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  • Articles  (5,510)
  • American Chemical Society  (5,036)
  • American Institute of Physics (AIP)  (474)
  • 1990-1994  (5,510)
  • 1940-1944
  • 1992  (5,510)
  • Process Engineering, Biotechnology, Nutrition Technology  (3,977)
  • Energy, Environment Protection, Nuclear Power Engineering  (1,326)
  • Mathematics  (474)
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  • Articles  (5,510)
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  • 1990-1994  (5,510)
  • 1940-1944
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  • 1
    Electronic Resource
    Electronic Resource
    Comment on "Oxidation-reduction capacities of aquifer solids" (1992)
    s.l. : American Chemical Society
    Environmental science & technology 26 (1992), S. 2537-2538 
    Details
    ISSN: 1520-5851
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology , Energy, Environment Protection, Nuclear Power Engineering
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1021/es00036a031
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  • 2
    Electronic Resource
    Electronic Resource
    ES&T Letters. Hazardous Waste Trade (1992)
    s.l. : American Chemical Society
    Environmental science & technology 26 (1992), S. 2309-2309 
    Details
    ISSN: 1520-5851
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology , Energy, Environment Protection, Nuclear Power Engineering
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1021/es00036a606
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  • 3
    Electronic Resource
    Electronic Resource
    ES&T Letters. Authors Reply to "Hazardous Waste Trade" (1992)
    s.l. : American Chemical Society
    Environmental science & technology 26 (1992), S. 2309-2310 
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    ISSN: 1520-5851
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology , Energy, Environment Protection, Nuclear Power Engineering
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1021/es00036a607
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  • 4
    Electronic Resource
    Electronic Resource
    ES&T Products (1992)
    s.l. : American Chemical Society
    Environmental science & technology 26 (1992), S. 2350-2353 
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    ISSN: 1520-5851
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology , Energy, Environment Protection, Nuclear Power Engineering
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1021/es00036a612
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  • 5
    Electronic Resource
    Electronic Resource
    ES&T Books (1992)
    s.l. : American Chemical Society
    Environmental science & technology 26 (1992), S. 2346-2347 
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    ISSN: 1520-5851
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology , Energy, Environment Protection, Nuclear Power Engineering
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1021/es00036a610
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  • 6
    Electronic Resource
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    ES&T Meetings (1992)
    s.l. : American Chemical Society
    Environmental science & technology 26 (1992), S. 2348-2349 
    Details
    ISSN: 1520-5851
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology , Energy, Environment Protection, Nuclear Power Engineering
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1021/es00036a611
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  • 7
    Electronic Resource
    Electronic Resource
    Reply to comments on "Oxidation-reduction capacities of aquifer solids" (1992)
    s.l. : American Chemical Society
    Environmental science & technology 26 (1992), S. 2538-2539 
    Details
    ISSN: 1520-5851
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology , Energy, Environment Protection, Nuclear Power Engineering
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1021/es00036a032
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  • 8
    Electronic Resource
    Electronic Resource
    ES&T Currents. International Agreements Show Poor Reporting (1992)
    s.l. : American Chemical Society
    Environmental science & technology 26 (1992), S. 2314-2314 
    Details
    ISSN: 1520-5851
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology , Energy, Environment Protection, Nuclear Power Engineering
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1021/es00036a609
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  • 9
    Electronic Resource
    Electronic Resource
    ES&T Books (1992)
    s.l. : American Chemical Society
    Environmental science & technology 26 (1992), S. 249-249 
    Details
    ISSN: 1520-5851
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology , Energy, Environment Protection, Nuclear Power Engineering
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1021/es00026a601
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  • 10
    Electronic Resource
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    Effect of deicing salts on metal and organic matter mobilization in roadside soils (1992)
    s.l. : American Chemical Society
    Environmental science & technology 26 (1992), S. 703-709 
    Details
    ISSN: 1520-5851
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology , Energy, Environment Protection, Nuclear Power Engineering
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1021/es00028a006
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  • 11
    Electronic Resource
    Electronic Resource
    Design and evaluation of a long-term soil gas flux sampler (1992)
    s.l. : American Chemical Society
    Environmental science & technology 26 (1992), S. 709-714 
    Details
    ISSN: 1520-5851
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology , Energy, Environment Protection, Nuclear Power Engineering
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1021/es00028a007
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  • 12
    Electronic Resource
    Electronic Resource
    Chemical contamination and associated fish diseases in San Diego Bay (1992)
    s.l. : American Chemical Society
    Environmental science & technology 26 (1992), S. 725-733 
    Details
    ISSN: 1520-5851
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology , Energy, Environment Protection, Nuclear Power Engineering
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1021/es00028a009
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  • 13
    Electronic Resource
    Electronic Resource
    Comparison of semianalytical methods to analyze complexation with heterogeneous ligands (1992)
    s.l. : American Chemical Society
    Environmental science & technology 26 (1992), S. 763-771 
    Details
    ISSN: 1520-5851
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology , Energy, Environment Protection, Nuclear Power Engineering
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1021/es00028a015
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  • 14
    Electronic Resource
    Electronic Resource
    Natural sorbents in oil spill cleanup (1992)
    s.l. : American Chemical Society
    Environmental science & technology 26 (1992), S. 772-776 
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    ISSN: 1520-5851
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology , Energy, Environment Protection, Nuclear Power Engineering
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1021/es00028a016
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  • 15
    Electronic Resource
    Electronic Resource
    ES&T Currents (1992)
    s.l. : American Chemical Society
    Environmental science & technology 26 (1992), S. 847-849 
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    ISSN: 1520-5851
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology , Energy, Environment Protection, Nuclear Power Engineering
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1021/es00029a613
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  • 16
    Electronic Resource
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    ES&T Letters. Nuclear power plants (1992)
    s.l. : American Chemical Society
    Environmental science & technology 26 (1992), S. 846-846 
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    ISSN: 1520-5851
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology , Energy, Environment Protection, Nuclear Power Engineering
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1021/es00029a612
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  • 17
    Electronic Resource
    Electronic Resource
    ES&T Currents (1992)
    s.l. : American Chemical Society
    Environmental science & technology 26 (1992), S. 1071-1073 
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    ISSN: 1520-5851
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology , Energy, Environment Protection, Nuclear Power Engineering
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1021/es50002a002
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  • 18
    Electronic Resource
    Electronic Resource
    ES&T Currents. (1992)
    s.l. : American Chemical Society
