Fractals, Wavelets, and their Applications

Part I: Fractal Theory.- Introduction to Fractals.- Geometry of self similar sets.- An introduction to Julia and Fatou set.- Crazy topology in complex dynamics.- Measure preserving fractal homeomorphisms.- The dimension theory of almost self affine sets and measures.- Countable alphabet non autonomous self affine sets.- On transverse hyperplanes to self similar Jordan arcs.- Fractals in product fuzzy metric space.- Some properties on Koch curve.- Projections of Mandelbrot percolation in higher dimensions.- Some examples of finite type fractals in three dimensional space.- Fractals in partial metric spaces.- Part II: Wavelet Theory.- Frames and extension problems I.- Frames and extension problems II.- Local fractal functions and function spaces.- Some historical precedents of the fractal functions.- A new class of rational quadratic fractal function with positive shape preservation.- Interval wavelets determined by points on the circle.- Construction of multi scaling functions using matrix polynomials.- A remark on reconstruction of splines from their local weighted average samples.- C1rational cubic fractal interpolation surface using functional values.- On fractal rational functions.- Part III: Applications of Fractals and Wavelets.- Innovation on the tortuous path: Fractal Electronics.- Permutation entropy analysis of EEG of mild cognitive impairment patients during memory activation task.- A multifractal based image analysis for cervical dysplasia classification.- Self similar network traffic modeling using fractal point process Markovian approach.- Validation of variance based fitting for self similar network traffic.- Self similar network traffic modeling using circulant Markov modulated poisson process.- Investigation of priority based optical packet switch under self similar variable length input traffic using matrix queuing theory.- Computationally efficient wavelet domain solver for fluorescence diffuse optical tomography.- Implementation of wavelet based and discrete cosine based algorithms on panchromatic image.- Trend, time series and wavelet analysis of river water dynamics.- An efficient wavelet based approximation method to film – pore diffusion model arising in chemical engineering.- A new wavelet based hybrid method for Fisher type equations.