This article is the continued version of the analytical solutions for the pressureless Navier-Stokes equations with density-dependent viscosity [9]. We are able to extend the similar solutions structure to the case with pressure under some restriction to the constants γ and θ.

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Abstract. We study some particular solutions to the Navier-Stokes-Poisson equations with density-dependent viscosity and with pressure, in radial symmetry. With an extension of the previous known blow-up solutions for the EulerPoisson equations with pressureless Navier-Stokes-Poisson density-dependent viscosity, we constructed the corresponding self-similar blow-up solutions for the Navier-Stokes-Poisson equations with density-dependent viscosity and with pressure. Our solutions can provide concrete examples for testing the validation and stabilities of numerical methods for the systems.

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This paper is to apply Rough Set to data mining of time series. Firstly, we process the time series data by attribute selection and similarity sequence search. Secondly, the time series is partitioned into some sets of pattern by Mobile Window Method (MWM) and each pattern is a trend of time series. Thirdly, an information table is made by predicting attributes and targeting attribute in trending variation ratio structure sequence (TVRSS). Then, the original information table is made suitably for rough set to discover knowledge. Finally, the extracting rules can predict the time series behavior in the future. The total process is four steps. In the end, we show some examples to demonstrate our method on the time series data of stock market.