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  • 11
    Electronic Resource
    Electronic Resource
    On the spectral decompositions of the linear transport operator with periodic boundary conditions (1976)
    Springer
    Letters in mathematical physics 1 (1976), S. 329-333 
    Details
    ISSN: 1573-0530
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract It is shown that the linear transport operator for a slab with periodic boundary conditions, or for infinite medium, can be analyzed within the Friedrichs' model of perturbation for non-selfadjoint operators. This leads to rephrasing Case's generalized eigenfunction expansion in terms of Hilbert space operators only.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00398489
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  • 12
    Electronic Resource
    Electronic Resource
    Asymptotic equivalence between the hydrodynamic and kinetic stages for the Lorentz model (1979)
    Springer
    Letters in mathematical physics 3 (1979), S. 87-92 
    Details
    ISSN: 1573-0530
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract The asymptotic equivalence between the kinetic and hydrodynamic evolutions for the Lorentz model in a semi-infinite medium with a perfectly reflecting boundary is proved in a Hilbert space formalism.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00400061
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  • 13
    Electronic Resource
    Electronic Resource
    Exact solutions for a semilinear hyperbolic system with general quadratic interactions (1990)
    Springer
    Il nuovo cimento della Società Italiana di Fisica 12 (1990), S. 1153-1163 
    Details
    ISSN: 0392-6737
    Keywords: Kinetic and transport theory ; Other topics in mathematical methods in physics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Summary The approximate conservation laws for a binary gas mixture with quadratic interactions can be written as a system of two semilinear hyperbolic equations. By using the method of characteristics the study of this system is reduced to the study of a system of nonlinear ordinary differential equations, for which we find several classes of exact solutions. Exact integrability conditions are found for ODE systems of generalized Lotka-Volterra type. Some situations are also considered, in which the characteristic method cannot be applied and exact solutions are obtained via an operator method.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02451957
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  • 14
    Electronic Resource
    Electronic Resource
    A minimax problem for semilinear nonlocal competitive systems (1993)
    Springer
    Applied mathematics & optimization 28 (1993), S. 113-132 
    Details
    ISSN: 1432-0606
    Keywords: Elliptic systems ; Nonlinear competitive interactions ; Game theory ; Optimal control ; 49A45 ; 35K10
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A two-sided game for the control of a stationary semilinear competitive system with autonomous sources is considered, where the controls are the kernels of the nonlocal interaction terms. The saddle point (the optimal solution of the game) is characterized as the unique solution of the associated optimality system, which is solved by an iterative scheme.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01182976
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  • 15
    Electronic Resource
    Electronic Resource
    On stable potentials (1971)
    Springer
    Communications in mathematical physics 22 (1971), S. 162-165 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract Examples are given of one- and two-dimensional stable potentials which cannot be decomposed into the sum of a non-negative function and a continuous stable potential.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01651335
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  • 16
    Electronic Resource
    Electronic Resource
    Single-Iteration Training Algorithm for Multi-Layer Feed-Forward Neural Networks (2000)
    Springer
    Neural processing letters 11 (2000), S. 113-129 
    Details
    ISSN: 1573-773X
    Keywords: virtual input layer ; neural network training ; fast learning ; SVD
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract A new methodology for neural learning is presented. Only a single iteration is needed to train a feed-forward network with near-optimal results. This is achieved by introducing a key modification to the conventional multi-layer architecture. A virtual input layer is implemented, which is connected to the nominal input layer by a special nonlinear transfer function, and to the first hidden layer by regular (linear) synapses. A sequence of alternating direction singular value decompositions is then used to determine precisely the inter-layer synaptic weights. This computational paradigm exploits the known separability of the linear (inter-layer propagation) and nonlinear (neuron activation) aspects of information transfer within a neural network. Examples show that the trained neural networks generalize well.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1009682730770
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  • 17
    Electronic Resource
    Electronic Resource
    The spectral decomposition for a class of linear transport operators (1982)
    Springer
    Journal of statistical physics 29 (1982), S. 363-374 
    Details
    ISSN: 1572-9613
    Keywords: Linear transport (Boltzmann) operator ; two-dimensional spectrum ; spectral decomposition ; generalized eigenfunction expansion
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The spectral decomposition theorem is proved for linear transport operators with separable scattering kernels and energy-dependent collision frequency in both one- and three-dimensional geometries.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01020792
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  • 18
    Electronic Resource
    Electronic Resource
    Half-range completeness for the Fokker-Planck equation (1983)
    Springer
    Journal of statistical physics 32 (1983), S. 565-584 
    Details
    ISSN: 1572-9613
    Keywords: Fokker-Planck equation (stationary and time dependent) ; boundary conditions (perfectly absorbing, partially absorbing, purely specularly reflecting) ; half-range completeness ; semi-infinite medium ; slab geometry
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Half-range completeness theorems are proved for eigenfunctions associated to the one-dimensional Fokker-Planck equation in a semi-infinite medium. Existence and uniqueness results for perfectly absorbing, partially absorbing, and purely specularly reflecting boundary conditions are deduced for the stationary and time-dependent problems. Similar results are obtained for a slab geometry.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01008957
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  • 19
    Electronic Resource
    Electronic Resource
    Optimal control for parabolic systems with competitive interactions (1994)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 17 (1994), S. 509-524 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider a two-dimensional parabolic system with general competitive interactions as a two-player game with conflicting objectives and with controls on the inhomogencous (source) terms. We show the existence of an optimal solution of the game as the saddle point of a suitable objective functional.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670170703
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  • 20
    Electronic Resource
    Electronic Resource
    Relationship Between the Albedo and Scattering Operators for the Boltzmann Equation with Semi-transparent Boundary Conditions (1996)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 19 (1996), S. 1-13 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The albedo and scattering operators are central objects in the time-dependent transport theory. Their mutual relationship has recently been established by Arianfar and Emamirad for the case of transparent boundaries. In this paper, we extend the result to general boundary conditions. To allow for this extension, the scattering theory for a transport-like equation is generalized to include partially reflecting boundary conditions. The existence of the wave and scattering operators is directly inferred from the properties of the evolution operators that are determined, in turn, by the physics of collisions within and at the boundaries of the scattering domain.
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