bluuebunny/crossref_metadata_2025 huggingface dataset:
Energy And Momentum Relaxation Of Hot Electrons By Acoustic Phonon Emission
Authors: Kent A J
Published: November 2023

At low electron temperatures the dominant process of energy relaxation by hot electrons in semiconductors is by acoustic phonon emission. The rate of energy loss due to electromagnetic (far infra-red) radiation is absolutely tiny by comparison. At higher electron temperatures optic phonon emission takes over. The carrier temperature at which the changeover from acoustic to optic phonon emission takes place depends on the optic phonon energy. In gallium arsenide the optic phonon energy is about 36 meV and the changeover is at between 30 and 50 K (Hawker et al. 1992). In gallium nitride, which has a much larger optic phonon energy( 100 meV), the changeover is expected to occur at a higher temperature. At room temperature optic phonon emission is dominant. This is due to an exponential dependence of the optic phonon emission rate on carrier temperature, while the energy relaxation rate through acoustic phonon emission saturates because emission of large wave vector (high-energy) acoustic phonons is forbidden by momentum conservation considerations. This effect is particularly important in low-dimensional electron systems, in which the reduction of phase space for electron scattering can significantly suppress the energy relaxation by acoustic phonon emission.
Kinematic Theory
Authors: Peng L -M , Dudarev S L , Whelan M J
Published: November 2023

Since high-energy electrons interact strongly with solids it is likely that scattering will occur more than once as electrons propagate through the specimen. This also means that the single scattering, or kinematic, approximation cannot be applied to the interpretation of experimental observations. Nevertheless, there are some interesting situations where the single scattering approximation does provide a useful means for understanding experimental results and in particular for understanding the geometry of electron diffraction patterns. In general, to develop a useful single scattering approximation we need to represent the potential V (r) by a sum of two terms
Temperature-Dependent Debye–Waller Factors
Authors: Peng L -M , Dudarev S L , Whelan M J
Published: November 2023

The Debye–Waller factor is a parameter widely used in both X-ray and electron crystallography to account for the effect of thermal vibrations of atoms in the lattice on the intensity of diffracted beams (Willis and Pryor, 1975). Thermal vibrations smear the periodic potential of the crystal. The instantaneous positions of atoms in the crystal are no longer periodic. However, an average periodic potential can be defined, which gives rise to discrete diffracted beams satisfying the same Bragg law that applies to the static crystal potential in the absence of thermal vibrations. The real-space distribution of the average potential is more smeared out in comparison with the distribution of potential in a static crystal. In real space within the harmonic approximation the effect may be described by a convolution of the potential corresponding to atoms frozen at their equilibrium positions with a Gaussian function describing the statistical distribution of thermal atomic displacements. Alternatively, in reciprocal space the effect of thermal vibrations on the average potential is described by the multiplication of the corresponding atomic electron scattering factor of the static crystal by the temperature factor Tk(James, 1948)
Statistical tests
Authors: Cowan Glen
Published: November 2023

In this chapter some basic concepts of statistical test theory are presented. As this is a broad topic, after a general introduction we will limit the discussion to several aspects that are most relevant to particle physics. Here one could be interested, for example, in the particles resulting from an interaction (an event), or one might consider an individual particle within an event. An immediate application of statistical tests in this context is the selection of candidate particles or events which are then used for further analysis. Here one is concerned with distinguishing events of interest (signal) from other types (background). These questions are addressed in Sections 4.2-4.4. Another important aspect of statistical tests concerns goodness-of-fit; this is discussed in Sections 4.5-4.7.
Unfolding
Authors: Cowan Glen
Published: November 2023

Up to now we have considered random variables such as particle energies, decay times, etc., usually with the assumption that their values can be measured without error. The present chapter concerns the distortions to distributions which occur when the values of these variables are subject to additional random fluctuations due to the limited resolution of the measuring device. The procedure of correcting for these distortions is known as unfolding. The same mathematics can be found under the general heading of inverse problems, and is also called deconvolution or unsmearing. Although the presentation here is mainly in the context of particle physics, the concepts have been developed and applied in fields such as optical image reconstruction, radio astronomy, crystallography and medical imaging.
The Molecular Astrophysics of Stars and Galaxies
Authors: Hartquist Thomas W , Williams David A
Published: November 2023

This book provides a comprehensive survey of modern molecular astrophysics. It includes an introduction to molecular spectroscopy and then addresses the main areas of current molecular astrophysics, including galaxy formation, star forming regions, mass loss from young as well as highly evolved stars and supernovae, starburst galaxies plus the tori and discs near the central engines of active galactic nuclei. All chapters have been written by invited authors who are acknowledged experts in their fields. The thorough editorial process has ensured a uniformly high standard of exposition and a coherent style. The book is unique in giving a detailed view of its wide-ranging subject. It will provide the standard introduction for research students in molecular astrophysics. The book will be read by research astronomers and astrophysicists who wish to broaden the basis of their knowledge or are moving their activities into this burgeoning field. It will enable chemists to learn the astrophysics most related to chemistry as well as instruct physicists about the molecular processes most important in astronomy.
Molecules in the Early Universe and Primordial Structure Formation
Authors: Lepp Stephen , Stancil Phillip C
Published: November 2023

