In this paper, the optimal filtering problem for polynomial system states over polynomial observations is studied proceeding from the general expression for the stochastic Ito differentials of the optimal estimate and the error variance. In contrast to the previously obtained results, the paper deals with the general case of nonlinear polynomial states and observations. As a result, the Ito dif...

The major aim of this article is modeling of nonlinear systems with friction structure that, thismethod is essentially extended based on taylore expansion polynomial. So in this study, thetaylore expansion was extended in the generalized form for the differential equations of the statespaceform. The proposed structure is based on multi independent variables taylore extended.According to the pro...

Abstract Kumar et al. (2006) obtained a fifth order polynomial in ω for the dispersion relation and pointed out that the calculations preformed by Porter et al. (1994) and by Dwivedi & Pandey (2003) seem to be in error, as they obtained a sixth order polynomial. The energy equation of Dwivedi & Pandey (2003) was dimensionally wrong. Dwivedi & Pandey (2006) corrected the energy equation and stil...

We describe an algorithm for deciding whether or not a real polynomial is positive semideenite. The question is reduced to deciding whether or not a certain zero-dimensional system of polynomial equations has a real root.