bluuebunny/crossref_metadata_2025_split huggingface dataset:
Interaction Of Two Black Holes In The Slow-Motion Limit
Authors: D'eath P D 
Published: November 2023

Abstract
Following the ideas of Chapter 3, in this chapter we shall describe a method of analysing the interaction of two black holes in a wide variety of physical situations (D’Eath 1975b). The black holes may be rotating and are permitted in our approach to have comparable masses, subject to two types of restriction on the interaction. First, it is assumed that the spatial separation of the black holes is large compared to the radii of their event horizons, so that each black hole is in the far field of the other. Second, we suppose that the relative velocity of the black holes is small compared to the speed of light, so that their combined gravitational field can be described in terms of a slow-motion approximation scheme. Then we should expect that the dominant interaction between them is just that between a pair of Newtonian point particles; it is further assumed in a slow-motion scheme that the Newtonian potential energy of the interaction is comparable to the relative kinetic energy. This allows one to consider a bound system of two black holes moving at non-relativistic speeds. It also allows one to study a quasiNewtonian scattering of two black holes at non-relativistic speeds in which the scattering angle may be quite large (Ruffini and Wheeler 1971; Hansen 1972). These two types of interaction are described by the same equations. The aim is then to find more and more accurate approximations to the dynamical spacetime geometry, subject to the vacuum Einstein field equations, and from this description of the geometry to find more and more accurate approximation to the equations of motion and spin propagation of the black holes.
Axisymmetric Black-Hole Collisions At The Speed Of Light: Perturbation Treatment Of Gravitational Radiation
Authors: D'eath P D 
Published: November 2023

Abstract
As remarked in Chapter 5, in the many years since general relativity was originally formulated by Einstein, no-one has found, owing to the complexity and nonlinearity of the field equations, any physically realistic analytic solution which does not possess a large number of simplifying symmetries. However, if one is interested in studying the generation of gravitational radiation by realistic physical sources, then one must of necessity consider isolated gravitating systems that are time-dependent and which can have no simplifying features apart from axisymmetry. General reviews of the subject of gravitational waves are given by Thorne (1977, 1987).
Axisymmetric Black-Hole Collisions At The Speed Of Light: Gravitational Radiation - Results And Conclusions
Authors: D'eath P D 
Published: November 2023

Abstract
In Chapters 6 and 7, the axisymmetric collision of two black holes was studied in the case in which the black holes approach at the speed of light, each with energyµ in the centre-of-mass frame. A perturbation approach was used, in which a large Lorentz boost is applied to the incoming data, so that the energies. λ, ν of the resulting incoming shock waves obey λ « ν. The subsequent evolution is described by a singular perturbation problem, with small parameter (.λ/ ν). When one boosts back to the centre-of-mass frame, successive terms of the perturbation series provide information on gravitational radiation which propagates at small angles from the symmetry axis near the curved shock 2 which has been distorted and deflected in the collision. (By symmetry, the same holds for radiation near the backward direction.) The gravitational radiation is described by the news function (Bondi et al. 1962) which is expected to have the convergent expansion (eqn (6.1.3))
On the Classification of Homotopy Types
Authors: Baues Hans-Joachim 
Published: November 2023

Abstract
In this chapter we describe fundamental new results on the classification of homotopy types. On the one hand, we get a classification by Postnikov invariants (k-invariants); on the other hand, we obtain a classification by boundary invariants. The general properties of these invariants lead us to introduce algebraic concepts which we call ‘kype functors’ E and ‘bype functors’ F, respectively. Here kype is a new word derived from the words k-invariant and type and similarly bype is derived from boundary invariant and type.
Duality theory of locally convex spaces
Authors: Meise Reinhold , Vogt Dietmar 
Published: November 2023

Abstract
As we have already seen, in general there exists no distinguished topology on the dual space E′; of a locally convex space E, except in the case of normed spaces. We shall therefore explore in this section possible and meaningful locally convex topologies on E′;. Thereby we shall also establish that certain notions in E do not depend on the topology given on E, rather only on the dual space E′;.
Non-Degenerate Elastic Multi-Structures
Authors: Kozlov Vladimir , Maz’ya Vladimir , Movchan Alexander 
Published: November 2023

Abstract
The analysis of the elasticity problems in Chapter 4 shows that for multi-structures consisting of a set of parallel thin rods and a three-dimensional finite body the resistance to loads applied along thin rods is much larger than the resistance to forces associated with bending of thin rods. That is, with applied loads of the same order, the transverse displacements of the multi-structure are much larger compared with the order displacements along the rods. This phenomenon is connected with the special geometry of the multi-structure we dealt with.
Enumeration
Authors: Read Ronald C 
Published: November 2023