Molecular astrophysics began in the recombination era. As soon as electrons and nuclei combined to form atoms these atoms began combining to form molecular ions and molecules. The appearance of the first molecules marked the dawn of chemistry and set the stage for the subsequent evolution of the Universe.
Dust Formation in M Stars
Authors: Gail Hans-Peter , Sedlmayr Erwin
Published: November 2023

Stars with initial masses between ≈2M0 and ≈8 M0 on the main sequence develop first through the red giant phase until they ignite central helium burning. Later they start to climb up the Asymptotic Giant Branch (AGB) where they alternately burn helium and hydrogen in two thin shells over a degenerated carbon-oxygen core. In this stage, the thermal pulsing AGB stage (TP-AGB), they are cool (Teff . ≈ 2000–2500 K),· luminous (L ≈104 £0) and very extended (R. ≈103 Rd giant stars. For further discussion see Chapter 11. Observationally they are found to be emitters of a strong infrared emission and a rich zoo of molecular microwave emission lines which originate in a dense and very extended (L ≈ 104 I(..) circumstellar shell of cool gas and dust. The central stars are usually obscured by the circumstellar dust and in many cases they are even optically invisible· and can only be identified by the IR-emission from warm dust and by microwave molecular line emission.
Models of Circumstellar Masers
Authors: Field David
Published: November 2023

Maser emission involving SiO, H2O and OH has been observed in the direction of a large number of AGB stars. These stars have the characteristic that they lose mass with rates between 10-8 solar masses per year to as much as 10.,..4 solar masses per year. Maser emission may occur in the circumstellar envelope (CSE) of AGB. stars and is belived to be closely connected with the phenomenon of mass loss. Maser emission may be used as a sensitive probe of the number density, temperature and velocity fields in the CSE. In regions close to the photosphere SiO masers, to tens of stellar radii distant H20 masers and to hundreds of stellar radii distant OH masers provide information about physical properties. The evolution and development of the CSE may be studied in depth by combining models of masers with hydrodyna,mic pulsation models of the circumstellar envelope (CSE) of a M-Mira (Bowen 1988, 1989; Pijpers and Hearn 1989; Bowen and Wilsson 1991; Fleischer et al. 1991, 1992; Humphreys et al. 1996 (H96); Bessell et al. 1996; Haefner et al. 1996 and references therein). The present chapter outlines how this may be carried out for M-Miras, the largest class of AGB stars. We start with a brief review ot observational data.
Dust Formation in the Environments of Hot Stars
Authors: Beck Holger , Sedlmayr Erwin
Published: November 2023

Dust is a ubiquitous component of the interstellar medium (see Chapter 4 and 5) and plays a vital and indispensable role in the overall cycle of cosmic material processing. During stellar evolution, from stellar birth up to the late stages, the solid phase is intimately interwoven with the gas component and the radiation field (see Chapters 11–13). The processes of nucleation and grain growth are well known to occur in the outflows of cool late-type stars.
Excitation and Detectability of Molecules in Active Galactic Nuclei
Authors: Black John H
Published: November 2023

It is paradoxical that low-energy molecular processes might be important in the hostile, energetic environments near active galactic nuclei (AGNs). It now appears that observations of the molecular component of the central gas offer crucial insight into the physics of the AGN phenomenon. As reviewed in the preceding chapter, activity in galactic centres is displayed by nuclear starbursts on scales of 102 to 103 pc as well as the true AGNs, which are the compact, luminous sources that reside in the central 10 pc of quasi-stellar objects (QSOs), radio galaxies, and Seyfert galaxies. In this chapter we are concerned with the possible ways in which molecules can be used to investigate the inner workings of the true AGN. Observations throughout the electromagnetic spectnim now suggest that many AGN are buried inside small-scale discs or tori of gas and dust. These central gas systems reprocess the non-thermal continuum into complex emission-line spectra and shield the central source from view over much of the electromagnetic spectrum. Chapter 20 contains a brief introduction to a unification hypothesis, which has been proposed in order to explain the observations of Seyfert 1 and Seyfert 2 galaxies with a single model in which the spectroscopic differences reflect different orientations of the observer’s line of sight to the central obscuring disc or torus (see Antonucci 1993 for a review). There is some hope that the descriptions of radio galaxies, BL Lacertae objects, radio-quiet QSOs, and radio-loud QSOs (the true quasars) can be unified similarly. A compact system of gas and dust is central to the unification hypothesis. Theory suggests that such a system will exist as small dense clouds (Krolik and Begelman 1986, 1988), which will be partly molecular if the pressure is sufficiently high (Krolik and Lepp 1989; Maloney, Hollenbach and Tielens 1996). Photoionization of gas by a non-thermal X-ray source allows atoms in a wide range of states of ionization to co-exist with molecules. Molecules can respond to heating and ionization by X-rays with unusual abundances (e.g. Lepp and Dalgarno 1996) and distinctive excitation patterns (Draine and Woods 1990; Gredel and Dalgarno 1995; Tine et al. 1997).
General Presentation
Authors: Catto Isabelle , Bris Claude Le , Lions Pierre-Louis
Published: November 2023

