bluuebunny/crossref_metadata_2025 huggingface dataset:
Pseudochaos
Authors: Zaslavsky George M
Published: November 2023

Integrable systems in a compact phase space have a full set of integrals of motion and simple periodic or quasi-periodic dynamics. Systems with chaotic dynamics have a positive Lyapunov exponent and uniform mixing in phase space. There are different ways to fill the gap between integrability and chaoticity.
Interaction Of Motor and Language Factors In The Development Of Speech Production
Authors: Smith Anne , Goffman Lisa
Published: November 2023

In general, models of language development in childhood (Locke 1993) and language production in adults (Levelt 1989; Levelt et al. 1999) do not include explicit accounts of the production process at the level of speech motor control. Models of the control and coordination of speech movements (Barlow and Farley 1989; Smith 1992) are written in the language of motor control theory,for example, of reflexes and centrally generated motor commands, and do not account for the question of how linguistic units act as input to, or emerge from, the production process (one exception to this is the theory of articulatory phonology of Browman and Goldstein 1992, which we discuss below). The growing literature on speech motor development, however, forces our attention on potential language/motor interactions. Clearly, language and speech motor processes codevelop in the child. How does language acquisition affect speech motor development, and how do basic motor processes affect language acquisition? These questions are the central focus of this chapter.
Duality
Authors: Kantorovitz Shmuel
Published: November 2023

We studied in preceding chapters the conjugate space X* for various special normed spaces. Our purpose in the present chapter is to examine X* and its relationship to X for a general normed space X.
Bounded operators
Authors: Kantorovitz Shmuel
Published: November 2023

We recall that B(X, K) denotes the normed space of all bounded linear mappings from the normed space X to the normed space Y. The norm on B(X, K) is the operator norm. The elements of B(X, Y) will be referred to briefly as operators. Two of the basic theorems about B(X, Y), the Uniform Boundedness Theorem and the Open Mapping Theorem, use so-called category arguments in their proofs. These are based on Baire’s theorem about complete metric spaces.
Integral representation
Authors: Kantorovitz Shmuel
Published: November 2023

Let X be a Banach space. A Banach subspa ce Z of X is a subspace of X in the algebraic sense, which is a Banach space for a norm II • llz larger than or equal to the given norm II · II of X. Clearly, if Zand X are Banach subspaces of each other, then they coincide as Banach spaces (with equality of norms).
Indices of quality
Authors: Smith John Maynard , Harper David
Published: November 2023

A crucial distinction we have tried to draw has been between ‘indices’, signals that are reliable because they cannot be faked, and ‘handicaps’, signals that are reliable because they are costly to produce. The distinction is clear enough in a model, and there are examples that fall easily into one or other category. Fights between funnel-web spiders are settled in favour of the heavier spider if the weight difference is greater than about 10 per cent. A spider can signal its weight cost-free by vibrating the web. Female stalk-eyed fiies prefer males with long eye-stalks—eye-stalk length is associated with good condition, and hence with ‘good genes’, because it would be too expensive for low quality males to grow long eye-stalks. These are examples of an index, and a handicap, respectively.
Endometrial cancer
Authors: Terry Paul D , Rohan Thomas E , Franceschi Silvia , Weiderpass Elisabete
Published: November 2023

Endometrial adenocarinoma accounts for approximately one of every 10 cancers diagnosed among women worldwide, with incidence rates varying at least 10-fold between areas of low incidence (such as North Africa and China) and high incidence (such as North America) (Parker et al. 1997; Parkin et al. 1999). The use of exogenous estrogens, and of estrogen replacement therapy in particular, has been strongly related to increased risk in epidemiological studies (IARC 1999; Akhmedkhanov et al. 2001). Exogenous estrogens unopposed by progesterone have been hypothesized to increase the risk of this malignancy through increased mitotic activity of endometrial cells, increased number of DNA replication errors, and somatic mutations resulting in the malignant phenotype (Akhmedkhanov et al. 2001).
Tobacco and cardiovascular disease
Authors: Jamrozik Konrad
Published: November 2023

At the level of the whole population, tobacco causes far more harm via its contribution to cardiovascular disease (CVD) than it does through its effects on either the risk of lung cancer or of chronic obstructive pulmonary disease (COPD). This occurs because, in the absence of smoking, lung cancer and COPD are both very rare conditions. CVD, by contrast, is now the commonest cause of death of Homo sapiens (World Health Organization 1999). Thus, for a given prevalence of smoking in a population, the small increase in risk of CVD, in relative terms, that is associated with smoking generates many additional cases of CVD. By contrast, the much larger relative risks for lung cancer and COPD associated with smoking generate fewer additional cases of these conditions because these risks are applied to ‘background’ incidence rates that are much lower than the lifetime risk of CVD in non-smokers (Wald 1978).
Fundamentals
Authors: Witten T , Pincus P
Published: November 2023

