bluuebunny/crossref_metadata_2025_split huggingface dataset:
Melting curves of two- and three-dimensional Wigner electron crystals in a magnetic field
Authors: Lea M J , March N H 
Published: November 2023

Abstract
It is a pleasure to present this work on Wigner electron crystallization in an applied magnetic field in this volume honouring Roger Elliott. It is now more than two decades since one of us (NHM), his then research student, John Durkan, and Professor Elliott, presented work at the San Francisco Conference on the Metal-Insulator Transition, on the way in which Wigner electron crystallization could be aided by the application of a magnetic field (Durkan et al. 1968).
Quantum optical properties of the exciton--polariton: new families of excitonic quasiparticles
Authors: Birman Joseph L 
Published: November 2023

Abstract
In this chapter I want to present some highlights of our group’s recent research on novel quantum optical properties of the familiar exciton-polariton and a few results on new composite quasiparticles related to excitons in semiconductors. This family of quasiparticles includes the familiar exciton-polariton which comprises exciton plus coupled photon as well as two extensions of the polariton: the phonoriton, invented by L. V. Keldysh and collaborators, which is a composite of exciton and photon and phonon; and the photoriton, a parametrically created composite of two off-resonance photons and the exciton-this was also introduced by the L. V. Keldysh group.
Albrecht Durer
Authors: Coolidge Julian Lowell , Gray Jeremy 
Published: November 2023

Abstract
It is a noteworthy fact in geometry that the study of figures in three or more dimensions has lagged very far behind that of figures which are in one plane. We have already mentioned on p. 12 that this was a source of regret to Plato. There was really a deep underlying reason for this, even if Plato were unaware of the fact. It can be shown that the geometry of the plane is not only simpler than that of higher spaces, but actually richer in interesting results. Such matters are not, however, our present concern; historically the lag of solid geometry behind plane geometry has persisted from Plato’s time to our own.
Afterword (1992): a revolution in the historiography of mathematics?
Authors: Crowe Michael 
Published: November 2023

Abstract
The revolution has begun! The concluding words in my 1975 paper, which appears as Chapter 1 of this volume, were that whether or not revolutions happen in mathematics, revolutions can ‘occur in mathematical nomenclature, symbolism, metamathematics (e.g. the metaphysics of mathematics), methodology (e.g. standards of rigour), and perhaps even in the historiography of mathematics’. No more compelling evidence that a revolution in the historiography of mathematics is under way could be found than the essays that Donald Gilles has collected for inclusion in this volume. Written by a distinguished group of historians and philosophers from a variety of countries, these papers collectively demonstrate that new and sophisticated approaches to the history of mathematics are being employed with success. Never before has this claim seemed so justified.
Vortices And Fluids: From Gravity To Elasticity
Authors: Meli Domenico Bertoloni 
Published: November 2023

Abstract
In the second half of the seventeenth century natural philosophy relied heavily on Cartesian explanations of phenomena in terms of the motion of particles of different shape and size. Even if the specific mechanism devised by Descartes was questioned, vortices and subtle fluids were the cornerstone for an intelligible explanation of the universe. The following two sections examine some aspects of the vortex theories framed by Descartes and Huygens in order to gain some familiarity with this material. The examples I have selected were well known to Leibniz and Newton, and were important in the formation of their views; we shall find several references to them in Leibniz’s manuscripts.
The Private Itinerary
Authors: Meli Domenico Bertoloni 
Published: November 2023

Abstract
This chapter outlines the itinerary leading from the Notes, namely Leibniz’s working sheets containing his immediate thoughts on the Principia, to the Tentamen. All the manuscripts discussed here are unpublished: those marking the most significant stages in Leibniz’s itinerary are reproduced in the Appendix, where I also provide a detailed textual analysis. In this chapter, however, I present a broader picture, including some manuscripts which are not reproduced later and the relevant Marginalia. Indeed, in some cases Leibniz’s isolated annotations in his own copy of Newton’s masterpiece can only be understood in relation to the texts presented here.
Reflections On Leibniz’s Theory And Its Development
Authors: Meli Domenico Bertoloni 
Published: November 2023

Abstract
The previous two chapters have charted the formation and development of Leibniz’s theory from his reading of the Principia, through a series of manuscript essays and calculations, to the published Tentamen. A comparative study of the material presented so far and of further private manuscripts, letters, and public texts discussed in this chapter allows us to grasp the problems met by Leibniz. Taking into account the contrast between these different genres, and the style of writing in the Tentamen, it is possible to appreciate the development of his theory and strategy. The following section examines the structure and style of the Tentamen, emphasizing the difference between the genesis of Leibniz’s ideas and the order of presentation. I also select two examples relevant to the relationships between mathematical theory and physical interpretation, namely the generalization of the expression for centripetal force attained in De Conatu, and the law of the harmonic circulation. My contention is that in the first case the link between mathematics and physics was lacking and Leibniz’s result was therefore unsuitable for a response to Newton. The second example, however, in which mathematics and physics are brought together, appeared in print in a prominent position.
The proposal
Authors: Fowler D H 
Published: November 2023

