We consider the half-linear second order differential equation which is viewed as a perturbation of the so-called Riemann-Weber half-linear differential equation. We present a comparison theorem with respect to the power of the half-linearity in the equation under consideration. Our research is motivated by the recent results published by J. Sugie, N. Yamaoka, Acta Math. Hungar. 111 (2006), 165–179.
The so-called “invariance under twisting” for twisted tensor products of algebras is a result stating that, if we start with a twisted tensor product, under certain circumstances we can “deform” the twisting map and we obtain a new twisted tensor product, isomorphic to the given one. It was proved before that a number of independent and previously unrelated results from Hopf algebra theory are particular cases of this theorem. In this article we show that some more results from literature are particular cases of invariance under twisting, for instance a result of Beattie-Chen-Zhang that implies the Blattner-Montgomery duality theorem.
Presented study is aimed at using additional information to improve process represen-tativity of hydrological modelling. The study region is the Haute-Mentue catchment lo-cated in the western part of Switzerland, 20 km north of Lausanne. Previous research in this catchment allowed improving of the understanding of the runoff generation by combining point soil moisture measurements (TDR) and integrating measurements both at the hillslope scale (dye tracing) and at the catchment scale (environmental tracing). In this work, environmental tracing information will be integrated into a semi-distributed hydrological model, which is a modified version of TOPMODEL taking into account a rapid stormflow generation above a less permeable soil horizon. Additional information has been incorporated by using a version of simulated annealing adapted for multi-criteria optimisation. and Štúdia je venovaná využitiu dodatkových informácií pri reálnejšej simulácii hydrologických procesov v zrážkovo-odtokovom modeli. Študovanou oblasťou je povodie Haute-Mentue, ležiace v západnej časti Švajčiarska, 20 km od Lausanne. Predchádzajúci výskum v tomto povodí, založený na kombinácii bodových meraní (TDR) a integrovaných meraní v mierke svahu (farbiace skúšky) a povodia (prirodzené stopovače), zlepšil vedomosti o tvorbe odtoku. V tejto štúdii sú informácie získané prirodzenými stopovačmi použité pri posudzovaní výsledkov simulácie odtoku pomocou semidistribuovaného hydrologického modelu (modifikovaná verzia modelu TOPMODEL, ktorá uvažuje s mechanizmom tvorby odtoku nasýtením nad vrstvou pôdy s nižšou priepustnosťou). Ďalšou dodatkovou informáciou boli výsledky automatickej optimalizácie parametrov modelu pmocou metódy vychádzajúcej z analógie medzi optimalizáciou parametrov modelu a rozdelením častíc v tuhnúcej kvapaline (tzv. simulated annealing), adaptovanej na optimalizáciu podľa viacerých kritérií.