    Environmental science & technology 26 (1992), S. 1473-1475 
    Details
    ISSN: 1520-5851
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology , Energy, Environment Protection, Nuclear Power Engineering
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1021/es00032a607
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  • 19
    Electronic Resource
    Electronic Resource
    Additions and Corrections. Estimating Trophospheric Lifetimes and Ozone-Depletion Potentials of One- and Two-Carbon Hydrofluorocarbons and Hydrochlorofluorocarbons (1992)
    s.l. : American Chemical Society
    Environmental science & technology 26 (1992), S. 1672-1672 
    Details
    ISSN: 1520-5851
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology , Energy, Environment Protection, Nuclear Power Engineering
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1021/es00032a608
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  • 20
    Electronic Resource
    Electronic Resource
    Field study and numerical simulation of subslab ventilation systems (1992)
    s.l. : American Chemical Society
    Environmental science & technology 26 (1992), S. 1752-1759 
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    ISSN: 1520-5851
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology , Energy, Environment Protection, Nuclear Power Engineering
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1021/es00033a006
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  • 21
    Electronic Resource
    Electronic Resource
    Diffusional transport of solutes through clay: use of clay-modified electrodes (1992)
    s.l. : American Chemical Society
    Environmental science & technology 26 (1992), S. 1775-1779 
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    ISSN: 1520-5851
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology , Energy, Environment Protection, Nuclear Power Engineering
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1021/es00033a010
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  • 22
    Electronic Resource
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    Boson–fermion and baryon mapping: Construction of collective subspaces. III. Application of the baryon mapping to many-baryon states (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 3463-3467 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The theory developed in Paper I of this series is applied to the general case of a system consisting of colorfree quark triplets, whose quantum numbers are chosen as collective trifermion indices. The appropriate mapping technique to be used here is the baryon mapping. It is demonstrated that the original multiquark states can be exactly represented by states of colorfree ideal baryons. Besides, collective extended images are derived for a class of fermionic operators leaving the collective fermion space invariant.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529894
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  • 23
    Electronic Resource
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    Gravitational equations in space-time with torsion (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 3509-3520 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Various representations of equations of gravitational theories in space-time with torsion are considered. Special attention is paid to the case of quadratic Poincaré gauge theory of gravity. Advantages of each representation are discussed. The complete algorithm for calculation of gravitational equations in the framework of the most efficient formalism of spinor-valued exterior forms is presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529902
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  • 24
    Electronic Resource
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    The Barut–Girardello coherent states (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 114-121 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: It is shown that the completeness problem of the SL(2,R) coherent states proposed by Barut and Girardello leads to a moment problem, not a Mellin transform. This moment problem, which also appears in the theory of para-Bose oscillators, has been solved following the Sharma–Mehta–Mukunda–Sudarshan solution of the problem. The matrix element of finite transformation in the coherent state basis is shown to satisfy a "quasiorthogonality'' condition analogous to the orthogonality condition of the matrix element in the canonical basis. Finally, the Barut–Girardello "Hilbert space of entire analytic functions of growth (1,1)'' turns out to be only a subspace of Bargmann's well-known Hilbert space of analytic functions. This subspace, which has been called "the reduced Bargmann space'' in a previous paper, is an invariant subspace of SL(2,R). With this identification the generators of the group in this realization turn out to be the well-known boson operators of Holman and Biedenharn.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529951
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  • 25
    Electronic Resource
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    On supersymmetries in nonrelativistic quantum mechanics (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 152-160 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: One-dimensional nonrelativistic systems are studied when time-independent potential interactions are involved. Their supersymmetries are determined and their closed subsets generating kinematical invariance Lie superalgebras are pointed out. The study of even supersymmetries is particularly enlightened through the already known symmetries of the corresponding Schrödinger equation. Three tables collect the even, odd, and total supersymmetries as well as the invariance (super)algebras.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529954
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  • 26
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    On the evaluation of the U(3) content of the matrix elements of one- and two-body operators (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1550-1565 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: An expression for the U(3) content of the matrix elements of one- and two-body operators in Elliott's basis is obtained. Three alternative ways of evaluating this content with increasing performance in computing time are presented. All of them allow an exact representation of that content in terms of integers, avoiding rounding errors in the computer codes. The role of dual bases in dealing with nonorthogonal bases is also clarified.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529680
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  • 27
    Electronic Resource
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    Matrix elements and Wigner coefficients for Uq[gl(n)] (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1008-1022 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: In this series of papers the fundamental Wigner coefficients and the matrix elements of the generators for the quantum group Uq[gl(n)] are derived. The Uq[gl(n)]:Uq[gl(n−1)] reduced Wigner coefficients and reduced matrix elements are determined algebraically as eigenvalues of certain Uq[gl(n−1)] invariants in the quantum group Uq[gl(n)]. The matrix elements of the elementary quantum group generators, in the Gel'fand–Tsetlin basis, are derived below, while all fundamental Wigner coefficients are derived in the second paper of the series.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529986
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  • 28
    Electronic Resource
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    Reduced Wigner coefficients for Uq[gl(n)] (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1023-1031 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: This is the second paper in a series concerned with the Racah–Wigner calculus for the quantum group Uq[gl(n)]. In this approach all reduced Wigner coefficients are determined algebraically by the eigenvalues of certain generalized Casimir invariants. Here the method is applied to evaluate all fundamental Wigner coefficients and reduced Wigner coefficients for Uq[gl(n)].
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529764
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  • 29
    Electronic Resource
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    The initial value problem for a class of general relativistic fluid bodies (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1047-1053 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A body or collection of bodies made of perfect fluid can be described in general relativity by a solution of the Einstein–Euler system where the mass density has spatially compact support. It is shown that for certain equations of state there exists a wide class of solutions of this type corresponding to appropriate initial data given on a spacelike hypersurface. This class is not constrained by any symmetry requirements. The key element of the proof is to write the equations as a symmetric hyperbolic system which is regular both for nonvanishing density and in vacuum.
