122312791
STOCHASTIC FORCING OF OCEANIC MOTIONS
Most oceanic motions are forced by stresses and heat and fresh water fluxes at the air-sea interface. When these forcing fields are assumed to be prescribed and stochastic and when the oceanic response is assumed to be linear then the forcing problem reduces to a set of stochastically forced linear oscillators. This set can in principle be decoupled. The asymptotic response of a linear oscillator to stationary random forcing is well understood and depends on whether the oscillator is stable, unstable or neutral. The explicit decoupling requires additional simplifying assumptions as exemplified by the stochastic forcing of surface gravity waves, internal gravity waves, Rossby waves and sea-surface temperature anomalies A powerful diagnostic tool is a coherence map which desribes the coherence between the oceanic response at one location and the atmospheric forcing at another location as a function of separation for different frequancies. A simple model of the stochastic forcing of barotropic Rossby waves by fluctuations in the atmospheric windstress reproduces basic features of observed coherence maps. The model expecially accounts for the qualitative changes that occur when different oceanic variables are considered or when the frequency is changed.
118540313
On the diffusion of momentum and mass by internal gravity waves
123589108
On simple semiabelian p-adic lie algebras
120429370
Reducibility behavior of polynomials with varying coefficients
AbstractLetK be a number field, and leth∈K[Y] be a polynomial of degreen. Fix an integer 0≤i≤n and compare the set ν of those integersa ofK such thath(Y)−aYihas a root inK with the set
$$\mathcal{R}$$
 of those integersa, such thath(Y)−aYiis reducible overK. Ifi is coprime ton, then we classify the rare cases where ν is not cofinite in
$$\mathcal{R}$$
. The main tools are a theorem of Siegel about integral points on algebraic curves and the theory of finite groups.
121536074
Sharply transitive linear algebraic groups
We study Zariski-closed linear groupsG ≤ GLn(k) over fieldsk of characteristic 0 which act sharply transitively on the non-zero vectors ofkn. For square-freen, orn⩽15, or ifk has cohomological dimension ⩽1 we obtain a complete classification (i.e. a reduction to questions about associative division algebras). The main tools are representation theory of Lie algebras over algebraically closed and non-closed fields, and results about simple associative algebras in order to control the interplay between linear Lie algebras and the associative algebras generated by them. The relation to nearfields and left-symmetric division algebras is also discussed.