Abstract
In this chapter we present the basic problem of graphical enumeration-the enumeration of unlabelled graphs. In particular, we look at Pólya‘s Enumeration Theorem and some problems to which it can be applied. We then consider the enumeration of some other kinds of graphs. The chapter concludes with some remarks about unsolved problems of graphical enumeration. How many graphs are there on four vertices? This question can easily be resolved by a process of trial and error, but if we ask how many graphs there are on ten vertices, the answer can be reliably found only by theoretical means, while the similar question for an indefinite number of vertices clearly requires a formula of some kind. In this chapter we shall be largely concerned with deriving such a formula, and some similar results.
Groups
Authors: Cameron Peter J 
Published: November 2023

Abstract
In this chapter, the connections between a graph and its automorphism group are described. The main themes are that most graphs have very little symmetry; abstract automorphism groups can be prescribed independently of most graph- theoretic properties; vertex-transitivity, however, entails various structural properties; and still higher degrees of symmetry can be expected to lead to a complete classification. The most important connection between graphs and groups is the fact that every graph G has an automorphism group, consisting of all permutations of the vertex set which map edges to edges and non-edges to non-edges. For most graphs, the automorphism group is trivial, consisting of only the identity permutation. However, every group is the automorphism group of some graph, and highly symmetric graphs have a number of special properties not shared by arbitrary graphs.
Probability
Authors: Mcdiarmid Colin 
Published: November 2023

Abstract
What are ‘typical’ properties of a graph? How can random methods yield existence results for graphs? What will randomized graph algorithms do? What have isoperimetric inequalities for graphs to do with probability? This chapter gives an introductory taste of the fertile area of graphs and probability. Since Paul Erdős brought together the subjects of graph theory and probability some forty years ago, the relationship has flowered marvellously.
Genetic markers for population studies-II Molecular markers
Authors: Burnett John 
Published: November 2023

Abstract
A wide range of natural molecules exist such as particular secondary metabolites like the lichen acids which are produced by the fungal component, the whole protein content or specific polymorphic enzyme proteins. Unfortunately, characteristic species-specific molecules only occur sporadically amongst the fungi so that their use as markers is limited, although they are often characteristic of higher groups such as genera, sections or families.
The generation of variation-I Mutation and migration
Authors: Burnett John 
Published: November 2023

Abstract
Strictly, mutation is the sole source of new variation, although it is recombination (see Chapter 7) which mainly generates novel multilocus genotypes. Mutations can occur in both nDNA and mtDNA, and the latter are quite common in fungi. Before the structure of DNA had been elucidated, mutations were recognized by the phenotypic changes they caused.
Student years and Greenland
Authors: Kruuk Hans 
Published: November 2023

Abstract
Leiden was only some 15 km from The Hague, a short trip by train, and Niko studied from home. He did not have to leave his stamping grounds and his friends, and for him the change from school to university was not the upheaval that it was for most other students. But what he found himself studying was something different, and totally new territory.
The classification of surfaces
Authors: Lawson Terry 
Published: November 2023

Abstract
In this chapter we discuss surfaces and classify them up to homeomorphism. A surface is a topological space which locally looks like a piece of the plane, such as a sphere or the exterior of a donut (a torus). Before specializing to surfaces, we begin by introducing the concept of an n-manifold, where a surface is a 2-manifold. Manifolds constitute one of the primary areas of study in topology. Our study of surfaces will introduce us to many of the key ideas in manifold theory in a fairly concrete geometric setting.
Sketches of an Elephant A Topos Theory Compendium
Authors: Johnstone Peter T 
Published: November 2023

Abstract
Topos Theory is a subject that stands at the junction of geometry, mathematical logic and theoretical computer science, and it derives much of its power from the interplay of ideas drawn from these different areas. Because of this, an account of topos theory which approaches the subject from one particular direction can only hope to give a partial picture; the aim of this compendium is to present as comprehensive an account as possible of all the main approaches and thereby to demonstrate the overall unity of the subject. The material is organized in such a way that readers interested in following a particular line of approach may do so by starting at an appropriate point in the text.
D3
Authors: Johnstone Peter T 
Published: November 2023

