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  • Mathematics and Statistics  (340)
  • Wiley-Blackwell  (340)
  • American Meteorological Society
  • Springer Nature
  • 1985-1989  (340)
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Keywords
Publisher
  • Wiley-Blackwell  (340)
  • American Meteorological Society
  • Springer Nature
Years
Year
  • 1
    Electronic Resource
    Electronic Resource
    Finite elements for the eigenvalue problem of differential operators in unbounded intervals (1985)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 7 (1985), S. 1-39 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The eigenvalue problem for one-dimensional differential operators with a possible essential spectrum is discretized with finite elements defined on a bounded interval together with a fundamental system of the differential equation outside of the interval. A non-pollution property of the discrete spectra is proved and the error in the approximation of isolated eigenvalues and corresponding eigenvectors is estimated. The convergence of some numerical algorithms for the solution of the subsequent discrete nonlinear eigenvalue problem is proved. The method is tested in some numerical examples.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670070102
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  • 2
    Electronic Resource
    Electronic Resource
    On spline collocation methods for boundary integral equations in the plane (1985)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 7 (1985), S. 74-89 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Nowadays boundary elemen; methods belong to the most popular numerical methods for solving elliptic boundary value problems. They consist in the reduction of the problem to equivalent integral equations (or certain generalizations) on the boundary Γ of the given domain and the approximate solution of these boundary equations. For the numerical treatment the boundary surface is decomposed into a finite number of segments and the unknown functions are approximated by corresponding finite elements and usually determined by collocation and Galerkin procedures. One finds the least difficulties in the theoretical foundation of the convergence of Galerkin methods for certain classes of equations, whereas the convergence of collocation methods, which are mostly used in numerical computations, has yet been proved only for special equations and methods.In the present paper we analyse spline collocation methods on uniform meshes with variable collocation points for one-dimensional pseudodifferential equations on a closed curve with convolutional principal parts, which encompass many classes of boundary integral equations in the plane. We give necessary and sufficient conditions for convergence and prove asymptotic error estimates. In particular we generalize some results on nodal and midpoint collocation obtained in [2], [7] and [8].The paper is organized as follows. In Section 1 we formulate the problems and the results, Section 2 deals with spline interpolation in periodic Sobolev spaces, and in Section 3 we prove the convergence theorems for the considered collocation methods.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670070105
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  • 3
    Electronic Resource
    Electronic Resource
    A method of iterative data refinement and its applications (1985)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 7 (1985), S. 108-123 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Iterative data refinement (IDR) is a general procedure for producing a sequence of estimates of the data that would be collected by a measuring device which is idealized to a certain extent, starting from the data that are collected by an actual measuring device. Following a discussion of the fundamentals of IDR, we present a number of previously published procedures which are special cases of it. We concentrate on examples from medical imaging. In particular, we discuss beam hardening correction in x-ray computerized tomography, attenuation correction in emission computerized tomography, and compensation for missing data in reconstruction from projections. We also show that a standard method of numerical mathematics (the parallel chord method) as well as a whole family of constrained iterative restoration algorithms are special cases of IDR. Thus IDR provides a common framework within which a number of originally different looking procedures are presented and discussed. We also present a result of theoretical nature concerning the initial behavior of IDR.
    Additional Material: 2 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670070108
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  • 4
    Electronic Resource
    Electronic Resource
    Zur Asymptotik der wellengleichung und der wärmeleitungsgleichung in zweidimensionalen außenräumenHerrn Professor Claus Müller zum 65. Geburtstag am 20. 2. 1985 gewidmet. (1985)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 7 (1985), S. 170-201 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We study initial and boundary value problems for the wave equation and the heat equation with a time-independent right-hand term f in two space dimensions in the exterior of a closed curve C. In the case of Neumann's boundary condition ∂u/∂n = 0 on C, the solutions increase with a logarithmic rate as t → ∞ if ∫ fdx ≠ 0. In contrast to this, the solutions of the corresponding Dirichlet problems converge to the solution of the related static problem as t → ∞. In the case of the wave equation, these results have already been obtained by L: A. Muravei under the additional assumption that the curvature of C is positive, by using high frequency estimates for the reduced wave equation Δ U + ϰ2 U = 0. The analysis presented here is based on different methods, which can be applied to arbitrary smooth curves.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670070111
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  • 5
    Electronic Resource
    Electronic Resource
    Asymptotic analysis of differential-delay equations and nonuniqueness of periodic solutions (1985)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 7 (1985), S. 223-237 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We study the differential-delay equation x′(t) = -αf(x(t-1)), where α is a positive parameter and f is an odd function which decays like x-r at infinity. In particular, we consider the case r ≤ 2, and prove the existence of periodic solutions with special symmetries which are different from previously known periodic solutions of minimal period 4. For r = 2 we prove sharp asymptotic estimates for the minimal periods of these solutions.Our results disprove a conjecture of R. D. Nussbaum.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670070114
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  • 6
    Electronic Resource
    Electronic Resource
    An integral equation of elasticity (1985)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 7 (1985), S. 261-268 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this work a certain mixed problem in R+3 for the Lamé equations in the theory of elasticity is reduced to the integral equationAn explicit formula for the solutions is given for either Ω = {x:x2 〉 0} or Ω = {x:∥x∥〈r}. The question of smoothness of the solutions is also discused. Another formulae on Ω = {x:∥x∥〈r} are found in [5], [4]. It seems that the techniques used below allows a deeper investigation of properties of the solutions to problem (*).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670070117
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  • 7
    Electronic Resource
    Electronic Resource
    Addendum (1985)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 7 (1985), S. 330-331 
    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.1670070121
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  • 8
    Electronic Resource
    Electronic Resource
    Relative influence of two small parameters in non uniformly elliptic homogenization problems (1985)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 7 (1985), S. 367-381 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We study three elliptic problems depending on two small parameters (∊ = homogenization parameter and δ = perturbation parameter which causes non uniform ellipticity). In each case, the homogenized operator corresponding to the second order operator is independent of the way (∊, δ) → (0, 0), but the convergence results and the limit solution do depend on the relative size of ∊ and δ; the relevant parameter is δ∊-2.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670070125
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  • 9
    Electronic Resource
    Electronic Resource
    On the absolutely continuous spectrum of MHD plasma confined in the flat torus (1985)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 7 (1985), S. 432-442 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The spectral properties of the linearized MHD operator are investigated applying the theory of trace class perturbation. Especially, it is shown that the essential spectrum in the positive (stable) part of the spectrum contains the absolutely continuous one and the corresponding part of the spectrum is unitarily equivalent to some multiplication operator.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670070130
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  • 10
    Electronic Resource
    Electronic Resource
    On the existence of optimum large amplitude hydrofoil propulsion (1985)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 7 (1985), S. 125-153 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The possibility of optimum thrust-production by means of periodic motions of a flexible wing is discussed. The disturbance velocities are assumed to be small so that a linearized theory is valid. It is proved that when adequate constraints are put upon the amplitude of the path of the wing and on the amplitude of its slopes and curvature, an optimum path exists.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670070109
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