From One To Two Dimensions

This book has been conceived to extend the generally published work on one- and two-dimensional digital filters in order to include some of the more recently developed ideas. It is intended to supplement and build on the classical books which cover the fundamental concepts of the topic. As a consequence of this, the basic theory is stated in a compact manner and is not developed thoroughly, as this would result in considerable duplication of existing books. The main theme of the book has been to provide a comprehensive background to the methods available for the realization of both recursive and nonrecursive digital filters, and to give an insight into some of the more recent implementation procedures. The book is planned to cover one- and two-dimensional systems in parallel, showing the techniques which are applicable in both areas, and also the limitations and constraints necessary when a one-dimensional technique is extended to systems of higher dimensionality. The theme of the book commences with several chapters on the design of filter transfer functions to meet given specifications. This is followed by a discussion of methods of implementing these in a practical system and the limitations imposed as a result of noise and finite word length. Finally, a discussion of some applications is included.

The field of nuclear magnetic resonance spectroscopy has undergone explosive development during the last decade with the advent of new one- and two-dimensional techniques. The author has had extensive experience in the use of these techniques for the structure elucidation of complex natural products, and in this book he gives a comprehensive, up-to-date and very readable account of these developments. The book's scope is very wide. It starts from fundamental principles of modern NMR spectroscopy, describing the instrumentation and its optimum use, and extends to the latest developments such as inverse measurements. Emphasis is on problem-solving so as to be useful to a large number of organic chemists, biochemists and medicinal chemists. The problems and worked solutions at the end of the chapters will help students to gain proficiency in the application of these new techniques. Those who are learning how to operate modern NMR spectrometers will find particularly useful the description of such basic aspects as shimming, probe tuning, and methods for improvement of resolution and sensitivity.

Two-dimensional calculus is vital to the mastery of the broader field, and this text presents an extensive treatment. Advantages include the thorough integration of linear algebra and development of geometric intuition. 1986 edition.

A visual, intuitive introduction in the form of a tour with side-quests, using direct probabilistic insight rather than technical tools.

A classic book about life in a two-dimensional universe, written by a well-known author. Now brought back into print in this revised and updated edition, the book is written within the great tradition of Abbott's Flatland, and Hinton's famous Sphereland. Accessible, imaginative, and clever, it will appeal to a wide array of readers, from serious mathematicians and computer scientists, to science fiction fans.

Superfluid helium is a quantum liquid that exhibits a range of counter-intuitive phenomena such as frictionless flow. Quantized vortices are a particularly important feature of superfluid helium, and all superfluids, characterized by a circulation that can only take prescribed integer values. However, the strong interactions between atoms in superfluid helium prohibit quantitative theory of vortex behaviour. Experiments have similarly not been able to observe coherent vortex dynamics. This thesis resolves this challenge, bringing microphotonic techniques to bear on two-dimensional superfluid helium, observing coherent vortex dynamics for the first time, and achieving this on a silicon chip. This represents a major scientific contribution, as it opens the door not only to providing a better understanding of this esoteric quantum state of matter, but also to building new quantum technologies based upon it, and to understanding the dynamics of astrophysical superfluids such as those thought to exist in the core of neutron stars.

Examines the structural anatomy of patterns, shows how reflections, rotations, and translations create symmetrical patterns, and shows examples from textiles, pottery, mosaics, natural forms, and Escher prints

The discrete Fourier transform (DFT) is an extremely useful tool that finds application in many different disciplines. However, its use requires caution. The aim of this book is to explain the DFT and its various artifacts and pitfalls and to show how to avoid these (whenever possible), or at least how to recognize them in order to avoid misinterpretations. This concentrated treatment of the DFT artifacts and pitfalls in a single volume is, indeed, new, and it makes this book a valuable source of information for the widest possible range of DFT users. Special attention is given to the one and two dimensional cases due to their particular importance, but the discussion covers the general multidimensional case, too. The book favours a pictorial, intuitive approach which is supported by mathematics, and the discussion is accompanied by a large number of figures and illustrative examples, some of which are visually attractive and even spectacular. Mastering the Discrete Fourier Transform in One, Two or Several Dimensions is intended for scientists, engineers, students and any readers who wish to widen their knowledge of the DFT and its practical use. This book will also be very useful for ‘naive’ users from various scientific or technical disciplines who have to use the DFT for their respective applications. The prerequisite mathematical background is limited to an elementary familiarity with calculus and with the continuous and discrete Fourier theory.

An important introduction to graphene, its physics and potentially significant applications, for graduate students, physicists and materials science researchers.