This textbook introduces readers to real analysis in one and n dimensions. It is divided into two parts: Part I explores real analysis in one variable, starting with key concepts such as the construction of the real number system, metric spaces, and real sequences and series. In turn, Part II addresses the multi-variable aspects of real analysis. Further, the book presents detailed, rigorous proofs of the implicit theorem for the vectorial case by applying the Banach fixed-point theorem and the differential forms concept to surfaces in Rn. It also provides a brief introduction to Riemannian geometry. With its rigorous, elegant proofs, this self-contained work is easy to read, making it suitable for undergraduate and beginning graduate students seeking a deeper understanding of real analysis and applications, and for all those looking for a well-founded, detailed approach to real analysis.

The first part of this book reviews some key topics on multi-variable advanced calculus. The approach presented includes detailed and rigorous studies on surfaces in Rn which comprises items such as differential forms and an abstract version of the Stokes Theorem in Rn. The conclusion section introduces readers to Riemannian geometry, which is used in the subsequent chapters. The second part reviews applications, specifically in variational quantum mechanics and relativity theory. Topics such as a variational formulation for the relativistic Klein-Gordon equation, the derivation of a variational formulation for relativistic mechanics firstly through (semi)-Riemannian geometry are covered. The second part has a more general context. It includes fundamentals of differential geometry. The later chapters describe a new interpretation for the Bohr atomic model through a semi-classical approach. The book concludes with a classical description of the radiating cavity model in quantum mechanics.

The book discusses basic concepts of functional analysis, measure and integration theory, calculus of variations and duality and its applications to variational problems of non-convex nature, such as the Ginzburg-Landau system in superconductivity, shape optimization models, dual variational formulations for micro-magnetism and others. Numerical Methods for such and similar problems, such as models in flight mechanics and the Navier-Stokes system in fluid mechanics have been developed through the generalized method of lines, including their matrix finite dimensional approximations. It concludes with a review of recent research on Riemannian geometry applied to Quantum Mechanics and Relativity. The book will be of interest to applied mathematicians and graduate students in applied mathematics. Physicists, engineers and researchers in related fields will also find the book useful in providing a mathematical background applicable to their respective professional areas.

The first part of this book reviews some key topics on multi-variable advanced calculus. The approach presented includes detailed and rigorous studies on surfaces in Rn which comprises items such as differential forms and an abstract version of the Stokes Theorem in Rn. The conclusion section introduces readers to Riemannian geometry, which is used in the subsequent chapters. The second part reviews applications, specifically in variational quantum mechanics and relativity theory. Topics such as a variational formulation for the relativistic Klein-Gordon equation, the derivation of a variational formulation for relativistic mechanics firstly through (semi)-Riemannian geometry are covered. The second part has a more general context. It includes fundamentals of differential geometry. The later chapters describe a new interpretation for the Bohr atomic model through a semi-classical approach. The book concludes with a classical description of the radiating cavity model in quantum mechanics.

The book discusses basic concepts of functional analysis, measure and integration theory, calculus of variations and duality and its applications to variational problems of non-convex nature, such as the Ginzburg-Landau system in superconductivity, shape optimization models, dual variational formulations for micro-magnetism and others. Numerical Methods for such and similar problems, such as models in flight mechanics and the Navier-Stokes system in fluid mechanics have been developed through the generalized method of lines, including their matrix finite dimensional approximations. It concludes with a review of recent research on Riemannian geometry applied to Quantum Mechanics and Relativity. The book will be of interest to applied mathematicians and graduate students in applied mathematics. Physicists, engineers and researchers in related fields will also find the book useful in providing a mathematical background applicable to their respective professional areas.

Frequency-Domain Receiver Design for Doubly-Selective Channels discusses broadband wireless transmission techniques, which are serious candidates to be implemented in future broadband wireless and cellular systems, aiming at providing high and reliable data transmission and concomitantly high mobility. This book provides an overview of the channel impairments that may affect performance of single carrier and multi-carrier block transmission techniques in mobile environments. Moreover, it also provides a new insight into the new receiver designs able to cope with double selectivity that affects present and future broadband high speed mobile communication systems.

