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This paper discusses the well known Lorenz system under the in-uence of white noise. We prove the existence of a unique solution, a stationary distribution and a random attractor. Furthermore, the random attractor contains for particular parameters only one point. Numerical experiments illustrate the results.
Suppose we are able to write the matrix A as a product of two matrices, L · U = A (2.3.1) where L is lower triangular (has elements only on the diagonal and below) and U is upper triangular (has elements only on the diagonal and above). For the case of a 4 × 4 matrix A, for example, equation (2.3.
We prove the existence of random attractors for nonlinear sto-chastic hyperbolic diierential equations. The nonlinearity of this equation has similar properties as the nonlinearity of the Sine Gordon equation. We consider a diiusion term depending on the state variable. To prove the existence of a random attractor we transform the stochastic hyperbolic… (More)
PURPOSE The values in a PET image which represent activity concentrations of a radioactive tracer are influenced by a large number of parameters including patient conditions as well as image acquisition and reconstruction. This work investigates noise characteristics in PET images for various image acquisition and image reconstruction parameters. METHODS… (More)
We evaluated the usefulness of a recently described procedure to assess the analytical performance of an assay. To demonstrate the advantages of this approach, we compared the performance of two analytical systems for determining prostate-specific antigen (PSA). Triplicate measurements of PSA with the IMx (Abbott) and the ACS 180 (Ciba Corning) were used to… (More)