Synthesis of time-optimal control of a second-order nonlinear process

The time-optimal control of a soft spring is discussed. The domain of controllability and the switching locus are described. It is shown that the switching locus changes in a discontinuous manner as the nonlinearity varies continuously.This research was partially supported by the Joint Services Electronics Program, Grant No. (4711) N00014-67-A-0226 ARPA 1129, and by NASA, Grant No. NGR 15-005-021.     

Mikrochemie

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Die Mikrogaskammermethode und die Mikrosublimation als Hilfsmittel bei der Bewertung von pflanzlichen Warenproben

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The reals as full and balanced biframe

This paper is the first part of a two-part investigation. It introduces full and balanced biframes which capture useful properties of the reals viewed as a biframe (or bitopological space). The subsequent paper will apply these concepts to the study of completions of quasi-nearness biframes.We start with the smallest dense quotient for biframes. Next we discuss the reals as a biframe and introduce the key ideas of balanced, full and stable biframes. The crucial tool here is the frame pseudocomplement. We include a discussion of the relations between the newly introduced ideas and regularity. Order topology biframes are all regular, normal and balanced but not necessarily full. We consider the plane and various examples related to zero-dimensionality. We provide methods of transferring fullness and balancedness from domain to codomain and conversely under various kinds of maps.Of particular importance to our later study of completions is the idea of a biframe map whose right adjoint preserves the first and second parts of the biframe. We give a result providing sufficient conditions for a map to have a part-preserving right adjoint. We present an example of a dense onto map (which is in fact a compactification) between normal, regular biframes whose right adjoint is not part-preserving. The paper concludes with internal properties of full and balanced biframes showing the particularly close connection between the first and second parts and ends with a final visit to the biframe of reals.     

Faber-Theorie für Riemannsche Flächen

Ohne ZusammenfassungHerrnHermann Schmidt zum 60. Geburtstag     

Zur Biosynthese pflanzlicher Stilbene, 4. Mitt.: Die Bildung von Ring A des Oxyresveratrols

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