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1994 (2)
1Author    Dirk-A BeckerRequires cookie*
 Title    A Simplified Algorithm for Finding Partially Invariant Solutions of Quasilinear Systems  
 Abstract    The method of partially invariant solutions of PDE systems was introduced by Ovsiannikov as a generalization of the classical similarity analysis. It offers a possibility to calculate exact solutions possessing a higher degree of freedom than similarity solutions. Ovsiannikov's algorithm, however, is somewhat hard to apply because one has to deal with three equation systems derived from the original PDE system. By means of the two-dimensional Euler equations, we show how the algorithm can be essentially simplified if classical similarity solutions are already known. Further, we prove a necessary criterion for the simplified algorithm to be senseful. 
  Reference    Z. Naturforsch. 49a, 458—464 (1994); received October 7 1993 
  Published    1994 
  Keywords    Hydrodynamics, Nonlinear systems, Group theory 
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 TEI-XML for    default:Reihe_A/49/ZNA-1994-49a-0458.pdf 
 Identifier    ZNA-1994-49a-0458 
 Volume    49 
2Author    K.-P Zeyer, G. Dechert, W. H. Ohm, Ann, R. Blittersdorf, F. W. SchneiderRequires cookie*
 Abstract    o u p l e d B i s t a b l e C h e m i c a l S y s t e m s -E x p e r i m e n t a l R e a l i z a t i o n o f B o o l e a n F u n c t i o n s U s i n g a S i m p l e F e e d f o r w a r d N e t We use the BZ-reaction and the M BO-reaction to implement the Boolean functions A N D , OR, N A N D , and N O R by the coupling of three chemical reactors. The experimental setup is analogous to a simple neural feedforward network with two reactors serving as the input layer and one reactor as the output layer. Coupling between the input and output reactors is carried out through the flow rate (BZ-and M BO-reaction) and through the electrical current by the use o f Pt working electrodes (BZ-reaction). The XOR-and X N O R functions may be realized with 5 reactors using com binations o f the A N D , N O R , N O R -and the A N D , NO R, Or-chemical gates, respectively. 
  Reference    Z. Naturforsch. 49a, 953 (1994); received M ay 28 1994 
  Published    1994 
  Keywords    Nonlinear systems, Flow-rate-coupling, functions 
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 TEI-XML for    default:Reihe_A/49/ZNA-1994-49a-0953.pdf 
 Identifier    ZNA-1994-49a-0953 
 Volume    49