Calculus on time scales was established in 1988 by Stefan Hilger. It includes both the classical derivative and the forward difference operator as special cases. It also includes Riemann integrals and finite sums as inverse operations. However, it does not include the Jackson q-difference operator on R and the Jackson q-integral on R. Also, it does not include neither the difference operator on...

! Abstract Molecular clocks have profoundly influenced modern views on the timing of important events in evolutionary history. We review recent advances in estimating divergence times from molecular data, emphasizing the continuum between processes at the phylogenetic and population genetic scales. On the phylogenetic scale, we address the complexities of DNA sequence evolution as they relate t...

The North Paci c thermocline (250m to 400m) is studied using XBT observations acquired during the 1970s and 1980s. Interannual variations (3-5 year time scales) in thermocline temperature, with O(0.1 C) amplitude at 400m, are found to exhibit westward propagation throughout the extra-tropical North Paci c up to 45N. Southwards of 30N, the features propagate intact across the basin from the east...

Here first we collect and develop necessary background on time scales required for this article. Then we present time scales integral inequalities of types: Poincaré, Sobolev, Opial, Ostrowski and Hilbert–Pachpatte. We give also the generalized analogs of all these inequalities involving high order delta derivatives of functions on time scales. We finish with lots of applications: all these ine...

Starbursts are associated with distinct time scales spanning at least three orders of magnitude from 10 to 10 yr. The triggering of nuclear starbursts occurs over 10 to 10 yr, when gas is flowing to the galaxy center due to angular momentum loss, thereby raising the nuclear gas density. Star formation then increases as a result of the increased gas pressure. In addition, spontaneous star format...

[This corrects the article on p. 439 in vol. 108.].

We establish WKB estimates for 2 × 2 linear dynamic systems with a small parameter ε on a time scale unifying continuous and discrete WKB method. We introduce an adiabatic invariant for 2 × 2 dynamic system on a time scale, which is a generalization of adiabatic invariant of Lorentz’s pendulum. As an application we prove that the change of adiabatic invariant is vanishing as ε approaches zero. ...