Abstract
Plato’s Meno is an enquiry into virtue. As part of the discussion, Plato’s Socrates digresses to illustrate his opinion that we cannot teach anything, but can only prompt recollection of the opinions of a disembodied soul. But Socrates’ digression takes him into the subject of our enquiry here, so let us begin with this passage, Meno 8le-85d. The translation is by W. K. C. Guthrie; I have suppressed all editorial additions, made one very slight alteration throughout which will be explained in Section 1.2(c), below, and restored two speeches at the end of 83b that have unaccountably been omitted.
PLato’s Mathematics Curriculum In Republic Vii
Authors: Fowler D H 
Published: November 2023

Abstract
My attitude to Plato and the Academy has been greatly influenced by the sceptical and rigorous analysis described in Cherniss, The Riddle of the Early Academy, especially Lectures 1 and 3 therein. And, to a historian of ancient mathematics, an additional riddle is raised by Cherniss’s scrupulous exploration of the fragmentary evidence, in the tension between his conclusion, on the one hand, that: Philodemus says that mathematics made great progress under the direction of Plato, who formulated problems which the mathematicians zealously investigated.
Elements Iv, X, And Xiii: The Circumdiameter And Side
Authors: Fowler D H 
Published: November 2023

Abstract
Let us now turn to the problem of the circumdiameter and side, introduced by my Socrates at S41 It is very similar in spirit to the very fruitful problem of the diagonal and side, discussed in Section 2.2, out of which grew the remarkable discoveries of the dimension of squares in Chapter 3. We take a regular polygon with its circumscribed circle, and try to describe the relation between the circumdiameter and a side. Instead of the side we can take a diagonal; and instead of the diameter, we can take the radius, since doubling or halving a ratio has an effect on the anthyphairesis that seems difficult to elucidate. We can also consider the inscribed circle, or investigate the similar three-dimensional problems associated with an edge or diagonal of a regular polyhedron inscribed in or circumscribed around a sphere.
Numbers And Fractions
Authors: Fowler D H 
Published: November 2023

Abstract
Almost the only notation for numbers (i.e. numerals) found in the earliest and best manuscripts of Euclid’s works (apart from the Sectio Canonis) is used to label the propositions; with the exception of four numerals in Elements XIII 11, those few numbers that are used in the text are written out as words. This is an extreme case; most mathematical texts, and all manner of financial, administrative, and legal documents, employ a notation that will underly the main topic of this chapter.
Later Interpretations
Authors: Fowler D H 
Published: November 2023

Abstract
It has been an oft-repeated story since antiquity that the origins of Greek geometry are to be found in Egyptian land measurement; for a discussion of some of the texts, see Heath, HGM i, 121-8. The earliest such possible reference comes from Herodotus, Histories ii, 109, written in the fifth century BC: This king [the semi-mythical Sesostris] moreover (so they said) divided the country among all the Egyptians by giving each an equal square parcel of land, and made this his source of revenue, appointing the payment of a yearly tax.
Symphonies Of Stone
Authors: Macintosh Wilson Alistair 
Published: November 2023

Abstract
Around 10 000 BC, the glaciers of the Great Ice Age began to retreat from off the face of the continent of Europe. As the land was freed from their grip, people started to move back northward. At first these were small tribes of hunters and gatherers, following the herds, coming together where the hunting was good, breaking apart to search for food where it was not. Slowly these tribes pressed further north and west, finally reaching the natural barriers of the continent: the coast of the North Sea and the Atlantic, and the islands of the sea—Britain and Ireland. There was no further to go. The wanderers settled, beginning to cultivate the land, and raise livestock. As further immigrants arrived, the population began to rise.
The Theban Mysteries
Authors: Macintosh Wilson Alistair 
Published: November 2023

Abstract
During the Eighteenth Dynasty of the New Kingdom (1550-1307 BC), the power of the priestly caste began to rise rapidly. This coincided with the removal of the capital of Egypt from Memphis in the north to the southern city of Waset, which the Greeks called Thebes. The greatest temple complex in ancient Egypt was built just north of Thebes—the temple of Amon-Re at Karnak. Originally each temple had been satisfied with a single officiant, a ritual specialist or lector priest, and a few part-time priests to look after less sacred functions. But at Karnak, there were priests ranged in four orders at the head of a vast staff. The temple complex at Karnak consisted of precincts dedicated to the Theban triad, the local god Amon in his aspect as Re the sun-god, Montu the hawk-headed war-god, and Mut the local war-goddess, who usually wore the vulture headdress.
The Thoughts Of Zeus
Authors: Macintosh Wilson Alistair 
Published: November 2023

