Chapter1: Low-resistivity structures in the seismically active lithosphere zones and observations of EM signals of seismic origination -- Chapter2: Theory of magnetic location of the epicentre area of a possible earthquake -- Chapter3: Tsunami precursors: mathematical model and applications -- Chapter4: Space Weather -- Chapter5: Structure of a Brain -- Chapter6: Space weather influence on bioe…
Arnold's Problems contains mathematical problems brought up by Vladimir Arnold in his famous seminar at Moscow State University over several decades. In addition, there are problems published in his numerous papers and books. The invariable peculiarity of these problems was that Arnold did not consider mathematics a game with deductive reasoning and symbols, but a part of natural science (espec…
Introduction: Signals and Signal Processing. Local Analysis. A Roadmap for the Book -- Continuous Analysis: The Short Time Fourier Transform STFT. The Continuous Wavelet Transform CWT. Case Studies. Notes and Exercises -- The Discrete Wavelet Transform: Redundancy of the CWT and the STFT. The Haar-System. Generalization to Daubechies Wavelets. Multiscale Analysis. A Unifying Viewpoint: Basis Sy…
Stochastic Differential Equations with Jumps in Rd -- Martingale Theory and the Stochastic Integral for Point Processes -- Brownian Motion, Stochastic Integral and Ito's Formula -- Stochastic Differential Equations -- Some Useful Tools in Stochastic Differential Equations -- Stochastic Differential Equations with Non-Lipschitzian Coefficients -- Applications -- How to Use the Stochastic Calculu…
Mathematical Preliminaries -- Introductory Applications -- Further Applications -- The Method of Multiple Scales -- Some Worked Examples Arising from Physical Problems.Many areas of science and engineering produce difficult mathematical problems , i.e., problems that cannot be solved in any conventional sense. In many cases, against all the apparent odds, it is possible to construct systematic …
Methods to Produce Biaxially Textured Substrates -- IBAD Template Films for HTS Coated Conductors -- Epitaxial Superconductors on Rolling-Assisted-Biaxially-Textured-Substrates (RABiTS) -- Inclined Substrate Deposition -- ISD by Thermal Evaporation -- Methods of YBa2Cu3O7?? Deposition and Related Issues -- Pulsed Laser Deposition of YBa2Cu2O7?? for Coated Conductor Applications: Current Status …
Topological Aspects of Four-Manifolds -- The Theory of Donaldson Invariants -- The Theory of Seiberg-Witten Invariants -- Supersymmetry in Four Dimensions -- Topological Quantum Field Theories in Four Dimensions -- The Mathai-Quillen Formalism -- The Seiberg-Witten Solution of N = 2 SUSY Yang-Mills Theory -- The u-plane Integral -- Some Applications of the u-plane Integral -- Further Developmen…
The intriguing mechanism of spontaneous symmetry breaking is a powerful innovative idea at the basis of most of the recent developments in theoretical physics, from statistical mechanics to many-body theory to elementary particles theory; for infinitely extended systems a symmetric Hamiltonian can account for non symmetric behaviours, giving rise to non symmetric realizations of a physical syst…
Why Symmetry? -- J-Pairing Interractions of Fermions in a Single-J Shell -- Supersymmetry in Nuclei -- The Relativistic Many Body Problem in Quantum Mechanics -- Gauge Invariance and the E1 Sum Rule in Nuclei -- The Heisenberg Group in Classical and Quantum Information Transmission -- Quantum Field Theory of Particle Mixing and Oscillations -- Two-Photon Interactions in Cavity QED -- Low-Dimens…