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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Manuscripta mathematica 28 (1979), S. 317-336 
    ISSN: 1432-1785
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract It is a well known theorem for Sturmian boundary value problems Lx=r Rx=0 that the pair (L, R=0) is inverse monotone (i. e. Lx ≧0, Rx=0 ⇒ x≧0) if there exists a weak majorizing element, i. e. a function z≧0 satisfying Lz≧0, Rz=0. We show that this criterion carries over to ordinary boundary value problems of arbitrary order if in addition there exists an inverse monotone pair ‘larger” than (L, R) in a certain sense. This follows from a variant of Schröder's theorem [10] combined with a result on strict monotonicity of nonnegative Green's functions. However, it will also be shown that the additional condition can only be dispensed with, if the boundary value problem is at most of the second order. Furthermore an analogous result holds, for elliptic boundary value problems in arbitrary dimensions.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Numerische Mathematik 29 (1978), S. 209-226 
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65L 10 ; CR: 5.17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary In this paper we give a simple stability theory for finite difference approximations to linear ordinary boundary value problems. In particular we consider stability with respect to a maximum norm including all difference quotients up to the order of the differential equation. It is shown that stability in this sense holds if and only if the principal part of the differential equation is discretized in a “stable way”. This last property is characterized by root conditions which we prove to be satisfied for some classes of finite difference schemes. Our approach simplifies and generalizes some known results of the literature where Sobolev norms or merely the maximum norm are used.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Numerische Mathematik 80 (1998), S. 1-38 
    ISSN: 0945-3245
    Keywords: Mathematics Subject Classification (1991): 34C35, 58F14, 65F50, 65H17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary. In this paper we develop a numerical method for computing higher order local approximations of invariant manifolds, such as stable, unstable or center manifolds near steady states of a dynamical system. The underlying system is assumed to be large in the sense that a large sparse Jacobian at the equilibrium occurs, for which only a linear (black box) solver and a low dimensional invariant subspace is available, but for which methods like the QR–Algorithm are considered to be too expensive. Our method is based on an analysis of the multilinear Sylvester equations for the higher derivatives which can be solved under certain nonresonance conditions. These conditions are weaker than the standard gap conditions on the spectrum which guarantee the existence of the invariant manifold. The final algorithm requires the solution of several large linear systems with a bordered Jacobian. To these systems we apply a block elimination method recently developed by Govaerts and Pryce [12, 14].
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Numerische Mathematik 51 (1987), S. 103-122 
    ISSN: 0945-3245
    Keywords: AMS(MOS) 65L05, 58F08, 58F22 ; CR: G1.7
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We show that a one-step method as applied to a dynamical system with a hyperbolic periodic orbit, exhibits an invariant closed curve for sufficiently small step size. This invariant curve converges to the periodic orbit with the order of the method and it inherits the stability of the periodic orbit. The dynamics of the one-step method on the invariant curve can be described by the rotation number for which we derive an asymptotic expression. Our results complement those of [2, 3] where one-step methods were shown to create invariant curves if the dynamical system has a periodic orbit which is stable in either time direction or if the system undergoes a Hopf bifurcation.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    s.l. : American Chemical Society
    The @journal of organic chemistry 46 (1981), S. 5119-5124 
    ISSN: 1520-6904
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Review of Scientific Instruments 63 (1992), S. 3752-3756 
    ISSN: 1089-7623
    Source: AIP Digital Archive
    Topics: Physics , Electrical Engineering, Measurement and Control Technology
    Notes: In this article, a new curve of the correction factor for the measurement of sheet resistance of a square sample with a square four-point probe is presented by using the theory of conformal transformation. This curve is quite different from that obtained by using the theory of infinite dipoles. An experimental curve is recommended to use. The function of the conformal transformation used in this article is simple and can be easily used for solving the problem of boundary effect of current field. The theoretical curve is suitable to the boundary areas of wafers.
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Review of Scientific Instruments 63 (1992), S. 3757-3762 
    ISSN: 1089-7623
    Source: AIP Digital Archive
    Topics: Physics , Electrical Engineering, Measurement and Control Technology
    Notes: By using conformal transformation to take account of the boundary effect, it has been confirmed that there are some areas of a square sample near the corners besides the boundary suitable to the resistance measurement of Van der Pauw's method. The theoretical criterion of the suitability is whether Van der Pauw's formula for calculation of the sheet resistance is still valid provided the voltage values in the formula for two times the measurement are substituted with those obtained by using the theory of conformal transformation. The experimental criterion is whether the experimental values of sheet resistance for probes in some areas are equal to that for them at the boundary for the same sample. The experimentally confirmed areas are larger than what the theory predicts. Our repeated experiments show that the areas out of the circle tangent to the boundary are suitable to Van der Pauw's method.
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 65 (1989), S. 3983-3986 
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The X-band electron-spin-resonance spectra of Fe-doped [Ca,Y](Ti,Al)O3 perovskite single crystals show five resonant lines. Two of the five lines have an inverse phase in the first-derivative curve. The possibility of emission transition of a paramagnetic ion in an anisotropic environment and/or in the presence of oscillating distortions is discussed in this paper.
    Type of Medium: Electronic Resource
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  • 9
    Electronic Resource
    Electronic Resource
    Cambridge : Cambridge University Press
    Ageing and society 3 (1983), S. 23-42 
    ISSN: 0144-686X
    Source: Cambridge Journals Digital Archives
    Topics: Medicine , Sociology
    Notes: The analysis of modern-age stratification systems must be based on the social organisation of work. This requires a theoretical approach that takes into account the structure of economic production, but also the fact that work is a meaningful activity of human beings within their life-world. The task therefore consists of integrating ‘materialist’ and ‘interpretive’ approaches to social reality. This integration is attempted in an examination of the special problems encountered by workers in the second half of their work life, as created by the ‘construction of ageing’ in the industrial firm. Existing approaches drawn from industrial sociology, stress structural features of the production process, whilst labelling theory stresses culturally induced age labels. Both are one-sided. A more comprehensive approach has to conceptualise the industrial firm as an actor with strategies based on economic rationality and as a life-world constituted by what is taken for granted by its members. The final section applies this framework to an empirical case study.
    Type of Medium: Electronic Resource
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  • 10
    ISSN: 1438-2385
    Source: Springer Online Journal Archives 1860-2000
    Topics: Process Engineering, Biotechnology, Nutrition Technology
    Notes: Zusammenfassung Für die Bestimmung des monomeren Acrylnitrils und Styrols einzeln und nebeneinander in Styrolpolymerisaten wurde eine besonders einfache Apparatur zur Isolierung der Monomeren aus den flüchtigen Bestandteilen entwickelt. Die in Dimethylformamid absorbierten monomeren Verbindungen werden nach Zusatz des Leitelektrolyten polarographisch bestimmt. Die Nachweisempfindlichkeit des polarographischen Verfahrens liegt bei 2 μg Acrylnitril bzw. 4 μg Styrol/ml Mcßlösung. Die Methode wird zur schnellen and einfachen Prüfung von Polystyrol und Polystyrol-Mischpolymerisaten als Bedarfsgegenstände im Sinne des Lebensmittelgesetzes vorgeschlagen und ermöglicht mit Sicherheit, Acrylnitril und Styrol in Plasten in Konzentrationen bis zu 0,01 % herab zu bestimmen.
    Type of Medium: Electronic Resource
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