Albert Einstein's Weekend Home; Caputh, near Berlin Architecture; Residences; Exterior

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Deck; Albert Einstein's Weekend Home; Caputh, near Berlin Architecture; Residences; Exterior

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Study; Albert Einstein's Weekend Home; Caputh, near Berlin Architecture; Residences; Interior

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Staircase; Albert Einstein's Weekend Home; Caputh, near Berlin Architecture; Residences; Interior

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Albert Einstein's Weekend Home; Caputh, near Berlin Architecture; Residences; Exterior

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Deck; Albert Einstein's Weekend Home; Caputh, near Berlin Architecture; Residences; Exterior

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View from Deck; Albert Einstein's Weekend Home; Caputh, near Berlin Architecture; Residences; Exterior

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Elsa Einstein with unidentified woman sitting on the porch of Albert Einstein's Weekend Home; Caputh, near Berlin Architecture; Residences; Exterior

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Albert Einstein Portraits; Men

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Studio portraits of Henry H. Goldschmidt Gould and his sister Ruth Augusta Beatrice Goldschmidt Portraits Children

Some signed by photographer Jacobi

Albert Einstein in his study; Haberlandstrasse 5, Berlin Portraits Men

Signed Jacobi

Margarete Oppenheimer geb. Busch : 29. Mai 1883 - 8. August 1935.

Memorial book with the speeches by Leo Baeck and Hugo Jacobi.

The Wieruszowski ancestry : from the mid 1700’s to the late 1900’s /

Family trees of the descendants of the Wieruszowski and of the Apt families from the mid 1700’s to the late 1900’s, from family sources and from other places.

The averaging principle and the diagram technique

Rae and Davidson have found a striking connection between the averaging method generalised by Kruskal and the diagram technique used by the Brussels school in statistical mechanics. They have considered conservative systems whose evolution is governed by the Liouville equation. In this paper we have considered a class of dissipative systems whose evolution is governed not by the Liouville equation but by the last-multiplier equation of Jacobi whose Fourier transform has been shown to be the Hopf equation. The application of the diagram technique to the interaction representation of the Jacobi equation reveals the presence of two kinds of interactions, namely the transition from one mode to another and the persistence of a mode. The first kind occurs in the treatment of conservative systems while the latter type is unique to dissipative fields and is precisely the one that determines the asymptotic Jacobi equation. The dynamical equations of motion equivalent to this limiting Jacobi equation have been shown to be the same as averaged equations.

Continuous-time Single Network Adaptive Critic for Regulator Design of Nonlinear Control Affine Systems

An optimal control law for a general nonlinear system can be obtained by solving Hamilton-Jacobi-Bellman equation. However, it is difficult to obtain an analytical solution of this equation even for a moderately complex system. In this paper, we propose a continuoustime single network adaptive critic scheme for nonlinear control affine systems where the optimal cost-to-go function is approximated using a parametric positive semi-definite function. Unlike earlier approaches, a continuous-time weight update law is derived from the HJB equation. The stability of the system is analysed during the evolution of weights using Lyapunov theory. The effectiveness of the scheme is demonstrated through simulation examples.