On positive solutions for some semilinear periodic parabolic eigenvalue problems

AbstractFor a bounded domain Ω in RN, N⩾2, satisfying a weak regularity condition, we study existence of positive and T-periodic weak solutions for the periodic parabolic problem Luλ=λg(x,t,uλ) in Ω×R, uλ=0 on ∂Ω×R. We characterize the set of positive eigenvalues with positive eigenfunctions associated, under the assumptions that g is a Caratheodory function such that ξ→g(x,t,ξ)/ξ is nonincreasing in (0,∞) a.e. (x,t)∈Ω×R satisfying some integrability conditions in (x,t) and ∫0Tesssupx∈Ωinfξ>0g(x,t,ξ)ξdt>0

Periodic parabolic problems with nonlinearities indefinite in sign

Let Ω ⊂ RN be a smooth bounded domain. We give sufficient conditions (which are also necessary in many cases) on two nonnegative functions a, b that are possibly discontinuous and unbounded for the existence of nonnegative solutions for semilinear Dirichlet periodic parabolic problems of the form Lu =λa (x, t) u p − b (x, t) u q in Ω × R, where 0 0. In some cases we also show the existence of solutions uλ in the interior of the positive cone and that uλ can be chosen such that λ → uλ is differentiable and increasing. A uniqueness theorem is also given in the case p ≤ q. All results remain valid for the corresponding elliptic problems

Towards practical permutation routing on meshes

We consider the permutation routing problem on two-dimensional $n \times n$ meshes. To be practical, a routing algorithm is required to ensure very small queue sizes $Q$, and very low running time $T$, not only asymptotically but particularly also for the practically important $n$ up to $1000$. With a technique inspired by a scheme of Kaklamanis/Krizanc/Rao, we obtain a near-optimal result: $T = 2 \cdot n + {\cal O}(1)$ with $Q = 2$. Although $Q$ is very attractive now, the lower order terms in $T$ make this algorithm highly impractical. Therefore we present simple schemes which are asymptotically slower, but have $T$ around $3 \cdot n$ for {\em all} $n$ and $Q$ between 2 and 8

Duale Genetiken als Legehennen für die ökologische Legehennenhaltung

Debates on culling day-old male egg type chicks are constantly growing. The current study investigated the performance of two dual purpose breeds in a mobile production system under organic conditions. 509 Lohmann Dual (LD) and 505 Lohmann Dualexperimental (LDex) day old chicks were reared in two mobile stable barns as hatched. The cockerels were slaughtered on day 70, 80 and 85, the hens remained in their respective mobile barn for a prolonged laying period. Average bodyweight of cockerels at d 85 was 2650 g in LD and 2176 g in LDex. In 68 weeks of production, an average LD hen produced 289 eggs whereas it was 307 eggs in LDex. The performance of the dual purpose breeds is not comparable with those of specialized hybrids however it may still be sufficient if the products realize higher prices at the market

CEREBROVASCULAR CARBON DIOXIDE REACTIVITY DURING EXPOSURE TO EQUIPOTENT ISOFLURANE AND ISOFLURANE IN NITROUS OXIDE ANAESTHESIA

We have studied the effects of hypocapnia on cerebrovascular changes in two MAC-equivalent anaesthetic regimens, using the transcranial Doppler technique as an index of cerebral blood flow (CBF) in 24healthy ASA I patients undergoing spinal surgery. Eight of the patients were subjected to carbon dioxide reactivity challenges in the awake state. Before surgery, the other 16 patients received, in random order, either 1.15% isoflurane in oxygen or 0.5% isoflurane with 70% nitrous oxide. Carbon dioxide reactivity was calculated for each group as the increase in flow velocity per kPa change in PÉCO2 (cm s−1 kPa−1). It was significantly greater for the isoflurane group (14.09 (SD 2.44) cm s−1 kPa−1) and significantly less for the isoflurane—nitrous oxide group (7.95 (1.32) cm s-−1 kPa−1) compared with the awake group (11.24 (0.95) cm s−1 kPa−1). We conclude that cerebrovascular responsiveness to changes in arterial carbon dioxide concentration is influenced markedly by the anaesthetic procedure. Hyperventilation is more likely to affect CBF during isoflurane anaesthesia than during an MAC-equivalent isoflurane—nitrous oxide anaesthesi