Pseudo-Riemannian metrics on closed surfaces whose geodesic flows admit nontrivial integrals quadratic in momenta, and proof of the projective Obata conjecture for two-dimensional pseudo-Riemannian metrics

We describe all pseudo-Riemannian metrics on closed surfaces whose geodesic flows admit nontrivial integrals quadratic in momenta. As an application, we solve the Beltrami problem on closed surfaces, prove the nonexistence of quadratically-superintegrable metrics of nonconstant curvature on closed surfaces, and prove the two-dimensional pseudo-Riemannian version of the projective Obata conjecture.Comment: 33 pages, 7 pictures. This paper replaces arXiv:0911.3521v1 and arXiv:1002.013

There exist no locally symmetric Finsler spaces of positive or negative flag curvature

We show that the results of Foulon (1997 an 2002) and Kim (2007) (independently, Deng and Hou (2007)) about the nonexistence of locally symmetric Finsler metrics of positive or negative flag curvature are in fact local

Closed manifolds admitting metrics with the same geodesics

The goal of this survey is to give a list of resent results about topology of manifolds admitting different metrics with the same geodesics. We emphasize the role of the theory of integrable systems in obtaining these results.Comment: Submitted to Conference Proceedings SPT2004: Symmetry and perturbation theory (Cala Gonone

Comment: Food web interactions and biomanipulation in Australian reservoirs

The authors have been studying the control of phytoplankton biomass in several Australian reservoirs. To manipulate fish communities in order to reduce phytoplankton biomass, one needs a thorough understanding of processes in the plankton-associated food webs. In contrast to the situation found in lakes of the northern hemisphere, the planktivorous fish of Australian reservoirs are relatively small and they may deplete small rather than large zooplankters, so that animals as large as the adults of Daphnia carinata may avoid predation. This would result in promotion of Daphnia, particularly if fish eliminate its smaller competitors. The aim of biomanipulation should be the establishment and maintenance of a proper ratio of planktivores/piscivores, adequate for water quality requirements. Successful selection of the appropriate ratio for a given reservoir will depend on the extent of our understanding of its food web interactions. For practical application of biomanipulation in management, further development of the food web theory under Australian conditions is needed

Competetive exclusion in Cladocera through elevated mortality of adults

The population dynamics of two cladocerans, Ceriodaphnia pulchella and Diaphanosoma brachyurum competing under laboratory conditions in lake water was analysed using crosscorrelations. Both mixed and isolated populations of the two cladocerans showed delayed density dependence in the death rates of juveniles and adults as well as in fecundity rate. The regressions for each of the three rates on total density of competitors were compared between the two species. There were no significant differences in the slopes of regressions for fecundity rates and the death rates of juveniles. However, in the inferior competitor (Diaphanosoma) which went extinct in all treatments, the death rate of adults increased with total density much more quickly than in the superior competitor (Ceriodaphnia). The intraspecific comparisons indicated that while Ceriodaphnia adults survived better than juveniles under conditions of crowding, in Diaphanosoma, juveniles were better survivors than adults. These data suggest that the contention of higher vulnerability of cladoceran juveniles than adults to starvation and crowding may prove to be not a universal phenomenon