Physiological constraints in insects are related to several large-scale processes such as species distribution and thermal adaptation. Here, we fill an important gap in ecophysiology knowledge by accessing the relationship between temperature and embrionary development time in four dragonfly species. We evaluated two questions (1) what is the effect of temperature on the development time of Odonata eggs, and (2) considering a degree-day relationship, could a simple linear model describe the dependence of embrionary development time on temperature or it is better described by a more complex non-linear relation. Egg development time of Erythrodiplax fusca (Rambur), Micrathyria hesperis Ris, Perithemis mooma Kirby, and Miathyria simplex (Rambur) (Odonata: Libellulidae) were evaluated. We put the eggs at different temperatures (15, 20, 25, and 30=C2=B0C) and counted the number of hatched larvae daily. A nonlinear response of the development to the temperature was found, differing from the expected pattern for standard degree-day analysis. Furthermore, we observed that there is a similar process in the development time and hatching synchronization between species, with all species presenting faster egg development at high temperatures. Species-specific differences are more evident at lower temperatures (15=C2=B0C), with no egg development in M. simplex. Only E. fusca was relatively insensitive to temperature changes with similar hatching rates in all treatments.=20

We give an explicit (new) morphism of modules between H*(T)(G/P) circle times H*(T)(P/B) and H*(T)(G/B) and prove (the known result) that the two modules are isomorphic. Our map identifies submodules of the cohomology of the flag variety that are isomorphic to each of H*(T)(G/P) and H*(T)(P/B). With this identification, the map is simply the product within the ring H*(T)(G/B). We use this map in two ways. First, we describe module bases for H*(T)(G/B) that are different from traditional Schubert classes and from each other. Second, we analyze a W-representation on H*(T)(G/B) via restriction to subgroups W-P. In particular, we show that the character of the Springer representation on H*(T)(G/B) is a multiple of the restricted representation of W-P on H*(T)(P/B).

Let H be a compact subgroup of a locally compact group G. We consider the homogeneous space G/H equipped with a strongly quasi-invariant Radon measure mu. For 1 <= p <= +infinity, we introduce a norm decreasing linear map from L-p(G) onto L-p(G/H, mu) and show that L-p(G/H, mu) may be identified with a quotient space of L-p(G). Also, we prove that L-p(G/H, mu) is isometrically isomorphic to a closed subspace of L-p(G). These help us study the structure of the classical Banach spaces constructed on a homogeneous space via those created on topological groups.

No abstract is available for this article.

This paper explains how the discovery of a pocket notebook brings to light P G Tait's surprising involvement in statistics. Tait (1831-1901) was Professor of Mathematics at the Queen's College, Belfast and later of Natural Philosophy at the University of Edinburgh. He was a Fellow of the Royal Society of Edinburgh and a former Fellow of Peterhouse, Cambridge (senior wrangler and first Smith's prizeman in 1852).

The goal of this article is two-fold. First, we consider a class of hyperholomorphic functions, the so called Bp, q(G) space in 3. Then, we use the Bp, q(G) space to characterize the hyperholomorphic -Bloch space. Second, we obtain characterizations of the weighted hyperholomorphic Bp, q(G)-functions by the coefficients of certain lacunary series expansions in Clifford Analysis.