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.

Regulation and consequences of differential gene expression in diabetic kidney disease

DIN (diabetic nephropathy) is the leading cause of end-stage renal disease worldwide and develops in 25-40% of patients with Type 1 or Type 2 diabetes mellitus. Elevated blood glucose over long periods together with glomerular hypertension leads to progressive glomerulosclerosis and tubulointerstitial fibrosis in susceptible individuals. Central to the pathology of DIN are cytokines and growth factors such as TGF-beta (transforming growth factor beta) superfamily members, including BMPs (bone morphogenetic protein) and TGF-beta 1, which play key roles in fibrogenic responses of the kidney, including podocyte loss, mesangial cell hypertrophy, matrix accumulation and tubulointerstitial fibrosis. Many of these responses can be mimicked in in vitro models of cells cultured in high glucose. We have applied differential gene expression technologies to identify novel genes expressed in in vitro and in vivo models of DN and, importantly, in human renal tissue. By mining these datasets and probing the regulation of expression and actions of specific molecules, we have identified novel roles for molecules such as Gremlin, IHG-1 (induced in high glucose-1) and CTGF (connective tissue growth factor) in DIN and potential regulators of their bioactions.