This chapter is a global presentation of the problems we are going to consider in this book, and also in a forthcoming work [17]. We therefore successively define the problem of investigating the thermodynamic limit of a given model in quantum molecular chemistry and survey the main mathematical difficulties encountered (Section 1.2), give some clues on the physical background of this mathematical problem (Section 1.3), and briefly review the state of the art of the mathematical knowledge on this type of problem (Section 1.4). Next, we introduce the thermodynamic limit problem for the Thomas-Fermi-von Weizsacker model for a crystal and some related models, detail the main results we have obtained in this setting, and indicate some extensions of our work to particular situations (Section 1.5).
Convergence of the Density for the Thomas-Fermi-Von Weizsä.Cker Model
Authors: Catto Isabelle , Bris Claude Le , Lions Pierre-Louis
Published: November 2023

In this chapter, we are concerned with the convergence of the electronic density when the size of the neutral molecular system goes to infinity, thereby approaching an infinite crystal whose nuclei are located at the points of a regular lattice.

Then, in Section 5.3, we establish a uniqueness result for the partial differential equations system obtained in the thermodynamic limit. The proof also applies to the Yukawa case, therefore providing another proof than the one given in Chapter 4. More precisely, in the point nuclei case we prove the following:
Convergence of the Energy Via the Convergence of the Density
Authors: Catto Isabelle , Bris Claude Le , Lions Pierre-Louis
Published: November 2023

In Chapters 2-5, we have shown that, both for Yukawa interaction and Coulomb interaction, there exists a thermodynamic limit for the energy per unit volume and for the electronic density, when the nuclei are located on a periodic cubic lattice. In addition, the density obtained in this limit is periodic, of the same period as the lattice. However, in the case of Coulomb forces, we have used some additional assumptions on the shape of the cell and of the nuclei, and also on the behaviour of the Van Hove sequence (see the statement of Theorem 3.1). The first goal of this chapter is to show that using a different strategy of proof allows us to get rid of these assumptions (see Section 6.2).
Evolution of small mammals
Authors: Berr R J
Published: November 2023

Islands have long held a fascination for biologists and those interested in natural history. The distinctive biotas of oceanic islands were of considerable significance to Darwin and Wallace in developing their ideas on evolution and the recognition that islands act as ‘evolutionary laboratories’ has stimulated considerable modern work on the systematics, genetics, and ecology of island groups.
Natural selection and random genetic drift as causes of evolution on islands
Authors: Barton N H
Published: November 2023

Evolution on islands may differ in many ways from that on the mainland. A novel physical environment, and fewer competing species, may allow unusual adaptive radiations (Schluter 1996). The total number of individuals in the species may be low, giving fewer advantageous mutations, and allowing deleterious mutations to accumulate (Kondrashov 1995; Lynch et al. 1995). Finally, populations may be founded by one or a few colonists, giving an immediate burst of random drift (Mayr 1954). I will concentrate on this last aspect of evolution on islands, and in particular, on the idea that genetic drift in founder events may lead to the formation of new species. Because random drift is a well understood and ubiquitous process, its effects are most amenable to theoretical generalities; indeed, most discussions of speciation on islands (verbal and mathematical) have concentrated on drift in founder events. However, this should not lead us to neglect the importance of natural selection: while it is hard to say much in general, its importance in particular cases is clear (e.g. Schluter 1996; Chapters 5, 9-11).
Ecological and evolutionary determinants of the species-area relationship in Caribbean anoline lizards
Authors: Loso Jonathan B
Published: November 2023

Explaining differences in species diversity among areas has been a central goal of ecology with studies traditionally focusing either on historical or ecological factors (see recent reviews in Ricklefs and Schluter 1993; Brown 1995; Rosenzweig 1995). Studies of insular faunas and floras have played a prominent role in the development of theories of species diversity beginning with the work of the naturalists of the latter half of the nineteenth century and continuing to this day. MacArthur and Wilson ‘s (1967) equilibrium theory of island biogeography, which explained differences in diversity in terms of the ecological processes of colonization and extinction rates, was particularly influential. Nonetheless, as MacArthur and Wilson (1967, Chapter 7) noted, ecological factors are only part of the explanation
Lake level fluctuations and speciation in rock-dwelling cichlid fish in Lake Tanganyika, East Africa
Authors: Rüber Lukas , Verheyen Erik , Sturmbauer Christian , Meyer Axel
Published: November 2023