This chapter assembles some underlying concepts that we will need through-out our study of structured fluids. The first section reviews the main needed ideas from statistical mechanics. For systems in equilibrium, we recall how probabilities of states are determined, and the connection between probability and the work to alter a system’s state. We also describe ways to estimate the time for a system to reach equilibrium. The second section is about the orders of magnitude common to the liquid environment of structured fluids. In this section we justify the magnitude of a simple liquid’s viscosity. The final section surveys the experimental probes that determine the useful questions we can ask about structured fluids.
Surface tension
Authors: Pelcé Pierre , Brujić Jasna , Costier Laurent
Published: November 2023

The origin of interfacial tension is the interaction energy between the molecules in the two media present. The first approach by Laplace involves calculating the energy required to divide two parts of an infinite fluid into two parts with a planar separation surface.
A Bird’s Eye View Of Liquid Crystal Elastomers
Authors: Warner M , Terentjev E M
Published: November 2023

Liquid crystal elastomers bring together, as nowhere else, three important ideas: orien-tational order order in amorphous soft materials, responsive molecular shape and quenched topological constraints. Acting together, they create many new physical phenomena that are the subject of this book. This bird’s eye view sketches how these themes come together and thereby explains the approach of our book.
Distortions of Nematic Elastomers
Authors: Warner M , Terentjev E M
Published: November 2023

Soft or semi-soft deformations are energetically the best response to shape changes imposed on a nematic elastomer. When the director can be rotated, then an elastomer will always deform softly, if the accompanying relaxations can be reconciled with the boundary conditions. In this chapter we examine distortions of nematic elastomers where the imperative to deform softly is in conflict with the external constraints imposed on them. There are generically two ways to resolve this conflict.
Review Of Environmental Health And Epidemiological Principles
Authors: Baker Dean
Published: November 2023

A major aim of environmental epidemiological studies is to determine if exposure to an environmental factor or factors is associated with an effect, or change in health status. If there is an association, it is desirable to be able to show an exposure–response relationship, i.e., a relationship in which an increase in the level of exposure is associated with an increase in the rate of a health effect. This section will review basic principles and terms that are used in environmental health and that are relevant to understanding environmental epidemiology.
Health Risk Assessment
Authors: KüNzli Nino , Perez Laura
Published: November 2023

Epidemiological studies usually result in estimates of the quantitative associations between environmental factors and health in humans. These risk functions–the odds ratio (OR), relative risk (RR), or a regression coefficient–are not of direct public health relevance. Such measures of risk do not take into account the absolute level of risk, the range or distribution of an environmental exposure, the health state of a population, or the distribution of susceptibility factors. Risk assessors need to translate this information into quantities relevant to policy makers and the public. As will be shown, environmental epidemiology can make important contributions to environmental health risk assessment procedures.
Atom optics
Authors: Letokhov Vladilen
Published: November 2023

The methods developed formanipulating atomic motion with laser light, briefly described in Chapters 5 and 6, have led naturally to the creation of atom optics.
From laser-cooled and trapped atoms to atomic and molecular quantum gases
Authors: Letokhov Vladilen
Published: November 2023

The invention and development of laser methods for cooling and trapping atoms have led to the advent of the physics of ultracold matter. Low-temperature quantum physics has so far dealt with condensed media, wherein quantum phenomena (superﬂuidity and superconductivity) usually manifest themselves at temperatures of a few kelvin. Laser cooling and trapping of atoms have made it possible to successively attain millikelvin, microkelvin, and nanokelvin temperatures, at which the de Broglie wavelength of the atoms becomes commensurable with the interatomic separation, even in dilute gases. The interaction of atoms in ultracold dilute gases becomes essentially quantum mechanical. The physics of such quantum gases is more akin to the well-developed physics of condensed matter at low temperatures. It is in essence a boundary field between atomic, laser, and condensed-matter physics. Following the first, pioneering experiments on the Bose–Einstein condensation of alkali-metal atoms, this field has continued to develop at a very fast pace, which can be explained by the vast variety of particles (atoms, isotopes, and molecules) that can be laser cooled and trapped under degeneracy conditions. This is much more than physicists had at their disposal previously (3,4He). Moreover, laser radiation and magnetic fields additionally make it possible to control not only the intrinsic quantum state of the interacting ultracold particle species, but also the interaction of the particles. All this makes the research in the field of quantum gases a great breakthrough, both in atomic–molecular physics and in many-body-interaction physics, which heretofore was the prerogative of low-temperature condensed-matter physics.
Multiphoton ionization of molecules
Authors: Letokhov Vladilen
Published: November 2023

