Detection Of Edges And Approximation Problems In Mechanical Engineering

Detection of singularities of a function from spectral data and the closely related problems arise in many important applications.Determination of jumps for functions is an important part of detection of singularities of a function.Now,many authors are interested in this area.Recently,X.L.Shi and L.Hu published the method of concentration factors for determination of jumps of functions via MCM conjugate wavelets.Usually,it is difficult to calculate the Hilbert transform of general window functions.The aim of this paper is to discuss determination of jumps for functions based on derivative Gabor series.The results will simplify the calculation of jump values.We hope this research will be useful for application.The problem on approximation of continuous functions via Achimede spiral arises in the design of mechanical spares.The problem is how to find a broken line of best approximation to a continuous function.In Chapter 3 of this paper,we established a characterization for a Chebyshev broken line of best approximation to a continuous function.We also established a sufficient condition for a smooth spline of best approximation to a continuous function.