This book provides a comprehensive treatment of the logic behind hypothesis testing. Readers will learn to understand statistical hypothesis testing and how to interpret P-values under a variety of conditions including a single hypothesis test, a collection of hypothesis tests, and tests performed on accumulating data. The author explains how a hypothesis test can be interpreted to draw conclusions, and descriptions of the logic behind frequentist (classical) and Bayesian approaches to interpret the results of a statistical hypothesis test are provided. Both approaches have their...
This book provides a comprehensive treatment of the logic behind hypothesis testing. Readers will learn to understand statistical hypothesis testin...
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 time-independent variant on cotangent bundles. Two parts are presented to include both geometrical theory and the applicative models: Part One: Time-dependent Hamilton Geometry and Part Two: Applications to Dynamical Systems, Economy and Theoretical Physics. The authors present 1-jet spaces and their duals as appropriate...
This book studies a category of mathematical objects called Hamiltonians, which are dependent on both time and momenta. The authors address the dev...
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 develop a theory of almost periodic fuzzy multidimensional dynamic systems on time scales. Several applications are studied; in particular, a new type of fuzzy dynamic systems called fuzzy q-dynamic systems (i.e. fuzzy quantum dynamic systems) is presented. The results are not only effective on classical fuzzy dynamic systems,...
This book systematically establishes the almost periodic theory of dynamic equations and presents applications on time scales in fuzzy mathematics and...
This book explores the relationships between music, the sciences, and mathematics, both ancient and modern, with a focus on the big picture for a general audience as opposed to delving into very technical details. The language of music is deciphered through the language of mathematics. Readers are shown how apparently unrelated areas of knowledge complement each other and in fact propel each other’s advancement. The presentation as well as the collection of topics covered throughout is unique and serves to encourage exploration and also, very concretely, illustrates the cross- and...
This book explores the relationships between music, the sciences, and mathematics, both ancient and modern, with a focus on the big picture for a gene...
This textbook provides an introduction to methods for solving nonlinear partial differential equations (NLPDEs). After the introduction of several PDEs drawn from science and engineering, readers are introduced to techniques to obtain exact solutions of NLPDEs. The chapters include the following topics: Nonlinear PDEs are Everywhere; Differential Substitutions; Point and Contact Transformations; First Integrals; and Functional Separability. Readers are guided through these chapters and are provided with several detailed examples. Each chapter ends with a series of exercises illustrating...
This textbook provides an introduction to methods for solving nonlinear partial differential equations (NLPDEs). After the introduction of several PD...
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 the determination of asymptotic formulas for Fourier coefficients of different types of special functions. A detailed account of recent applications of modular forms in number theory with a focus on using computer algorithms is provided. Computer algorithms are included for each presented application to help readers put the...
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 ...
This book presents a comprehensive overview of Structural Equation Modeling and how it can be applied to address research issues in different disciplines. The authors employ a ‘simple to complex’ approach. The book reviews topics such as variance, covariance, correlation, multiple regression, mediation, moderation, path analysis, and confirmatory factor analysis. The authors then discuss the initial steps for performing structural equation modeling, including model specification, model identification, model estimation, model testing, and model modification. The book includes an...
This book presents a comprehensive overview of Structural Equation Modeling and how it can be applied to address research issues in different discipli...
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 extension of metric spaces. Readers are introduced to general fixed-point theorems while comparing and contrasting important and insignificant metric spaces. The book is intended to be self-contained and serves as a unique resource for researchers in various disciplines.
This book presents fixed point theory, one of the crucial tools in applied mathematics, functional analysis, and topology, which has been used to solv...
