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In this article we discuss how the existence of Kaehler metrics with constant scalar curvature on the projectivization of a holomorphic vector bundle over a Kaehler manifold M is related to a moment map condition for the action of the automorphism group of M on the moduli of vector bundles.

The purpose of this paper is to work out the theoretical aspects of the vibration problem of rubber wiper blade on convex windshield. Over the past 20 years, some 2-dimensional spring-mass models were presented in engineering science to simulate the vibration of rubber wiper blade on windshield. In this paper, we will consider the elasticity perspective on this 3-dimensional vibration problem. Our theoretical analysis suggests that there should exist two classes of vibration frequencies corresponding to " * -exact deformations (Class I)" and " * -closed deformations (Class II)". We prove mathematical theorems on the characterization of deformations of Class I. We also explain how elementary deformations of Class II can be constructed. We then deduce two mathematical formulas, for the vibration problem of rubber wiper blade on convex windshield, from our theoretical analysis. Our theoretical predictions are in almost perfect agreement with experimental data. One of the crucial steps of our analysis is a decomposition theorem motivated by the de Rham Cohomology and the Hodge Theory.

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