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    URL: http://dx.doi.org/10.1063/1.529766
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  • 30
    Electronic Resource
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    A superversion of quasifree second quantization. I. Charged particles (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1032-1046 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A formalism comprising and extending quasifree second quantization of charged bosons and fermions is presented. The second quantization of one-particle observables leads to current superalgebras, and a super-Schwinger term shows up. Anticommuting parameters are introduced in order to construct super-Bogoliubov transformations mixing bosons and fermions. As an application, representations of Lie superalgebras are given which are semidirect products of extensions of affine Kac–Moody algebras and the Virasoro algebra, and of the super-Virasoro algebra.
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    URL: http://dx.doi.org/10.1063/1.529765
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  • 31
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    Head-on collision of gravitational plane waves with noncollinear polarization: A new class of analytic models (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1054-1064 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A new four-parameter class of exact solutions of Einstein's field equations is obtained, using the inverse scattering method of Belinsky and Zakharov. Its members represent the head-on collision of a variably polarized gravitational plane wave with one having constant polarization and, in general, different profile, or with an infinitely thin shell of null dust. In some of these models no curvature singularity develops along the future boundary of the region of interaction. In certain cases the singularity avoidance is the direct result of the noncollinear polarization of the waves involved in the collision.
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    URL: http://dx.doi.org/10.1063/1.529767
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  • 32
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    A supersymmetric Dirac oscillator with scalar coupling (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1114-1117 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: It is shown that a relativistic wave equation with a scalar coupling correctly describes the Dirac oscillator in the sense that in the nonrelativistic limit this results in the Schrödinger equation for the harmonic oscillator with an extra σ⋅rˆ term. It is demonstrated that this equation has built-in supersymmetry, and that it guarantees the stability of the Dirac vacuum.
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    URL: http://dx.doi.org/10.1063/1.529775
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  • 33
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    Linear undulator brightness: Exact analytical treatment (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1200-1207 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: In this paper it is shown that the calculation of linearly polarized undulator brightness can be worked out exactly using elliptic functions and multivariable generalized Bessel functions. The obtained results are shown to be valid both in nonrelativistic and ultrarelativistic regimes. The physical relevance of the obtained results are discussed and the "low-energy'' corrections to the resonance condition are derived.
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    URL: http://dx.doi.org/10.1063/1.529731
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  • 34
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    Movable singularities in Sigma and Skyrme models (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1185-1199 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The singularity structure of the solutions of the equations of motion for the Sigma and Skyrme model Lagrangians with the hedgehog ansatz is investigated. In both cases the solutions present superposed a polelike term and a logarithmic branch point. The set of solitonic configurations of the Skyrme model is characterized by the sequence of locations of their singularities on the negative real axis of the dimensionless variable z = (eFπr)2, with an accumulation point at z=0. The first few terms of the Laurent series representing the Skyrme soliton profile are shown to reproduce well the exact values in an interval about the origin. Padé approximants to the residual power series obtained after subtraction of the dominant pole term are modified in order to satisfy the constraints imposed by the asymptotic power series expansion, and approximate representations are built for the Skyrme soliton configuration, which are shown to combine simplicity with accuracy.
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    URL: http://dx.doi.org/10.1063/1.529730
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  • 35
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    An application of first integrals method in magnetic diffusion problem (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1216-1220 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: In this paper a rigorous approach to the magnetic diffusion problem is presented under the assumption that the random fluid velocity field is independent of x and completely determined by a prescribed probability measure on the space of symmetric velocity field u(t)=u(−t). By adopting the first integrals method developed by Visik and Fursikov [Mat. Sb. 92, 347 (1973)], the space characteristic functional associated with the random induction equation has been expressed by a functional power series. The explicit formula for this functional has been obtained, without deriving and solving a suitable functional equation for the [u,B] field.
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    URL: http://dx.doi.org/10.1063/1.529984
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  • 36
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    An existence theorem for perturbed Newtonian cosmological models (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1224-1233 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Given a Newtonian Friedmann-like cosmological model MO, there exist, locally in time, spatially periodic solutions close to MO. Such solutions represent inhomogeneous models that are homogenous and isotropic on a large scale. The Euler–Poisson system is shown to be linearization stable at MO.
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    URL: http://dx.doi.org/10.1063/1.529734
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  • 37
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    A simple method for group analysis and its application to a model of detonation (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 3931-3937 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A simple procedure is suggested to obtain extensions of the principal Lie algebra, for invariance transformations of a given family of equations, by using an equivalence algebra. An application to a qualitative model of detonation is performed.
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    Exact wave functions of an electron on a quasiperiodic lattice: Definition of an infinite-dimensional Riemann theta function (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 3938-3947 
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    Notes: A scheme for obtaining the exact wave functions of an electron on a quasiperiodic lattice is presented. It is shown that the trace map plays a very important role for construction of the infinite-dimensional Riemann theta function in terms of which the wave functions can be represented.
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    Structure of matrices transforming Stokes parameters (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 3574-3584 
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    Notes: The structure of matrices that represent a linear transformation of the Stokes parameters of a beam of light into the Stokes parameters of another beam of light is investigated by means of the so-called Stokes criterion. This holds that the degree of polarization of a beam of light can never be changed into a number larger than unity. Several general properties are derived for matrices satisfying the Stokes criterion. These are used to establish conditions for the elements of such matrices. Conditions that are either necessary, or sufficient or both are presented. General 4×4 matrices are treated and a number of special cases is worked out analytically. Several applications are pointed out.
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    Schrödinger–Fuerth quantum diffusion theory: Generalized complex diffusion equation (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 111-113 
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    Notes: According to Schrödinger–Fuerth quantum diffusion theory the equations of quantum theory can be derived by applying the Fuerth transformation to the equations of diffusion theory. By introducing a complex flux whose real and imaginary parts are the x and y components of the flux, a complex form of the two-dimensional diffusion equation is obtained and the equation is then generalized to three dimensions. Application of the Fuerth transformation to the generalized complex diffusion equation yields a quantum equation, which is shown to be equivalent to the Dirac equation.
