For a zero-mean, unit-variance stationary univariate Gaussian process we derive the probability that a record at the time n, say $X_n$ , takes place, and derive its distribution function. We study the joint distribution of the arrival time process of records and the distribution of the increments between records. We compute the expected number of records. We also consider two consecutive and non-consecutive records, one at time j and one at time n, and we derive the probability that the joint records $(X_j,X_n)$ occur, as well as their distribution function. The probability that the records $X_n$ and $(X_j,X_n)$ take place and the arrival time of the nth record are independent of the marginal distribution function, provided that it is continuous. These results actually hold for a strictly stationary process with Gaussian copulas.

Mosasaurs are an extinct group of secondarily adapted aquatic lizards that became the dominant marine tetrapods in the Late Cretaceous oceans. They continuously shed and replaced their teeth in order to maintain a functional dentition at all times; however, the process of tooth development in mosasaurs is still incompletely known. Based on incremental line width measurements and growth line counts, we assess dentine formation rates in three mosasaur taxa (Dollosaurus, cf. Platecarpus and Tylosaurus) and one genus of marine crocodylian (Aigialosuchus), all from the lower Campanian (Upper Cretaceous) of southernmost Sweden. Two sets of periodic dentinal markings characterized by concentric, alternating opaque and transparent laminae are recognized: one set comprising thin bands situated 6–34 μm apart (depending on taxon), which is superimposed onto a second set of coarser bands where spaces vary between 102 and 275 μm. Assuming that the finer striations represent daily increments (i.e. lines of von Ebner), it is estimated that the deposition of dentine at the sectioned level of the tooth-crowns took 342 (cf. Platecarpus), 426 (Dollosaurus), 487 (Tylosaurus) and 259 (Aigialosuchus) days, respectively. The coarser bands contain between 11 and 13 thin striations each, and are thus considered to be homologous to similar periodic dentinal markings in extant vertebrates, i.e. Andresen lines. Prolonged tooth development times in large-toothed taxa, such as Tylosaurus, presumably increased the risk of long-term incapacity to capture prey after dental trauma, an evolutionary trade-off which may have been compensated for by allometric modifications of the teeth.

Diameter increments, recruitment and mortality were studied over a six-year period in a 3.02 ha sample in an area of 64 ha of undisturbed gallery forest alongside the Gama stream. The study site is located in Fazenda Água Limpa in Brasília, Federal District, Brazil. Trees ≥ 31 cm gbh (10 cm dbh) were measured every three years from 1985 in 151 (10 m × 20 m) permanent plots in Gama forest.

The mean annual diameter increment for trees ≥ 10 cm dbh was 0.25 cm y-1. Variability was high with coefficients of variation c. 100% or more. Light-demanding and large upper storey species tended to grow faster than shade-tolerant and lower storey species. Mean increments for the community increased with increasing diameter classes.

The mean annual mortality rate for the community was 3.5% y−1 while the recruitment was 2.7%. The community was dynamic with 86% of all species either suffering mortality or gaining recruits or both during the six years. The net difference between recruitment and mortality was zero for 55 species. The recruitment compensated for the mortality of most of the abundant species.

Modern theories of brightness induction include an influence from regions that do not share a border with the target. This study tested whether the spatial range of neural integration is the same with incremental versus decremental contrast edges in relatively remote parts of the background. Using an asymmetric matching task, observers set the brightness of a comparison ring, within its own uniform surround, to match the brightness of a test ring within a contiguous surround and a noncontiguous background. The measurements showed that the area of integration depended on the incremental versus decremental contrast polarity at the edge between the surround and background. This implies that brightness induction from an inhomogeneous background must consider the polarity of contrast edges within the whole scene.

The statolith microstructure was examined from seven species of seven families of Antarctic squid captured in Prydz Bay (n=23). Five of the species (Kondakovia longimana, Psychroteuthis glacialis, Brachioteuthis sp., Mastigoteuthis psychrophila, Galiteuthis glacialis) had very clear statolith growth increments which could be enumerated from the nucleus to the statolith margin. These increments were similar in appearance to daily statolith increments in other temperate and tropical squids. Psychroteuthis glacialis also had two distinct zones which may reflect growth during the pelagic and demersal phases of the life cycle. Total statolith increment counts were not possible on two of the species (Bathyteuthis abyssicola and Alluroteuthis antarcticus). The statolith microstructure of Bathyteuthis abyssicola had some very faint increments near the nucleus but increments were not visible in most of the statolith microstructure, while the statolith microstructure of A. antarcticus was indistinct in the nuclear region (possibly due to the formation of a second primordium during ontogenesis). Future research may reveal that statolith increments are useful tools for Antarctic squid age and growth studies.

This paper has as its main theme the fitting in practice of the variance-gamma distribution, which allows for skewness, by moment methods. This fitting procedure allows for possible dependence of increments in log returns, while retaining their stationarity. It is intended as a step in a partial synthesis of some ideas of Madan, Carr and Chang (1998) and of Heyde (1999). Standard estimation and hypothesis-testing theory depends on a large sample of observations which are independently as well as identically distributed and consequently may give inappropriate conclusions in the presence of dependence.

If T is a stopping time on a martingale {St}, the mth order moments of T and ST (for integers m ≧ 2) are related by an identity known as a Wald equation of order m. Wald equations hold under certain conditions, which are simplified in this paper by showing that among the set of previously known conditions, some are implied by the others.