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The application of cumulants to flow routing

Romanowicz Renata J., Doroszkiewicz Joanna

Meteorology Hydrology and Water Management. Research and Operational Applications

2019

Vol. 7, Iss. 1

15--21

This paper aims to fill a gap between present and past research approaches to modelling flow in open channels. In particular, a history of the analytical solutions of a linearized St. Venant equation is presented. A solution of the linearized St. Venant equation, describing the response of a river channel to a single impulse forcing, the so called Instantaneous Unit Hydrograph (IUH), can be described using cumulants, defined as the moments of a logarithm of a variable. A comparison of analytical and numerical solutions of flood wave propagation under various flow conditions is given. The river reach of Biała Tarnowska is used as an illustration of both approaches. A practical application of simplified solutions to the emulator of a flood wave propagation is suggested showing a link between theory and practice.

Technique of ultra wideband radar target discrimination using natural frequencies and cumulant preprocessing

Baev A. B., Kuznetsov Y. V.

Kwartalnik Elektroniki i Telekomunikacji

2004

Vol. 50, z. 4

605-616

A modification of ultra wideband aspect independent radar target discrimination method using fourth-order cumulant preprocessing is introduced. It based on the natural frequencies of the objects. The increasing of the accuracy of parameter estimation can be achieved if the correct choice of one-dimensional slice of 3-D fourth-order cumulant sequence is made. The usage of this technique with signature algorithm leads to the increasing of the true discrimination probability if the space of attributes includes the most informative parameters of the objects. The results of experimental research of the signals scattered by the scaled aircraft models by using the signature algorithm with fourth-order cumulant preprocessing are presented.

The generalization of the Kac-Bernstein Theorem

Quine M. P., Seneta E.

Probability and Mathematical Statistics

1999

Vol. 19, Fasc. 2

441--452

The Skitovich-Darmois Theorem of the early 1950's establishes the normality of independent X1, X2,…, Xn from the independence of two linear forms in these random variables. Existing proofs generally rely on the theorems of Marcinkiewicz and Cramér, which are based on analytic function theory. We present a self-contained real-variable proof of the essence of this theorem viewed as a generalization of the case n = 2, which is generally called Bernstein's Theorem, and also adapt an early little known argument of Kac to provide a direct simple proof when n = 2. A large bibliography is provided.