"2015-04-23+02:00"^^ . "sequence distribution function uniform distribution irrationality measure randomness arithmetic density"@en . . "2014-04-28+02:00"^^ . . "http://www.isvav.cz/projectDetail.do?rowId=GAP201/12/2351"^^ . "2012-01-01+01:00"^^ . "1"^^ . . "GAP201/12/2351" . . . "1"^^ . . "Distribu\u010Dn\u00ED a metrick\u00E9 vlastnosti \u010D\u00EDseln\u00FDch posloupnost\u00ED a jejich aplikace" . . . . "2015-12-31+01:00"^^ . "0"^^ . "Distribution and metric properties of number sequences and their applications"@en . . . "C\u00EDlem projektu je naj\u00EDt nov\u00E9 a rozvinout pou\u017E\u00EDvan\u00E9 metody analytick\u00E9 a kombinatorick\u00E9 teorie \u010D\u00EDsel pro studium distribu\u010Dn\u00EDch a metrick\u00FDch vlastnost\u00ED konkr\u00E9tn\u00EDch \u010D\u00EDseln\u00FDch posloupnost\u00ED nebo jejich t\u0159\u00EDd. V oblasti distribu\u010Dn\u00EDch vlastnost\u00ED budou p\u0159edm\u011Btem studia glob\u00E1ln\u00ED charakteristiky mno\u017Einy v\u0161ech distribu\u010Dn\u00EDch funkc\u00ED, jako\u017E i podm\u00EDnky existence n\u011Bkter\u00FDch jejich specifick\u00FDch vlastnost\u00ED ud\u00E1vaj\u00EDc\u00EDch typ rozd\u011Blen\u00ED posloupnost\u00ED a jejich vliv na vlastnosti charakterizuj\u00EDc\u00ED n\u00E1hodnost a aritmetiku podkladov\u00FDch posloupnost\u00ED. Bude studov\u00E1n i vliv aritmetick\u00FDch charakteristik (nap\u0159. diskrepance, hustota, apod.) posloupnost\u00ED na jejich mno\u017Einu distribu\u010Dn\u00EDch funkci\u00ED a posloupnost\u00ED od n\u00ED odvozen\u00FDch (nap\u0159. blokov\u00E9, troj\u00FAheln\u00EDkov\u00E9, apod.), jako i vz\u00E1jemn\u00E9 vztahy mezi jejich mno\u017Einami distribu\u010Dn\u00EDch funkc\u00ED. P\u0159edm\u011Btem studia budou i souvislosti distribu\u010Dn\u00EDch a metrick\u00FDch charakteristik (jako Hausdorffova dimenze, Baireova klasifikace apod.) mno\u017Ein \u010D\u00EDseln\u00FDch posloupnost\u00ED a jejich s aritmetick\u00FDmi vlastnostmi, jako iracionalita, nebo m\u00EDry iracion\u00E1lnosti \u010D\u00EDseln\u00FDch posloupnost\u00ED a jejich t\u0159\u00EDd." . . . "The aim of the project is to develop new and to generalize used methods of the analytic and combinatorial number theory employed in the study of distribution and metric properties of number sequences or their families. In the area of distribution properties the aim of study will be global characteristics of the set of all distribution functions, as well as conditions for the existence of their specific properties indicating the distribution type and their impact on the randomness and the arithmetics of the underlying sequences. The aim of the study will also be the interference between arithmetic characteristics (discrepancy, density etc.) of sequences and their sets of distribution functions and the sets of distribution functions of derived sequences (e.g. block, triangle, etc.), as well as the mutual relationships of these two sets. The aim of study will also be the interference between distribution and metric characteristics (as Hausdorff dimension, Baires classification, etc) of number sequences and their arithmetic properties, as irrationality, or measures of irrationality."@en . . "16"^^ . . "16"^^ . . .