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  • 1
    Electronic Resource
    Electronic Resource
    State function and spectral properties of a two-component interacting Fermi gas (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 164-169 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Rules are derived for the computation of the spectrum and state function of a system of N fermions in one dimension interacting with a delta function potential. The system is composed of fermions of two types of internal symmetry. The rules are valid for an arbitrary number of either symmetry type and any value of the delta function interaction strength. The state functions satisfy periodic boundary conditions, and therefore describe the interacting system at nonzero density.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528855
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Three interacting particles in one dimension: An algebraic approach (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 155-168 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: An algebraic formulation of the problem of three particles in one dimension is given, where the particles interact with delta function potentials of arbitrary strength and have almost arbitrary mass. An algebraic formulation is taken to mean that the steps implied from formulation to solution involve finite algebra. The canonical example is equal mass particles interacting with equal strength delta function potentials, where the Bethe ansatz holds and the solution involves only sums of products of matrices with elements that are rational functions of a complex variable. When the Bethe ansatz fails the Sommerfeld diffraction ansatz is satisfied if a condition of internal consistency is met. This condition of internal consistency requires the solution to a Riemann–Hilbert functional equation with an algebraic coefficient. The solution to this functional equation is an analytic, but not generally a meromorphic function. It is demonstrated that an asymptotic solution may be constructed within the domain of algebraic functions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528168
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Simulation of nonlinear reaction-diffusion equations (1977)
    Springer
    Bulletin of mathematical biology 39 (1977), S. 391-396 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Discrete particle simulation techniques developed for problems in plasma physics have been adapted to investigate one-dimensional dissipative structures. The results of the model are found to be consistent with bifurcation analysis of nonlinear reaction-diffusion equations. Two distinct type of behavior are observed corresponding to a localized steady-state solution and a time-dependent solution.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02462918
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    On limits to perception and pattern recognition (1989)
    Springer
    Bulletin of mathematical biology 51 (1989), S. 681-686 
    Details
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract We propose certain general conditions that we believe are reasonable for any pattern recognition algorithm. We find that these conditions give rise to paradoxical identification. The algorithms are incapable of distinguishing composite patterns and must be able to distinguish patterns at an atomistic level.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02459655
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  • 5
    Electronic Resource
    Electronic Resource
    The spherical hierarchical model (1973)
    Springer
    Communications in mathematical physics 32 (1973), S. 215-230 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract The spherical version of Dyson's hierarchical model is analyzed. A particular case which is designed to simulate the long-range Ising problem is dealt with in detail. A phase transition is found with critical temperature $$\beta _c = \tfrac{1}{2}(2^\alpha - 2)(4 - 2^\alpha )^{ - 1} $$ wheren th neighbor spins interact with a strength ofn −α. Critical exponents are calculated for this particular case and are found to be identical with the critical exponents of the long-range spherical Ising model.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01645593
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    Paper (German National Licenses)
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  • 6
    Electronic Resource
    Electronic Resource
    Book review (1994)
    Springer
    Foundations of physics 24 (1994), S. 811-812 
    Details
    ISSN: 1572-9516
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02054676
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    Paper (German National Licenses)
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  • 7
    Electronic Resource
    Electronic Resource
    Asymptotic and essentially singular solutions of the Feigenbaum equation (1988)
    Springer
    Journal of statistical physics 51 (1988), S. 991-1007 
    Details
    ISSN: 1572-9613
    Keywords: Feigenbaum ; largeN ; iteration ; doubling transformation ; universal ; fixed point ; feigenvalue
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract For suitably defined largeN, we express Feigenbaum's equation as a singular Schroder functional equation whose solution is obtained using a scaling ansatz. In the limit of infiniteN certain self-consistency conditions on the scaled Schroder solution lead to an essentially singular solution of Feigenbaum's equation with a length scale factor of α≅ 0.0333 and. a limiting feigenvalue of δ∞≃30.50, in agreement with Eckmann and Wittwer's value of α=0.0333831... and their conjectured estimate of δ∞≲30.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01014896
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    Paper (German National Licenses)
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