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North Holland

Progress in Optics
1st Edition
Volume 41
English
The first volume of this text was published in 1961, only a few months after the invention of the laser. This event triggered a wealth of developments, many of which were reported in the 240 review articles which were published in this series since its inception. The present volume contains seven articles covering a wide range of subjects. The first article presents a review of various optical effects in spherical and circular micro-cavities capable of supporting high-Q resonant modes (commonly referred to as morphology-dependent resonances (MDRs) or whispering gallery modes (WGMs)). The second presents a comprehensive review of the theory and practice of optical disk data storage. Other articles include discussions on delay control systems for wideband phased array antennas, and quantum statistical properties of optical beams interacting in nonlinear couplers.
Measurement Error and Latent Variables in Econometrics
1st Edition
Volume 37
T. Wansbeek + 1 more
English
The book first discusses in depth various aspects of the well-known inconsistency that arises when explanatory variables in a linear regression model are measured with error. Despite this inconsistency, the region where the true regression coeffecients lies can sometimes be characterized in a useful way, especially when bounds are known on the measurement error variance but also when such information is absent. Wage discrimination with imperfect productivity measurement is discussed as an important special case. Next, it is shown that the inconsistency is not accidental but fundamental. Due to an identification problem, no consistent estimators may exist at all. Additional information is desirable. This information can be of various types. One type is exact prior knowledge about functions of the parameters. This leads to the CALS estimator. Another major type is in the form of instrumental variables. Many aspects of this are discussed, including heteroskedasticity, combination of data from different sources, construction of instruments from the available data, and the LIML estimator, which is especially relevant when the instruments are weak. The scope is then widened to an embedding of the regression equation with measurement error in a multiple equations setting, leading to the exploratory factor analysis (EFA) model. This marks the step from measurement error to latent variables. Estimation of the EFA model leads to an eigenvalue problem. A variety of models is reviewed that involve eignevalue problems as their common characteristic. EFA is extended to confirmatory factor analysis (CFA) by including restrictions on the parameters of the factor analysis model, and next by relating the factors to background variables. These models are all structural equation models (SEMs), a very general and important class of models, with the LISREL model as its best-known representation, encompassing almost all linear equation systems with latent variables. Estimation of SEMs can be viewed as an application of the generalized method of moments (GMM). GMM in general and for SEM in particular is discussed at great length, including the generality of GMM, optimal weighting, conditional moments, continuous updating, simulation estimation, the link with the method of maximum likelihood, and in particular testing and model evaluation for GMM. The discussion concludes with nonlinear models. The emphasis is on polynomial models and models that are nonlinear due to a filter on the dependent variables, like discrete choice models or models with ordered categorical variables.
Quantum Theoretic Machines
What is thought from the point of view of Physics?
1st Edition
A. Stern
English
Making Sense of Inner Sense'Terra cognita' is terra incognita. It is difficult to find someone not taken abackand fascinated by the incomprehensible but indisputable fact: there are material systems which are aware of themselves. Consciousness is self-cognizing code. During homo sapiens's relentness and often frustrated search for self-understanding various theories of consciousness have been and continue to be proposed. However, it remains unclear whether and at what level the problems of consciousness and intelligent thought can be resolved. Science's greatest challenge is to answer the fundamental question: what precisely does a cognitive state amount to in physical terms?Albert Einstein insisted that the fundamental ideas of science are essentially simple and can be expressed in a language comprehensible to everyone. When one thinks about the complexities which present themselves in modern physics and even more so in the physics of life, one may wonder whether Einstein really meant what he said. Are we to consider the fundamental problem of the mind, whose understanding seems to lie outside the limits of the mind, to be essentially simple too? Knowledge is neither automatic nor universally deductive. Great new ideas are typically counterintuitive and outrageous, and connecting them by simple logical steps to existing knowledge is often a hard undertaking. The notion of a tensor was needed to provide the general theory of relativity; the notion of entropy had to be developed before we could get full insight into the laws of thermodynamics; the notice of information bit is crucial for communication theory, just as the concept of a Turing machine is instrumental in the deep understanding of a computer. To understand something, consciousness must reach an adequate intellectual level, even more so in order to understand itself. Reality is full of unending mysteries, the true explanation of which requires very technical knowledge, often involving notions not given directly to intuition. Even though the entire content and the results of this study are contained in the eight pages of the mathematical abstract, it would be unrealistic and impractical to suggest that anyone can gain full insight into the theory that presented here after just reading abstract.In our quest for knowledge we are exploring the remotest areas of the macrocosm and probing the invisible particles of the microcosm, from tiny neutrinos and strange quarks to black holes and the Big Bang. But the greatest mystery is very close to home: the greatest mystery is human consciousness. The question before us is whether the logical brain has evolved to a conceptual level where it is able to understand itself.