Abstract
We saw in Section D1.4 that, for each cartesian (resp. regular, coherent, geometric) theory 𝕋, there is a category C𝕋 of the appropriate kind containing a model of 𝕋 which is generic, in the sense defined there. Since we are mainly interested in models which live in toposes, it would be convenient to be able to construct a topos containing a model of a given theory which is generic amongst models in toposes. There are various methods for doing this. One, which was sketched in Section B4.2, relies on the 2-categorical structure of (Grothendieck) toposes, in order to build up (the topos containing) the generic model by an inductive process. Here we shall give a more ‘pedestrian’, but also more explicit, method, which has the advantage that the explicit description of the generic model which we obtain allows us to establish results about models of a theory by first proving them in the generic case, and then transferring them along inverse image functors.
The experimental side
Authors: Balucani Umberto , Zoppi Marco 
Published: November 2023

Abstract
In Chapter 1 we have provided some intuitive arguments for restricting our attention to a limited class of liquids, namely those approximately described by the Hamiltonian (1.1), (1.2). Such a picture of ‘simple’ liquids deserves a more detailed discussion if we wish to make contact with the real liquids which can be investigated experimentally. In principle, a liquid can be described as a state of matter occurring in a limited range of pressures and densities, where it exhibits peculiar macroscopic properties (absence of a definite shape, very low compressibility, fluidity, etc.) well known from everyday experience. Microscopically, we deal with a system of interacting particles (henceforth referred to as the ‘molecules’). In a first idealization, we may assume that the molecules are individually characterized by a well- defined set of properties, independent of the overall state of the system. This assumption has important consequences even from an experimental point of view, since it implies that collective properties can be studied by assuming that the relevant ‘single-molecule’ parameters (such as the dipole moment or the polarizability) can be used as a basic set, independent of the thermodynamic conditions such as temperature and pressure.
Collective properties
Authors: Balucani Umberto , Zoppi Marco 
Published: November 2023

Abstract
In Section 3.4 we saw that all the results of ordinary Navier-Stokes hydrodynamics can formally be deduced by a microscopic memory function approach. In perspective, this success stems from the slow character of the hydrodynamic variables in the limit of small wave vectors, which in turn implies the validity of a Markovian ansatz for the corresponding memory functions. As a by-product of the approach, it was moreover possible to establish ‘Green-Kubo relations’ for the macroscopic transport coefficients, which can be expressed as time integrals of ordinary correlation functions.
The ideal gas temperature
Authors: Carrington Gerald 
Published: November 2023

Abstract
We shall introduce first the properties of an ideal gas, starting with the ideal gas law and the elementary kinetic theory of gases. In effect we begin by taking a microscopic approach because most beginners feel comfortable with the basic concepts involved. Remember that the primary purpose of this chapter, and the two which follow, is not to develop the physical properties of ideal gases as such. Instead we shall use the ideal gas as an example to introduce some important thermodynamic ideas. An ideal gas is one in which the long-range interactions between the atoms or molecules can be ignored. I assume that you know the atoms of the gas move about incessantly, colliding with the walls of the containing vessel and with each other. In an ideal gas the duration of these encounters is short compared with the time the atoms spend in free motion between collisions.
Zeroth and first laws
Authors: Carrington Gerald 
Published: November 2023

Abstract
In Chapters 2-4 we introduced a number of thermodynamic functions for ideal gases. Because we knew the primary equations of state, such as (2.1.1) and (2.2.2), it was not necessary to introduce the underlying laws of thermodynamics in a formal way. Instead we explored some basic thermodynamic concepts without the need to establish the general theory first. In this chapter we shall develop the notions of states and processes further. The aim is to enlarge upon ideas that are already familiar. Although we might proceed in a number of ways, we shall follow a traditional route which is based on the classical laws of thermodynamics. This approach acknowledges how firmly the classical laws are embedded in the literature and language of physics.
Superconducting states
Authors: Kuramoto Y , Kitaoka Y 
Published: November 2023

Abstract
Superconductivity, one of the best understood many-body problems in physics 11 J, again became a challenging problem when a new kind of superconducting phenomenon was discovered in CeCu2Siz by Steglich et al. [2] in 1979. The system behaves as a heavy-electron material close to magnetic instability. In the subsequent decade, intensive investigations of a class of uranium compounds established a new field of heavyelectron superconductivity by successive discoveries of superconductivity in UBe13, UPl3, URu2Si2, UPd2Al3 and UNi2Al3 [3,4]. The most important characteristics for a series of uranium heavy-electron superconductors, except for UBen, are that superconductivity coexists with antiferromagnetism and that the specific heat coefficient γ lies in a broad range from 700 mJ/(mol K2) (lJBe13) to 60 mJ/(mol K2) (URu2Si2). The f-shell electrons, which are strongly correlated by Coulomb repulsive interaction, determine the properties of heavy quasi-particles at the Fermi level.
Elastic Scattering
Authors: Boffi Sigfrido , Franco Davide Pacati Carlotta Giusti , Radici Marco 
Published: November 2023

