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This book discusses the theory and practice of random number generators that are useful for computer simulation and computer security applications. Random numbers are ubiquitous in computation. They are used in randomized algorithms to perform sampling or choose...
This book aims to introduce readers without a strong mathematical background to the basic ideas of fuzzy set theory and logic. Fuzzy mathematics is the mathematics of vagueness, a universal property of this world. There are many objects that are called vague because...
This book explores boundary value problems for fractional dynamic equations on arbitrary time scales, including Caputo fractional dynamic equations, impulsive Caputo fractional dynamic equations, and impulsive Riemann-Liouville fractional dynamic equations. The author...
This book explores boundary value problems for Riemann-Liouville fractional dynamic equations on arbitrary time scales as well as the shifting problem on the whole time scale. The author includes an introductory overview of fractional dynamic calculus on time scales....
This book presents practical demonstrations of numerically calculating or obtaining Fourier Transform. In particular, the authors demonstrate how to obtain frequencies that are present in numerical data and utilizes Mathematica to illustrate the calculations.This book...
This book is a self-contained treatment for those who study or work on the computational aspects of classical modular forms. The author describes the theory of modular forms and its applications in number theoretic problems such as representations by quadratic forms and...
This book revises and expands upon the prior edition, The Navier-Stokes Problem. The focus of this book is to provide a mathematical analysis of the Navier-Stokes Problem (NSP) in R^3 without boundaries. Before delving...
This book provides the essential theoretical tools for stochastic modeling. The authors address the most used models in applications such as Markov chains with discrete-time parameters, hidden Markov chains, Poisson processes, and birth and death processes.This...
This book ?offers step-by-step descriptions of various random systems and explores the world of computer simulations. In addition, this book offers a working introduction to those who want to learn how to create and run Monte Carlo simulations. Monte Carlo...
This book discusses the modern theory of Laplace eigenfunctions through the lens of a new tool called geodesic beams. The authors provide a brief introduction to the theory of Laplace eigenfunctions followed by an accessible treatment of geodesic beams and their...
This book describes how complex systems from a variety of fields can be modeled using quantum mechanical ideas; from biology and ecology, to sociology and decision-making. Quantum mechanics is traditionally associated with microscopic systems; however, quantum concepts...
This book examines the most fundamental parts of convex analysis and its applications to optimization and location problems. Accessible techniques of variational analysis are employed to clarify and simplify some basic proofs in convex analysis and to build...
This book is intended for a first-semester course in calculus, which begins by posing a question: how do we model an epidemic mathematically? The authors use this question as a natural motivation for the study of calculus and as a context through which central calculus...
This book presents fixed point theory, one of the crucial tools in applied mathematics, functional analysis, and topology, which has been used to solve distinct real-world problems in computer science, engineering, and physics. The authors begin with an overview of the...
This book reviews the construction of elementary systems living in de Sitter (dS) spacetime, in both the classical and quantum senses. Field theories on dS spacetime are among the most studied mathematical models of the Universe, whether for its earlier period...
Statistics is the activity of inferring results about a population given a sample. Historically, statistics books assume an underlying distribution to the data (typically, the normal distribution) and derive results under that assumption. Unfortunately, in real life,...
This book systematically establishes the almost periodic theory of dynamic equations and presents applications on time scales in fuzzy mathematics and uncertainty theory. The authors introduce a new division of fuzzy vectors depending on a determinant algorithm and...
This book studies a category of mathematical objects called Hamiltonians, which are dependent on both time and momenta. The authors address the development of the distinguished geometrization on dual 1-jet spaces for time-dependent Hamiltonians, in contrast with the...
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