The multiphoton ionization techniques for molecules were developed in parallel with the studies into the resonance multistep ionization of atoms, but their aim was to achieve photo selective laser detection of molecular traces in combination with mass spectrometry of the photoions produced, that is, to create what is called a “laser two- dimensional optical mass spectrometer” (Letokhov 1976). However, the more complex structure of molecular spectra, the high photoionization potentials of molecules (8–12 eV), and the absence of tunable laser sources operable in the UV region of the spectrum made it necessary to use the available UV excimer lasers capable of photoionizing molecules by “brute force.” In that case, the low selectivity of the optical channel was compensated by the extra selectivity of the mass spectrometer. Figure 10.1 schematically illustrates the main methods of multiphoton ionization of molecules: (a) resonance stepwise ionization, (b) resonance-enhanced two-photon (or multiphoton) ionization (RETPI or REMPI), and (c) nonresonance multiphoton ionization. The stepwise photoionization technique provides good spectral selectivity; it requires a tunable laser radiation source of moderate power output (kW–MW/cm2). The REMPI technique is of limited selectivity and requires higher radiation powers (MW–GW/cm2); it is especially convenient where use is made of ultrashort laser pulses. And, finally, the nonresonance multiphoton ionization (MPI) technique features no spectral selectivity; it is a “brute-force” method, where the necessary chemical selectivity is attained solely in the mass-spectrometer channel. Therefore, the last two techniques are unsuitable for the detection of trace molecules in a mixture of organic molecules, because many of the molecules simultaneously suffer photoionization and photo fragmentation. However, when combined with the cooling of molecules in a pulsed supersonic jet, which prevents their distribution among many sublevels and thus makes their spectra sharper, the REMPI technique proves very effective (Reisler and Wittig 1985; Lubman 1990).
The outlook for single molecule fluorescence measurements
Authors: Gell Chris , Brockwell David , Smith Alastair
Published: November 2023

Single molecule sensitivity provides a platform for fundamental and applied studies that are increasing in their complexity and ambition at a fast pace. There are undoubtedly exciting discoveries to be made in many areas, particularly in biophysics. Even in the few brief examples that have been given in this book we have had a glimpse of the insights that single molecule measurements have already provided. The roles which structural and functional heterogeneity play in many biological processes, revealed by single molecule methods, will be a topic of intense study in the coming years.
How to use this book
Authors: Drummond Michael E , Sculpher Mark J , Torrance George W , O’Brien Bernie J , Stoddart Greg L
Published: November 2023

There is a growing literature on economic evaluation in health care. Studies have been conducted by economists, medical researchers, clinicians, and multidisciplinary teams containing one or more of these parties. The studies go under a confusing range of labels, such as cost-effectiveness analysis (CEA), cost-benefit analysis (CBA), and cost-utility analysis (CUA). They also vary greatly in quality, as methodological critiques have shown (Drummond et al. 1986; Adams et al. 1992; Gerard 1992; Udvarhelyi et al. 1992; Donaldson and Shackley 1997; Neumann et al. 2005).
Presentation and use of economic evaluation results
Authors: Drummond Michael E , Sculpher Mark J , Torrance George W , O’Brien Bernie J , Stoddart Greg L
Published: November 2023

The implicit or explicit objective of economic evaluation is to improve decisions about the allocation of health care resources. Therefore, in this penultimate chapter we discuss issues relating to the presentation and use of economic evaluation results. In Chapter 3 we pointed out that, in order to assess the usefulness of economic evaluation results, readers (users) of studies needed to answer the following questions.
Introduction
Authors: Harrigan Jinni A , Rosenthal, Robert , Scherer Klaus R
Published: November 2023

The renaissance of theorizing and research on emotion in the last 30 years (after decades of neglect during the hegemony first of learning theory and then the excesses of the cognitive revolution) has been primarily due to the influential work on facial expression pioneered by Tomkins (1962, 1963) and vigorously pursued by Ekman (Ekman & Friesen 1975, 1978), Izard (1971, 1991), and their collaborators (Ekman et al. 1972, 1982, 1987; Ekman & Rosenberg 1997; Izard et al. 1980). Photos with the prototypical expressions of the basic emotions adorn most textbooks of psychology and remind students and researchers alike of the powerful role of nonverbal behavior during emotional episodes.
Nonverbal behavior and interpersonal Sensitivity
Authors: Hall Judith A , Bernieri, Frank J , Carney Dana R
Published: November 2023

Although questions about how people respond to others’ nonverbal cues have always been central to the study of nonverbal communication, the study of individual differences in accuracy of nonverbal cue processing, or interpersonal sensitivity, is a more recent endeavor. This chapter focuses on assessment of individual differences, emphasizing the major paradigms and instruments for assessing accuracy of nonverbal cue processing, and discussing characteristics of the stimuli and judgment methodologies (e.g. what state or trait is being judged, who is being judged, what cue channels are available, whether the cues are posed or spontaneous, whether judgment is done in live interaction or from standard stimuli, what judgment format is used, what criteria and methods are used for scoring).
Nonverbal Behavior In Education page 283
Authors: Babad Elisha
Published: November 2023

