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The unique continuation property of -harmonic functions on the Heisenberg group
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10.1017/S000497271800101
Periods of Ducci sequences and odd solutions to a Pellian equation
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10.1017/S000497271900021
Amenable semigroups of nonlinear operators in uniformly complex Banach spaces
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10.1017/S000497271800107
On generators and disturbances of dynamical systems in the context of chaotic points
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10.1017/S000497271800145
Dichotomy property for maximal operators in a nondoubling setting
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10.1017/S000497271800120
Geometric and fixed point properties in products of normed spaces
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10.1017/S000497271800114
Numerical solution of nonlinear elliptic systems by block monotone iterations
Get PDFWe present numerical methods for solving a coupled system of nonlinear elliptic problems, where reaction functions are quasimonotone nondecreasing. We utilize block monotone iterative methods based on the Jacobi and Gauss--Seidel methods incorporated with the upper and lower solutions method. A convergence analysis and the theorem on uniqueness of solutions are discussed. Numerical experiments are presented.
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The effects of model climate bias on ENSO variability and ensemble prediction
Get PDFNew methods are presented for determining the role of coupled ocean-atmosphere model climate bias on the strength and variability of the El Nino-Southern Oscillation (ENSO) and on the seasonal ensemble prediction of El Nino and La Nina events. An intermediate complexity model with a global atmosphere coupled to a Pacific basin ocean is executed with parallelised algorithms to produce computationally efficient year-long forecasts of large ensembles of coupled flow fields, beginning every month between 1980 and 1999. Firstly, the model is provided with forcing functions that reproduce the average annual cycle of climatology of the atmosphere and ocean based on reanalysed observations. We also configure the model to generate realistic ENSO fluctuations. Next, an ensemble prediction scheme is employed which produces perturbations that amplify rapidly over a month. These perturbations are added to the analyses and give the initial conditions for the ensemble forecasts. The skill of the forecasts is presented and the dependency on the annual and ENSO cycles determined. Secondly, we replace the forcing functions in our model with functions that reproduce the averaged annual cycles of climatology of two state of the art, comprehensive Coupled General Circulation Models. The changes in skill of subsequent ensemble forecasts elucidate the roles of model bias in error growth and potential predictability.
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