The East African Lakes Tanganyika, Malawi, and Victoria each harbour hundreds of endemic invertebrate and vertebrate species. The endemic cichlid fish faunas of the East African Lakes are biologically astonishingly diverse and each of the lakes contains its distinct species flock of cichlid fishes. These species flocks are viewed as the most spectacular example among living vertebrates for evolutionary phenomena termed adaptive radiation, and explosive speciation (Fryer and Iles 1972; Futuyma 1986; Coulter 1991; Martens et al. 1994) and provide ample opportunity of the study of the evolutionary mechanisms that might be responsible for the formation of these species flocks (Fryer and Iles 1972).
Biotic drift or the shifting balance did forest islands drive the diversity of warningly coloured butterflies?
Authors: Mallet James L B , Turner John R G
Published: November 2023

According to Stephen Hawking ‘God does throw dice ‘. Our question will be ‘When are the dice thrown? ‘ It has been customary to think of Wright ‘s shifting balance as a stochastic theory of evolution and Fisherian natural selection as deterministic; contrariwise both R. A. Fisher and Sewall Wright believed in fundamental stochasticity (Turner 1987, 1992). We propose a different dichotomy: that divergence can take place as an adaptive response either to stochastic changes in the genetic structure of the population, or to stochastic changes in the biotic environment, or of course, both. We will explore this through the spectacular evolutionary divergence of the colour patterns of South American butterflies, particularly Heliconius.
Introduction: The photon
Authors: Loudon Rodney
Published: November 2023

The use of the word ‘photon’ to describe the quantum of electromagnetic radiation can lead to confusion and misunderstanding. It is often used in the context of interference experiments, for example Young’s slits, in such phrases as ‘which slit does the photon pass through?’ and ‘where do the photons hit the screen when one of the slits is covered up’. The impression is given of a fuzzy globule of light that travels this way or that way through pieces of optical equipment or that light beams consists of streams of the globules, like bullets from a machine gun. Lamb has even argued that there is no such thing as a photon [11 and he has proposed that the word should be used only under licence by properly qualified people! It is, however, difficult to disagree with some of his concerns.
Conservation
Authors: Monk Kathryn A , Fretes Yance de , Reksodiharjo-Lilley Gayatri
Published: November 2023

This chapter discusses the principles of conservation in Indonesia, especially reserve management and species protection in Nusa Tenggara and Maluku (NT&M). It also discusses problems and constraints in reserve management and species protection, and offers recommendations. More over, the chapter covers some basic principles on conservation biology and their application for the management of reserves and species in NT&M. Considering that many people in NT&M still greatly depend on the natural resources to fulfill their daily needs, the chapter offers ideas on how resources should be managed through wildlife trade or ecotourism, and points to the research needed to support conservation in NT&M.
Graphs: an introduction
Authors: Matoušek Jiří , Nešetřil Jaroslav
Published: November 2023

For example, the points may represent participants at a birthday party and the joins correspond to pairs of participants who know each other. Or the points can represent street crossings in a city and the joins the streets. Also a municipal transport network or a railway network is usually displayed as a scheme of this type (see Fig. 3.1), and electrotechnical schemes often have a similar character as well. In such cases, the points are commonly called vertices (or also nodes) and the joins are called edges. If we disregard the length, shape, and other properties of the joins and we only pay attention to which pairs of points are joined and which are not, we arrive at the mathematical notion of a graph. Although very simple, a graph is one of the key concepts in discrete mathematics. This is also illustrated in the subsequent sections.
Trees
Authors: Matoušek Jiří , Nešetřil Jaroslav
Published: November 2023

Even very abstract and elusive concepts in mathematics are often given names from common language. Similarly as mathematical definitions are not at all arbitrary, the name for a notion may be quite important. Sometimes the name helps to communicate, on an intuitive level, some key property of the object which is not easy to notice behind the formal definition. Other names may sound quite illogical in today’s context without knowing their often convoluted history. For example, fields in mathematics are neither green fields nor strawberry fields nor any other kind of fields most people may be used to, and it is hard to imagine why something in the plane should be called a vertex (see Chapter 5 for the origin of this name). And, an unfitting name may lead one completely astray. In this chapter, the reader can judge how well mathematicians succeeded in choosing a name for a simple and fundamental graph-theoretic concept-a tree. While trees in mathematics perhaps cannot match those in nature for beauty or diversity, they still form quite a rich area in graph theory, and closely related concepts of trees appear in other branches of mathematics and of computer science as well.
Double-counting
Authors: Matoušek Jiří , Nešetřil Jaroslav
Published: November 2023

In pre-computer ages, double-counting was used by accountants. When adding up the numbers in a table, they first found the sum of the row totals and then they compared it to the sum of the column totals. If their computation was correct, both results were the same. In other words, the order of summation in a double sum like this may be changed. This simple idea underlies many mathematical tricks and proofs; in more complex cases it is accompanied by other ideas, of course. The main difficulty is usually in figuring out what exactly should be double-counted.
The number of spanning trees
Authors: Matoušek Jiří , Nešetřil Jaroslav
Published: November 2023

