02448oam 2200625 450 991071174310332120190107094428.0(CKB)5470000002486642(OCoLC)960761830(EXLCZ)99547000000248664220161015d2013 ua 0engurbn||||||abpurbn||||||adatxtrdacontentcrdamediacrrdacarrierTotal body bone area, bone mineral content, and bone mineral density for individuals aged 8 years and over United States, 1999-2006Hyattsville, Maryland :U.S. Department of Health and Human Services, Centers for Disease Control and Prevention, National Center for Health Statistics,2013.1 online resource (iv, 78 pages) illustrations (some color)Vital and health statistics, series 11, data from the National Health Examination Survey, the National Health and Nutrition Examination Surveys, and the Hispanic Health and Nutrition Examination Survey ;number 253DHHS publication ;pub number 2013-1603"August 2013.""CS240914"--Page 4 of cover.Includes bibliographical references.Total body bone area, bone mineral content, and bone mineral density for individuals aged 8 years and over BonesUnited StatesGrowthStatisticsBoneDensityStatisticsBone densitometryUnited StatesStatisticsHealth surveysUnited StatesStatisticsBone densitometryfastBonesGrowthfastHealth surveysfastUnited StatesfastStatistics.lcgftStatistics.fastBonesGrowthBoneDensityBone densitometryHealth surveysBone densitometry.BonesGrowth.Health surveys.National Center for Health Statistics (U.S.),OCLCEOCLCEOCLCQOCLCFOCLCOOCLCAGPOBOOK9910711743103321Total body bone area, bone mineral content, and bone mineral density for individuals aged 8 years and over3474080UNINA03699oam 2200613zu 450 991048288570332120240724212510.03-662-21676-0(CKB)1000000000751035(SSID)ssj0000508723(PQKBManifestationID)12183167(PQKBTitleCode)TC0000508723(PQKBWorkID)10562778(PQKB)11207601(MiAaPQ)EBC3099502(Au-PeEL)EBL3099502(CaPaEBR)ebr10974403(OCoLC)934997347(BIP)47313338(EXLCZ)99100000000075103520160829d1997 uy engurcnu||||||||txtccrBounded variable logics and counting : a study in finite models1st ed.[Place of publication not identified]Springer19971 online resource (190 pages)Lecture notes in logic Bounded variable logics and countingBibliographic Level Mode of Issuance: Monograph3-540-62037-0 Lecture Notes in Logic 9 Bounded Variable Logics and Counting A Study in Finite Models -- Bounded Variable Logics and Counting -- Copyright -- Preface -- Table of Contents -- 0. Introduction -- 1. Definitions and Preliminaries -- 2. The Games and Their Analysis -- 3. The Invariants -- 4. Fixed-Point Logic with Counting -- 5. Related Lindström Extensions -- 6. Canonization Problems -- 7. Canonization for Two Variables -- Bibliography -- Index.Viewed as a branch of model theory, finite model theory is concerned with finite structures and their properties under logical, combinatorial, algorithmic and complexity theoretic aspects. The connection of classical concerns of logic and model theory with issues in complexity theory has contributed very much to the development of finite model theory into a field with its own specific flavour. I like to think of this monograph as a study which - with a partic­ ular theme of its own - exemplifies and reflects some central ideas and lines of research in finite model theory. The particular theme is that of bounded variable infinitary logics, with and without counting quantifiers, related fixed-point logics, and corresponding fragments of PTIME. The re­ lations with PTIME exhibit that fruitful exchange between ideas from logic and from complexity theory that is characteristic of finite model theory and, more specifically, of the research programme of descriptive complexity. Among the main particular topics and techniques I would emphasize: - the importance of games as a fundamental tool from classical logic; their use in the analysis of finite structures also with respect to algorithmic and complexity theoretic concerns is amply illustrated. - the role of cardinality phenomena, which clearly are amongst the most fundamental guidelines in the analysis of finite structures.Lecture Notes in LogicBOUNDED VARIABLE LOGICS AND COUNTINGModel theoryComputational complexityMathematicsHILCCPhysical Sciences & MathematicsHILCCMathematical TheoryHILCCModel theory.Computational complexity.MathematicsPhysical Sciences & MathematicsMathematical Theory511.3/3Otto Martin1225992PQKBBOOK9910482885703321Bounded variable logics and counting : a study in finite models2846465UNINA