There are two methods of Automatic Theorem Proving in Geometry: the Gröbner bases method and Wu’s pseudo-remainder method. The idea in the behind both methods is this: some hypotheses and a thesis are given. Instead of working with a geometric drawing of the configuration and reasoning “mathematically”, the hypotheses and the thesis are, respectively, translated into a set of polynomials and (u...

LINKÖPING This report and other reports from the automatic control group in Linkk oping are available by anonymous Abstract. We analyze Glad/Fliess algebraic observability for polynomial control systems from a commutative algebraic/algebro-geometric point of view. Furthermore we show some relations between algebraic observabil-ity and realization theory for polynomial diierential equations. Mos...

We explore the evolution of the probability density function (PDF) for an initially deterministic passive scalar diffusing in the presence of a uni-directional, white-noise Gaussian velocity field. For a spatially Gaussian initial profile, we derive an exact spatiotemporal PDF for the scalar field renormalized by its spatial maximum. We use this problem as a test-bed for validating a numerical ...

Abstract—Novel encoding scheme for algebraic codes, such as codes on algebraic curves, multidimensional cyclic codes, and hyperbolic cascaded Reed–Solomon codes, is proposed with numerical examples. We make use of the 2-dimensional inverse discrete Fourier transform, which generalizes the Mattson–Solomon polynomial for Reed–Solomon codes. We also generalize the workings of the generator polynom...

Mathematical modelling of dynamical processes often yields systems of ordinary differential equations (ODEs) or differential algebraic equations (DAEs). We investigate corresponding boundary value problems. Considering uncertainties in physical parameters of the systems, we introduce random variables. This stochastic model is resolved by the strategy of the polynomial chaos. A non-intrusive app...