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  • 1
    Electronic Resource
    Electronic Resource
    Structure of matrices transforming Stokes parameters (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 3574-3584 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529906
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Well-posedness of stationary and time-dependent Spencer–Lewis equations modeling electron slowing down (1989)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 30 (1989), S. 158-165 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The unique solvability of the time-dependent and stationary Spencer–Lewis equations is established under natural assumptions on the solution and the data of the problem. The strategy used is the method of characteristics followed by perturbation and monotone approximation arguments. The evolution operator in the time-dependent Spencer–Lewis equation is proved to generate a strongly continuous contraction semigroup.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528580
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    An eigenvalue criterion for matrices transforming Stokes parameters (1993)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 34 (1993), S. 5072-5088 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Simple eigenvalue tests are given to ascertain that a given real 4×4 matrix transforms the four-vector of Stokes parameters of a beam of light into the four-vector of Stokes parameters of another beam of light, and to determine whether a given 4×4 matrix is a weighted sum of pure Mueller matrices. The latter result is derived for matrices satisfying a certain symmetry condition. To derive these results indefinite inner products are applied.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530343
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Multigroup transport equations with nondiagonal cross-section matrices (1986)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 27 (1986), S. 1633-1638 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Multigroup transport equations with nondiagonal cross-section matrices are studied using the Wiener–Hopf method. Formulas for the solution and the exit distribution are given in terms of the factorization of the symbol of the Wiener–Hopf equation. Unlike the formulas for a diagonal cross-section matrix, these formulas involve derivatives of the H-functions. For the case of two groups, the H-functions are computed explicitly.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.527078
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  • 5
    Electronic Resource
    Electronic Resource
    Stationary solutions of the non-linear Boltzmann equation in a bounded spatial domain (1989)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 11 (1989), S. 471-481 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A contraction mapping (or, alternatively, an implicit function theory) argument is applied in combination with the Fredholm alternative to prove the existence of a unique stationary solution of the non-linear Boltzmann equation on a bounded spatial domain under a rather general reflection law at the piecewise C1 boundary. The boundary data are to be small in a weighted L∞-norm.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670110405
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  • 6
    Electronic Resource
    Electronic Resource
    Transport equations with boundary conditions of reverse reflection type (1988)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 10 (1988), S. 15-35 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A study is performed of transport equations on arbitrary three-dimensional domains with boundary conditions of reverse reflection type. The existence of the dominant eigenvalue of the criticality problem is proved and its independence of the functional setting and its continuous dependence on a variety of data are established. The corresponding time-dependent problem is shown to be well-posed, also for a conservative boundary. The relationship between the criticality and the time-dependent problem is given explicitly.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670100103
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  • 7
    Electronic Resource
    Electronic Resource
    Polarized light transfer above a reflecting surface (1986)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 8 (1986), S. 311-327 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The existence and uniqueness are established for the solution of the equation of transfer of polarized light in a homogeneous atmosphere of finite optical thickness, assuming reflection by the planetary surface. A general Lp-space formulation is adopted. The boundary value problem is first written as a vector-valued integral equation. Using monotonicity properties of the spectral radii of the integral operators involved as well as recent half-range completeness results for kinetic equations with reflective boundary conditions, the present results follow as a corollary.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670080121
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    Paper (German National Licenses)
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