scholarly journals A variational characterization of profile curves of invariant linear Weingarten surfaces

2020 ◽  
Vol 68 ◽  
pp. 101564
Author(s):  
A. Pámpano
Keyword(s):  
Variational Characterization ◽  
Weingarten Surfaces

Variational characterization of real eigenvalues in linear viscoelastic oscillators

2017 ◽  
Vol 23 (10) ◽  
pp. 1377-1388 ◽  
Author(s):  
Seyyed Abbas Mohammadi ◽  
Heinrich Voss
Keyword(s):  
Degrees Of Freedom ◽  
Nonlinear Eigenvalue Problem ◽  
Eigenvalues And Eigenvectors ◽  
Variational Characterization ◽  
Viscoelastic System ◽  
New Approach ◽  
Motion Equations ◽  
Multiple Degrees Of Freedom ◽  
Linear Viscoelastic

This paper proposes a new approach for computing the real eigenvalues of a multiple-degrees-of-freedom viscoelastic system in which we assume an exponentially decaying damping. The free-motion equations lead to a nonlinear eigenvalue problem. If the system matrices are symmetric, the eigenvalues allow for a variational characterization of maxmin type, and the eigenvalues and eigenvectors can be determined very efficiently by the safeguarded iteration, which converges quadratically and, for extreme eigenvalues, monotonically. Numerical methods demonstrate the performance and the reliability of the approach. The method succeeds where some current approaches, with restrictive physical assumptions, fail.

scholarly journals Variational characterization of Hp

2019 ◽  
Vol 149 (5) ◽  
pp. 1123-1134 ◽  
Author(s):  
Honghai Liu
Keyword(s):  
Hardy Space ◽  
Approximate Identity ◽  
Jump Operator ◽  
Variational Characterization ◽  
Approximate Identities ◽  
Oscillation Operator

AbstractIn this paper, we obtain the variational characterization of Hardy space Hp for $p\in (((n)/({n+1})),1]$, and get estimates for the oscillation operator and the λ-jump operator associated with approximate identities acting on Hp for $p\in (((n)/({n+1})),1]$. Moreover, we give counterexamples to show that the oscillation and λ-jump associated with some approximate identity cannot be used to characterize Hp for $p\in (((n)/({n+1})),1]$.

scholarly journals Locating real eigenvalues of a spectral problem in fluid-solid type structures

2005 ◽  
Vol 2005 (1) ◽  
pp. 37-48 ◽  
Author(s):  
Heinrich Voss
Keyword(s):  
Viscous Fluid ◽  
Spectral Problem ◽  
Eigenvalue Problems ◽  
Tube Bundle ◽  
Incompressible Viscous Fluid ◽  
Mechanical Vibrations ◽  
Variational Characterization ◽  
Solid Type

Exploiting minmax characterizations for nonlinear and nonoverdamped eigenvalue problems, we prove the existence of a countable set of eigenvalues converging to∞and inclusion theorems for a rational spectral problem governing mechanical vibrations of a tube bundle immersed in an incompressible viscous fluid. The paper demonstrates that the variational characterization of eigenvalues is a powerful tool for studying nonoverdamped eigenproblems, and that the appropriate enumeration of the eigenvalues is of predominant importance, whereas the natural ordering of the eigenvalues may yield false conclusions.

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