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  • Mathematics and Statistics
  • Wiley-Blackwell  (109)
  • American Meteorological Society
  • Blackwell Publishing Ltd
  • Springer Nature
  • 1990-1994  (76)
  • 1980-1984  (33)
  • 1960-1964
  • 1991  (76)
  • 1983  (33)
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  • Wiley-Blackwell  (109)
  • American Meteorological Society
  • Blackwell Publishing Ltd
  • Springer Nature
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  • 1990-1994  (76)
  • 1980-1984  (33)
  • 1960-1964
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  • 1
    Electronic Resource
    Electronic Resource
    The sommerfeld half-plane problem revisited, II the factoring of a matrix of analytic functionsThese results were announced at the XXth General Assembly of the U.R.S.I. held in Washington, D.C., August 1981. (1983)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 5 (1983), S. 14-21 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A half-plane under plane wave excitation obeys a Dirichlet boundary condition on one side and a Neumann boundary condition on the other. These boundary conditions contrast the ones used by A. Sommerfeld in his classical paper. The present problem leads to a system of integral equations of the Wiener-Hopf type which may be solved by a matrix factoring method suggested by A. E. Heins in 1950.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670050103
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  • 2
    Electronic Resource
    Electronic Resource
    Asymptotic equipartition of energy for equations of elasticity (1983)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 5 (1983), S. 186-194 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we give a review of the equipartition of energy results of Goldstein and Sandefur [3], [4], [5] as well as proving a new result in the case of a particular fourth order equation. These results are then applied to the equations of elasticity to give a weak asymptotic orthogonality for the shear and pressure waves. In the case of boundary value problems in the interior of a bounded domain we get weak asymptotic orthogonality in the average.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670050114
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  • 3
    Electronic Resource
    Electronic Resource
    Variational derivatives and p-gradients of functionals on spaces of continuously differentiable functions (1983)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 5 (1983), S. 530-543 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The purpose of this paper is to introduce and study a new type of derivative - the variational gradient - for a functional on Cn[a, b]. Local and global versions of this concept are analyzed. This notion provides a natural approach to variational derivatives on Cn[a, b] under rather mild smoothness assumptions on the functional. When applied in the context of the Calculus of Variations, the notion of the variational gradient captures the natural boundary conditions (as well as the Euler-Lagrange equations) under weaker smoothness assumptions than those usually required using Gǎteaux variations.Conditions are established for the existence of the variational derivative and an integral representation for the Gǎteaux variation in terms of the variational derivative is derived. Conditions for the variational derivative to be differentiable are also established.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670050132
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  • 4
    Electronic Resource
    Electronic Resource
    On mathematical modelling of absorption and dispersion of seismic waves for low frequencies (1991)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 14 (1991), S. 563-572 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The problem of determining the dispersion and absorption of plane seismic waves by a given seismic quality factor is dealt with in the case that the quality factor tends to a positive limit as the frequency goes to zero.General formulae are derived for the phase velocity and the attenuation coefficient by solving the corresponding Riemann-Hilbert problems for analytic functions in the upper half-plane.
    Additional Material: 3 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670140804
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  • 5
    Electronic Resource
    Electronic Resource
    Wiener-hopf equations for waves scattered by a system of parallel sommerfeld half-planes (1991)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 14 (1991), S. 525-552 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A scalar time-harmonic wave (governed by Helmholtz's equation) impinges on N semi-infinite half-planes. The scattered field is sought when first, second, and third-kind boundary conditions or even general linear transmission conditions on the plates ∑m and their complementary parts ∑m′ are prescribed. Making use of the Fourier transform a representation formula for H1 (Ω) solutions is presented. The boundary/transmission problem is shown to be equivalent to a (2N × 2N)-Wiener-Hopf (WH) system for jumps of the Dirichlet-and Neumann-Cauchy data across the semi-infinite screens ∑m. The (2N × 2N)-Fourier symbol matrix SP contains N block matrices on the diagonal corresponding to Sommerfeld boundary/transmission problems for a single plate. These (2 × 2)-symbol matrices are factorizable and thus the full WH system is invertible by a perturbation argument for not too small spacings of neighbouring screens ∑m.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670140802
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  • 6
    Electronic Resource
    Electronic Resource
    Convergence analysis for a multiplicatively relaxed EM algorithm (1991)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 14 (1991), S. 573-593 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The expectation maximization (EM) algorithm is an iterative procedure used to determine maximum likelihood estimators in situations of incomplete data. In the case of independent Poisson variables it converges to a solution of a problem of the form min ∑[〈ai,x〉 - bi log 〈ai, x〉] such that x ≥0. Thus, it can be used to solve systems of the form Ax = b, x≥0 (with A stochastic and b positive.) It converges to a feasible solution if it exists and to an approximate one otherwise (the one that minimizes d (b, Ax), where d is the Kullback-Leibler information divergence). We study the convergence of the multiplicatively relaxed version proposed by Tanaka for use in positron emission tomography. We prove global convergence in the underrelaxed and unrelaxed cases. In the overrelaxed case we present a local convergence theorem together with two partial global results: the sequence generated by the algorithm is bounded and, if it converges, its limit point is a solution of the aforementioned problem.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670140805
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  • 7
    Electronic Resource
    Electronic Resource
    The three-dimensional wigner-poisson problem: Existence, uniqueness and approximation (1991)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 14 (1991), S. 35-61 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We prove the existence of a unique, global classical solution of the quantum Vlasov-Poisson problem posed on the phase space ∝x3 × ∝v3. The proof is based on a reformulation of the quantum Vlasov-Poisson problem as a system of countably many Schrödinger equations coupled to a Poisson equation for the potential. The Schrödinger-Poisson problem is first analysed on a bounded domain in ∝x3 and the solution of the whole-space problem is then obtained by a limiting procedure in which the domains ‘tend’ to ∝x3.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670140103
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  • 8
    Electronic Resource
    Electronic Resource
    Dynamical shape control and the stabilization of non-linear thin rods (1991)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 14 (1991), S. 63-78 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we consider the problem of stabilizing the motion of the tip of a thin rod by controlling the shape of the rod, that is its length, dynamically. Well-posedness of the associated state equations, valid on a moving domain, is proved, and the necessary conditions of optimality for the control problem are derived. The theory applies to materials where the stress-strain relation is both non-linear and non monotone, so that hysteresis effects arising from solid-solid phase transitions in the rod are included.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670140104
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  • 9
    Electronic Resource
    Electronic Resource
    Masthead (1991)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 14 (1991) 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670140301
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  • 10
    Electronic Resource
    Electronic Resource
    Entropy compactification in Lagrangean gas dynamics (1991)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 14 (1991), S. 207-216 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670140305
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