Although T(Kn) can be expressed in such a nice and simple way, no completely straightforward method is known for deriving the formula. In the course of time, many proofs have been discovered. Their basic ideas differ substantially, but each of them involves a clever trick or follows from a nontrivial theory. We have collected several of these proofs into this chapter (by far not all known ones!), mainly as an illustration of the richness of mathematical thought.
Finite projective planes
Authors: Matoušek Jiří , Nešetřil Jaroslav
Published: November 2023

Mathematicians are often interested in objects that are highly regular in some sense. A good example is the regular Platonic solids we have seen in Section 5.3. They are scarce, beautiful, and also very useful. For instance, symmetry groups related to them play an important role in physics. In this chapter, we will consider certain very regular families of finite sets, the so-called finite projective planes. As the name suggests, this notion has a geometric inspiration. Finite projective planes are highly symmetric and also somewhat rare. Appreciating their mathematical usefulness, and maybe also their beauty, requires learning something about them first. Let us remark that the study of regular configurations of sets with a flavor somewhat similar to finite projective planes is an extensive branch of combinatorial mathematics (we will say a little more about such objects in Chapter 11).
Probability and probabilistic proofs
Authors: Matoušek Jiří , Nešetřil Jaroslav
Published: November 2023

The reader will most likely know various problems about determining the probability of some event (several such problems are also scattered in the other chapters). Textbooks often contain such problems taken “from real life”, or at least pretending to be real life problems. They speak about shuffling and drawing cards, tossing coins or even needles, or also about of defunct lightbulbs, defunct phone lines, or decaying radioactive atoms-depending on the author’s inclinations and fantasy. In this chapter we want to show a remarkable mathematical application of probability, namely how mathematical statements can be proved using elementary probability theory, although they don’t mention any probability or randomness. Alon and Spencer [10] is an excellent book for studying probabilistic methods in combinatorics in more depth, and Grimmett and Stirzaker [18) can be recommended as a probability theory textbook.
Linear Algebra
Authors: Kaye Richard , Wilson Robert
Published: November 2023

This book covers the basic theory of matrices and vector spaces. The book's three main parts cover (i) matrices, vector spaces, bases and dimension; (ii) inner products bilinear and sesquilinear forms over vector spaces; (iii) linear transformations, eigenvalues and eigenvectors, diagonalization, and Jordan normal form. An introduction to fields and polynomials over fields is also provided, and examples and applications are provided throughout. The approach throughout is rigorous, but without being unnecessarily abstract. In particular, this book would be suitable reading for a student with no prior exposure to abstract algebra. Although intended as a `second course', the book is completely self-contained and all the material usually given in a `first course' is presented fully in Part One, so the book provides a useful guide to the entire theory of vector spaces as usually studied in an undergraduate degree. Abstract methods are illustrated with concrete examples throughout, and more detailed examples highlight applications of linear algebra to analysis, geometry, differential equations, relativity and quantum mechanics. As such, the book provides a valuable introduction to a wide variety of mathematical methods.
Polynomials
Authors: Kaye Richard , Wilson Robert
Published: November 2023

In the last chapter we saw how we can add and multiply linear transformations in ℒ (V,V), i.e. how ℒ (V,V) is given arithmetic operations analogous to the matrix operations of addition and multiplication. Much of the study of linear transformations f: V → V concerns their properties under these arithmetic operations, and before we can take this further we must review some material on polynomials and discuss how polynomials can be applied to linear transformations such as f.
Higher-Order Electroweak And Qcd Corrections
Authors: Bardin Dima , Passarino Giampiero
Published: November 2023

In the preceding chapters each amplitude in the Standard Model (SM) has been written as the sum of an improved Born-like term plus a remainder. In the improved component we make a (partial) re-summation of potentially large one-loop terms while the remainder is expanded up to one-loop in perturbation theory to guarantee the proper cancellation of gauge parameter dependent contributions.
Qcd Corrections For Two-Fermion Production
Authors: Bardin Dima , Passarino Giampiero
Published: November 2023

The couplings to the fermion current can be considered as the Born ones or the effective ones, including the bulk of the electroweak radiative corrections. To this decay rate we have to add final state radiation, both QED and QCD. When the couplings are effective ones an additional problem arises. The naive factorization that effectively amounts to shrinking all weak corrections to a point before applying final state radiation is sometimes a poor approximation to the correct 𝒪 (α αs) result.
The Annihilation e+e-→ff Away From The Z-Resonance
Authors: Bardin Dima , Passarino Giampiero
Published: November 2023

Standard LEPl tests of the minimal Standard Model (MSM) involve a well-defined procedure where we start with pseudo-observables (PO), discussed in Chapter 9, and perform a fit to the MSM parameters at the Z peak (Grunewald 1998). There is a new situation when we compare with the first years of operation at LEP: the top quark mass now has the rank of a precision measurement, mt = 173.8 ± 5 GeV, and this will be accounted for in the fit by including the proper penalty function, as we have explained in Section 9.1.2.
A Determination Of The W Boson Mass
Authors: Bardin Dima , Passarino Giampiero
Published: November 2023

In this and the following chapters we shall see that several different analyses can be performed at LEP2, ranging from WW physics to Higgs boson physics.