The purpose of this chapter is to acquaint the reader with the various ways nonverbal (NV) research is used in education. ‘Research’ is taken here in a global and loose manner, covering the entire range of fact-seeking activities, from controlled experimental studies at one extreme, to informal gathering of NV information for purposes of teacher reflection and improvement at the other extreme. The chapter is intended to be descriptive and analytical.
Nonverbal communication coding systems of committed couples
Authors: Yoshimoto Dan K , Shapiro Alyson , O’Brien Kelly , Gottman John M
Published: November 2023

As discussed in previous chapters, the study and understanding of a single modality of nonverbal behavior, such as vocal or facial action, is rich in information regarding specific individual behavior. While this approach is useful, it is also somewhat artificial when it comes to understanding the complexities of real behavior. Generally, the expression of an emotion or other behavior involves the coordination of multiple modalities working concurrently, which requires an integrated approach for quantifying nonverbal behavior.
Technical Issues In Recording Nonverbal Beh Avior
Authors: Frank Mark G , Juslin Patrik N , Harrigan Jinni A
Published: November 2023

From the early days of recording nonverbal behavior using 16mm Wlm or paper and pencil reports, significant technological strides have been made. Such advances include the use of video and audio tapes, digital and 8mm recording, computer-driven data collection and analysis, scanning devices—all of which offer greater visual and auditory capture of the nonverbal data; greater clarity, precision, and comparability of data; and improved data storage and analysis than 20 years ago.
Theoretical Results For The Euler Equations
Authors: Novotný A , Straškraba I
Published: November 2023

This chapter is devoted to the study of qualitative properties of the Euler equations of compressible flow. In what follows basic properties of the Euler equations as a nonlinear hyperbolic system will be pointed out and the relevance of boundary conditions discussed. The method of characteristics is demonstrated on representative examples as is, for example, the piston problem. Then the existence of smooth solutions, loss of smoothness and lifespan of the smooth solution of the general hyperbolic system in connection with the Euler system is treated thoroughly. Special solutions as plane waves are also studied.
Principal ligand fields: σ interactions
Authors: Jean Yves
Published: November 2023

In this chapter, we shall construct the molecular orbitals (MO) of mono-metallic complexes MLl and thereby deduce their electronic structure by distributing the electrons in these orbitals. We shall study different types of ‘ligand field’, each one being characterized by the number of ligands and by their geometrical arrangement around the metal centre (octahedral complexes ML6, tetrahedral, or square-planar ML4, etc.).
The Inflationary Universe
Authors: Hawley John F , Holcomb Katherine A
Published: November 2023

The big bang model of cosmology is spectacularly successful as a scientific theory. Until quite recently, it would have seemed unthinkable that any physical model, much less one so elegant and simple, would enable us to begin to understand the universe as a whole, with all its daunting complexities. The big bang model makes definite predictions about observable quantities such as elemental abundances, and those predictions have been borne out to a remarkable degree.
Surfaces
Authors: Gilbert N D , Porter T
Published: November 2023

Knots are one-dimensional objects living in three-dimensional space. Surfaces are two-dimensional objects. Some of the ideas that help in understanding knots can also be adapted to help study surfaces. The flow of ideas is two way and we shall see later on how surfaces help us to study knots. The study of surfaces, however, has no need of knot theory for motivation. There are important applications of the classification theorem for surfaces in other areas of mathematics, perhaps most notably in complex analysis, but we will not be going in that direction here.
Graphs and trees
Authors: Gilbert N D , Porter T
Published: November 2023

The theory of graphs impinges on the study of knots and surfaces in four significant ways. We shall see how knots can be studied by graph theory applied to their diagrams, and how graphs can be studied by embedding them in surfaces. We have already met (in Chapter 6) the Cayley graph of a group presentation, which produces a geometric representation of a group from sets of generators and defining relations, and later on we shall meet covering graphs that give a proof, via Van Kampen’s theorem, of a fundamental result about free groups. It is not our aim to compress a complete introduction to graph theory into this single chapter; rather, we select the essential facts and leave the reader to pursue the wider subject in texts intended for that purpose. We mention Wilson (l 985) and White (1984) as being particularly suitable.
The fundamental group
Authors: Gilbert N D , Porter T
Published: November 2023

The fundamental group is an algebraic label attached to a topological space. Naturally enough, it is a group and is constructed using paths in the space, continuous analogues of the sequences of edges constituting paths in a graph. The more convoluted is the shape of the space, the more variety there will be among the paths in that space and the larger will be the fundamental group. The fundamental group first arose in Poincare’s work on the three-body problem. His idea was to classify the possible evolutions of a system of three bodies moving under mutual gravitational forces as paths in the phase space with coordinates given by the bodies’ positions and velocities, but to regard nearby paths as the same. This led to the notion of deformation of one path into another, now formalized as homotopy of paths. The fundamental group consists of homotopy classes of paths in a space. The notion of homotopy is also crucial in complex analysis: Cauchy’s theorem on contour integration may be phrased as saying that the integrals of a holomorphic function around two homotopic contours are the same (see e.g. Priestley 1990). Further development of the extensive theory of the fundamental group, beyond that covered here, may be found in Armstrong (1983) and Brown (1988). Our principal application will be to knots: any knot yields a group, namely the fundamental group of its complement in 3, and algebraic properties of the group reflect properties of the knot.
Lattice rules as multiple sums
Authors: Sloan I H , Joe S
Published: November 2023

