EDvan\u00FDm modelem pro n\u00E1hodn\u00E9 mno\u017Einy v euklidovsk\u00E9m prostoru jsou sjednocen\u00ED (stacion\u00E1rn\u00EDho, ev. izotropn\u00EDho) procesu (n\u00E1hodn\u00E9ho pole) \u010D\u00E1stic (bod\u016F, \u00FAse\u010Dek, vl\u00E1ken, konvexn\u00EDch t\u011Bles atp.). V r\u00E1mci projektu budou studov\u00E1ny integr\u00E1ln\u011B-geometrick\u00E9 (translativn\u00ED i kinematick\u00E9) vztahy pro integr\u00E1ly k\u0159ivost\u00ED jednotliv\u00FDch \u010D\u00E1stic i v\u00FDsledn\u00E9 n\u00E1hodn\u00E9 mno\u017Einy. Tyto vztahy budou pou\u017Eity pro vy\u0161et\u0159ov\u00E1n\u00ED zvolen\u00FDch statistick\u00FDch estim\u00E1tor\u016F k\u0159ivost\u00ED. D\u00E1le budou p\u0159edm\u011Btem v\u00FDzkumu rozptyly estim\u00E1tor\u016F d\u00E9lky, resppovrchu \u010D\u00E1stic. D\u016Fraz bude kladen zejm\u00E9na na teoretick\u00E9 i numerick\u00E9 odvozen\u00ED vztah\u016F pro rozptyly odhad\u016F zalo\u017Een\u00FDch na systematick\u00E9m v\u00FDb\u011Bru. V oblasti simulace proces\u016F vl\u00E1ken \u010Di povrch\u016F budou vyu\u017Eity sou\u010Dasn\u00E9 v\u00FDsledky zn\u00E1m\u00E9 pro bodov\u00E9 procesy. V r\u00E1mci p\u0159edchoz\u00EDho projektu GA \u010CR 201/96/0226 byla prov\u00E1d\u011Bna statistick\u00E1 anal\u00FDza shlukov\u00FDch bodov\u00FDch proces\u016F pomoc\u00ED p\u0159\u00EDslu\u0161n\u00E9 Voronoiovy mozaiky. Tento v\u00FDzkum bude pokra\u010Dovat, nyn\u00ED s d\u016Frazem na procesy s pevn\u00FDm j\u00E1drem, \u0161iroce vyu\u017E\u00EDvan\u00E9 ve fyzice a nauce o mater" . . . "Integral geometry and statistics of random set components"@en . "GA201/99/0269" . . . . "Neuvedeno."@en . . "0"^^ . . "Integr\u00E1ln\u00ED geometrie a statistick\u00E1 anal\u00FDza komponent n\u00E1hodn\u00FDch mno\u017Ein" . . "1"^^ . "2"^^ . . . "Random sets in an Euclidean space are usually modelled as union sets of (stationary, ev. isotropic) processes (random fields) of primary components-particles (points,segments, fibres, convex bodies etc.) Integral-geometric relations (both kinematic and translative) for curvature integrals of individual particles as well as for their union will be investigated and applied to gain properties of chosen statistical curvatore estimators. Other estimators of length and surface area will be studied from the point of view of their variances and theoretical as well as numerical evaluation of the systematic sampling will be carried out in some particular cases. Recent methods of simulation of point processes will be applied to gain new results on sampling of fibre and surface processes. Statistical interference of point processes bymeans of the related Voronoi tesselation, which has been proposed and tested by simulations under the previous project (GACR 201/96/0226) for cluster fields, will continue with an"@en . "Jedn\u00E1 se o odborn\u011B n\u00E1ro\u010Dn\u00FD teoreticky orientovan\u00FD projekt se zna\u010Dn\u00FDm p\u0159\u00EDnosem pro rozvoj oboru. Dosa\u017Een\u00E9 v\u00FDsledky jsou vesm\u011Bs netrivi\u00E1ln\u00ED a publikace jsou v\u011Bt\u0161inou v presti\u017En\u00EDch \u010Dasopisech a sborn\u00EDc\u00EDch. Projekt je sice teoretick\u00FD, ve zpr\u00E1v\u011B jsou c\u00EDle uve"@cs . .