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  • 1
    Electronic Resource
    Electronic Resource
    Extraction of Mercaptans from Light Distillate Fuels (1952)
    s.l. : American Chemical Society
    Industrial & engineering chemistry 44 (1952), S. 1486-1489 
    Details
    ISSN: 1520-5045
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1021/ie50510a074
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  • 2
    Electronic Resource
    Electronic Resource
    SL(3,R) as the group of symmetry transformations for all one-dimensional linear systems. III. Equivalent Lagrangian formalisms (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1571-1578 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The SL(3,R) theory of projective transformations of the plane is applied to the Lagrangians of all one-dimensional Newtonian linear systems. Noether and non-Noether equivalent Lagrangians, as well as the associated Noether and non-Noether constants of motion, are thus obtained in a completely general and systematic way. Complete unification is achieved by this group-theoretic approach to Lagrangians of one-dimensional linear systems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529681
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  • 3
    Electronic Resource
    Electronic Resource
    Non-Abelian group quantization and quantum kinematic invariants of some noncompact Lie groups (1991)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 32 (1991), S. 348-355 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The formalism of non-Abelian group quantization is briefly revisited, within the regular representation of noncompact Lie groups. It is shown that some of such r-dimensional groups have a set of r basic quantum-kinematic invariants, which substantially differ from the traditional invariants. The relation of the traditional invariants of the Lie algebra with the new quantum-kinematic invariants is also briefly examined. This paper contains two miscellaneous examples of quantum-kinematic invariant operators.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529420
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  • 4
    Electronic Resource
    Electronic Resource
    Infinitesimal symmetry transformations. II. Some one-dimensional nonlinear systems (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 593-600 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The converse problem of similarity analysis is discussed for the infinitesimal symmetry transformations of ordinary second-order differential equations which are nonlinear in x(overdot) (and may be linear or nonlinear in x). A natural classification of the problem arises, according to the highest order N of nonlinearity in x(overdot). The completely general maximal Lie algebra is obtained for the case N≤3. In the case N≥4 one has, besides the system of differential equations for the infinitesimal generators, an extra set of anholonomic constraints, which operates as a symmetry-breaking mechanism producing a strong reduction in the number of surviving parameters. Miscellaneous examples are given, which illustrate some features of similarity analysis of nonlinear systems. The infinitesimal point transformation symmetries of the Van der Pol oscillator are also briefly discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.526595
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  • 5
    Electronic Resource
    Electronic Resource
    SL(3,R) as the group of symmetry transformations for all one-dimensional linear systems. II. Realizations of the Lie algebra (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 1746-1752 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The two-dimensional space-time realizations of the Lie algebra of SL(3,R) are obtained, when the group acts as the maximal point symmetry group of any given one-dimensional Newtonian linear system. It is shown that these realizations are isomorphic with the realization of the Lie algebra of the projective group in the plane. Next an active point of view is introduced, and SL(3,R) is interpreted as a group of mappings that transform one admissible world line of the system into another. Thus a new mechanical realization of the sl(3,R) algebra comes to the fore. Some miscellaneous examples are included.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.527872
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  • 6
    Electronic Resource
    Electronic Resource
    Pedestrian approach to two-cocycles for unitary ray representations of Lie groups (1987)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 28 (1987), S. 2268-2279 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Necessary and sufficient conditions for unitary ray representations of connected Lie groups are reexamined. Thus a systematic constructive method is obtained for calculating the admissible exponent factors (two-cocycles). The gauge freedom of the unitary ray representation formalism is also considered. This introduces the distinction between trivial and genuine ray representations. A special gauge is then adopted, within which the two-cocycle is almost unique. The only prerequisite of the exponent factor calculus is the knowledge of the binary combination rules for the essential parameters of the group. The attained method affords a simple, general, and explicit (i.e., coordinate-dependent) two-cocycle calculus. The aim of this paper is merely instrumental.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.527760
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  • 7
    Electronic Resource
    Electronic Resource
    SU(2) quantum kinematics: Rotation-observable versus angular-momentum generalized commutation relations (1998)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 5798-5810 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The canonical commutation relations of quantum mechanics are generalized to the case where appropriate dynamical variables are angular-momentum, rotation-angle, and rotation-axis observables. To this end, SU(2) is "quantized" on the compact group manifold, according to the standard procedure of non-Abelian quantum kinematics. Quantum-kinematic invariant operators are introduced, and their commutation relations with the rotation variables are found in an explicit manner. The quantum-kinematic invariants yield superselection rules in the form of eigenvalue equations of an isotopic structure (which one should solve in the applications, in order to get multiplets that carry the irreducible representations of the underlying quantum kinematic models). A wide range of applicability of SU(2) quantum kinematics is suggested. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.532594
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  • 8
    Electronic Resource
    Electronic Resource
    SL(3,R) as the group of symmetry transformations for all one-dimensional linear systems (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 9-15 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The converse problem of similarity analysis is solved in general for the finite symmetry transformations of any inhomogeneous ordinary linear differential equation of the second order x¨+f2(t)x(overdot)+f1(t)x =f0(t). The eight-parameter realizations of the symmetry group are obtained in the form F−1P2 F, where F stands for transformations of (t,x) that depend exclusively on the fundamental solutions of the equation, and where P2 is an arbitrary projective transformation in the plane. Thus it is shown that the full point symmetry group corresponds to SL(3,R) indeed, without recourse to the Lie algebra. Also, a technique is obtained for calculating the finite point symmetry realization of SL(3,R) for any given one-dimensional linear system. Some miscellaneous examples are given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528139
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  • 9
    Electronic Resource
    Electronic Resource
    On the complete symmetry group of the classical Kepler system (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 5734-5748 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A rather strong concept of symmetry is introduced in classical mechanics, in the sense that some mechanical systems can be completely characterized by the symmetry laws they obey. Accordingly, a "complete symmetry group'' realization in mechanics must be endowed with the following two features: (1) the group acts freely and transitively on the manifold of all allowed motions of the system; (2) the given equations of motion are the only ordinary differential equations that remain invariant under the specified action of the group. This program is applied successfully to the classical Kepler problem, since the complete symmetry group for this particular system is here obtained. The importance of this result for the quantum kinematic theory of the Kepler system is emphasized.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530708
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  • 10
    Electronic Resource
    Electronic Resource
    Ion-molecule reactions in silane-tetrafluoromethane mixtures (1977)
    s.l. : American Chemical Society
    The @journal of physical chemistry 〈Washington, DC〉 81 (1977), S. 281-286 
    Details
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1021/j100519a001
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