Synthesis and reactions of some dihydro and tetrahydro-4H-imidazo[5,4,1-ij]quinoline derivatives

Reaction of phenyl N-(8-quinolinyl)carbamate with sodium borohydride afforded 1,2-dihydro-4H-imidazo-[5,4,1-ij]quinolin-2-one, 2a . The 5,6-double bond of 2a was functionalized by reaction with nitrosyl chloride to give the nitroolefin 4 and by reaction with hypobromous acid to give the trans-bromohydrin 5 . Reaction of 5 with sodium azide led to the rearranged trans-6-azido-5-ol 7 , the structure of which was determined by ¹H nmr studies.     

Relations between subclasses of greedoids

In previous papers many different classes and constructions of greedoids have been defined and studied. This paper documents inclusion relations among all subclasses of greedoids which are known so far. It will be shown that all inclusion relations are proper and that all but one subclasses of interval greedoids are distinct.

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Zusammenfassung In früheren Arbeiten wurden viele verschiedene Klassen und Konstruktionen für Greedoide eingeführt und studiert. In dieser Arbeit werden alle bekannten Inklusionsbeziehungen zwischen Unterklassen von Greedoiden dokumentiert. Es wird gezeigt, daß alle Inklusionsbeziehungen echt und alle Unterklassen mit einer Ausnahme tatsächlich verschieden sind.

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Supported by the joint research project Algorithmic Aspects of Combinatorial Optimization of the Hungarian Academy of Sciences (Magyar Tudományos Akadémia) and the German Research Association (Deutsche Forschungsgemeinschaft, SFB 21). Part of this research was done while the first author was visiting the Department of Combinatorics and Optimization, University of Waterloo.     

Absence of De Giorgi-type theorems for strongly elliptic equations with complex coefficients

One constructs examples of strongly elliptic second-order differential equations in the divergence form with measurable bounded complex coefficients in Rⁿ, n3, whose generalized solutions are not bounded in any neighborhood of the origin.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta, im. V. A. Steklova AN SSSR, Vol. 115, pp. 156–168, 1982.     

Multipliers on Besov spaces

It is proved in this paper that the characteristic function of the half-space is not a multiplier for the pair (B _pq ^1/p , B _p ^1/p ), 1<p<, 1<q . In addition, necessary and sufficient conditions are found for the validity of the inclusion.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 135, pp. 36–50, 1984.     

Uncertainty principle and uncertainty relations

It is generally believed that the uncertainty relation q p1/2, where q and p are standard deviations, is the precise mathematical expression of the uncertainty principle for position and momentum in quantum mechanics. We show that actually it is not possible to derive from this relation two central claims of the uncertainty principle, namely, the impossibility of an arbitrarily sharp specification of both position and momentum (as in the single-slit diffraction experiment), and the impossibility of the determination of the path of a particle in an interference experiment (such as the double-slit experiment).The failure of the uncertainty relation to produce these results is not a question of the interpretation of the formalism; it is a mathematical fact which follows from general considerations about the widths of wave functions.To express the uncertainty principle, one must distinguish two aspects of the spread of a wave function: its extent and its fine structure. We define the overall widthW and the mean peak width w of a general wave function and show that the productW w is bounded from below if is the Fourier transform of . It is shown that this relation expresses the uncertainty principle as it is used in the single- and double-slit experiments.     

Recovery and recrystallization in AISI 321 steel under static conditions

Static softening of AISI 321 steel after cold and hot deformation characterizing the industrial thermomechanical treatment was studied by means of tensile tests and TEM. The deformation temperature, the strain and the grain size were the main parameters determining the final softening. The results can be applied for optimization of the solution annealing.