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    Limiting Gibbs states and dynamics for thermal photons (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 143-151 
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    Notes: For thermal photons, the limiting Gibbs state is investigated in the framework of algebraic quantum theory. For the one-particle Hamiltonian, the square root of the local Laplacians with Dirichlet boundary conditions is used. The local regions are only demanded to have the segment property and the thermodynamic limit is performed along a nearly arbitrary family of such local regions. Also, the limiting dynamics as a noncontinuous group of Bogoliubov transformations on an extension of the quasilocal Weyl algebra and as a W* dynamics on the GNS–von Neumann algebra is derived. After having performed the limits, the photon algebra is restricted to the physical (transversal) photons. The crucial mathematical method in verifying these results are comparisons of the semigroups of the square root of the Laplacians in different regions of the ν-dimensional Euclidean space by means of the ordering of positivity preserving operators.
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    Geometric superalgebra and the Dirac equation (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 161-170 
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    Notes: A unified mathematical approach to spinors and multivectors or superalgebra is constructed in a form useful to study the mathematical description of matter and its interaction fields. The formalism then encompasses both points of view: multivectors for the description of (space-time) geometry and the description of the integer spin, interaction fields, and spinor representations suitable for the description of half odd integer, matter fields. An application is made to study the change of the Dirac equation under the spinors to multivectors (to scalars) mapping. The physical and geometric content of the multivector solutions of the Dirac–Hestenes equation is clearly shown.
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    On the quantum differential calculus and the quantum holomorphicity (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 19-24 
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    Notes: Under some natural assumptions [less restrictive than in the paper by Wess and Zumino (preprint CERN-TH-5697/90, LAPP-TH-284/90)] differential calculi on the quantum plane are found and investigated. Complex structure, complex derivatives, and holomorphic functions on the quantum plane are defined. Generalized Cauchy–Riemann equations are given and solved.
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    Unified models from gauged supergroups. II. Exceptional series D(2,1;α), G(3), F(4) (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 399-402 
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    Notes: Previously elaborated principles [J. Math. Phys. 31, 1783 (1990)] for dimensional reduction of models of gauged supergroups over supercoset spaces are applied to the exceptional superalgebras. The superspace is parametrized by a pair of Grassmann coordinates.
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    Representations and traces of the Hecke algebras Hn(q) of type An−1 (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 4-14 
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    Notes: The notion of the connectivity class of minimal words in the algebra Hn(q) is introduced and a method of explicitly constructing irreducible representation matrices is described and implemented. Guided by these results, the connection between the Ocneanu trace on Hn(q) and Schur functions is exploited to derive a very simple prescription for calculating the irreducible characters of Hn(q). They appear as the elements of the transition matrix relating certain generalized power sum symmetric functions to Schur functions. Their evaluation involves the use of the Littlewood–Richardson rule, which is proved to apply to Hn(q) just as it does to Sn. Both representation matrices and characters are tabulated.
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    A note on the Lorentz transformations linking initial and final four-vectors (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 84-85 
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    Notes: The set of all (homogeneous, proper, orthochronous) Lorentz transformations that link two given forward-timelike four-vectors with equal norms, as well as the condition under which a unique Lorentz transformation is singled out, is completely determined, and presented in a form suitable for immediate reduction to Galilean transformations by letting c→∞,c being the speed of light in empty space. Analogies to the intuitively well-understood Galilean transformation group are obvious. Thus, for instance, the ordinary velocity addition operator "+'' involved in the determination of a Galilean transformation link becomes ⊕, the relativistic velocity addition operator involved in the determination of a Lorentz transformation link. The analogies shared by Galilean and Lorentz transformation links were overlooked by explorers since, as opposed to the associative–commutative binary operation + in the Euclidean three-space R3, the binary operation ⊕ in R3c = {v∈R3:||v||〈c} is neither associative nor commutative.
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    Linearization of polynomials (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 3356-3366 
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    Notes: It is well known that the linearization of quadratic forms is accomplished using Dirac matrices. The general problem of linearization of any polynomial of degree n having p variables is considered. First the homogeneous polynomials are considered and it is shown that we only need to study two basic homogeneous forms, namely, the sum and the product one. The sum is linearized using matrices which turn out to be a matrix representation of a generalized Clifford algebra. The homogeneous form is linearized using matrices, the size of which is large for practical use. Some clues are given to reduce their size. Since any polynomial of degree n can be made homogeneous by introducing a supplementary variable, the method proposed is quite general. It constitutes an algorithm for the linearization of any polynomial.
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    Green's function for crossed time-dependent electric and magnetic fields. Phase-space quantum mechanics approach (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 3402-3409 
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    Notes: In the present paper, the Moyal propagator is obtained for an electron inmersed in a constant uniform magnetic field crossed with a uniform electric field having arbitrary time dependence, using the techniques of phase space quantum mechanics. All the interesting magnitudes can be evaluated from it, and one can make quantum physics remaining in the context of phase space. Making use of these methods, the corresponding Green's function is also obtained.
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    Boson–fermion and baryon mapping: Construction of collective subspaces. I. Theory (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 3445-3453 
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    Notes: Recently, the mathematical formalism of the Dyson boson mapping has been extended to a system of 3n fermions, leading to the boson–fermion and the baryon mapping. In the present paper, the case of a restriction to a subset of three-fermion quantum numbers, the collective indices, is discussed. A theory is developed for the representation of fermionic states and operators in a truncated ideal space where only collective boson–fermion pairs or collective ideal baryons are allowed. An exact reproduction of physical properties is proved to be possible provided that the original fermionic problem can be solved in a subspace where all three-fermion subsystems carry collective indices. Examples of simple applications are presented in the two subsequent papers of this series.
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    Square-well representations for potentials in quantum mechanics (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 3472-3476 
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    Notes: A single particle moves in one dimension and obeys nonrelativistic quantum mechanics. If the potential shape f(x) is symmetric and vanishes at infinity, then, without loss of generality, it can be represented in the form of a mixture f(x)=∫0∞A(t)w(x/t)dt of square wells w(x). It is shown that A(t)=f'(t) and that the discrete eigenvalues of the Schrödinger operator H=−D2+vf(x) are given approximately by the general formula En(approximately-equal-to)EAn=mins(approximately-greater-than)0[s+v∫0∞f'(t)w¯n(st2)dt], where {w¯n(s)}n=0∞ are the known "kinetic potentials'' associated with the simple square-well problem. For n=0 or 1, the approximations EnA are lower bounds to the corresponding exact energies En. The general formula is applied to the sech-squared potential and to the truncated quartic oscillator.
