Nicholas Declaris – författare

Stories About Sets discusses the cardinality of sets and mathematical concepts, such as function, curve, surface, dimensions, and the paradoxical properties of curves and surfaces. The book reviews sets, operations on sets, the empty set, subsets, the universal sets, intersection of sets, union of sets, partitioning of sets, and boolean algebras. The text also discusses the cardinality of sets, including equality between sets, countable sets, unequal sets, the uncountability of the continuum, the existence of transcendental numbers, and the enigmatic axiom. The book analyzes if a part can be equal to the whole (which turns out to be true if it is applied to infinite sets). The text also discusses the arithmetic of the infinite such as involving the multiplication of infinite cardinalities. The book explains some remarkable functions and curves, the Dirichlet''s function, Cantor''s set, points of fracture, and continuous functions whose graphs possess a tangent at no point. The text shows how to construct a closed curve of infinite length or a curve passing through all the points of a square. The book can prove interesting and highly educational for students with mathematic or algebra subjects, as well as for academicians involved in teaching statistics or mathematics.

The Theory of Linear Systems presents the state-phase analysis of linear systems. This book deals with the transform theory of linear systems, which had most of its success when applied to time-invariant systems. Organized into nine chapters, this book begins with an overview of the development of some properties of simple differential systems that are mostly of a nonalgebraic nature. This text then presents a brief treatment of vector spaces, matrices, transformations, norms, and inner products. Other chapters deal with the inductive process used to define dynamical systems. This book discusses as well the existence and uniqueness theorem for the solutions of a homogeneous linear differential system. The final chapter deals with the abstract concept of a dynamical system and derives properties of these systems. This book is a valuable resource for advanced graduate students in areas such as economics and bioengineering. Engineers engaged in systems design will also find this book useful.

Analysis of Reflector Antennas provides information pertinent to the analysis of reflector-antenna systems. This book provides an understanding of how design data have been and can be derived. Organized into four chapters, this book begins with an overview of the history of focusing reflector-antenna systems characterized by a highly variable level of general interest. This text then examines the solutions of the scalar Helmholtz equation in rectangular and spherical coordinates. Other chapters consider antenna performance described in terms of several fundamental properties, including capture area, directivity, gain, beam efficiency, aperture efficiency, polarization, effective noise temperature, and phase center. This book discusses as well the resulting functional dependence between axial ratio and component amplitude, which is the same as that between voltage standing wave ratio and voltage reflection coefficient. The final chapter deals with the role of the special-purpose digital computers. This book is a valuable resource for research and development engineers.

Radiation and Propagation of Electromagnetic Waves serves as a text in electrical engineering or electrophysics. The book discusses the electromagnetic theory; plane electromagnetic waves in homogenous isotropic and anisotropic media; and plane electromagnetic waves in inhomogenous stratified media. The text also describes the spectral representation of elementary electromagnetic sources; the field of a dipole in a stratified medium; and radiation in anisotropic plasma. The properties and the procedures of Green''s function method of solution, axial currents, as well as cylindrical boundaries are also considered. The book further tackles diffraction by cylindrical structures and apertures on cylindrical structures. Students taking electrical engineering or electrophysics will find the book useful.

Detection of Signals in Noise serves as an introduction to the principles and applications of the statistical theory of signal detection. The book discusses probability and random processes; narrowband signals, their complex representation, and their properties described with the aid of the Hilbert transform; and Gaussian-derived processes. The text also describes the application of hypothesis testing for the detection of signals and the fundamentals required for statistical detection of signals in noise. Problem exercises, references, and a supplementary bibliography are included after each chapter. Students taking a graduate course in signal detection theory.

Lumped and Distributed Passive Networks: A Generalized and Advanced Viewpoint considers the mathematical study of a subset of passive linear operators. This five-chapter focuses on the questions of analysis and representation of such operators and illustrates the results of these analyses by obtaining some of the limitations that are imposed on the performance of passive systems. The first two chapters deal with the structure of general linear passive operators. These chapters specifically look into the theory of distributions, called generalized functions. The third and fourth chapters illustrate the application of passive operator theory to rational (lumped) and irrational (distributed) systems. The fifth chapter discusses some applications of optimization theory to the study of networks.

Crystals: Their Role in Nature and in Science provides the description of the phenomena and concepts and essential facts and ideas in the study of crystals. The book is divided into two parts. Part 1 discusses the growth and various forms of crystals. Under this section, topics on the etymology of the word "crystal", the existence of crystals, how crystals grow, stacking patterns, and various crystal symmetries are presented. Part 2 covers the crystal structure and how it interacts with light and X-rays. This part discusses some strange light effects that some crystals make; the production of beautiful and scientifically significant color patterns; the possible types of space patterns in crystals; and the use of X-ray in finding the details of the internal atomic pattern of crystals. Crystallographers and laymen interested in the study and appreciation of crystals will find the book invaluable.

