Geometry in preduals of spaces of 2-homogeneous polynomials on Hilbert spaces

Let H be a (real or complex) Hilbert space. Using spectral theory and properties of the Schatten–Von Neumann operators, we prove that every symmetric tensor of unit norm in HoH is an infinite absolute convex combination of points of the form xox with x in the unit sphere of the Hilbert space. We use this to obtain explicit characterizations of the smooth points of the unit ball of HoH .

Modulated temperature differential scanning calorimetry and its application to freeze-drying

MTDSC is a software modification of the traditional DSC thermal analysis technique that allows more accurate determination of the glass transition as well as measurement of the endothermic relaxation that often accompanies the transition. The glass transition is an essential parameterboth of the original frozen solution and of the end product. Measurement of endothermic relaxation allows the determination of molecularrelaxation times in the freeze-dried product that may be useful in predicting the effect of formulation variables and storage conditions on physical stability.

On solvability of linear differential equations in ${\Bbb R}^{\Bbb N}$

We construct $x^0$ in ${\Bbb R}^{\Bbb N}$ and a row-finite matrix $T=\{T_{i,j}(t)\}_{i,j\in\N}$ of polynomials of one real variable $t$ such that the Cauchy problem $\dot x(t)=T_tx(t)$, $x(0)=x^0$ in the Fr\'echet space $\R^\N$ has no solutions. We also construct a row-finite matrix $A=\{A_{i,j}(t)\}_{i,j\in\N}$ of $C^\infty(\R)$ functions such that the Cauchy problem $\dot x(t)=A_tx(t)$, $x(0)=x^0$ in ${\Bbb R}^{\Bbb N}$ has no solutions for any $x^0\in{\Bbb R}^{\Bbb N}\setminus\{0\}$. We provide some sufficient condition of solvability and of unique solvability for linear ordinary differential equations $\dot x(t)=T_tx(t)$ with matrix elements $T_{i,j}(t)$ analytically dependent on $t$.

Some results on solvability of ordinary linear differential equations in locally convex spaces

Let $\Gamma$ be the class of sequentially complete locally convex spaces such that an existence theorem holds for the linear Cauchy problem $\dot x = Ax$, $x(0) = x_0$ with respect to functions $x: R\to E$. It is proved that if $E\in \Gamma$, then $E\times R^A$ is-an-element-of $\Gamma$ for an arbitrary set $A$. It is also proved that a topological product of infinitely many infinite-dimensional Frechet spaces, each not isomorphic to $\omega$, does not belong to $\Gamma$.

Ovariole number - a predictor of differential reproductive success among worker subfamilies in queenless honeybee (Apis mellifera L.) colonies

A honeybee queen normally mates with 10-20 drones, and reproductive conflicts may arise among a colony's different worker patrilines, especially after a colony has lost its single queen and the workers commence egg laying. In this study, we employed microsatellite markers to study aspects of worker reproductive competition in two queenless Africanized honeybee colonies. First, we determined whether there was a bias among worker patrilines in their maternity of drones and, second, we asked whether this bias could be attributed to differences in the degree of ovary activation of workers. Third, we relate these behavioral and physiological factors to ontogenetic differences between workers with respect to ovariole number. Workers from each of three (colony A) and one (colony B) patrilineal genotypes represented less than 6% of the worker population, yet each produced at least 13% of the drones in a colony, and collectively they produced 73% of the drones. Workers representing these genotypes also had more developed follicles and a greater number of ovarioles per ovary. Across all workers, ovariole development and number were closely correlated. This suggests a strong effect of worker genotype on the development of the ovary already in the postembryonic stages and sets a precedent to adult fertility, so that

Differential osmoregulatory capabilities of common spiny mice (Acomys cahirinus) from adjacent microhabitats

The osmoregulatory function of common spiny mice Acomys cahirinus living on opposite slopes of the lower Nahal Oren ('Evolution Canyon') on mount Carmel, Israel, was investigated by increasing the salinity of the water source whilst maintaining a high-protein diet. The southern-facing slope (SFS) of this canyon differs from the northern-facing slope (NFS) as it receives considerably more solar radiation and consequently forms a more xeric, sparsely vegetated habitat. During the summer, mice living on the two opposite slopes significantly differed in their urine osmolality, which also increased significantly as dietary salinity increased. Offspring of wild-captured mice, born in captivity, and examined during the winter, continued to show a difference in osmoregulatory function depending on the slope of origin. However, they differed from wild-captured mice, as they did not respond to the increase in dietary salinity by increasing the concentration of their urine, but rather by increasing the volume of urine produced. This study shows that A. cahirinus occupying different microhabitats may exhibit differences in their ability to concentrate urine and thus in their ability to withstand xeric conditions. We suggest that they may also differ genetically, as offspring from the NFS and SFS retain physiological differences, but further studies will be needed to confirm this hypothesis.

Differential energy costs of winter acclimatized common spiny mice Acomys cahirinus from two adjacent habitats

The common spiny mouse Acomys cahirinus, of Ethiopian origin, has a widespread distribution across arid, semi-arid and Mediterranean parts of the Arabian sub-region. We compared the daily energy expenditure (DEE), water turnover NTTO) and sustained metabolic scope (SusMS = DEE/resting metabolic rate) of two adjacent populations during the winter. Mice were captured from North- and South- facing slopes (NFS and SFS) of the same valley, comprising mesic and xeric habitats, respectively. Both DEE and SusMS winter values were greater in NFS than SFS mice and were significantly greater than values previously measured in the summer for these two populations in the same environments. However, WTO values were consistent with previously established values and were not significantly different from allometric predictions for desert eutherians. We suggest that physiological plasticity in energy expenditure, which exists both temporally and spatially, combined with stable WTO, perhaps reflecting a xeric ancestry, has enabled A. cahirinus to invade a wide range of habitats. (C) 2003 Elsevier Inc. All rights reserved.