In the preceding chapter we have seen that a lattice rule Q is an equal weight quadrature rule in which the quadrature points are all the points belonging to some integration lattice L that lie in us. However, that rather abstract definition does not tell us how lattice rules may be written down, or implemented in a computer program.
Introduction
Authors: Prutton M
Published: November 2023

All the properties of a piece of bulk material are determined by the number and types of atoms it contains and by their arrangement in space with respect to each other. Some properties can be related in a straightforward manner, both theoretically and experimentally, to the chemical composition and to the crystal structure by using the large body of understanding provided by the band theory of solids (Rosenberg 1975; Kittel 1986). Thus, for instance, the division of crystalline solids into insulators, semiconductors, and conductors, the explanation of the relationship between thermal and electrical properties, and the occurrence of both Hall and magneto-resistance effects can all be satisfactorily explained within the framework of the band theory of solids. It may be less straightforward to relate other properties to a theoretical model of a solid, and a more empirical approach may have to be adopted. One example of such a property is the ferromagnetism of some metals. This depends upon small differences between large interactions in the solid, and demands a difficult and sophisticated theory for its explanation. Mechanical creep and fatigue failure are examples of phenomena requiring an understand¬ing of faults which occur in crystalline solids and the way in which they move in response to applied forces. Again, the theoretical description of these processes is difficult. Nevertheless these properties are still determined in principle, provided that the composition and structure of the material are sufficiently well defined.
Surface chemical composition
Authors: Prutton M
Published: November 2023

The first questions to be asked about a surface are: what atoms are present and what are their concentrations? If techniques can be found to provide the answers to these questions, then the next, more detailed, question is: how are the atoms bound to each other? These are the questions of surface chemistry.
The Loop Formulation of Gauge Theory and Gravity
Authors: Loll Renate
Published: November 2023

This chapter contains an overview of the loop formulation of Yang- Mills theory and 3+1-dimensional gravity in the Ashtekar form. Since the configuration spaces of these theories are spaces of gauge potentials, their classical and quantum descriptions may be given in terms of gauge-invariant Wilson loops. I discuss some mathematical problems that arise in the loop formulation and illustrate parallels and differences between the gauge theoretic and gravitational applications. Some remarks are made on the discretized lattice approach.
Knotted Surfaces, Braid Movies, and Beyond
Authors: Carter J Scott , Saito Masahico
Published: November 2023

Knotted surfaces embedded in 4-space can be visualized by means of a variety of diagrammatic methods. We review recent developments in this direction. In particular, generalizations of braids are explained. We discuss generalizations of the Yang-Baxter equation that correspond to diagrams appearing in the study of knotted surfaces. Our diagrammatic methods of producing new solutions to these generalizations are reviewed. We observe 2-categorical aspects of these diagrammatic methods. Finally, we present new observations on algebraic/algebraic-topological aspects of these approaches. In particular, they are related to identities among relations that appear in combinatorial group theory, and cycles in Cayley complexes. We propose generalizations of these concepts from braid groups to groups that have certain types of Wirtinger presentations.
Single-Step Approximations
Authors: Fröbrich P , Lipperheide R
Published: November 2023

The formal theory of reactions developed in Chapter 5 has provided us with rigorous expressions for the cross section of any type of transition from one two-body channel to another. These can be used as the starting point for the explicit calculation of reaction cross sections to be compared with experimental data. We shall demonstrate this using as examples a number of specific reactions for which the cross section will be derived in detail.
Many-Valued Logics
Authors: Malinowski Grzegorz
Published: November 2023

The book attempts an elementary exposition of the topics connected with many-valued logics. It gives an account of the constructions being "many-valued" at their origin, i.e. those obtained through intended introduction of logical values next to truth and falsity. To this aim, the matrix method has been chosen as a prevailing manner of presenting the subject. The inquiry throws light upon the profound problem of the criteria of many-valuedness and its classical characterizations. Besides, the reader can find information concerning the main systems of many-valued logic, related axiomatic constructions, and conceptions inspired by many valuedness. The examples of various applications to philosophical logic and some practical domains, as switching theory or Computer Science, helps to see many-valuedness in a wider perspective. Together with a selective bibliography and historical references it makes the work especially useful as a survey and guide in this field of logic.
Quantifiers in rr1any-valued logic
Authors: Malinowski Grzegorz
Published: November 2023