The correlation between precision measurements and theoretical calculations is, of course, one of the main issues to be discussed.
Phenomenology Of The Msm Higgs Boson
Authors: Bardin Dima , Passarino Giampiero
Published: November 2023

With the new experimental data from the LEP /SLD Collaborations and the increasing experimental accuracy that has been achieved, there is indirect evidence (from Z-resonance data) for a Higgs boson with a mass below 262GeV (at 95 per cent C.L.) in the Minimal Standard Model (MSM) of the unified electroweak interactions. From the point of view of direct searches, we should keep in mind that in the near future LEP2 will be the only opportunity for a direct search of a Higgs boson of mass> 90 GeV, see (LEPEWWG 1998).
The evolution of diversity in ancient ecosystems: a review
Authors: Morris S Conway
Published: November 2023

It is John Phillips (1860) who is generally credited with first plotting a history of diversity as revealed by the fossil record (Figure 14.1, upper left). Although schematic his diagram has several features of interest. It depicts the triple peaks of Palaeozoic, Mesozoic and Cainozoic diversity, divided by the caesuras of the end Permian and end-Cretaceous events. Interestingly, the respective dips in the highs of Paleozoic and Mesozoic diversity were attributed to techonomic failure, a problem that still dogs any analysis of ancient diversity. Phillips (1860) also recognized the precipitous increase in Cainozoic diversity. Thus, within a year of the first edition of Darwin ‘s Origin of Speciesthe basic information on the history of organic diversity was available, with Phillips (1860) not only drawing attention to techonomic lacunae but also in the pages preceding his figure 4 making some preliminary attempts to quantify his analysis. It took more than a hundred years, however, for serious interest in this history to be rekindled. First were the pioneering formulations of Newell (1967), Valentine (1969, 1973) and Tappan (1969), but the subsequent enterprise has been strongly influenced by the massive compilations, in part unpublished, by Sepkoski (1992) (Figure 14.1) and an important series of analytical papers (Sepkoski 1978, 1979, 1981, 1988, 1993; see also Sepkoski 1997).
“Moulding The Mathematical Education Of 55 Million” Americans
Authors: Parshall Karen Hunger
Published: November 2023

Sylvester faced a new challenge when The Johns Hopkins University finally opened for instruction in October of 1876. He had not taught in a formal, classroom setting since his forced retirement from the Royal Military Academy in 1870, and he had never before taught at the graduate level. How best to convey the spirit and the techniques of mathematical research to the six graduate students who had come to study with him at Hopkins during that first year? Initially, he was unsure, and this uncertainty reflected itself in the fact that he chose not to offer a regularly scheduled course during the first term, opting instead to meet with students more informally in his office and to focus on rekindling his own mathematical flame. As he confided to his long-time friend, Barbara Bodichon (letter 84), while he found his new position refreshing in its seemingly total freedom, he wondered just how the students were supposed to learn. He was succeeding in resuscitating his research on the theory of invariants (letters 86−89), and he was actively involved in trying to solicit support nationally for a research-level mathematics journal (letter 85), but what about the students? In the second and subsequent terms, he gave scheduled courses in addition to instituting the practice of speaking formally and informally on his current research interests. The liberality of the Hopkins atmosphere allowed Sylvester, in a very real way, to define the role of a mathematics research professor for the first time in the American context.
Mapping Time
Authors: Richards E G
Published: November 2023

The Calendar’ contains descriptions of a selection of the calendars of the world and their history. There are introductory chapters on the nature of calendars, their astronomical background, and the history of writing and counting. There are also Chapters on the Week and on the history of Calendar reform. There is a section on methods of converting dates in one calendar to dates in another which are suitable for implementation on a hand calculator or computer; these include a discussion of the calculation of the date of Easter. The book is intended for the general reader rather than for the specialist but contains much material not otherwise easily accessible. There is an extensive bibliography.
ThEegyptian Calendar
Authors: Richards E G
Published: November 2023

The second civilization on earth started along the fertile banks of the Nile. Each year, water from the mountains of East Africa poured down, causing the Nile to flood its banks and fertilizing the valley with the silt washed down with it. Egyptian agriculture was dominated by this inundation.
Four European Calendars
Authors: Richards E G
Published: November 2023

Our knowledge of the calendars in use in the Greek cities is surprisingly meagre. It comes in part from classical authors such as Geminus and Censori nus, and in part from dates inscribed on tombs and the like. Certainly, a lunar or lunisolar calendar underlay Greek calendars, but the latter varied in detail from one city state to another-different names were used, the year began at different times, intercalations were managed differently, and the years were counted in various ways. It is often very unclear how one month in one state corresponded to a month in another.
HIV
Authors: Nowak Martin A , May Robert M
Published: November 2023