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    Phase-space representations of general statistical physical theories (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 131-142 
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    Notes: It is shown that Hilbert-space quantum mechanics and many other statistical theories can be represented on some phase space, in the sense that states can be identified with probability measures and observables can be described by functions. In the general context of statistical dualities, informationally complete observables are introduced and a theorem on their existence is proven. The correspondence between these observables and the injective affine mappings from the states into the probability measures on phase space, i.e., the phase-space representations, is pointed out. In particular, a description of all observables by functions is presented, such that all expectation values can, in arbitrarily good physical approximation, be calculated as integrals. Moreover, some new aspects of the particular case of those phase-space representations of quantum mechanics that are related to certain joint position-momentum observables are discussed.
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    Quantum quaternions (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 171-173 
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    Notes: The notion of quantum quaternions is introduced as a one-parametric quantum deformation of the quaternion algebra. An appriopriate noncommutative differential calculus is developed and the quantum version of the Fueter equation is founded.
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    Asymmetric anharmonic oscillators in the Hill-determinant picture (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 213-221 
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    Notes: A new version of the Hill-determinant construction of bound states is proposed. It is based on the matching of two suitable power-series Ansätze for the wave function. For the asymmetric well potential V(x)=ax+bx2+cx3+dx4 the convergence of the approximants to the physical solutions is proved. For b(approximately-greater-than)bminimal, the Taylor coefficients for this anharmonic oscillator's wave function are specified by four-term recurrences.
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    Hidden symmetries of two-dimensional systems with local degeneracies (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 203-212 
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    Notes: The energy spectrum of a nonrelativistic particle in radial potentials of the form V(r) = αr 2d−2 − βr d−2 shows one level with a singularly high multiplicity. The two-dimensional problems are focused upon and the constants of motion that generate the symmetries responsible for this local accidental degeneracy are determined. The conserved operators realize an SU(2) algebra and the bound states are seen to fall into either finite, semibounded, or unbounded representations of this algebra. An SO(3,2) module encompassing the eigenstates associated to the whole set of potentials is also identified. It is further shown that there exists a second coordinate system besides the polar one in which the Schrödinger equation separates. Finally, it is indicated how the two-dimensional Coulomb and harmonic oscillator problems arise as special cases.
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    Isometry groups of three-dimensional Riemannian metrics (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 267-272 
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    Notes: The necessary and sufficient conditions for a three-dimensional Riemannian metric to admit a group Gr of isometries acting on s-dimensional orbits are given. This provides the list of (abstract) groups that can act isometrically and maximally on such metrics. The conditions are expressed in terms of the eigenvalues and eigenvectors of the Ricci tensor. In any case, the order of differentiability of these data necessary to determine the isometry group is less than 4.
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    On the instability of the n=1 Einstein–Yang–Mills black holes and mathematically related systems (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 248-255 
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    Notes: The usual approach to analyze the linear stability of a static solution of some system of equations consists of searching for linearized solutions which satisfy suitable boundary conditions spatially and which grow exponentially in time. In the case of the n=1 Einstein–Yang–Mills (EYM) black hole, an interesting situation occurs. There exists a perturbation which grows exponentially in time−and spatially decreases to zero at the horizon−but nevertheless is physically singular on the horizon. Thus, this unstable mode is unacceptable as initial data, and the question arises as to whether the n=1 EYM black hole is stable. We analyze this issue here in the more general case of a scalar field φ satisfying the wave equation ∂2φ/∂t2 = (DaDa − V)φ on a manifold R×M, where Da is the derivative operator associated with a complete Riemannian metric on M and V is a bounded function on M whose derivatives also are bounded. We prove that if the operator A = −DaDa + V fails to be a strictly positive operator on the Hilbert space L2(M), then there exists smooth initial data of compact support in M which give rise to a solution which grows unboundedly with time. This implies that the n=1 EYM black hole and other mathematically similar systems are unstable despite the nonexistence of physically acceptable exponentially growing modes. Rigorous criteria for linear stability are also obtained.
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    Dirac equation in external fields: Separation of variables in nondiagonal metrics (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 297-303 
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    Notes: The algebraic method of separation of variables in the Dirac equation proposed in earlier works by one of the present authors [Theor. Math. Phys. 70, 204 (1987); J. Math. Phys. 30, 2132 (1989)] is developed for the space-time with nondiagonal metrics. The essence of the method consists of the separation of the first-order matricial differential operators that define the dependence of the Dirac's bispinor on the related variables. In contrast to some other authors the pairs of operators are commuted on each step of separation including the variables mixed by nondiagonal elements of fundamental tensor of space-time. There are reasons to believe that it must be some local similarity transformation connected these commuted operators with noncommuted corresponding operators of other authors, although such transformation in view of mathematical difficulties of problem, in general, were not successfully found.
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    Singularities in the solutions of the massive Skyrme model (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 2626-2632 
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    Notes: The equation of motion for the Skyrme model with a pion mass term is studied in the framework of the Painlevé analysis, and information is obtained about the singularity structure of its solutions. As in the massless case, singularities exist, consisting of a first-order pole term superposed to a logarithmic branch point. For the solitonic solutions, the singularities form an infinite sequence of points located on the negative real axis of the squared radial variable, accumulating at the origin. Based on this property and on the asymptotic behavior of the solitonic solutions, an approximate representation is built for the baryonic soliton, which is extremely accurate.
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    Weyl manifolds and connections (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 2633-2638 
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    Notes: A study is made of Weyl connections and their associated holonomy groups. The extent to which a Weyl connection determines its associated metric and 1-form structures is also discussed. Finally, the related concept of a locally metric connection is introduced and some relations between metric, locally metric, and Weyl connections are established.
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    Asymptotically exact diffusive boundary conditions in linear kinetic theory (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 2639-2647 
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    Notes: In a recent article in this journal, asymptotic considerations were used to define appropriate boundary conditions for diffusive approximations to linear kinetic equations. A variational treatment was invoked to carry out the details of the analysis. Here these details are carried out exactly, and it is shown that the earlier variational results are accurate to a few percent.
