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The Handbook of Cubic Math unveils the theory involved in Rubik's Cube's solution, the potential applications of that theory to other similar puzzles, and how the cube provides a physical example for many concepts in mathematics where such examples are difficult to find. Nonetheless, the authors have been able to cover and explain these topics in a way which is easily understandable to the layman, suitable for a junior-high-school or high-school course in math, and appropriate for a college course in modern algebra. This manual will satisfy the experts' curiosity about the moves that lead to the solution of the cube and will offer a useful supplementary teaching aid to the beginners.

The Handbook of Cubic Math unveils the theory involved in Rubik's Cube's solution, the potential applications of that theory to other similar puzzles, and how the cube provides a physical example for many concepts in mathematics where such examples are difficult to find. Nonetheless, the authors have been able to cover and explain these topics in a way which is easily understandable to the layman, suitable for a junior-high-school or high-school course in math, and appropriate for a college course in modern algebra. This manual will satisfy the experts' curiosity about the moves that lead to the solution of the cube and will offer a useful supplementary teaching aid to the beginners.

Atlantic menhaden, Brevootia tyrannus, the object of a major purse-seine fishery along the U.S. east coast, are landed at plants from northern Florida to central Maine. The National Marine Fisheries Service has sampled these landings since 1955 for length, weight, and age. Together with records of landings at each plant, the samples are used to estimate numbers of fish landed at each age. This report analyzes the sampling design in terms of probability sampling theory. The design is classified as two-stage cluster sampling, the first stage consisting of purse-seine sets randomly selected from the population of all sets landed, and the second state consisting of fish randomly selected from each sample set. Implicit assumptions of this design are discussed with special attention to current sampling procedures. Methods are developed for estimating mean fish weight, numbers of fish landed, and age composition of the catch, with approximate 95% confidence intervals. Based on specific results from three ports (Port Monmouth, N.J., Reedville, Va., and Beaufort, N.C.) for the 1979 fishing season, recommendations are made for improving sampling procedures to comply more exactly with assumptions of the sampling design. These recommendations include adopting more formal methods for randomizing set and fish selection, increasing the number of sets sampled, considering the bias introduced by unequal set sizes, and developing methods to optimize the use of funds and personnel.

The enlarged new edition of this textbook provides a comprehensive introduction to the basic processes in plasmas and demonstrates that the same fundamental concepts describe cold gas-discharge plasmas, space plasmas, and hot fusion plasmas. Starting from particle drifts in magnetic fields, the principles of magnetic confinement fusion are explained and compared with laser fusion. Collective processes are discussed in terms of plasma waves and instabilities. The concepts of plasma description by magnetohydrodynamics, kinetic theory, and particle simulation are stepwise introduced. Space charge effects in sheath regions, double layers and plasma diodes are given the necessary attention. The novel fundamental mechanisms of dusty plasmas are explored and integrated into the framework of conventional plasmas. The book concludes with a concise description of modern plasma discharges. Written by an internationally renowned researcher in experimental plasma physics, the text keeps the mathematical apparatus simple and emphasizes the underlying concepts. The guidelines of plasma physics are illustrated by a host of practical examples, preferentially from plasma diagnostics. There, Langmuir probe methods, laser interferometry, ionospheric sounding, Faraday rotation, and diagnostics of dusty plasmas are discussed. Though primarily addressing students in plasma physics, the book is easily accessible for researchers in neighboring disciplines, such as space science, astrophysics, material science, applied physics, and electrical engineering. This second edition has been thoroughly revised and contains substantially enlarged chapters on plasma diagnostics, dusty plasmas and plasma discharges. Probe techniques have been rearranged into basic theory and a host of practical examples for probe techniques in dc, rf, and space plasmas. New topics in dusty plasmas, such as plasma crystals, Yukawa balls, phase transitions and attractive forces have been adopted. The chapter on plasma discharges now contains a new section on conventional and high-power impulse magnetron sputtering. The recently discovered electrical asymmetry effect in capacitive rf-discharges is described. The text is based on an introductory course to plasma physics and advanced courses in plasma diagnostics, dusty plasmas, and plasma waves, which the author has taught at Kiel University for three decades. The pedagogical approach combines detailed explanations, a large number of illustrative figures, short summaries of the basics at the end of each chapter, and a selection of problems with detailed solutions.

First published in 2001. The classical Fourier transform is one of the most widely used mathematical tools in engineering. However, few engineers know that extensions of harmonic analysis to functions on groups holds great potential for solving problems in robotics, image analysis, mechanics, and other areas. For those that may be aware of its potential value, there is still no place they can turn to for a clear presentation of the background they need to apply the concept to engineering problems. Engineering Applications of Noncommutative Harmonic Analysis brings this powerful tool to the engineering world. Written specifically for engineers and computer scientists, it offers a practical treatment of harmonic analysis in the context of particular Lie groups (rotation and Euclidean motion). It presents only a limited number of proofs, focusing instead on providing a review of the fundamental mathematical results unknown to most engineers and detailed discussions of specific applications. Advances in pure mathematics can lead to very tangible advances in engineering, but only if they are available and accessible to engineers. Engineering Applications of Noncommutative Harmonic Analysis provides the means for adding this valuable and effective technique to the engineer's toolbox.

Although the Fourier transform is among engineering's most widely used mathematical tools, few engineers realize that the extension of harmonic analysis to functions on groups holds great potential for solving problems in robotics, image analysis, mechanics, and other areas. This self-contained approach, geared toward readers with a standard background in engineering mathematics, explores the widest possible range of applications to fields such as robotics, mechanics, tomography, sensor calibration, estimation and control, liquid crystal analysis, and conformational statistics of macromolecules. Harmonic analysis is explored in terms of particular Lie groups, and the text deals with only a limited number of proofs, focusing instead on specific applications and fundamental mathematical results. Forming a bridge between pure mathematics and the challenges of modern engineering, this updated and expanded volume offers a concrete, accessible treatment that places the general theory in the context of specific groups.

Although deconstruction has become a popular catchword, as an intellectual movement it has never entirely caught on within the university. For some in the academy, deconstruction, and Jacques Derrida in particular, are responsible for the demise of accountability in the study of literature. Countering these facile dismissals of Derrida and deconstruction, Herman Rapaport explores the incoherence that has plagued critical theory since the 1960s and the resulting legitimacy crisis in the humanities. Against the backdrop of a rich, informed discussion of Derrida's writings -- and how they have been misconstrued by critics and admirers alike -- The Theory Mess investigates the vicissitudes of Anglo-American criticism over the past thirty years and proposes some possibilities for reform.