The effective equation method

In this chapter we present a general method of constructing the effective equation which describes the behaviour of small-amplitude solutions for a nonlinear PDE in finite volume, provided that the linear part of the equation is a hamiltonian system with a pure imaginary discrete spectrum. The effective equation is obtained by retaining only the resonant terms of the nonlinearity (which may be hamiltonian, or may be not); the assertion that it describes the limiting behaviour of small-amplitude solutions is a rigorous mathematical theorem. In particular, the method applies to the three-- and four--wave systems. We demonstrate that different possible types of energy transport are covered by this method, depending on whether the set of resonances splits into finite clusters (this happens, e.g. in case of the Charney-Hasegawa-Mima equation), or is connected (this happens, e.g. in the case of the NLS equation if the space-dimension is at least two). For equations of the first type the energy transition to high frequencies does not hold, while for equations of the second type it may take place. In the case of the NLS equation we use next some heuristic approximation from the arsenal of wave turbulence to show that under the iterated limit "the volume goes to infinity", taken after the limit "the amplitude of oscillations goes to zero", the energy spectrum of solutions for the effective equation is described by a Zakharov-type kinetic equation. Evoking the Zakharov ansatz we show that stationary in time and homogeneous in space solutions for the latter equation have a power law form. Our method applies to various weakly nonlinear wave systems, appearing in plasma, meteorology and oceanology

Tuberous Sclerosis: a Review of Literature and Own Clinical Observation

This article provides information on the origins, prevalence and clinical manifestations of tuberous sclerosis in children. The own clinical observation of a child with severe clinical course of this disease, caused by the early onset of neurological symptoms, multiple rhabdomyomas and skin manifestations

A systematic survey of floral nectaries

The construction of classifications, as well as the understanding of biological diversity, depends upon a careful comparison of attributes of the organisms studied (Stuessy, 1990). It is widely known that data from diverse sources showing differences from taxon to taxon are of systematic significance. Dur-ing the 20th century, systematists have emphasized that their discipline involves a synthesis of all knowledge (Stevens, 1994) or, in other words, the variation of as many relevant characters as possible should be incorporated into the natural system to be constructed. The extent to which particular characters are constant or labile will determine their usefulness to syste-matics. In general, more conservative characters will be valuable in defining families and orders, whereas more labile characters may be useful at the ge-neric and specific levels (Webb, 1984). There is no doubt that floral characters are among the most used in the classification of flowering plants. At the same time, they constitute essential features in diagnostic keys to taxa in both taxonomic treatments and Floras (Cronquist, 1981, 1988).Fil: Bernardello, Gabriel Luis Mario. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto Multidisciplinario de Biología Vegetal. Universidad Nacional de Córdoba. Facultad de Ciencias Exactas Físicas y Naturales. Instituto Multidisciplinario de Biología Vegetal; Argentin