A necessary flexibility condition of a nondegenerate suspension in Lobachevsky 3-space

We show that some combination of the lengths of all edges of the equator of a flexible suspension in Lobachevsky 3-space is equal to zero (each length is taken either positive or negative in this combination).Comment: 20 pages, 13 figure

Female length at sexual maturity for pygmy and Antarctic blue whales based on Soviet ovarian corpora, 1961-72

Female blue whale ovarian corpora data were translated and encoded from the USSR’s Slava (1961/62–1965/66) and Sovietskaya Ukraina (1961/62–1971/72) expeditions. Complete ovarian data were available for 1,425 blue whales (1,272 pygmy, 153 Antarctic). Catches north of 52°S were assumed to be pygmy blue whales (Balaenoptera musculus brevicauda), while those south of 56°S were assumed to be Antarctic (true) blue whales (B. m. intermedia), although there was some evidence for a small proportion (<1%) of both Antarctic blue whales north of 52°S and pygmy blue whales south of 56°S. A small proportion of lengths were rounded to the nearest metre, and many whales shorter than 18.0 were recorded as 18.0 m or greater (whale stretching). A Bayesian logistic model fitted to the data provided estimates of L50 and L95 (the lengths at which 50% and 95% of females are sexually mature). For pygmy blue whales L50 was 19.2 m (95% interval 19.1–19.3 m) and L95 was 20.5 m (95% interval 20.4–20.7 m). These estimates are more precise than those from Japanese data because the Soviet vessels recorded 32 times more pygmy blue whales shorter than the legal minimum length (21.3 m). Among small areas, L50 varied from 18.4 to 19.9 m for pygmy blue whales; all estimates were much shorter than the 23.4 m from the Antarctic. The status of northern Indian Ocean pygmy blue whales is unclear: L50 for these blue whales was statistically significantly shorter than L50 for both the southern Indian Ocean and around Australia, but the magnitude of the differences was small: 0.5–0.6 m

Time dependent correlations in marine stratocumulus cloud base height records

The scaling ranges of time correlations in the cloud base height records of marine boundary layer stratocumulus are studied applying the Detrended Fluctuation Analysis statistical method. We have found that time dependent variations in the evolution of the $\alpha$ exponent reflect the diurnal dynamics of cloud base height fluctuations in the marine boundary layer. In general, a more stable structure of the boundary layer corresponds to a lower value of the $\alpha$ - indicator, i.e. larger anti-persistence, thus a set of fluctuations tending to induce a greater stability of the stratocumulus. In contrast, during periods of higher instability in the marine boundary, less anti-persistent (more persistent like) behavior of the system drags it out of equilibrium, corresponding to larger $\alpha$ values. From an analysis of the frequency spectrum, the stratocumulus base height evolution is found to be a non-stationary process with stationary increments. The occurrence of these statistics in cloud base height fluctuations suggests the usefulness of similar studies for the radiation transfer dynamics modeling.Comment: 12 pages, 6 figures; to appear in Int. J. Mod. Phys. C, Vol. 13, No. 2 (2002