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  • 1975-1979  (15)
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Year
  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Letters in mathematical physics 1 (1975), S. 23-29 
    ISSN: 1573-0530
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract Given a Banach representation of a Hilbert Lie group, the Lie algebra $$\mathfrak{G}$$ of which is the closure of the union of an increasing sequence of finite dimensional subalgebras, we construct a Gårding domain on which we differentiate the group representation to a representation of a dense subalgebra of $$\mathfrak{G}$$ .
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Letters in mathematical physics 1 (1975), S. 83-91 
    ISSN: 1573-0530
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract Given a continous representation of a Lie group in a Banach space we study its 1-cohomology. We prove that the computation of the 1-cocycles can be reduced to that of the 1-cocycles of the differential of the representation. When the group is semi-simple and the representation is K-finite, we prove that the cohomology is equivalent to the cohomology of the Lie algebra representation on K-finite vectors. We prove, using Casimir operators, that there exist only a finite number of irreducible representation of a semi-simple Lie group with a non-trivial cohomology. Exemples of such representations are given.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Letters in mathematical physics 3 (1979), S. 279-283 
    ISSN: 1573-0530
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract It is proved, in the framework of a recent theory of non-linear group representations elaborated by the authors, that the non-linear Yang-Mills equations are formally linearizable: there exists a formal non-linear operator which intertwins the non-linear Yang-Mills equations with their free (linear) part.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Letters in mathematical physics 2 (1977), S. 155-160 
    ISSN: 1573-0530
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract A discussion about the connection between non-linear wave equations covariant under the action of a Lie group on one hand, and the theory of non-linear representations of the covariance group developed elsewhere [1] on the other hand, is presented here. Applications to a class of relativistic non-linear wave-equations are then suggested.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Letters in mathematical physics 2 (1978), S. 499-504 
    ISSN: 1573-0530
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We classify the analytic actions, having a fixed point, of the classical inhomogeneous groups, such that the linear part of this action restricted to a Levi factor is the natural action defining this Levi factor as a classical simple group.
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  • 6
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    Organic Magnetic Resonance 7 (1975), S. 334-338 
    ISSN: 0030-4921
    Keywords: Chemistry ; Analytical Chemistry and Spectroscopy
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Description / Table of Contents: Phosphorus chemical shifts have been evaluated by means of the perturbation theory using CNDO/S wave functions in phosphine, phosphite, phosphonate and phosphate derivatives. The necessity of introducing 3d orbitals of phosphorus and of using Zeff3d as an adjustable parameter for each family of compounds is shown. Calculated values agree with experimental ones.
    Notes: La méthode des perturbations est appliquée aux fonctions d'onde CNDO/S pour calculer les déplacements chimiques du phosphore de quelques phosphines, phosphites, phosphonates et phosphates. Nous montrons la nécessité d'introduire les orbitales 3d du phosphore et de considérer Zeff3d comme un paramètre à déterminer pour chaque famille de composés. Les valeurs calculées sont alors en bon accord avecl' expérience.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
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  • 7
    ISSN: 0018-019X
    Keywords: Chemistry ; Organic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The cylindrical macrotricyclic ligands 1-3 yield inclusion complexes, [3]-cryptates, with various metal cations. NMR. studies indicate the successive formation of a mononuclear and a binuclear complex. The former is probably unsymmetrical undergoing fast intramolecular cation exchange; the latter is symmetrical, with a cation located on each macrocyclic subunit of the macrotricyclic system. A heteronuclear (Ag2+, Pb2+) complex has been observed. The stability constants of the mononuclear and binuclear alkali and alkaline-earth cation complexes of ligands 1-3 have been determined by potentiometric methods. The stabilities are comparable to those of the complexes of the isolated macrocyclic subunit 5b. The binuclear complexes are almost as stable as the mononuclear one even in highly charged species like for instance the complex of ligand 2 with two barium cations. Cylindrical macrotricyclic ligands are topologically well suited for the designed positioning of two metal cations in a binuclear inclusion complex.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
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  • 8
    ISSN: 0018-019X
    Keywords: Chemistry ; Organic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The optically active macrotricyclic cryptands 1 and 2, containing the binaphthyl group as chiral unit, have been synthesized. These compounds contain lateral cavities which may serve as anchoring sites for polar groups of the substrates and a central, chiral cavity large enough for including more or les completely the bulk of a molecular ion. Their complexation properties towards molecular ions give evidence for the occurrence of two types of processes: (a) direct complexation of primary ammonium cations, like phenylethyl ammonium chloride, occurs with either 1 or 2; (b) cascade binding, involving first complexation of an alkali cation followed by pairing with a molecular anion, takes place with 2. Process (b) may be considered as a metallo-receptor model system where binding of an anionic substrate is dependent on initial binding of a cation. In both cases (a) and (b) weak resolution of chiral racemic substrates has been observed by extraction and transport (through a bulk liquid membrane) experiments. This indicates that in the complex the bulk of the substrate should be located close to the chiral unit and therefore more or less in the central cavity. In the case of cryptand 2, the resolution achieved for the (±)-mandelate anion is markedly affected by the nature of the complexed cation.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
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  • 9
    Publication Date: 1975-12-01
    Print ISSN: 0377-9017
    Electronic ISSN: 1573-0530
    Topics: Mathematics , Physics
    Published by Springer
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  • 10
    Publication Date: 1979-07-01
    Print ISSN: 0377-9017
    Electronic ISSN: 1573-0530
    Topics: Mathematics , Physics
    Published by Springer
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