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  • Articles  (1,121)
  • Wiley-Blackwell  (1,121)
  • American Association for the Advancement of Science (AAAS)
  • 1980-1984  (1,121)
  • Mathematics  (1,121)
  • 1
    Electronic Resource
    Electronic Resource
    Masthead (1980)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 2 (1980) 
    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.1670020301
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  • 2
    Electronic Resource
    Electronic Resource
    Über das Verhalten der Lösungen der Maxwellschen Randwertaufgabe in Gebieten mit Kegelspitzen (1980)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 2 (1980), S. 235-250 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We study the behavior of the solution E of the Maxwell's boundary value problem ∇ × ∇ × E + λE = F, n × E|r = 0 in domains Ω which have conical boundary points. In a neighbourhood K(R) = B(a,R) ∩ Ω of a singular boundary point a the field E is expanded using a theorem of N. Weck. It e.g. turns out that the solution lies in H1(3)(K(R)) if K(R) is convex.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670020209
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  • 3
    Electronic Resource
    Electronic Resource
    Eigenvalue bounds for Hill's equationThis work was performed under the terms of the agreement on association between Max-Planck-Institut for Plasmaphysik and EURATOM. (1980)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 2 (1980), S. 288-302 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: For Hill's equation the lowest eigenvalue a0 of the boundary value problem y(x + 1) = y(x) is considered. Introducing Lp norms of the function f(x), lower bounds for a0 which depend only on this norm are derived for p = 1,2 and ∞ by solving a variational principle. For these lower bounds analytical expressions are obtained. The quality of the approximations thus obtained is discussed for Mathieu's equation and an application in magnetohydrodynamics is considered.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670020304
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  • 4
    Electronic Resource
    Electronic Resource
    A local compactness theorem for Maxwell's equations (1980)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 2 (1980), S. 12-25 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The paper gives a proof, valid for a large class of bounded domains, of the following compactness statements: Let G be a bounded domain, β be a tensor-valued function on G satisfying certain restrictions, and let {n} be a sequence of vector-valued functions on G where the L2-norms of {n}, {curl n}, and {div(β n)} are bounded, and where all n either satisfy x n = 0 or (β Fn) = 0 at the boundary ∂G of G ( = normal to ∂G): then {n} has a L2-convergent subsequence. The first boundary condition is satisfied by electric fields, the second one by magnetic fields at a perfectly conducting boundary ∂G if β is interpreted as electric dielectricity ∊ or as magnetic permeability μ, respectively.These compactness statements are essential for the application of abstract scattering theory to the boundary value problem for Maxwell's equations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670020103
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  • 5
    Electronic Resource
    Electronic Resource
    Gradient bounds for plasma confinement (1980)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 2 (1980), S. 68-72 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The problem of plasma confinement in a Tokomak machine has recently attracted considerable mathematical attention. In the present article, gradient bounds for the solution are obtained through the use of differential inequalities and the Hopf maximum principle. These estimates, which take slightly different forms in the plasma and vacuum regions, become exact in the one-dimensional case. An estimate is also given for the distance from the boundary of the interior point where the maximum of the solution is attained.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670020107
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  • 6
    Electronic Resource
    Electronic Resource
    Differentiable dependence upon the data in a one-phase Stefan problem (1980)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 2 (1980), S. 73-90 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: It is well known that the free boundary of the one-phase Stefan problem (1.1-5) depends continuously on the boundary data [1]. In this paper we prove that, in addition, the solution operator S which, to each g. assigns the corresponding free boundary, is continuously Frechet differentiable and we give the defining formulas of the Frechet derivative.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670020108
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  • 7
    Electronic Resource
    Electronic Resource
    Über die Radon-Transformation kreissymmetrischer Funktionen und ihre Beziehung zur Sommerfeldschen Theorie der Hankelfunktionen (1980)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 2 (1980), S. 108-129 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: For the Radon transform of functions with circular symmetry an inversion formula is proved in a new and elementary way. The inversion formula combined with Fourier theory is applied to Sommer-feld's integral for Hv1, yielding a representation of products which generalizes Nicholson's integral for |Hv(1)| 2.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670020110
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  • 8
    Electronic Resource
    Electronic Resource
    A finite element method for the double-layer potential solutions of the Neumann exterior problem (1980)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 2 (1980), S. 191-208 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A variational formulation for the integral equation used for the double layer potential solution of the Neumann exterior problem in the Laplace equation was proposed in [4]. This formulation allows the use of a finite element method which we describe and experiment here.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670020206
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  • 9
    Electronic Resource
    Electronic Resource
    Uniform convergence of the horizontal line method for solutions and free boundaries in Stefan evolution inequalities (1980)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 2 (1980), S. 149-167 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The change of variable for the temperature Θ in the one-phase Stefan problem leads to the evolution inequality, (ut - Δu - f)(v - u) ≥ 0 for all regular v ≥ 0, where u ≥ 0 is required. This inequality is to hold over a space-time domain D = Ω × (0, T) with a Dirichlet boundary condition imposed on ∂ Ω × (0, T) and a zero initial condition. The free boundary phase interface is given in one space dimension by The fully implicit divided difference scheme leads to a sequence of elliptic variational inequalities for {um}. The sequence {um} may be interpolated linearly in t to obtain an approximation UΔt of u. The following results are obtained in this paper: (i) a two-sided weak maximum principle for um - um-1 in N space dimensions, hence the free boundary approximation for N = 1, is a monotone increasing step function; (ii) the uniform convergence of UΔt and ∇UΔt, to u and ∇u, respectively, on D; (iii) the uniform convergence to the Hölder continuous, monotone increasing free boundary x on [0, T] of the piecewise linear sequence xΔt, where xΔt interpolates xΔt, in one space dimension; (iv) a constructive existence proof for u and x in prescribed regularity classes.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670020203
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  • 10
    Electronic Resource
    Electronic Resource
    Picture reconstruction from projections in restricted range (1980)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 2 (1980), S. 209-220 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In order to reduce scanning time modern x-ray scanners provide projections only in a restricted range [0, φ] with φ 〈 π. We consider the reconstruction of pictures from p + 1 complete projections in [0, φ]. An extrapolation procedure is given to achieve approximations gp of the data in the whole range. We show that the L2-error of the corresponding picture is of order p-α if the original belongs to the Sobolev space Hoα. The validity of our error estimate is investigated by numerical experiments.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670020207
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