This textbook introduces readers to real analysis in one and n dimensions. It is divided into two parts: Part I explores real analysis in one variable, starting with key concepts such as the construction of the real number system, metric spaces, and real sequences and series. In turn, Part II addresses the multi-variable aspects of real analysis. Further, the book presents detailed, rigorous proofs of the implicit theorem for the vectorial case by applying the Banach fixed-point theorem and the differential forms concept to surfaces in Rn. It also provides a brief introduction to Riemannian geometry. With its rigorous, elegant proofs, this self-contained work is easy to read, making it suitable for undergraduate and beginning graduate students seeking a deeper understanding of real analysis and applications, and for all those looking for a well-founded, detailed approach to real analysis.

This book provides up-to-date and comprehensive coverage of the research and application of Integrated Pest Management (IPM) in tropical regions. The first section explores the agro-ecological framework that represents the foundations of IPM, in addition to emerging technologies in chemical and biological methods that are core to pest control in tropical crops. The second section follows a crop-based approach and provides details of current IPM applications in the main tropical food crops (such as cereals, legumes, root and tuber crops, sugarcane, vegetables, banana and plantain, citrus, oil palm, tea, cocoa and coffee) and also fibre crops (such as cotton) and tropical forests. Integrated Pest Management in Tropical Regions: * Explores the techniques aimed at controlling pests in agro-ecosystems sustainably while reducing secondary effects on the environment and on plant, animal and human health * Contextualizes IPM within our current knowledge of climate change and the global movement of organisms * Covers integrated strategies to contains pests in major tropical food crops, fibre crops and trees * Discusses options and challenges for pest control in tropical agriculture

In the United Kingdom and Europe generally, the study of prehistoric monuments has long been the domain of archaeologists who excavate, measure, date and record them. From the 1960s onwards, archaeoastronomers provided an alternative picture based on their belief that the builders understood celestial movements and consequently enshrined astronomical alignments into their monuments. This picture was highly contested by most archaeologists and the two fields, archaeology and archaeoastronomy, have gone their separate ways. One of the scholars who broke this stalemate was Lionel Sims who, as an anthropologist, had a wealth of ethnographic material to draw from, allowing him to envision archaeoastronomy from a multidisciplinary perspective by combining a number of methodologies and approaches to examine how archaeoastronomy could deal with cultural complexity. Lionel Sims has produced an influential body of work which has challenged existing narratives about British prehistoric monuments and, equally importantly, provided innovative ways to approach and think about skyscapes. His work is not without controversy, but his unique take and thought-provoking conclusions have had an impact on the thinking of numerous students and collaborators. This festschrift gathers contributions from many of his colleagues who wish to honour and pay their respects to him. Following an introduction that discusses the legacy of his work, the volume delves deeper into three areas: Anthropology and Human Origins, Prehistory and Megalithic Monuments, and Theory. Its thirteen chapters contextualise Lionel's work and expand it in new and exciting directions for skyscape archaeology.

In this text, the author establishes a connection between classical and quantum mechanics through the normal field definition and related wave function concept. Indeed, the author proposes a new energy which includes both classical and quantum mechanics in a unified framework. Concerning such energy, they show that if m, where m denotes the total system mass, then the energy is experienced in a classical mechanics context, whereas if the approximation r(x,t) x is assumed, where r(x,t) denotes point-wise the particle classical field of position, and for appropriate m values the standard Schroedinger energies are re-obtained. Among the examples of applications concerning the proposal, the author highlights the hydrogen atom as one example, where both the proton and electron are allowed to move. The consistent result of a proton mass concentration at r = 0 is obtained. The author also develops a procedure to obtain eigenvalues of a positive definite symmetric matrix. The novelty here, concerning previous results in the book entitled Functional Analysis and Applied Optimization in Banach Spaces, are the rigorous proofs presented. Indeed, the results seem to be applicable to more general matrices. However, the author postpones the proof of such general results for future research. In the last chapter, a complete and rigorous existence result for the Ginzburg-Landau system of superconductivity is presented. A duality principle and related optimality conditions are also developed. In the final section, the author presents research concerning numerical results for three-dimensional models in superconductivity.