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    Representations of the quantum algebras Uq(ur,s) and Uq(ur+s) related to the quantum hyperboloid and sphere (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1937-1947 
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    Notes: Representations πΛμ of the principal degenerate series of the quantum algebra Uq(ur,s) are introduced. Structure of these representations is studied. Several classes of unitary irreducible representations of the algebra Uq(ur,s) are separated in the set of irreducible representations πΛμ and irreducible constituents of reducible representations πΛμ. The formulas of action of operators of irreducible representations of the quantum algebra Uq(ur+s) in the basis corresponding to restriction of representations onto the subalgebra Uq(ur+us) are given.
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    Computation of error effects in nonlinear Hamiltonian systems using Lie algebraic methods (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1948-1963 
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    Notes: There exist Lie algebraic methods for obtaining transfer maps around any given trajectory of a Hamiltonian system. This paper describes an iterative procedure for finding transfer maps around the same trajectory when the Hamiltonian is perturbed by small linear terms. Such terms often result when an actual system deviates from an ideal one due to errors. Two examples from accelerator physics are worked out. Comparisons with numerical computations, and in simple cases exact analytical calculations, demonstrate the validity of the procedure.
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    On some mathematical problems in the evaluation of fields produced by currents which are generalized functions (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 2164-2168 
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    Notes: A method is given to overcome the ambiguities in the order of integration in the calculation of potentials as reciprocal Fourier transform by φ=F˜Fφ=∫dk0∫dk when generalized functions are involved.
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    Dirac Hamiltonian with Coulomb potential and spherically symmetric shell contact interactiona) (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 2207-2214 
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    Notes: Spherically symmetric Hamiltonians describing a Dirac particle in Coulomb potential combined with contact interaction on a sphere (typically, a δ-shell interaction) are constructed. The point spectrum is studied numerically for the case of scalar and vector δ shells. A comparison of two possible definitions of δ-shell coupling constants is also given.
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    Green functions of the De Rham Laplacian in maximally symmetric spaces (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 2228-2231 
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    Notes: The massive p-form two-point functions in maximally symmetric spaces of arbitrary dimension n are obtained.
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    Generalization of the pseudopotential to an interaction with nonzero range (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 2215-2227 
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    Notes: The resonance properties of certain arrays of potentials defined by a self-adjoint integral operator of finite rank are studied. It is shown that a uniformly spaced infinite linear array of such potentials can admit zero-width resonances, and that a uniformly spaced circular array can admit resonances whose widths tend to zero exponentially, as the number of potentials tends to infinity while the arc-length spacing remains constant−properties that have previously been studied for the Fermi pseudopotential (point interaction). Additionally, it is demonstrated that the pseudopotential can be derived from such an integral-operator potential as an appropriate limit. The relevance of these calculations to the study of arrays of cylindrical dipoles in classical electromagnetism is discussed.
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    E. Cartan moment of rotation in Ashtekar's self-dual representation of gravitation (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 2242-2248 
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    Notes: The geometric construction of the E. Cartan moment of rotation associated to the spacetime curvature provides a geometric interpretation of the gravitational field sources and describes geometrically how the sources are "wired'' to the field in standard geometrodynamics. The E. Cartan moment of rotation yields an alternate way (as opposed to using variational principles) to obtain Einstein equations. The E. Cartan construction uses, in an essential way, the soldering structure of the frame bundle underlying the geometry of the gravitational field of general relativity. The geometry of Ashtekar's connection formulation of gravitation is based on a complex-valued self-dual connection that is not defined on the frame bundle of spacetime. It is shown how to transfer the construction of the E. Cartan moment of rotation of Ashtekar's formulation of the theory of gravity and demonstrate that no spurious equations are produced via this procedure.
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    A new topology on space-time (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 2232-2241 
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    Notes: A new topology, P˜, is suggested on space-time definable solely in terms of the causal structure, thus combining ideas of both Zeeman (and more specifically Hawking, King, and McCarthy) and Alexandrov to create a very "physical'' topology. It is proved that the distinguishing condition holds on a manifold if and only if this new topology is equivalent to the path topology of Hawking, King, and McCarthy. It is also found that the homeomorphism group of P˜ is the group of chronological and antichronological bijections in the case that the chronology condition holds on the space-time manifold. Thus, if the chronology condition holds P˜ determines the causal structure, and if the distinguishing condition holds P˜ determines the causal, differential, and conformal structures of space-time.
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    Cosmic censorship and pseudoconvexity (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 2249-2253 
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    Notes: It is shown that conditions of causal simplicity and pseudoconvexity are closely related. It is proved that under certain reasonable conditions space-time is maximally null pseudoconvex. It is indicated that pseudoconvexity may play the role of global hyperbolicity even though it is a weaker condition. Consequently, obtained results provide some tentative evidence for the validity of the cosmic censorship hypothesis.
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    Stationary axisymmetric charged perfect fluid type D solutions (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 2254-2257 
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    Notes: A complete class of stationary axisymmetric Wainwright class I charged perfect fluid solutions is given.
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    Nontrivial soliton scattering in an integrable chiral model in (2+1)-dimensions (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 2269-2278 
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    Notes: Soliton solutions of an integrable chiral model in (2+1)-dimensions are studied. Through the solution of a "Riemann problem with zeros'' solitons of this model have already been found [R. S. Ward, J. Math. Phys. 29, 386 (1988)] which scatter in a trivial manner. By exploiting a connection with the O(3) σ model, it is shown that the model also has solitons that are not contained in the above construction, and whose scattering properties are highly nontrivial. Soliton scattering is also discussed for a σ model which interpolates between this integrable model and the SU(2) chiral σ model.
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    Exact solutions of nonlinear Schrödinger equation for positive group velocity dispersion (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 2323-2328 
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    Notes: A method is given for obtaining new exact solutions of nonlinear Schrödinger equation describing the propagation of pulses in optical fibers for positive group-velocity dispersion. The method is based on the construction of a certain complete integrable finite-dimensional dynamical system, whose solutions determine the exact solutions of nonlinear Schrödinger equation. The set of exact analytic solutions contains dark solitary waves, dark soliton, periodic, and stationary solutions which are very important from a physical point of view.
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    Time-dependent rototranslational diffusion equation with multiple mixed boundary conditions: A formally exact analytical solution (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 2329-2335 
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    Notes: A formally exact analytical solution of the time-dependent rototranslational diffusion equation (RTDE) with mixed boundary conditions applied over both the translational and rotational variables has been derived. The approximation of isotropic translational motion has been imposed and no further approximations have been used in the calculations. The solution has been obtained in the form of a set of homogeneous linear algebraic equations.
