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Piezoelectric polymers based on polyvinylidene fluoride (PVDF) are of interest for large aperture spacebased telescopes as adaptive or smart materials. Dimensional adjustments of adaptive polymer films depend on controlled charge deposition. Predicting their long-term performance requires a detailed understanding of the piezoelectric material features, expected to suffer due to space environmental degradation. Hence, the degradation and performance of PVDF and its copolymers under various stress environments expected in low Earth orbit has been reviewed and investigated. Various experiments were conducted to expose these polymers to elevated temperature, vacuum UV, γ-radiation and atomic oxygen. The resulting degradative processes were evaluated. The overall materials performance is governed by a combination of chemical and physical degradation processes. Molecular changes are primarily induced via radiative damage, and physical damage from temperature and atomic oxygen exposure is evident as depoling, loss of orientation and surface erosion. The effects of combined vacuum UV radiation and atomic oxygen resulted in expected surface erosion and pitting rates that determine the lifetime of thin films. Interestingly, the piezo responsiveness in the underlying bulk material remained largely unchanged. This study has delivered a comprehensive framework for material properties and degradation sensitivities with variations in individual polymer performances clearly apparent. The results provide guidance for material selection, qualification, optimization strategies, feedback for manufacturing and processing, or alternative materials. Further material qualification should be conducted via experiments under actual space conditions. 3 4 AcknowledgementsThe authors express their appreciation to Bruce Tuttle for use of equipment to measure the d 33 coefficients, Jonathan Campbell for use of the evaporation chamber, Mark Stavig for DMA measurements, Gary Zender for acquiring the SEM images, Ralph

ABSTRACT. Relations are found between the nonvanishing of certain Wronskians and disconjugacy properties of Lny + py = 0, where Lny is a disconjugate operator and p is sign definite. The results are then used to show ways in which Lny + py can be factored.Introduction.In this paper we investigate possible ways of factoring certain nth order linear differential operators of the form

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SynopsisDominance properties of solutions to Lny + p(x)y = 0, where Ln is a disconjugate operator, are compared to dominance properties of solutions to its adjoint.