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  • 1
    Electronic Resource
    Electronic Resource
    Nonlinear operators and their propagators (1997)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 484-500 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Mathematical physicists are familiar with a large set of tools designed for dealing with linear operators, which are so common in both the classical and quantum theories; but many of those tools are useless with nonlinear equations of motion. In this work a general algebra and calculus is developed for working with nonlinear operators: The basic new tool being the "slash product," defined by A(1+εB) =A+εA/B+O(ε2). For a generic time development equation, the propagator is constructed and then there follows the formal version of time dependent perturbation theory, in remarkable similarity to the linear situation. A nonperturbative approximation scheme capable of producing high accuracy computations, previously developed for linear operators, is shown to be applicable as well in the nonlinear domain. A number of auxiliary mathematical properties and examples are given. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.531829
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  • 2
    Electronic Resource
    Electronic Resource
    Sodium Metaphosphate in Mechanical Dishwashing (1934)
    s.l. : American Chemical Society
    Industrial & engineering chemistry 26 (1934), S. 998-1001 
    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/ie50297a021
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  • 3
    Electronic Resource
    Electronic Resource
    Sanitary Value of Sodium Meta-Phosphate in Dishwashing (1938)
    s.l. : American Chemical Society
    Industrial & engineering chemistry 30 (1938), S. 23-26 
    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/ie50337a005
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  • 4
    Electronic Resource
    Electronic Resource
    Phosphates in Water Conditioning (1942)
    s.l. : American Chemical Society
    Industrial & engineering chemistry 34 (1942), S. 32-40 
    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/ie50385a007
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  • 5
    Electronic Resource
    Electronic Resource
    High-accuracy approximation techniques for analytic functions (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 411-415 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A generalization of the familiar mesh point technique for numerical approximation of functions is presented. High accuracy and very rapid convergence may be obtained by thoughtful choice of the reference function chosen for interpolation between the mesh points. In particular, derivative operators are represented by highly nonlocal matrices; but this is no drawback when one has computing machines to perform the algebraic manipulations. Some examples are given from familiar quantum mechanical problems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.526624
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  • 6
    Electronic Resource
    Electronic Resource
    Numerical integration in many dimensions. III (1986)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 27 (1986), S. 488-488 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Extending a previous line of work, a powerful computational method is found for numerical integration in many dimensions of functions of the form F( f1(x1 ,x2)+f2(x2 ,x3)+ f3(x3 ,x4) +⋅⋅⋅+fd(xd,x1)).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.527248
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  • 7
    Electronic Resource
    Electronic Resource
    Numerical integration in many dimensions. II (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 955-957 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Two new techniques are presented that appear to be useful in obtaining accurate numerical values for the numerical integration of fairly smooth functions in many dimensions. Both methods start with the idea of a mesh containing n points laid out in each of the d dimensions, then seek strategies that use far less than all nd points in some systematically improved sequence of approximations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.526554
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  • 8
    Electronic Resource
    Electronic Resource
    Numerical integration in many dimensions. I (1985)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 26 (1985), S. 951-954 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: If a d-dimensional integral involves an integrand of the functional form F( f1(x1)+f2(x2)+⋅⋅⋅), then one can introduce an integral transform (Fourier or Laplace or variants on those) which allows all the integrals over the coordinates xi to factor. Thus a d-dimensional integral is reduced to a one-dimensional integral over the transform variable. This is shown to be a very powerful and practical numerical approach to a number of problems of interest. Among the examples studied is the computation of the volume of phase space for an arbitrary collection of relativistic particles. One important aspect of the approach involves numerical integration along various contours in the complex plane.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.526553
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  • 9
    Electronic Resource
    Electronic Resource
    Nonlinear operators. II (1997)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 3841-3862 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: This work extends the previous development of new mathematical machinery for nonlinear operators acting on a vector space. Starting from the usual concept of inner product, we find that Hermitian, anti-Hermitian, and unitary nonlinear operators can be defined without bringing in the ideas of a dual vector space or adjoint operators. After looking briefly at how these general ideas might be used in classical mechanics and to extend the linear Schrödinger equation of quantum theory, the topic of Lie groups and Lie algebras is studied. Many, but not all, of the familiar features of that topic are extended to nonlinear operators. New representations are found for a few simple cases of interest to physics, and some provocative implications for elementary particle theory are discussed. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.532070
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  • 10
    Electronic Resource
    Electronic Resource
    ULTRAVIOLET RADIATION AND REDUCTION OF DEEP WOUND INFECTION FOLLOWING HIP AND KNEE ARTHROPLASTY (1980)
    Oxford, UK : Blackwell Publishing Ltd
    Annals of the New York Academy of Sciences 353 (1980), S. 0 
    Details
    ISSN: 1749-6632
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Natural Sciences in General
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1749-6632.1980.tb18931.x
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