Calculation of the Hessian for the Log-Log Frequency Distribution
We calculate the diagonal entries of the Hessian for our log-log frequency models.
On a class of -convex functions.
In this paper we define a general class of α-convex functions with respect to a convex domain D contained in the right half plane by using a generalized Sălăgean operator introduced by F.M. Al-Oboudi in [5] and we give some properties of this class. 2000 Mathematical Subject Classification: 30C45
High‐precision U‐Pb zircon age calibration of the global Carboniferous time scale and Milankovitch band cyclicity in the Donets Basin, eastern Ukraine
High‐precision ID‐TIMS U‐Pb zircon ages for 12 interstratified tuffs and tonsteins are used to radiometrically calibrate the detailed lithostratigraphic, cyclostratigraphic, and biostratigraphic framework of the Carboniferous Donets Basin of eastern Europe. Chemical abrasion of zircons, use of the internationally calibrated EARTHTIME mixed U‐Pb isotope dilution tracer, and improved mass spectrometry guided by detailed error analysis have resulted in an age resolution of <0.05%, or ∼100 ka, for these Carboniferous volcanics. This precision allows the resolution of time in the Milankovitch band and confirms the long‐standing hypothesis that individual high‐frequency Pennsylvanian cyclothems and bundles of cyclothems into fourth‐order sequences are the eustatic response to orbital eccentricity (∼100 and 400 ka) forcing. Tuning of the fourth‐order sequences in the Donets Basin to the long‐period eccentricity cycle results in a continuous age model for the Middle to Late Pennsylvanian (Moscovian‐Kasimovian‐Ghzelian) strata of the basin and their record of biological and climatic changes through the latter portion of the late Paleozoic Ice Age. Detailed fusulinid and conodont zonations allow the export of this age model to sections throughout Euramerica. Additional ages for Mississippian strata provide among the first robust radiometric calibration points within this subperiod and result in variable lowering of the base ages of its constituent stages compared to recent global time scale compilations.