In 1981 the Centers for Disease Control in Atlanta noticed an increase in rare diseases that are associated with suppression of the immune system. This observation was made in groups of homosexual men in Los Angeles, San Francisco and New York. Patients died from infectious diseases that were normally controlled by the immune system. There was also an increase in a rare cancer, called Kaposi’s sarcoma. The number of patients who succumbed to this new immunodeficiency disease increased dramatically. It became clear that a completely new disease with an unknown mechanism had suddenly appeared.
Timing The Emergence Of Resistance
Authors: Nowak Martin A , May Robert M
Published: November 2023

In this chapter we describe the detailed dynamics of the rise of resistant virus during (single)-drug therapy. We assume that resistant mutants pre-exist prior to treatment and calculate the rate at which their abundance increases during treatment. We provide an alytic approximations for the fall of wild-type virus and the rise of resistant virus. We calculate the time it takes until the resistant mutant reaches 50% prevalence in free virus and infected cell populations. The calculations in this chapter are based on the basic model of virus dynamics; the underlying central assumption is that resistant virus rises as a consequence of an increase in target cell numbers.
Iterative Methods for Toeplitz Systems
Authors: Ng Michael K
Published: November 2023

Toeplitz and Toeplitz-related systems arise in a variety of applications in mathematics and engineering, especially in signal and image processing. This book deals primarily with iterative methods for solving Toeplitz and Toeplitz-related linear systems, discussing both the algorithms and their convergence theories. A basic knowledge of real analysis, elementary numerical analysis and linear algebra is assumed. The first part of the book (chapters one and two) gives a brief review of some terms and results in linear algebra and the conjugate gradient method, which are important topics for handling the mathematics later on in the book. The second part of the book (chapters three to seven) presents the theory of using iterative methods for solving Toeplitz and Toeplitz-related systems. The third part of the book (chapters eight to twelve) presents recent results from applying the use of iterative methods in different fields of applications, such as partial differential equations, signal and image processing, integral equations and queuing networks. These chapters provide research and application-oriented readers with a thorough understanding of using iterative methods, enabling them not only to apply these methods to the problems discussed but also to derive and analyse new methods for other types of problems and applications.
Toeplitz Systems
Authors: Ng Michael K
Published: November 2023

In various application fields, the matrices encountered have special structures which can be exploited to facilitate the solution process. Sparsity is one of these features. However, the matrices we consider in this book are mostly dense matrices with a special structure. One interesting family consists of matrices having a Toeplitz form. A matrixTn∈ ℂn×nis said to be aToeplitzmatrix if it is of the form given in (1.5), i.e. it is constant along its diagonals. The name Toeplitz originates from the work of Otto Toeplitz (1911) in the early 1900s on bilinear forms related to Laurent series. More details about his work can be found in (Grenander and Szegö 1984).
Applications to ODEs and PDEs
Authors: Ng Michael K
Published: November 2023

In this chapter, we consider using the preconditioned conjugate gradient method with transform based preconditioners to solve ordinary and partial differential equations.
Applications to Queueing Networks
Authors: Ng Michael K
Published: November 2023

In this chapter we discuss numerical methods for queueing and stochastic manufacturing systems. We are interested in obtaining the steady state probability distribution. In queueing systems, many useful quantities, such as the blocking probability and the waiting time of customers in the queues, can be obtained from the steady state probability distributions. Moreover, the average running cost and profit of many manufacturing systems can also be written in terms of these steady state probability distributions. In matrix terms, we are interested in obtaining the normalized right-hand side null vectors of the generator matrices of the queueing and manufacturing systems. Definitions of queueing theory terminologies used below can be found in Cooper (1981).
Principles
Authors: Silk Joseph
Published: November 2023

The cosmologies of myth were characterized by the invention of deities to account for phenomena, such as the stars or the planets. There was one law for the heavens, where the gods dwelt for the most part, and another for the ordinary man. The modern scientist, and we can look back to Aristotle as being the first great natural scientist, commences his study of the universe by assuming that the laws of nature are universal. We do not need one law for the planetary motions, and another for walking along a road. In this spirit, cosmology, the scientific study of the universe, is developed by extrapolating locally verified laws of physics to remote locations in space and time. We do not need Atlas to hold up the heavens, but the orbits of the planets suffice to stop them falling on to the Earth like so many shooting stars. At first, crystalline spheres undergoing complex arrays of epicyclic motions were needed to account for the planetary motions. It took nearly 2000 years for the Copernican revolution to overthrow the epicycles of the geocentric universe, dethroning the Earth as the centre of the cosmos and setting the stage for modern astronomy.
Our Neighbourhood
Authors: Silk Joseph
Published: November 2023

Look up at the sky on a dark night. The thousands of twinkling points of light that you can see are mostly stars that are neighbours of the sun. Neighbourliness is a relative concept. Here it amounts to a distance of hundreds of light years. Stars come in many varieties, from red to blue, and even beyond the range of colours visible to the human eye. The bluer the colour, the hotter the star.

