Combination of pseudopotentials and density functionals

Semilocal pseudopotentials have been determined for first–row (Li to Ne), second row (Na to Ar), and third-row atoms (K, Ca). Core–valence correlation is included by adjusting the pseudopotentials to experimental energies of ions with a single valence electron. Correlation within the valence shell is taken into account by using the spin–density functional formalism. The approximations involved in this approach are tested for atomic ionization energies as well as binding energies of monohydrides and alkali diatomics, agreement with experiment is usually satisfactory, but in certain applications density functionals should be already included in the fitting of the local part of the pseudopotential. In addition, 3s/3p and 3s/2p basis sets (for first and second row, respectively), designed for use in connection with our pseudopotentials, are given; it is shown that they yield reasonable results for both SCF and correlation energies.     

On the Calculation of Stationary Solutions of Multi-Dimensional Fokker–Planck Equations by Orthogonal Functions

In this paper, nonlinear stochastic systems are investigatedvia associated Fokker–Planck equations. Their stationary solutions arecalculated by expansions into orthogonal functions, e.g. especiallyadjusted polynomials and Fourier series. The weighting functions of thenew polynomials are obtained by the application of the stochasticaveraging method. The proposed analysis is demonstrated with severalexamples. The first one is a two-dimensional problem of nonlinearoscillators driven by white noise. The second one describes two-massoscillators with independent coloured noise excitations leading tosix-dimensional probability density functions. The next example ispresenting a system driven by both harmonic and stochastic excitationleading to three-dimensional probability density functions. Finally,oscillators with dry friction characteristics are examined.     

Parameterschätzungen dynamischer systeme nach dem Prinzip der minimalen Anregungsenergie

Übersicht Bekanntlich liefert die Maximum Likelihood (ML) Methode die wirksamsten Algorithmen zur Schätzung von Parametern. Es wird gezeigt, daß die bisher bekannten ML-Schätzer mit dem Prinzip der minimalen Anregungsenergie stochastischer Systeme hergeleitet und damit auf allgemeinere Problemstellungen erweitert werden können.

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Parameter estimations of dynamic systems by means of the principle of minimal excitation energy

Summary The Maximum Likelihood (ML) method gives the most effective algorithms for problems of parameter estimation and system identification. It is shown that the known ML-estimators are derivable by means of the principle of minimal excitation energy in stochastic systems. Therewith, they can be extended to more general estimation problems.