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.
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.
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.
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.
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