bluuebunny/crossref_metadata_2025_split huggingface dataset:
Principal ligand fields: σ interactions
Authors: Jean Yves 
Published: November 2023

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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.
Introduction
Authors: Prutton M 
Published: November 2023

Abstract
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.
The Loop Formulation of Gauge Theory and Gravity
Authors: Loll Renate 
Published: November 2023

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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.
k-Space Microscopy in Biology and Materials Science
Authors: Callaghan Paul T 
Published: November 2023

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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

Abstract
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.