Many-valued predicate calculi are usually built along the classical pattern (compare 1.5). Then the enriched language also includes two quantifiers: universal and existential. Nonetheless, in many cases the difficulties arise either with getting an adequate semantic description of quantifiers, or with an axiomatization of a defined system of the first-order logic. On the other hand, there is a visible tendency to enlarge many-valued predicate logics with generalized quantifiers binding a number of nominal variables and predicates at a time (Rosser and Turquette (1952)) and also with generalized quantifiers in Mostowski’s sense (see e.g. Rescher (1969)). In this chapter, an account of ordinary and generalized forms of quantification in many-valued logic is given. Further, a very relevant topic, namely the problem of foundation of set theory on many-valued logic, is also outlined.
Introducing Labelled Deductive Systems
Authors: Gabbay Dov M
Published: November 2023

The previous chapter successively refined the notion of a logical system with a view of introducing LDS as the most general concept of a logic. This chapter motivates LDS through many examples from monotonic and nonmonotonic logics. Section 2.2 is mainly concerned with formulating known and familiar monotonic logics as LDS. This will persuade the reader that LDS is general enough. Section 2.3 presents many nonmonotonic systems and features as LDS. This should show that LDS is indeed a natural and comprehensive framework. Within LDS, the distinction between monotonic and nonmonotonic systems is not important.. Both kinds look essentially the same with some variations. The rest of the sections in the chapter present case studies in depth, showing how LDS presentations of known logics make us understand them much better and present them with technical simplicity and elegance. The chapter concludes with a discussion of the limitations of LDS.
Substructural Predicates
Authors: Dosen Kosta
Published: November 2023

In another paper by the author, of which this is a companion, it was suggested that equality principles should be restricted in substructural set theories or higher-order logics in order to prevent the banned structural rules from resurging. Underlying these restrictions are notions of predicate in which the use of predicate functors corresponding to contraction and thinning are restricted. These notions are here introduced and compared with the restrictions envisaged in the former paper.
Fine Hierarchy and Definability in the Lindenbaum Algebra
Authors: Selivanov Victor
Published: November 2023

The paper continues an earlier work on applications of a fine hierarchy defined by the author to the classification of index sets. We refine some results relating the fine hierarchy to Boolean terms, prove a useful completeness condition for the levels of the fine hierarchy, discuss a general scheme of the classification of definable index sets, and completely classify index sets of the predicates definable in the Lindenbaum algebra of sentences of any finite rich language.
Introduction to critical phenomena
Authors: Bellac Michel Le , Barton G
Published: November 2023

This first chapter is an elementary introduction to the models and methods that will be used later. The ferromagnetic (Curie) transition serves as our prototype for all second-order phase transitions, and serves also to introduce the notions of broken symmetry and of order parameter. The basic model of ferromagnetism, namely the Ising model, is described in Section 1.2, and solved for an elementary case. The reason why this model is so important is that it has an exact solution in two dimensions, which exhibits spontaneous magnetization. Section 1.3 is devoted to a first approach to mean-field methods, which remain amongst the most frequently exploited approximations even today. They will lead us to define a first set of critical exponents; the listing of such exponents will then be completed in Section 1.4, once correlation functions have been defined. Finally, in Section 1.5 a qualitative description of critical phenomena will enable us, in a first approximation, to define the concept of scale invariance and its relation to the behaviour of the theory under dilatations.
The perturbation expansion and Feynman diagrams
Authors: Bellac Michel Le , Barton G
Published: November 2023

The aim of this chapter is the systematic development of concepts and techniques that have been introduced in the first three chapters; namely correlation functions and generating functions (Section 1.4.1); Legendre transformations (Section 1.4.5); and perturbation expansions and expansions in the number of loops (Sections 2.4.2, 3.4.3, and 3.5.3). The tools we use are the generating functional and Gaussian integration. In several cases it proves possible to explain the method through an example with just one variable; a preliminary study of such examples then makes it much easier to follow the general discussion.
Green's functions and the S matrix
Authors: Bellac Michel Le , Barton G
Published: November 2023

In this chapter we study the Klein-Gordon field interacting with itself. This model has very limited physical applications, but it allows us to introduce several important ideas without having to use the more complicated formalism for particles of nonzero spin.
k-Space Microscopy in Biology and Materials Science
Authors: Callaghan Paul T
Published: November 2023

Because of its high gyromagnetic ratio and its abundance in natural materials, the hydrogen proton is the predominant nucleus of NM R microscopy. In biological tissue it is present in the major molecular species, water, lipids, proteins, and polysaccharides. Hydrogen is abundant in synthetic polymers and in natural oils, waxes, and tars. It is significant in some minerals such as coal, and in others it may be introduced by adsorption of water.
The echo phenomenon
Authors: Bagguley D M S
Published: November 2023

High frequency electromagnetic pulse methods are now widely used in a variety of modern scientific disciplines ... physics, chemistry, biochemistry, and medicine all find use for these techniques to complement steady state measurements. In the following Articles of this book distinguished scientists draw attention to specific applications which have stemmed from the early work on spin echoes in nuclear magnetic resonance. This field was pioneered by E. L. Hahn [1] and in presenting a book which is clearly interdisciplinary in subject matter it is appropriate to reconsider some of the basic principles of echo formation inherent in that work. These phenomena underlie many of the sophisticated techniques widely used in present day research and are often only marginally familiar to the experimentalist.
NMR and enzymes
Authors: Evans J N S
Published: November 2023

