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  • Articles  (9,040)
  • Wiley-Blackwell  (9,040)
  • American Association for the Advancement of Science (AAAS)
  • Mathematics  (9,040)
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  • 1
    Electronic Resource
    Electronic Resource
    Finite elements for incompressible flow (1979)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 1 (1979), S. 16-31 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We describe in this paper a finite element method for the solution of viscous incompressible flow problems which incorporates an approximate form of the incompressibility condition automatically into the finite element basis. Several examples of such finite elements are presented and applied to a simple test problem.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670010103
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  • 2
    Electronic Resource
    Electronic Resource
    On the limiting behaviour of solutions to boundary integral equations associated with time harmonic wave equations for small frequencies (1979)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 1 (1979), S. 89-100 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The treatment of boundary value problems for Helmholtz equation and for the time harmonic Maxwell's equations by boundary integral equations leads to integral equations of the second kind which are uniquely solvable for small positive frequencies λ. However, the integral equations obtained in the limiting case λ = 0 which are related to boundary value problems of potential theory in general are not uniquely solvable since the corresponding boundary value problems are not. By first considering in a general setting of a Banach space X the limiting behaviour of solutions φλ to the equation φλ - K λ φ λ = fλ as λ → 0 where {Kλ: X → X, λ ∊ (0,α)}, α 〉 0, denotes a family of compact linear operators such that I - Kλ (I identity) is bijective for λ∊(0,α) whilst I - K0 is not and ‖ Kλ - K0‖ →, 0, ‖fλ - f0‖ → 0, λ → 0, and then applying the results to the boundary integral operators, the limiting behaviour of the integral equations is considered. Thus, the results obtained by Mac Camey for the Helmholtz equation are extended to the case of non-connected boundaries and Werner's results on the integral equations for the Maxwell's equations are extended to the case of multiply connected boundaries.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670010108
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  • 3
    Electronic Resource
    Electronic Resource
    Zur Theorie der Integraltransformationen (1979)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 1 (1979), S. 114-125 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Let A be a selfadjoint uniformly elliptic differential operator. Let the underlying domain be bounded. Eigenvalue problems can be solved then, and an arbitrary square integrable function may be developed in a Fourier series relative to the eigenfunctions. In general elliptic differential operators have a continuous spectrum, if the underlying domain is unbounded. In this case the spectral theorem provides a representation of a given function by an integral transformation. The spectral projector can be calculated, if the outgoing and incoming solutions are known (radiation condition). Thus integral transformations may be derived very easily. Four examples will be given: the Fourier sine transform, the Lebedev transform, the transformation belonging to the Dirichlet problem of the plate equation and, finally, the Fourier transformation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670010110
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  • 4
    Electronic Resource
    Electronic Resource
    Ein algebraisches Verfahren zur Lösung von gemischten Anfangsrandwertproblemen aus der Theorie instationärer GitterströmungenHerrn Prof. Dr. H. Söhngen zu seinem 70. Geburtstage am 30. November 1978 gewidmet. (1979)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 1 (1979), S. 158-186 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Mixed boundary value problems for the wave-equation in the x-y-plane, with boundaries parallel to the x-axis, are usually treated by Laplacetransformation. To use this method numerically we present it here by means of the Mikusiński-calculus. In this paper our main interest lies in the treatment of mixed initial-boundary value problems arising in unsteady subsonic cascade flow.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670010204
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  • 5
    Electronic Resource
    Electronic Resource
    Asymptotic expansions for central limit theorems for general linear stochastic processes. I: General theorems on rates of convergence (1979)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 1 (1979), S. 241-264 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This paper deals with so-called general linear stochastic processes (GLSP), defined by T. Kawata in 1972 in generalization of work of R. Lugannani and J. B. Thomas of 1967/71. These second order processes (which are not necessarily stationary nor have independent increments) are described by rather weak requirements, so that several processes such as some random noise and pulse train processes are specific models of these GLSP. Part I is concerned with two general theorems giving asymptotic expansions (including those for the density function) in the central limit theorem for such GLSP, together with error rates. The assumptions for the corresponding θ- and o-error estimates seem rather natural: in the former, apart from assumptions on the inherent structure of such GLSP, the existence of certain moments of higher order as well as a Cramer-type condition are assumed, in the latter in addition a Lindeberg-type condition of higher order. Fourier analytic machinery is used for the proofs.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670010208
