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Otto Molerus 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1964,15(3):262-272
Résumé Les oscillations longitudinales par contraction et dilatation du pendule élastique double passent, pour certaines fréquences d'excitation, alternativement de mouvements longitudinaux à des mouvements transversaux. En première approximation, l'analyse de la stabilité des oscillations longitudinales aboutit à un système linéaire d'équations différentielles à coefficients périodiques. Par conséquent, l'instabilité des oscillations longitudinales par contraction et dilatation du pendule élastique double peut servir à la démonstration des régimes d'instabilité du premier et du second ordre se rapportant aux systèmes d'oscillations mécaniques et rhéolinéaires à plusieurs degrés de liberté. 相似文献
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Johann Radon 《Archiv der Mathematik》1954,5(4-6):309-316
Ohne Zusammenfassung
Alexander Ostrowski zum 60. Geburtstag gewidmet 相似文献
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Karlheinz Schüffler 《manuscripta mathematica》1982,40(1):1-15
In the Sobolev space Hm(B,?3), B the open unit disc in ?2, we consider the set Mn of all conformally parametrized surfaces of constant mean curvature H with exactly n simple interior branch points (and no others). We denote by M*n the set of all xεMn with the following properties:
- in every branch point the geometrical condition KG¦xZ¦≡O holds (KG is the Gauss curvature and xz is the complex gradient of the surface x).
- the corresponding boundary value problem Δh+×z{2(2H2-KG)h=O,hδB=O, is uniquely solvable.
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Karlheinz Schüffler 《manuscripta mathematica》1979,30(2):163-197
Multiply connected minimal surfaces of genus 0 with only simple interior branch points, for which the corresponding boundary value problem $$\Delta h - K|x_z |^2 h = 0; h_{|\partial \Omega } = 0$$ (K is the Gauss curvature and xz is the complex gradient of the surface x) is uniquely solvable and which have the property, that the condition K|xz|2≠0 holds in the branch points, are always isolated and stable solutions of the Plateau problem, corresponding to their boundary curves. To achieve these results one has to consider the conformal type as a variable. We give a method to perform the variation of the conformal type for holomorphic functions. Using the Weierstrass representation we thus obtain a differentiable structure on the set of multiply connected minimal surfaces. We find interesting connections between the classical Riemann-Hilbert problem and Fredholm properties of a projection operator on this manifold. 相似文献
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Summary Given the eigenvalue problem (A–E) x=0 for real or complex matricesA the number of eigenvalues with positive real parts is determined without evaluating the caracteristical polynomial. A proceeding is developed here to transform the given matrixA into a reduced form by applying a finite series of elementary transformations upon the matrix. The elements of the reduced matrix allow immediately to solve the problem. 相似文献