Since the first reported NMR study [1] of an enzyme, ribonuclease, in 1957, NMR spectroscopy has been applied with exponentially increasing frequency to a wide range and number of enzymes. Although the introduction and development of 2D1H NMR techniques over the last 10 years has revolutionized the structural elucidation of small proteins (molecular weightMr15 000), the majority of enzymes fall outside this molecular weight range. The recent introduction of heteronuclear multiple quantum coherence (HMQC) spectroscopy and 3D techniques has helped to extend this molecular weight limit, currently to aboutMr=25 000. For enzymes larger than this, the complete structure cannot currently be determined by NMR. But one of the distinguishing features of NMR spectroscopy as a technique for structural biology is its ability to provide crucial structural information about a specific part or region of a molecule. This sets NMR apart from other structural techniques such as X-ray crystallography, in which the whole structure must be solved completely before a selected region can be investigated. This ability to focus on structural regions of interest is nowhere more important than in the field of protein function, where the relationship between structure and function is intimately connected at the enzyme active site. The use of heteronuclear NMR, in particular nuclei such as13C,15N,19F, and31P, has been important in providing the means to focus on enzyme active sites for proteins whoseMr=25000-100000.
Electron spin echo envelope modulation studies of mixed valence manganese complexes: applications to the catalytic manganese cluster of photosynthetic oxygen evolution
Authors: Britt R D , Klein M P
Published: November 2023

Professor Erwin Hahn’s 1950 discovery of spin echoes has opened a number of areas in experimental physics and chemistry [ 1] . Among these is the use of the electron spin echo envelope modulation (ESEEM) technique, such as described by Rowanet al.[2], which has become an important tool for measuring the spin transitions of magnetic nuclei magnetically coupled to EPRvisible electron paramagnets. In our applications, we use the ESEEM technique to study the coordination of ligands containing magnetic nuclei to metal centres active in biological catalysis. Details of experimental and theoretical aspects of the use of the ESEEM technique are provided in a number of good references [3-11] . In a brief review, the ESEEM technique requires the use of a pulsed EPR spectrometer, in which powerful microwave pulses are employed to affect large rotations of the net electron spin magnetization on a time-scale short compared to the relaxation processes which return the electron spin magnetization to equilibrium. For very narrow EPR signals, the EPR spectrum can be obtained by Fourier analysis of the Free Induction Decay (FID) following a single microwave pulse. However, the large bandwidths of most EPR signals, in particular those associated with transition metals, preclude such simple pulsed EPR experiments. In such cases, only a small fraction of an inhomogeneously broadened EPR line is excited by the microwave pulse.
Time evolution of electron-nuclear cross-polarization in radiofrequency induced optical nuclear spin polarization (RF-ONP)
Authors: Stehlik D , Vieth H -M
Published: November 2023

One of the many ingenious ideas that Erwin Hahn and his group in Berkeley contributed in the early years of the newly developing field of NMR was the concept of Nuclear Double Resonance (DR) in solids [1,2] . It became important for the study of many phenomena in solid state physics, because by means of accumulative polarization exchange with an easily observable nuclear spin reservoir it permitted the sensitive detection of nuclear spin ensembles which have poor direct detectability due to a weak nuclear magnetic moment, low abundance, or similar reasons. Moreover, these experiments represented an early and far-reaching confirmation of the powerful spin temperature concept. Since pulsed NMR techniques were involved, it was possible to study the polarization transfer in its complete time development. Oscillatory exchange of spin order was also observed [3,4], which demonstrates the importance of spin coherence in the initial polarization exchange between the reservoirs and contains direct information on the coupling responsible for the cross-talk between the reservoirs.
Global themes in gravity
Authors: Joshi Pankaj S
Published: November 2023

Global considerations have been important in theories of gravitation right from the inception of the general theory of relativity, and also in cosmology, by the very definition and purpose of that science. It was realized then that even though locally the laws of physics are those of special relativity and space-time is very nearly flat, the space-time universe as a whole is made by joining such local patches and gives rise to a non-flat, curved continuum which would also admit a suitable differential structure. The matter and energy density distribution is then described in terms of tensor fields on such a differentiable manifold. These matter fields in turn generate the space-time curvature via the field equations of Einstein. Similar global features will arise in other theories of gravity as well, such as those of Brans and Dicke (1961), which are metric theories of gravitation based on a space-time manifold model.
Quantum effects near the space-time singularity
Authors: Joshi Pankaj S
Published: November 2023