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  • 6
    Electronic Resource
    Electronic Resource
    Asymptotic expansions for central limit theorems for general linear stochastic processes. II: Models of the general random noise and pulse train processes (1979)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 1 (1979), S. 346-353 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This part is concerned with the applications of the theorems on error estimates for asymptotic expansions in the central limit theorem for general linear stochastic processes of Part I to two important typical models. These are the general random noise process and a class of pulse train processes that occur in stochastic signal theory and in a variety of digital communication schemes. The assumptions on the inherent structure of the general theorems turn out to be simple here.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670010304
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  • 7
    Electronic Resource
    Electronic Resource
    On boundary controllability of one-dimensional vibrating systems (1979)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 1 (1979), S. 322-345 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper boundary controllability of one-dimensional vibrating system such as the vibrating string or the vibrating beam is studied. In particular we are concerned with the question whether it is possible to transfer a given initial state of vibration into rest within a given time such that the system stays in rest when the control is turned off.This problem is rephrased as a typical trigonometric moment problem which is solved within the framework of an abstract moment problem in a Hilbert space. The results of null-controllability which are obtained are substantially based on classical results of Ingham and Redheffer concerning trigonometric inequalities and incompleteness of certain sequences of trigonometric functions, respectively. The representation of the general statements follows closely the lines of a paper of Russell. Besides a special case is treated where explicit representations of boundary controls can be given that transfer the system to a permanent rest position. This special case includes amplitude boundary control of the vibrating string and the freely supported beam.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670010303
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  • 8
    Electronic Resource
    Electronic Resource
    On the integral equation method for the plane mixed boundary value problem of the Laplacian (1979)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 1 (1979), S. 265-321 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Although the plane boundary value problem for the Laplacian with given Dirichlet data on one part Γ2 and given Neumann data on the remaining part Γ2 of the boundary is the simplest case of mixed boundary value problems, we present several applications in classical mathematical physics. Using Green's formula the problem is converted into a system of Fredholm integral equations for the yet unknown values of the solution u on Γ2 and the also desired values of the normal derivatie on Γ1. One of these equations has principal part of the second kind, whereas that one of the other is of the first kind. Since any improvement of constructive methods requires higher regularity of u but, on the other hand, grad u possesses singularities at the collision points Γ1 ∩ Γ2 even for C∞ data, u is decomposed into special singular terms and a regular rest. This is incorporated into the integral equations and the modified system is solved in appropriate Sobolev spaces. The solution of the system requires to solve a Fredholm equation of the first kind on the arc Γ2 providing an improvement of regularity for the smooth part of u. Since the integral equations form a strongly elliptic system of pseudodifferential operators, the Galerkin procedure converges. Using regular finite element functions on Γ1 and Γ2 augmented by the special singular functions we obtain optimal order of asymptotic convergence in the norm corresponding to the energy norm of u and also superconvergence as well as high orders in smoother norms if the given data are smooth (and not the solution).
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670010302
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  • 9
    Electronic Resource
    Electronic Resource
    On a class of elliptic singular perturbations with applications in population genetics (1979)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 1 (1979), S. 432-441 
    Details
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: With the maximum principle for differential equations asymptotic estimates are made for a class of linear elliptic singular perturbation problems with resonant turning point behaviour in some of the independent variables. The method is applied to the stationary solution of the Kolmogorov backward equation in population genetics.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/mma.1670010308
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  • 10
    Electronic Resource
    Electronic Resource
    Zum 70. Geburtstag von Henry Görtler (1979)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 1 (1979), S. 443-444 
    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.1670010402
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