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    String cosmology in spherically symmetric space-time (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 2336-2338 
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    Notes: Cosmological solutions for the string model are done in a spherically symmetric Kantowski–Sachs metric ansatz. Solutions are evaluated for three equations of states for string density. Also, an analytic relation between the metric coefficients is assumed. A first-order autonomous system is developed from the field equations and a line singularity is found.
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    Real representations of Clifford algebras (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1579-1581 
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    Notes: Simple proof of classification theorem of all real irreducible representations of Clifford algebras is given.
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    Racah–Wigner calculus for the super-rotation algebra. I (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1582-1593 
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    Notes: The symmetry properties and the pseudo-orthogonality relations of the super-rotation Clebsh–Gordan coefficients for the tensor product of two irreducible representations of the super-rotation algebra are derived. The symmetric super-rotation 3-j symbol and the symmetric and invariant super-rotation 6-j symbol are defined, their basic properties are described, and their relations to the usual 3-j and 6-j symbols are given.
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    Graded algebras and geometry based on Yang–Baxter operators (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1631-1635 
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    Notes: The Γ-graded algebras such as the ε-symmetric algebra, generalized Lie algebras and the concept of generalized Lie–Cartan pairs are given in terms of graded Yang–Baxter operators.
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    Analysis on the p-adic superspace. I. Generalized functions: Gaussian distribution (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1636-1642 
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    Notes: The theory of generalized functions on the p-adic superspace Qn,mp over the (super)commutative Banach superalgebra Λ=Λ0⊕Λ1 with the trivial Λ1 annihilator is proposed. The p-adic Gaussian "supermeasure'' is defined as a generalized function on the p-adic superspace. The connection between the p-adic Gaussian integration and the p-adic gamma function of Morita is considered
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    Functional calculus of the Borel transform (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1648-1651 
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    Notes: An explicit form is given of the Borel transform B˜ of g(large-closed-square)f where g(large-closed-square)f(z):=g( f(z)) with f Borel summable and g analytic in f(0) and a detailed study of the singularities in B˜ (in the Borel variable) is made. Examples include g(ξ)=1/ξ, log ξ and eξ. The present paper generalizes results of Boenkost et al. [J. Math. Phys. 29, 1118 (1987)].
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    Jet methods in nonholonomic mechanics (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1652-1665 
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    Notes: Classical nonholonomic mechanical systems are studied whose evolution space is a fiber bundle τ: M→R. The framework is that of jet spaces in which the geometrical meaning of the theory emerges clearly. For systems with linear constraints a new interpretation is given of Appell's equations as first-order differential equations associated with a suitable vector field. The d'Alembert principle is formulated in an appropriate way to be generalized to systems with nonlinear constraints. The equivalence between the equations of motion arising from this generalization, the ones set up on Gauss' principle of least constraint and Hertz's principle of least curvature is established.
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    A new asymptotic form for the Laguerre polynomials (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1666-1671 
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    Notes: A new asymptotic formula in terms of elementary functions is demonstrated for the Laguerre polynomials Lαn(x) in the limit when all three parameters (n,α,x) become large. This asymptotic limit appears in the problem of obtaining the low-field semiclassical approximation from the full quantum mechanical behavior of a two-dimensional electron gas in a magnetic field.
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    Variational density of electrons for large closed shell atoms (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1672-1674 
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    Notes: An exact expression for the atomic form factor for closed shell atoms is derived using an antisymmetric multielectron wave function. It is shown that for large atoms it can be written as an integral over a Bessel function. Using the Hankel transform it gives an expression for the density of electrons which is of Thomas–Fermi form which was found earlier by Pucci and March.
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    Analysis on the p-adic superspace. II. Differential equations on p-adic superspace (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1643-1647 
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    Notes: The Cauchy problem for differential equations on the p-adic superspace is considered. The application of this mathematical theory to the model of the supersymmetric quantum mechanics on the p-adic Riemannian surface is proposed. The non-Archimedean superdiffusion is also considered.
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    The extension theory and the opening in semitransparent surface (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1685-1689 
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    Notes: The model of zero width slits based on the operator's extension theory for the wave scattering by a semitransparent surface with small aperture is constructed.
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    Super Wigner function (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1690-1694 
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    Notes: The phase-space representation of supersymmetric quantum mechanics is given. The super Wigner function is constructed and its transformation property is investigated. In the case of a supersymmetric oscillator, it is explicitly shown how the invariance under the supersymmetry transformation determines the form of the super Wigner function.
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    Note on the representation of many-particle dynamics as higher-order single-particle dynamics, with a means to relativistic elevation of Newtonian dynamics (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1675-1684 
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    Notes: It is shown how (first in Newtonian physics), by processes of repeated differentiation of equations of motion and of algebraic elimination, the dynamics of many particles may be brought to another equivalent representation, that of a single higher-order equation of motion for a single particle. Here a higher-order Lagrangian followed by an Ostrogradsky Hamiltonian may be brought into play. (This leads parenthetically to the construction of a considerable class of canonically inequivalent specifications of one basic set of equations of motion.) The higher-order one-particle representation translates simply and directly (but not uniquely) into relativistic generalization (because only a single world line is being described), in which the Poincaré group is canonically represented in an Ostrogradsky Hamiltonian formulation. The examples of the Kepler problem and the harmonic oscillator are elaborated in detail.
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    Novel solution of the one-dimensional quantum-mechanical harmonic oscillator (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1705-1709 
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    Notes: The classical solution is used as a variable for the one-dimensional quantum-mechanical oscillator, and this leads to a separable differential equation solvable in closed form which yields a set of new quantum mechanical solutions, not energy eigenfunctions, that have the property of being localized. These new solutions are shown to be eigenfunctions of a time-independent position operator. The operator algebra of that operator and an analogous momentum operator is given, as well as the relationship of the eigenfunctions to the energy eigenfunction set. The new eigenfunctions, which are not square integrable but possess a δ-function normalization, themselves represent wavepackets that at times corresponding to when the classical position is at an extremum collapse to Dirac δ functions.