Any discussion on space-time singularities cannot be considered complete without consideration of quantum effects in the vicinity of the same. The reason is, when the curvatures grow arbitrarily high near a space-time sin-gularity, especially when it is a scalar polynomial or strong curvature singularity, the classical general relativity can be relied upon less and less and the quantum effects must become important and may dominate. In fact, the very existence of singularity could become questionable, when quantum effects are taken into account. For example, DeWitt (1967) suggested the possibility for singularity avoidance within a quantum frame-work by imposing the condition 1µ[3g] = 0 at the singular boundary, where 3g denotes a three-geometry. Thus, the state functional for the universe vanishes at the singularity.
Background to quantum field theory
Authors: Dixon J M , Tuszynski J A , Clarkson P A
Published: November 2023

In the various series expansions considered, one always encounters a lack of analyticity in the dependence on the coupling constant . . . It could seem that nature does not believe in power-series expansions in the many-body problem; one suspects the same may hold true in other areas of physics (quantum electrodynamics, for example). . . . one cannot be sure, even when one is in a region in which well-defined series expansion appears to be converging, that there does not exist a ground state of the system with quite different character (more order, for example), from that assumed in the perturbation-theoretic calculation. What one can hope for from an incorrect perturbation-theoretic approach is that it will contain built-in danger signals. These danger signals take the form of inconsistencies; a quantity that should, but does not, satisfy causality requirements, or an instability of a given excitation mode of the system.
Mathematical methods and results
Authors: Dixon J M , Tuszynski J A , Clarkson P A
Published: November 2023

The significant problems we have cannot be solved at the same level of thinking with which we created them. In earlier chapters we have alluded frequently to the recent progress made in analysing nonlinear differential equations using both exact and approximate methods. This chapter is intended as a practical overview of the main developments in the field of nonlinear analysis. We have striven to make the exposition lucid, so that even an uninitiated reader can apply the methods presented to the physical problems at hand. Furthermore, many concrete examples have been provided, especially those which pertain to applications in condensed-matter systems described in Chapters 5 and 6.
Chaos and fractal basin boundaries in engineenng
Authors: Thompson J M T
Published: November 2023

The aim of this chapter is to sketch some of the applications of chaos, and more generally the global geometrical techniques of nonlinear dynamics, to practical problems in engineering. This is done in an informal, pictorial way, with a minimum of the underlying theory, which can be found elsewhere [1, 2). The material is based on recent research work at University College London directed towards current problems of marine technology encountered by the North Sea oil industry. This research has emphasized the importance of chaotic transients and the associated fractal basin boundaries, which are more important in an engineering context than the more familiar steady-state chaotic attractors. The only bit of theory that we shall need is given in Fig. 9.1, which shows the three-dimensional phase space of a general one-degree-of-freedom nonlinear oscillator under periodic forcing, spanned by the displacement, velocity, and time. Such oscillators are of continuous concern to mechanical and electrical engineers.
Nonlinearity and chaos in atoms and molecules
Authors: Child M S
Published: November 2023

The concepts of nonlinearity and chaos have been applied to two areas of atomic and molecular science. One, which is the subject of a recent text by Gray and Scott [I], relates to the sensitivity of certain complex reaction schemes to small changes in pressure, temperature, and concentration. The other, to which this chapter is devoted, concerns the internal dynamics of atoms and molecules at energies which approach their ionization or dissociation thresholds. To set the historical perspective, it has been known for many years that molecules undergo orderly normal mode vibrations in their lowest energy states [2]. On the other hand, modern theories of chemical dissociation [3] assume a statistical or chaotic distribution over all degrees of freedom. Hence a transition from order to chaos must have occurred at some intermediate energy. Experimental investigation of this interesting transitional region was until recently notoriously difficult but the advent of laser spectroscopy (see e.g. [41) has completely changed the picture. This chapter attempts to bring together the main theoretical insights stimulated by these new experiments.
Experimental Techniques
Authors: Ghosh Pradip K
Published: November 2023

The basic components of any ion trap experimental system are rather simple; they are: (i) a high vacuum enclosure wherein the trap is housed, (ii) the trap structure, (iii) an appropriate detector which detects the trapped ions, and (iv) associated electronics. In practice, however, depending on the nature and quality of information required, the experimental system can be extremely complex. In this chapter, we shall first present a brief and broad outline of general-purpose systems, and then, in order to provide some perception of the diversity in trap design, we shall describe a few actual traps. Some trap-based systems are described in later chapters on applications.
Collision Studies With Stored Ions
Authors: Ghosh Pradip K
Published: November 2023

Collision studies using ion traps, involving reactions of either positive or negative ions with neutrals or electrons, or photon-induced processes, have been relatively few. These include studies of ion-molecule reactions, ionelectron recombination reactions, charge exchange processes, photo dissociation of positive ions, and photo detachment from negative ions. Ionmolecule reactions have been studied both at room temperature and at near liquid helium temperature. While the results obtained do not go beyond integral cross sections and the methods employed to date do not offer state-selectivity, the medium offers both certain convenience and high sensitivity for collision studies. In this chapter we present some examples of trap-based studies of: (i) ion-molecule reactions, (ii) charge exchange reactions, (iii) ion-electron recombination reactions, (iv) photo dissociation processes, and (v) photo detachment processes.