Local stability implies global stability for the 2-dimensional Ricker map

Consider the difference equation $x_{k+1}=x_k e^{\alpha-x_{n-d}}$ where $\alpha$ is a positive parameter and d is a non-negative integer. The case d = 0 was introduced by W.E. Ricker in 1954. For the delayed version d >= 1 of the equation S. Levin and R. May conjectured in 1976 that local stability of the nontrivial equilibrium implies its global stability. Based on rigorous, computer aided calculations and analytical tools, we prove the conjecture for d = 1.Comment: for associated C++ program, mathematica worksheet and output, see http://www.math.u-szeged.hu/~krisztin/ricke

HEIGHT REFERENCE OF TERRAIN RELIEFS

The accuracy and resolution of real topographic heights in the terrain reliefs has a special importance in meteorology, hydrology and other Earth’s disciplines dealing with dynamical processes on regional scale. The accuracy of topographic height referencing of a region composed from several areas with independent national geodetic networks depends on the homogeneity of the applied measuring processes and geodetic datum on these areas.                  The territories falling out of homogeneity can be revealed by comparing their leveled height data to topographic heights produced from GPS measurements. The difference indicate either local gravity anomalies or height datum problem.  Two territories were selected (one in Hungary and one in Greece) to demonstrate this method what revealed a height datum problem on the Greek area.

Invasion impact is conditioned by initial vegetation states

Abstract Biological invasion is a crucial problem in the world because of its negative consequences for protected areas. The degradation stage of vegetation might affect the success of invasion. One of the most abundant and threatening invasive species is the common milkweed (Asclepias syriaca L.) which has invaded already 23 countries of Europe and in several habitat types its further spreading is promoted by climate change. Pannonian sand grassland is one of the most threatened habitat by common milkweed invasion. Therefore, invasion in sand grassland vegetation is an important issue. However, the effects of the invasive plant in the open sand grassland are rather controversial. In order to clarify the existing contradictory results, the study was carried out in a strictly protected area, near Fülöpháza (Hungary) in a reserve core area in a UNESCO biosphere reserve. Microcoenological study was applied to determinate the fine-scale community characteristics of non-invaded and invaded stands in natural and seminatural vegetation and data were processed by Juhász-Nagy's information theory models. Shannon diversity of species combinations (compositional diversity) which describes the ways of the coexistence of species, and the number of realized species combinations were used for measuring beta diversity. Differences between stands were analyzed by two-way ANOVA. The maximum compositional diversity of species and main life-forms (annuals, perennials and cryptogams) did not differ significantly between the non-invaded and invaded stands. In contrast, significantly larger characteristic areas of compositional diversity were detected in the invaded stands. Based on these results, it could be concluded that diversity of species combinations did not change but those values have shifted to coarser scales in case of invaded stands. The direction of this change suggests a kind of impoverishment in the presence of Asclepias. Thus, it is worth mentioning from the invasion management point of view that protection of the habitats against disturbance is a more cost-effective and successful way than protection against the establishment or extirpation of invasive species, since disturbance facilitates the invasions throughout the impoverishment of the community

Time evolution in the Morse potential using supersymmetry: dissociation of the NO molecule

We present an algebraic method for treating molecular vibrations in the Morse potential perturbed by an external laser field. By the help of a complete and normalizable basis we transform the Schr\"{o}dinger equation into a system of coupled ordinary differential equations. We apply our method to calculate the dissociation probability of the NO molecule excited by chirped laser pulses. The dependence of the molecular dipole-moment on the interatomic separation is determined by a quantum-chemical method, and the corresponding transition dipole moments are given by approximate analytic expressions. These turn out to be very small between neighboring stationary states around the vibrational quantum number $m=42$, therefore we propose to use additional pulses in order to skip this trapping state, and to obtain a reasonable dissociation probability.Comment: 4 pages, 3 figure