Let (M, g 0) be a closed Riemann surface (M, g 0) of genus γ(M) > 1 and let f 0 be a smooth, non-constant function with max p∈M f 0 (p) = 0, all of whose maximum points are non-degenerate. As shown in [11] for sufficiently small λ > 0 there exist at least two distinct conformal metrics g λ = e 2u λ g 0 , g λ = e 2u λ g 0 of Gauss curvature Kg λ = K g λ = f 0 + λ, where u λ is a relative minimizer of the associated variational integral and where u λ = u λ is a further critical point not of minimum type. Here, by means of a more refined mountain-pass technique we obtain additional estimates for the "large" solutions u λ that allow to characterize their "bubbling behavior" as λ ↓ 0.

The behaviour of adult winter moths Operophtera brumata (L.) (Lep., Geometridae) was investigated during the period of recolonization of fruit orchards in late autumn. Experiments were run simultaneously on both apple and cherry trees in order to detect differences and similarities on these two host plants. The study aimed at a better understanding of spatial and temporal aspects of recolonization of host plants and hence an improvement of monitoring methods.1. Male flight and female migration coincide well enough to guarantee reproductive success. Recolonization of apple and cherry trees occurs simultaneously, but is delayed with decreasing altitude. 2. Male flight activity starts at sunset and reaches its maximum 2 h later. During the night activity decreases gradually to a minimum at sunrise. 3. Females approach tree trunks covering more than 3" of the horizon. The dark part of the horizon appears to be the preferred crawling direction. The travelling time ranges from 1-10 days. 4. Within the tree crown the crawling paths of females are different on cherry and on apple. However, females preferably seek the top segment for oviposition on both cherry and apple trees. 5. On both cherry and apple significantly higher egg densities are found in the top part of the tree crown than in the lower parts. Older wood appears to be more attractive for oviposition probably due to better hiding places. Females seem to optimize between protection and access to food resources for their progeny.The implications of the results for winter moth monitoring in Swiss fruit orchards are discussed.

We show uniqueness of classical solutions of the normalised two-dimensional HamiltonRicci flow on closed, smooth manifolds for smooth data among solutions satisfying (essentially) only a uniform bound for the Liouville energy and a natural space-time L 2 -bound for the time derivative of the solution. The result is surprising when compared with results for the harmonic map heat flow, where non-uniqueness through reverse bubbling may occur.

Relations between root water uptake and soil moisture tension. The root water uptake Q expressed as sink term of the continuity equation was computed using exclusivly field measured data of a post‐irrigation water transport study. The experiment was carried out in an undisturbed Loess soil monolith. The soil moisture redistribution influenced by the evapotranspiration of the grass cover and the soil moisture characteristics were measured independently using the identical experimental layout. The data show a clear relationship between the root water uptake Q and the soil moisture tension S. Within the tension range of approx. 0–100 mbar the uptake Q decreases drastically with water desaturation. Within the upper part of the rooting zone this decrease is more pronounced and starts at a lower tension.

We model the Lights Out game on general simple graphs in the framework of linear algebra over the field F2. Based upon a version of the Fredholm alternative, we introduce a separating invariant of the game, i.e., an initial state can be transformed into a final state if and only if the invariant of both states agrees. We also investigate certain states with particularly interesting properties. Apart from the classical version of the game, we propose several variants, in particular a version with more than only two states (light on, light off), where the analysis resides on systems of linear equations over the ring Zn. Although it is easy to find a concrete solution of the Lights Out problem, we show that it is NP-hard to find a minimal solution. We also propose electric circuit diagrams to actually realize the Lights Out game.