The new field of semiconductor spintronics represents a possible direction towards the development of hybrid devices that could perform logic operations, communication and storage, within the same material technology. This book provides a critical analysis of the mechanisms responsible of spin relaxation and applied the Monte Carlo method to investigate the significant case of electrons in bulk GaAs. It includes the results obtained by Dr. Stefano Spezia during his three-year Ph.D. in Applied Physics, under the supervision of Prof. Dominique Persano Adorno, and in collaboration with Dr. Nicola Pizzolato and Prof. Bernardo Spagnolo, at the Department of Physics of the University of Palermo (Italy). The prediction of an increase of the spin lifetime in the presence of e-e scattering as well as at increasing lattice temperatures are relevant results from both a fundamental and an applied point of view. Also remarkable is the possibility to increase the spin lifetime by the simultaneous application of high fields and an external noise controlled by an extra fluctuating electric field. The experimental validation of these achievements offers valuable challenges to experimentalists.

Number Theory with Applications to Cryptography takes into account the application of number theory in the field of cryptography. It comprises elementary methods of Diophantine equations, the basic theorem of arithmetic and the Riemann Zeta function. This book also discusses about Congruences and their use in mock theta functions, Method of Iterative Sliding Window for Shorter Number of Operations in case of Modular Exponentiation and Scalar Multiplication, Discrete log problem, elliptic curves, matrices and public-key cryptography and Implementation of Pollard Rho over binary fields using Brent Cycle Detection Algorithm. It also provides the reader with the significant insights of number theory to the practice of cryptography in order to understand discrete log problem, matrices, elliptic curves and public-key cryptography and the applications of Fibonacci sequence on continued fractions.

Mathematics Education: History and Research takes into account the basic methodology used for the mathematics education in ancient times. It includes the advanced mathematical study and the development of conditional reasoning skills and certain challenges involved in the mathematical cognition. This book also discusses about the cultural diversity and its role in mathematical activities, exploring practices of teachers in teaching mathematics and statistics in kwazulu-natal schools, mathematics teachers' professional identity development in communities of practice, interactive whiteboards in mathematics teaching: a literature review, using technology in elementary mathematics teacher education and using historical perspective in designing discovery learning on integral for undergraduate students.

In the last half-century, financial derivatives have become progressively central in finance being actively traded on many exchanges throughout the world and entered into by financial institutions, fund managers, and corporate treasurers. Elements of Financial Mathematics: From Interest Theory to Options book presents those mathematical models that continue to reveal essentials for understanding the relationships among the actors in the financial world: annuities, bonds, portfolio theory, and derivatives.

During the last two decades, there has been an explosive growth in the telecommunications industry, characterized by an exponential increase in demand due to the addition of more and more individual computing devices. Digital Communication Systems: Signals, Channels, and Signaling book presents those concepts of mathematics that continue to reveal fundamentals for digital communication systems: principles of information theory, signaling over channels affected by additive white Gaussian noise, over band-limited channels, and fading channels.

Mathematical Theory and Applications of Error-Correcting Codes book presents those concepts of mathematics that continue to reveal essentials in making reliable the data exchange between systems and their parts. For such reason, its applications range over many areas, including physical science, engineering, and medicine. In particular, it treats of hard and soft-decision decoding, of cyclic and quasi-cyclic codes, of Reed-Solomon codes, of low density parity check codes, and quantum error-correcting codes.

Semiconductor Material Technologies examines various technologies related to semiconductor material that have been developed in the recent times. It includes five different sections corresponding to such technologies, where section 1 and 2 talks about semiconductor modeling and its manufacturing, section 3 and 4 highlights advanced plasma techniques for electronic applications and gallium nitride crystals and their application to the electronic devices. Section 5 describes about semiconductor structures for optoelectronic applications. Provide the reader with the insights into the development of these technologies helping the technicians adopt various techniques to build various products like integrated photovoltaic etc.

Basic Quantum Mechanics for Electrical Engineering examines the basics of Quantum mechanics and a must have for Electrical Engineering. Readers are provided with detailed information on basic quantum mechanics specifically focused on Electrical engineering.

Photon-Atom Processes Quantum Field Theory of Electrodynamics investigates various aspects of electrodynamics and various models of Quantized EM-Field. It includes five different sections where section 1 and 2 talks about quantum electrodynamics and scattering processes, and section 3 and 4 highlights Fermion and Boson Propagators and QED Processes. Section 5 has been dedicated to Feynman diagrams and Higher-Order Interactions in QED of Strong Fields. Provide the reader with the insights into the development of quantum electrodynamics, so as to understand various physical processes associated with photon-atom interactions.

This book introduces the field of neuroscience that theoretically and experimentally studies how neurons work. In particular, the conductance-based model of Hodgkin-Huxley, its simplified version of FitzHugh-Nagumo and nonlinear integrate-and-fire models are discussed. Moreover, the dynamics of both neuronal populations and cognition are considered. The aim of this book is to give an introduction to the mathematical modeling and analysis of networks of neurons in the perspective of dynamical systems.

This book focuses on the latest theoretical and experimental achievements in the field of spin-based electronics in semiconductors. In particular, the properties of dilute and ferromagnetic semiconductors, and the optical responses of electron spins are studied. Moreover, the dynamics, manipulation and transport of spin-polarized electrons are considered. It is intended to students to semiconductor physics and semiconductor devices as well as researchers in this field.

Focusing on the Clifford algebra as a unified mathematical language of Physics; the advantages of using Clifford algebra formalism in many fields of Theoretical Physics are discussed and new mathematical results in the relatively new branch of the real Clifford Analysis are presented as well. The chapters contributed by authors in this book provide a detailed examination of Clifford algebras and their significance to analysis, geometry, mathematical structures, physics, and applications in engineering.

This book brings together some of the most important scientific works in the Quantum Monte Carlo literature. In particular, Variational and Diffusion Monte Carlo, Auxiliary Fields or Shell Model Quantum Monte Carlo, Path Integral and Constrained Path Quantum Monte Carlo have been widely discussed interlacing together theory and applications. A new Quantum Monte Carlo scheme adept of a direct stochastic sampling of the density matrix is also addressed. For physical chemists and molecular physicists or any researcher interested in computer optimization or statistical sampling-this book is an invaluable source of cutting-edge techniques.

Advances in Applied Combinatorics talks about the subject of binomial coefficients, permutations, the combinational proofs, the graph theory, derangements, partitions, linear recurrences, graph algorithms and permutation groups, to give a far-fetched insight on applied combinatorics. This book also discusses about the fractional sums and the differences, harmonic numbers and the cubed binomial coefficients, the recursive algorithms, linear recurrences and the fibonacci numbers. The generating functions and the sequence of numbers and polynomials.

Linear Algebra, Matrix Theory and Applications gives insights into the various aspects related to the matrices including the concepts on vector spaces, least square regression, determinants, eigen values, eigen vectors, positive definite matrices, singular value decomposition and teaches the readers the methods of computation in matrices. This book also discusses about Reduced triangular form of polynomial, Gaussian Elimination-based correlation analysis, Shift-invert diagonalization of spin chains, Fast matrix multiplication, Finding the pth root of principal matrix and Quasi-rational canonical form of a matrix.