Mathematical Methods in Engineering

Since it covers recent applications of Fractional Calculus, Wavelets and Neutrices it will be attractive to many engineers, scientists, and mathematicians

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This book contains some of the contributions that have been carefully selected and peer-reviewed, which were presented at the International Symposium MME06 Mathematical Methods in Engineering, held in Cankaya University, Ankara, April 2006. The Symposium provided a setting for discussing recent developments in Fractional Mathematics, Neutrices and Generalized Functions, Boundary Value Problems, Applications of Wavelets, Dynamical Systems and Control Theory.

Contenu
Fractional Mathematics.- Fractional calculus and regularized residue of infinite dimensional space.- Fractional spaces generated by the positive differential and difference operators in a Banach space.- Sub-diffusion equations of fractional order and their fundamental solutions.- Neutrices and Generalized Functions.- The composition and neutrix composition of distributions.- A review on the products of distributions.- Some remarks on the incomplete gamma function.- Boundary Value Problems.- One-dimensional wave propagation in functionally graded cylindrical layered media.- Piecewise constant control of boundary value problem for linear impulsive differential systems.- On nonlocal boundary value problems for hyperbolic-parabolic equations.- On asymptotical behavior of solution of Riccati equation arising in linear filtering with shifted noises.- Isomorphism classes of ordinary elliptic curves over fields of characteristic 3.- Hidden symmetries of two dimensional superintegrable systems.- A fourth order accurate difference-analytical method for solving Laplace's boundary value problem with singularities.- Modeling of PDE processes with finite dimensional non-autonomous ODE systems.- On solutions of discrete nonlinear elliptic boundary value problems.- Some exact solutions of the (2 + 1)-dimensional Kadomtsev-Petviashvili equation.- Varadhan estimates without probability: lower bound.- Dirichlet problem for orthotropic bounded cylinder with combined boundary conditions.- A numerical analysis of variational finite difference schemes for steady state heat conduction problems with discontinuous coefficients.- On the solution of a mathematical model of a viscoelastic bar.- Dynamics of wall bounded flow.- Applications of Wavelets.- Wavelet transform for the simultaneousprediction of the colorants in food product.- A review on the wavelet transform applications in analytical chemistry.- Continuous wavelet analysis for the ratio signals of the absorption spectra of binary mixtures.- Improved incremental self-organizing map for the segmentation of ultrasound images.- An application of continuous wavelet transform to electrochemical signals for the quantitative analysis.- The threshold of compression in wavelet transform with Haar's coefficients - numerical examples.- Dynamical Systems and Control Theory.- 3-D Computerized ionospheric tomography with random field priors.- Comparison of fuzzy and Volterra series nonlinear system modeling approaches.- Novel hardware-oriented algorithms for TDOA positioning technique in cellular networks.- Unknown costs in a duopoly with differentiated products.- Bayesian price leadership.- Comparison of methodologies in river flow prediciton. The Paiva river case.- A XY Spin Chain Models on Space Curves and Analogy with Kirchhoff Rods.- Approximate controllability of one-dimensional SDE driven by countably many Brownian motions.- Synchronization between neuronal spiking activity and sub-threshold sinusoidal stimuli based on the FitzHugh-Nagumo model.- A characterization of the dynamics of Newton's derivative.- Dissipative solitons and nonlinear resonance dynamics in 2+1 dimensions.- Implementation of floating point arithmetics using an FPGA.- A method for the recovery of the electric field vibration inside vertical inhomogeneous anisotropic dielectrics.