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    Affine conformal vectors in space-time (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1754-1764 
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    Notes: All space-times admitting a proper affine conformal vector (ACV) are found. By using a theorem of Hall and da Costa, it is shown that such space-times either (i) admit a covariantly constant vector (timelike, spacelike, or null) and the ACV is the sum of a proper affine vector and a conformal Killing vector or (ii) the space-time is 2+2 decomposable, in which case it is shown that no ACV can exist (unless the space-time decomposes further). Furthermore, it is proved that all space-times admitting an ACV and a null covariantly constant vector (which are necessarily generalized pp-wave space-times) must have Ricci tensor of Segré type {2,(1,1)}. It follows that, among space-times admitting proper ACV, the Einstein static universe is the only perfect fluid space-time, there are no non-null Einstein–Maxwell space-times, and only the pp-wave space-times are representative of null Einstein–Maxwell solutions. Otherwise, the space-times can represent anisotropic fluids and viscous heat-conducting fluids, but only with restricted equations of state in each case.
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    Real trajectories in complex-time method and barrier penetrationlike phenomena (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1745-1753 
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    Notes: Various applications of the real trajectories in the complex-time method are discussed. It is shown that the proper way of summation over semiclassical orbits removes existing doubts and leads to the more general formulas than the standard WKB-type one in the energy eigenvalue problem. This method is also used in the description of explicitly time-dependent phenomena. In the problem of escaping from a metastable state, the estimation of a lifetime is in a good agreement with the inverse width of a false ground state energy.
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    Stochastic lengths (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1695-1704 
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    Notes: The autocorrelations of the line element for the sample paths of diffusion processes are computed. Lengths are defined for the sample paths of diffusions which depend upon an arbitrary function f and reduce to the classical relativistic length for differentiable trajectories. Their mean values are computed for a general diffusion and provide a family of stochastic actions labeled by f. In a variational principle, these actions are extremized over the drift and probability density and the equations characterizing the critical diffusions are derived. The Klein–Gordon equation is obtained from the variation of arbitrary f-dependent stochastic extensions of the length of trajectories.
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    Qualitative analysis of a class of Bianchi V imperfect fluid cosmologies (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1772-1779 
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    Notes: It has been shown that by utilizing a set of "dimensionless'' equations of state, the Einstein field equations governing Bianchi V imperfect fluid cosmologies reduce to a plane-autonomous system of equations. This plane-autonomous system shall be investigated here, and the qualitative behavior of the underlying cosmological models shall thereby be obtained.
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    Cosmological Yang–Mills hydrodynamics (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1782-1785 
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    Notes: The partial differential equations that govern the evolution of a self-gravitating fluid endowed with a density of charge taking its values in a Lie algebra, generating a Yang–Mills current, and hence a Yang–Mills field are written and studied. The local properties of the solutions are analogous to those of gravitating plasmas, but may be quite different globally.
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    A multipolar stationary object embedded in a gravitational field (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1780-1781 
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    Notes: The task of embedding a multipolar stationary object in a gravitational field is undertaken in this paper. It is believed that such an object will be astrophysically interesting.
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    The classical susceptibility and the temperature-dependent susceptibility of a free electron gas (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1799-1806 
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    Notes: The origin of dimensional independence in the classical susceptibility is studied. This study has led to an integral expression for the finite-temperature susceptibility of a free electron gas, given in terms of the zero-temperature susceptibility. At finite temperatures the susceptibility is regular. The singularity, which exists at twice the Fermi wave vector when T=0, vanishes. Thus the anomalous behavior associated with 2kF is expected to disappear when T≠0.
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    Nondispersive solutions of the Klein–Gordon equation (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1817-1821 
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    Notes: The nondispersive solutions of the Klein–Gordon equation, that is, solutions depending on an arbitrary function F(u), where u is itself a solution of the characteristic equation of the homogeneous three-dimensional scalar wave equation (∇u)2−(c−1∂tu)2=0, are discussed.
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    On a phenomenological generalized Boltzmann equation (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1786-1798 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: In this paper the existence and uniqueness of the solution for a generalized Boltzmann equation is proved and the positivity of this solution is discussed. Two series representations of the solution of the equation will be given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529656
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  • 97
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    Electronic Resource
    On the integrability aspects of the one-dimensional classical continuum isotropic biquadratic Heisenberg spin chain (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1807-1816 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The integrability aspects of a classical one-dimensional continuum isotropic biquadratic Heisenberg spin chain in its continuum limit up to order [O(a4)] in the lattice parameter "a'' are studied. Through a differential geometric approach, the dynamical equation for the spin chain is expressed in the form of a higher-order generalized nonlinear Schrödinger equation (GNLSE). An integrable biquadratic chain that is a deformation of the lower-order continuum isotropic spin chain, is identified by carrying out a Painlevé singularity structure analysis on the GNLSE (also through gauge analysis) and its properties are discussed briefly. For the nonintegrable chain, the perturbed soliton solution is obtained through a multiple scale analysis.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529658
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  • 98
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    Electronic Resource
    Nondispersive solutions of the Dirac equation (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1822-1830 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Nondipersive solutions of the Dirac equation, that is, solutions depending on an arbitrary function F(u), where u is itself a solution of the characteristic equation (∇u)2−(c−1∂tu)2=0, are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529659
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  • 99
    Electronic Resource
    Electronic Resource
    Conformal invariance in a Dirac oscillator (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1831-1836 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The conformal invariance properties of a Dirac oscillator are established. A set of operators is constructed whose algebra shows that it can be considered as a conformal system. The operators are then used to solve the problem using algebraic techniques. The superconformal generalization of the algebra is also worked out, and some consequences of these invariances for the properties of the model are mentioned.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529660
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  • 100
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    Electronic Resource
    Transformations of some induced osp(3/2) modules in an so(3)⊕sp(2) basis (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1841-1863 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The modules of the orthosymplectic Lie superalgebra osp(3/2), induced from finite-dimensional irreducible submodules of the stability subalgebra so(3)⊕gl(1) are investigated. The corresponding infinite-dimensional irreducible or indecomposable modules, the Kac modules, and the related typical and atypical modules are studied in detail. Every such module is decomposed into a direct sum of either indecomposable or irreducible modules of the even subalgebra so(3)⊕sp(2). For each of these (infinite-dimensional or finite-dimensional, irreducible or indecomposable) modules relations are written down, giving the transformations of the basis under the action of the algebra generators.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529662
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