Nonlinear Electron-Wave Interaction Phenomena explores the interaction between drifting streams of charged particles and propagating electromagnetic waves. Of particular concern are the situations in which the wave amplitude is large and there is strong coupling between the charged fluid and the wave. Emphasis is placed on those devices that utilize a defined injected stream of some type. Particle and electromagnetic wave velocities both small and comparable to the velocity of light are considered. Comprised of 16 chapters, this book begins with an introduction to the various classes of devices in which the drifting stream (charged fluid) is composed of electrons and/or ions coupled to a slow electromagnetic wave over an extended region. The discussion then turns to Eulerian versus Lagrangian formulation and radio-frequency equivalent circuits, along with space-charge-field expressions. Subsequent chapters focus on the interaction mechanisms in klystrons, traveling-wave amplifiers, and O-type backward-wave oscillators, as well as crossed-field forward- and backward-wave amplifiers, and traveling-wave energy converters. The book also evaluates multibeam and beam-plasma interactions; phase focusing of electron bunches; pre-bunched electron beams; collector depression techniques; and modulation characteristics. This monograph is designed to serve both as a research monograph for workers in the fields of microwave electron and plasma devices and as a text for advanced graduate students.

Finite Permutation Groups provides an introduction to the basic facts of both the theory of abstract finite groups and the theory of permutation groups. This book deals with older theorems on multiply transitive groups as well as on simply transitive groups. Organized into five chapters, this book begins with an overview of the fundamental concepts of notation and Frobenius group. This text then discusses the modifications of multiple transitivity and can be used to deduce an improved form of the classical theorem. Other chapters consider the concept of simply transitive permutation groups. This book discusses as well permutation groups in the framework of representation theory. The final chapter deals with Frobenius'' theory of group characters. This book is a valuable resource for engineers, mathematicians, and research workers. Graduate students and readers who are interested in finite permutation groups will also find this book useful.

Noneuclidean Geometry focuses on the principles, methodologies, approaches, and importance of noneuclidean geometry in the study of mathematics. The book first offers information on proofs and definitions and Hilbert''s system of axioms, including axioms of connection, order, congruence, and continuity and the axiom of parallels. The publication also ponders on lemmas, as well as pencil of circles, inversion, and cross ratio. The text examines the elementary theorems of hyperbolic geometry, particularly noting the value of hyperbolic geometry in noneuclidian geometry, use of the Poincaré model, and numerical principles in proving hyperparallels. The publication also tackles the issue of construction in the Poincaré model, verifying the relations of sides and angles of a plane through trigonometry, and the principles involved in elliptic geometry. The publication is a valuable source of data for mathematicians interested in the principles and applications of noneuclidean geometry.

Geometric Transformations, Volume 1: Euclidean and Affine Transformations focuses on the study of coordinates, trigonometry, transformations, and linear equations. The publication first takes a look at orthogonal transformations, including orthogonal transformations of the first and second kinds; representations of orthogonal transformations as the products of fundamental orthogonal transformations; and representation of an orthogonal transformation of space as a product of fundamental orthogonal transformations. The text then examines similarity and affine transformations. Topics include properties of affine mappings, Darboux''s lemma and its consequences, affine transformations in coordinates, homothetic transformations, similarity transformations of the plane in coordinates, and similarity mapping. The book takes a look at the representation of a similarity transformation as the product of a homothetic transformation and an orthogonal transformation; application of affine transformations to the investigation of properties of the ellipse; and representation of any affine transformation as a product of affine transformations of the simplest types. The manuscript is a valuable reference for high school teachers and readers interested in the Euclidean and affine transformations.

Geometric Transformations, Volume 2: Projective Transformations focuses on collinearity-preserving transformations of the projective plane. The book first offers information on projective transformations, as well as the concept of a projective plane, definition of a projective mapping, fundamental theorems on projective transformations, cross ratio, and harmonic sets. Examples of projective transformations, projective transformations in coordinates, quadratic curves in the projective plane, and projective transformations of space are also discussed. The text then examines inversion, including the power of a point with respect to a circle, definition and properties of inversion, and circle transformations and the fundamental theorem. The manuscript elaborates on the principle of duality. The manuscript is designed for use in geometry seminars in universities and teacher-training colleges. The text can also be used as supplementary reading by high school teachers who want to extend their range of knowledge on projective transformations.

Complex Numbers in Geometry focuses on the principles, interrelations, and applications of geometry and algebra. The book first offers information on the types and geometrical interpretation of complex numbers. Topics include interpretation of ordinary complex numbers in the Lobachevskii plane; double numbers as oriented lines of the Lobachevskii plane; dual numbers as oriented lines of a plane; most general complex numbers; and double, hypercomplex, and dual numbers. The text then takes a look at circular transformations and circular geometry, including ordinary circular transformations, axial circular transformations of the Lobachevskii plane, circular transformations of the Lobachevskii plane, axial circular transformations, and ordinary circular transformations. The manuscript is intended for pupils in high schools and students in the mathematics departments of universities and teachers'' colleges. The publication is also useful in the work of mathematical societies and teachers of mathematics in junior high and high schools.

Frequency Independent Antennas provides a reasonably complete coverage of frequency independent antennas from its inception until the middle of 1965. Most of the contents have not previously been published, except in scattered journal articles, and some are original. The first six chapters are written at a fairly easy level—about the level of a beginning graduate student or the more advanced undergraduate. The last two chapters, which deal with solutions of Maxwell''s equations, are at a somewhat higher level. The book opens with a discussion of some fundamental ideas about antennas. It shows how typical measurements can be understood in terms of classical electromagnetic theory: in other words, how to make sense of measured data, how to set up apparatus to get meaningful data, and how to test their significance. Separate chapters follow on the features of frequency independent, plane-sheet, spiral, and log-periodic antennas. Subsequent chapters discuss how the periodic structure theory provides a way of understanding the peculiarities of frequency independent antennas; and solutions of Maxwell''s equations for idealized spiral and idealized sinusoidal structures.