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 $t$.

Latin American migration in the central area of Iquique: New fronts of residential location and unequal forms of access to housing

Historically the central area of the city of Iquique has been established as residential space migrants choosing from different backgrounds , however since the late 2000s migration flows are diversified being mostly Latin American immigrants who live in precarious conditions , accessing tugurizados properties , deteriorated in an increasingly growing informal market. The results presented here are derived from quantitative residential location of migrants , as well as the implementation of 13 in-depth interviews . From these results emerge that Latin American migrants access to the same places where once lived internal migrants, however they inhabit a restrictive market , uneven and inadequate living conditions lease, but allows them to articulate residence and proximity to industrial networks , social and popular trade.

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 $\Gamma$.

Enhanced cAMP generation and insulin-releasing potency of two novel Tyr(1)-modified enzyme-resistant forms of glucose-dependent insulinotropic polypeptide is associated with significant antihyperglycaemic activity in spontaneous obesity-diabetes

Glucose-dependent insulinotropic polypeptide (GIP) is an important incretin hormone, which potentiates glucose-induced insulin secretion. Antihyperglycaemic actions of GIP provide significant potential in Type 11 diabetes therapy. However, inactivation of GIP by the enzyme dipeptidyl peptidase IV (DPP IV) and its consequent short circulating half-life limit its therapeutic use. Therefore two novel Tyr(1)-Modified analogues of GIP, N-Fmoc-GIP (where Fmoc is 9-fluorenylmethoxycarbonyl) and N-palmitate-GIP, were synthesized and tested for metabolic stability and biological activity. Both GIP analogues were resistant to degradation by DPP IV and human plasma. In Chinese hamster lung (CHL) cells expressing the cloned human GIP receptor, both analogues exhibited a 2-fold increase in cAMP-generating potency compared with native GIP (EC50 values of 9.4, 10.0 and 18.2 nM respectively). Using clonal BRIN-BD11 cells, both analogues demonstrated strong insulinotropic activity compared with native GIP (P <0.01 to P <0.001). In obese diabetic (ob/ob) mice, administration of N-Fmoc-GIP or N-palmitate-GIP (25 nmol/kg) together with glucose (18 mmol/kg) significantly reduced the peak 15 min glucose excursion (1.4- and 1.5-fold respectively; P <0.05 to P <0.01) compared with glucose alone. The area under the curve (AUC) for glucose was significantly lower after administration of either analogue compared with glucose administered alone or in combination with native GIP (1.5-fold; P <0.05). This was associated with a significantly greater AUC for insulin (2.1-fold; P <0.001) for both analogues compared with native GIP. A similar pattern of in vivo responsiveness was evident in lean control mice. These data indicate that novel N-terminal Tyr(1) modification of GIP with an Fmoc or palmitate group confers resistance to degradation by DPP IV in plasma, which is reflected by increased in vitro potency and greater insulinotropic and antihyperglycaemic activities in an animal model of Type 11 diabetes mellitus.

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 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.