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- PAUL BINDING
- 2005

We give an example of an indefinite weight Sturm-Liouville problem whose eigenfunctions form a Riesz basis under Dirichlet boundary conditions but not under anti-periodic boundary conditions.

We study the role played by the indefinite weight function a(x) on the existence of positive solutions to the problem −div (|∇u| p−2 ∇u) = λa(x)|u| p−2 u + b(x)|u| γ−2 u, x ∈ Ω, ∂u ∂n = 0, x ∈ ∂Ω, where Ω is a smooth bounded domain in R n , b changes sign, 1 < p < N, 1 < γ < Np/(N − p) and γ = p. We prove that (i) if Ω a(x) dx = 0 and b satisfies… (More)

It has been stated in the literature that static, nonlinear optimization approaches cannot predict coactivation of pairs of antagonistic muscles; however, numerical solutions of such approaches have predicted coactivation of pairs of one-joint and multijoint antagonists. Analytical support for either finding is not available in the literature for systems… (More)

We consider a regular indefinite Sturm-Liouville problem with two self-adjoint boundary conditions, one being affinely dependent on the eigen-parameter. We give sufficient conditions under which a basis of each root subspace for this Sturm-Liouville problem can be selected so that the union of all these bases constitutes a Riesz basis of a corresponding… (More)

Mathematical optimization of specific cost functions has been used in theoretical models to calculate individual muscle forces. Measurements of individual muscle forces and force sharing among individual muscles show an intensity-dependent, non-linear behavior. It has been demonstrated that the force sharing between the cat Gastrocnemius, Plantaris and… (More)

Optimization theory is used more often than any other method to predict individual muscle forces in human movement. One of the limitations frequently associated with optimization algorithms based on efficiency criteria is that they are thought to not provide solutions containing antagonistic muscular forces; however, it is well known that such forces exist.… (More)

It is well known that static, non-linear minimization of the sum of the stress in muscles to a certain power cannot predict cocontraction of pairs of one-joint antagonistic muscles. In this report, we prove that for a single joint either all agonistic muscles cocontract or all are silent. For two-joint muscles, we show that lengthening and shortening of… (More)

Prediction of accurate and meaningful force sharing among synergistic muscles is a major problem in biomechanics research. Given a resultant joint moment, a unique set of muscle forces can be obtained from this mathematically redundant system using nonlinear optimization. The classical cost functions for optimization involve a normalization of the muscle… (More)

We consider one dimensional p-Laplacian eigenvalue problems of the form −∆pu = (λ − q)|u| p−1 sgn u, on (0, b), together with periodic or separated boundary conditions, where p > 1, ∆p is the p-Laplacian, q ∈ C 1 [0, b], and b > 0, λ ∈ R. It will be shown that when p = 2, the structure of the spectrum in the general periodic case (that is, with q = 0 and… (More)