Molecular Mechanisms in Visual Transduction
1st Edition
Volume 3
D.G. Stavenga + 2 more
English
Molecular mechanisms in visual transduction is presently one of the most intensely studied areas in the field of signal transduction research in biological cells. Because the sense of vision plays a primary role in animal biology, and thus has been subject to long evolutionary development, the molecular and cellular mechanisms underlying vision have a high degree of sensitivity and versatility. The aims of visual transduction research are firstto determine which molecules participate, and then to understand how they act in concert to produce the exquisite electrical responses of the photoreceptor cells.Since the 1940s [1] we have known that rod vision begins with the capture of a quantum of energy, a photon, by a visual pigment molecule, rhodopsin. As the function of photon absorption is to convert the visual pigment molecule into a G-protein activating state, the structural details of the visual pigments must beexplained from the perspective of their role in activating their specific G-proteins. Thus, Chapters 1-3 of this Handbook extensively cover the physico-chemical molecular characteristics of the vertebrate rhodopsins. Following photoconversion and G-protein activation, the phototransduction cascade leads to modifications of the population of closed and open ion channels in the photoreceptor plasma membrane, and thereby to the electrical response. The nature of the channels of vertebrate photoreceptors is examined in Chapter 4, and Chapter 5 integrates the present body of knowledge of the activation steps in the cascade into a quantitative framework. Once the phototransduction cascade is activated, it must be subsequently silenced. The various molecular mechanisms participating in inactivation aretreated in Chapters 1-4 and especially Chapter 5. Molecular biology is now an indispensable tool in signal transduction studies. Numerous vertebrate (Chapter 6) and invertebrate (Chapter 7) visual pigments have been characterized and cloned. The genetics and evolutionary aspects of this great subfamily of G-protein activating receptors are intriguing as they present a natural probe for the intimate relationship between structure and function of the visual pigments. Understanding the spectral characteristics from the molecular composition can be expected to
Topological Algebras
1st Edition
Volume 185
V.K. Balachandran
English
This book consists of nine chapters. Chapter 1 is devoted to algebraic preliminaries. Chapter 2 deals with some of the basic definition and results concerning topological groups, topological linear spaces and topological algebras. Chapter 3 considered some generalizations of the norm. Chapter 4 is concerned with a generalization of the notion of convexity called p-convexity. In Chapter 5 some differential and integral analysis involving vector valued functions is developed. Chapter 6 is concerned with spectral analysis and applications. The Gelfand representation theory is the subject-matter of Chapter 7. Chapter 8 deals with commutative topological algebras. Finally in Chapter 9 an exposition of the norm uniqueness theorems of Gelfand and Johnson (extended to p-Banach algebras) is given.
From Peirce to Skolem
A Neglected Chapter in the History of Logic
1st Edition
Volume 4
Geraldine Brady
English
This book is an account of the important influence on the development of mathematical logic of Charles S. Peirce and his student O.H. Mitchell, through the work of Ernst Schröder, Leopold Löwenheim, and Thoralf Skolem. As far as we know, this book is the first work delineating this line of influence on modern mathematical logic.
A Psychological Approach to Ethical Reality
1st Edition
Volume 132
K. Hillner
English
The pre-eminent 19th century British ethicist, Henry Sidgwick once said: "All important ethical notions are also psychological, except perhaps the fundamental antitheses of 'good' and 'bad' and 'wrong', with which psychology, as it treats of what is and not of what ought to be, is not directly concerned" (quoted in T.N. Tice and T.P. Slavens, 1983). Sidgwick's statement can be interpreted to mean that psychology is relevant for ethics or that psychological knowledge contributes to the construction of an ethical reality. This interpretation serves as the basic impetus to this book, but Sidgwick's statement is also analyzed in detail to demonstrate why a current exposition on the relevance of psychology for ethical reality is necessary and germane.
Inflation, Employment and Business Fluctuations
1st Edition
Volume 35C
Bozzano G Luisa
English
A Textbook on Macroeconomic Knowledge and Analysis
Quantum Theory, Deformation and Integrability
1st Edition
Volume 186
R. Carroll
English
About four years ago a prominent string theorist was quoted as saying that it might be possible to understand quantum mechanics by the year 2000. Sometimes new mathematical developments make such understanding appear possible and even close, but on the other hand, increasing lack of experimental verification make it seem to be further distant. In any event one seems to arrive at new revolutions in physics and mathematics every year. This book hopes to convey some of the excitment of this period, but will adopt a relatively pedestrian approach designed to illuminate the relations between quantum and classical. There will be some discussion of philosophical matters such as measurement, uncertainty, decoherence, etc. but philosophy will not be emphasized; generally we want to enjoy the fruits of computation based on the operator formulation of QM and quantum field theory. In Chapter 1 connections of QM to deterministic behavior are exhibited in the trajectory representations of Faraggi-Matone. Chapter 1 also includes a review of KP theory and some preliminary remarks on coherent states, density matrices, etc. and more on deterministic theory. We develop in Chapter 4 relations between quantization and integrability based on Moyal brackets, discretizations, KP, strings and Hirota formulas, and in Chapter 2 we study the QM of embedded curves and surfaces illustrating some QM effects of geometry. Chapter 3 is on quantum integrable systems, quantum groups, and modern deformation quantization. Chapter 5 involves the Whitham equations in various roles mediating between QM and classical behavior. In particular, connections to Seiberg-Witten theory (arising in N = 2 supersymmetric (susy) Yang-Mills (YM) theory) are discussed and we would still like to understand more deeply what is going on. Thus in Chapter 5 we will try to give some conceptual background for susy, gauge theories, renormalization, etc. from both a physical and mathematical point of view. In Chapter 6 we continue the deformation quantization then by exhibiting material based on and related to noncommutative geometry and gauge theory.
Analysis, Manifolds and Physics, Part II - Revised and Enlarged Edition
1st Edition
Y. Choquet-Bruhat
C. DeWitt-Morette
English
Twelve problems have been added to the first edition; four of them are supplements to problems in the first edition. The others deal with issues that have become important, since the first edition of Volume II, in recent developments of various areas of physics. All the problems have their foundations in volume 1 of the 2-Volume set Analysis, Manifolds and Physics. It would have been prohibitively expensive to insert the new problems at their respective places. They are grouped together at the end of this volume, their logical place is indicated by a number of parenthesis following the title.

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