The distance to the nearest stars is determined by parallax. During the course of a year, as the Earth orbits the Sun, the apparent position of a star on the celestial sphere is displaced appreciably. The displacement depends on its distance from us. The parallax method can be used to measure stellar distances out to a hundred light years or so.
Supermassive Black Holes and Galaxy Formation
Authors: Silk Joseph
Published: November 2023

Predicted by the theory of general relativity, black holes are among the strangest objects known to exist. A point in space usually has a past and a future. An explosion is an example of a point in space–time. The explosion is both at a specific point in space and at a specific time. Any observer, or any light signal, can be said to move towards the future. If it travels far enough and long enough, it is in theory eventually able to reach any other point in space at some future time. The one exception to this rule is experienced by an object near a black hole. A black hole may be defined to be a region in space–time where there are events from which there is no escape, even for light signals. A black hole is a trapped surface: cross this surface, and there is no going back!
Beyond the Beginning
Authors: Silk Joseph
Published: November 2023

Quantum uncertainty is the key to understanding what, if anything, happened before the beginning; that is, time zero as measured by the cosmologist. The logic is worth examining. The universe is expanding, and therefore it had a beginning. Extrapolate known physics towards the beginning, and we reach a point of failure. Classical physics is inadequate to cope with the extremes of density and temperature that we know must have been present. So far, so good. Enter quantum cosmology: here is where the fun begins.
A Brief Moment in Time
Authors: Silk Joseph
Published: November 2023

The past is unique and inviolate from the wanderings of a future time traveller. It is not possible to travel back to an epoch where no time machine already existed. A time traveller needs an exit door as well as an entrance: for this, time machines are needed. Once some future civilization masters the techniques of time machines, from then onwards what we think of as space and time will never be the same again.

We can imagine the equivalent of super highways laid down in time as well as in space once time machine construction becomes routine engineering. The future will be multiply connected. Only the past is sacrosanct. We need not worry about time travellers appearing at our front door in the immediate future. Shakespeare can rest in peace: there is no danger that his greatest plays were written by some traveller from the future.
And so to God
Authors: Silk Joseph
Published: November 2023

The role of God in cosmology has both intrigued and plagued cosmologists since the earliest recorded writings on the nature of the cosmos. Some suffered: not only were their books banned or burnt, even they were not immune from similar treatment. In modern times, the Catholic Church at least developed more progressive views under the guidance of the eminent Jesuit cosmologist Georges Lemaître.

Born in 1894 at Charleroi, Belgium, Lemaître, as a young, unknown researcher and already ordained, was able to demonstrate in 1920 that Einstein’s static universe from 1917 was unstable to collapse.
Introduction
Authors: Wille Klaus
Published: November 2023

The study of the basic building blocks of matter and the forces which act between them is a fundamental area of physics. The structures under scrutiny are extraordinarily small, sometimes well below 10−15 m, and in order to perform experiments at this scale probes with correspondingly high spatial resolution are needed. Visible light, with a wavelength λ 500 nm, is wholly inadequate. In- stead, high energy photon or particle beams have proven to be excellent tools, and the results of elementary particle physics would be unimaginable without them. High energy particle beams are thus essential to this field of experimental physics.
RF systems for particle acceleration
Authors: Wille Klaus
Published: November 2023

In Chapter 1 we showed that the fundamental limitations to the final beam energy achievable in static accelerators may be overcome by the use of highfrequency voltages. Virtually all modern accelerators use powerful radiofrequency systems to produce the requisite strong electric fields, with frequencies ranging from a few hundred MHz to several GHz. In such systems waveguides are preferred as resonators and to conduct the beam, since they have low losses and can deliver very high power. We will begin by considering the physics of waveguides and resonant cavities, and will discuss their most important properties. Further details may be found, for example, in references [59], [110] and [109].
Radiative effects
Authors: Wille Klaus
Published: November 2023

In Chapter 2 we showed that electron beams of sufficiently high energy emit synchrotron radiation according to (2.15) with a power Because of their high rest mass, this effect is negligible for protons until they reach extremely high energies of at least 1 TeV. In this chapter we will consider how the emission of synchrotron radiation determines many of the properties of electron beams, in particular by damping synchrotron and betatron oscillations.
Diagnostics
Authors: Wille Klaus
Published: November 2023

The beam circulating inside a closed vacuum chamber is not visible from outside. Furthermore, no-one is usually allowed near the accelerator while it is in operation. In order to establish first of all whether a beam is present in the machine, and then to measure the physical parameters of that beam, the accelerator must therefore be equipped with a wide range of measuring instruments, often termed monitors. In this chapter we will discuss the most common beam monitors used in accelerators and introduce various diagnostics used to measure the key beam parameters.
Imaging and probing foam structure
Authors: Weaire Denis , Hutzler Stefan
Published: November 2023

If, however, the liquid be viscid and tenacious, like soap and wate1; the air is […] imprisoned in the mass, producing the appearance which is commonly called lather.

Philosophy in Sport Made Science in Earnest. (1853), John Murray, London.

An heroic labour, often discussed but never repeated, was undertaken by the botanist Edwin Matzke in the 1940s. Matzke produced soap bubbles of equal size by use of a syringe that he dipped into a soap solution. The bubbles were then placed one by one into a glass container.