Abstract
Measuring the angular distribution of an elastically scattered probe provides the first information on a system and, in particular, on its size, charge and/or matter distribution, magnetization density, and the role of its constituents. In the case of electron scattering this information is contained in the differential cross section in terns of the so-called electromagneticforn factors. In photon scattering electric polarizability and magnetic susceptibility of the target are the relevant quantities which represent its dynamic response. This chapter collects the formalism for elastic electron scattering which is the basis for further development and comparison in the following chapters dedicated to various inelastic processes. The role and meaning of the electromagnetic form factors come out very naturally in this context and are discussed in a number of cases, with particular emphasis on the nucleon form factors. This is because nucleon form factors play an important role when investigating the response of atomic nuclei. Without a good knowledge of the behaviour of free nucleons it would be dangerous to draw any conclusion about the nuclear response.
Inclusive Inelastic Scattering
Authors: Boffi Sigfrido , Franco Davide Pacati Carlotta Giusti , Radici Marco 
Published: November 2023

Abstract
Inelastic electron scattering has proved to be a very precise tool for studying the excitation spectrum of atomic nuclei owing to the possibility of simultaneously varying energy and momentum transfer. Since the very beginning of experimentation a large amount of work has been done in determining the energies and properties of excited states. Single-particle and collective excitations were identified and helped to understand the structure and dynamics of nuclei in terms of the motion of the constituent nucleons. We refer to the literature cited in Chapter 1 for a comprehensive account of the subject and to Fig. 1.1 for a schematic view of the nuclear response in the energy-momentum plane. Here we are interested in the nuclear response over a range of energies well above the region of giant resonances and below that of deep inelastic scattering, where two distinct features appear as large peaks with characteristic dependence on energy and momentum transfer.
Semi-Inclusive Inelastic Scattering
Authors: Boffi Sigfrido , Franco Davide Pacati Carlotta Giusti , Radici Marco 
Published: November 2023

Abstract
Semi-inclusive inelastic reactions are produced when one or more particles are ejected from the target and are detected in coincidence with the scattered electron, while the residual nucleus remains undetected. If the dynamical variables of all the final particles are determined, we have an exclusive reaction. The simplest case of semi-inclusive reaction is one-nucleon knockout. The kinematic variables of this process and the notation are shown in Fig. 6.1. In this situation, when the residual nucleus is left in its ground state or in a discrete excited state, we have an exclusive reaction.
Perspectives
Authors: Boffi Sigfrido , Franco Davide Pacati Carlotta Giusti , Radici Marco 
Published: November 2023

Abstract
Electron scattering and photon absorption at intermediate energies have been shown to provide rich information on nucleon interaction and nuclear structure. With presentday experimentation a large domain of the (ω, q)-plane is accessible to study the hadron response under a variety of kinematical conditions. Taking advantage of the unique precision of the electromagnetic probe this response can be studied in terms of measurable form factors and structure functions. Spin degrees of freedom can also be exploited, increasing the number of measured observables and enabling us to access the transition amplitudes of the process and therefore to obtain a complete determination of the scattering matrix. The continuous progress of experimental research both in detection systems and in the beam characteristics, the increasing precision of the measurements and the number of experimental facilities under construction will make available in the near future a large collection of new and appealing data.
Structure of molecules
Authors: Pettifor D G 
Published: November 2023

Abstract
Molecules show a wide variety of structure, the number of variants increasing dramatically with number of atoms in the molecule. Thus, whereas the dimer displays only one structure type, the trimer can be either linear like CO2 or bent like H20. Molecules with four atoms, on the other hand, can take the one-dimensional linear chain structures like H4, the two-dimensional square ring structure like S4 or the rhombic close-packed planar structure like Si4, the three-dimensional tetrahedral structure like P4, or numerous other distorted structural variants. The five-atom molecule, as we have already seen in Fig. 1.15, chooses the close-packed plane as its ground state structure for Na5, the trigonal bipyramid for Mg5 and Si5, the regular pyramid for Al5, and the envelope structure for S5 respectively. The six-atom molecule can choose between the one-dimensional linear chain, the two-dimensional hexagonal ring or close-packed plane, the three-dimensional pentagonal pyramid, trigonal tripyramid, trigonal prism, or octahedron-to name but a few! The energy difference between these competing structure types is usually very small, often being of the order of 1% of the binding energy or less. Hence, the reliable prediction of the ground-state structure of a particular molecule requires self-consistent quantum mechanical calculations of high precision that expend large amounts of computer time.