Abstract
In order to build the life in the sea and the rocks of the Earth’s surface, Zeus had to overcome certain problems. To see what these were, let’s return to our construction of the regular solids in the previous section. We remember that the regular polyhedra were formed in empty space by the random combination of regular polygons, which themselves arose directly from the numbers. Let’s now look in more detail at the process by which the regular polygons lock together.
Apollonius The I Great Geometer
Authors: Macintosh Wilson Alistair 
Published: November 2023

Abstract
Apollonius was born at Perga in Pamphylia, near Antalya in present-day Turkey, around 262 BC. He is believed to have studied at Alexandria, under the famous astronomer Aristarchus of Samos. Whilst studying with Aristarchus, Apollonius was given the nickname ‘Epsilon’, because of his interest in the theory of the Moon, whose crescent looks like that Greek letter. One of the major problems of Greek astronomy was why the planets sometimes appear to move backwards in the sky. For example, Fig. 14.1 shows the backward, or retrograde, motion of the planet Mars.
The Science Of Numbers
Authors: Macintosh Wilson Alistair 
Published: November 2023

Abstract
As we described in ‘A world made of numbers’ (Chapter 7), the Pythagoreans believed that everything which can be known can be described in terms of numbers. In about 450 BC Philolaus, the Pythagorean, wrote: ‘And really everything that is known has a number. For it is impossible that without it anything can be known or understood by reason. The one is the foundation of everything.’
The School Of Alexandria
Authors: Macintosh Wilson Alistair 
Published: November 2023

Abstract
The westernmost branch of the Nile is blocked from exit to the Mediterranean by a narrow limestone ridge running west to east from the Libyan desert. The Nile, diverted eastward along this ridge, forms Lake Mareotis, finally issuing to the sea at Abuqir. Seven miles west of Abuqir lies the small island of Pharos, offering a sheltered harbour from the prevailing northerly winds.
A Saxon mathematician
Authors: Fauvel John 
Published: November 2023

Abstract
August Ferdinand Mifoius was born on 17 November 1790 and died on 26 September 1868. During the course of his lifetime, the pursuit of mathematics in Germany was transformed. In 1790, it would be hard to find one German mathematician of international stature: by the time he died, Germany was the home and training ground of the world’s leading mathematicians, and the mathematics researched and taught there spread and came to influence the higher mathematical activity of the rest of the world. We touch on some of the factors effecting this transformation during the course of this book. The changes were not unrelated to the development of the entire German-speaking world over this period, from a gaggle of fairly independent states, through invasions, wars, revolutions, and other tribulations, to an empire united under the political and military might of Prussia.
The development of topology
Authors: Biggs Norman 
Published: November 2023

Abstract
In this chapter I shall discuss some of Mobius’s contributions to topology, and try to put them in the context of the general history of topological ideas in the nineteenth century. Mobius probably did not think of himself as a topologist, because at that time there was no general subject called topology; nevertheless, his ideas have had a profound influence on the development of the subject. The fascinating properties of the Mobius band are described earlier in the book; apart from that, I assume only a very vague knowledge of what topology is about.
Liquid semiconductors and metal-insulator transitions in liquids
Authors: Mott Sir Nevill 
Published: November 2023

Abstract
Liquid semiconductors were first studied systematically by the Leningrad school (see the review by loffe and Regel (1960) and the books by Gubanov (1963) and Glazov et al. (1969)). Recently many of them have been investigated in several other centres. In our view there is little difference in principle between the theories necessary to treat liquid and solid non-crystalline semiconducting materials, except that any defects (such as dangling bonds and valence alternation pairs described in Chapter 7), which may pin the Fermi energy, will have a concentration which minimizes the free energy and which varies strongly with temperature. Cutler and Rasmolondramanitra (1984) have analysed the properties of non-metallic Se-Te alloys in these terms; neutral and charged dangling bonds (valence alternating pair) may exist, with motion of charge between them (see also Cutler 1977). A main theme in this chapter is the discussion of the liquid divalent metal Hg, and the monovalent metals Cs and Rb, at temperatures and densities near to that at which a metal-insulator transition occurs, this involving work at high temperatures; we also give a short discussion of metal—ammonia solutions, which also show a transition with decreasing concentration of metal. We normally use a pseudogap model, though in some materials it is preferable to assume that defects exist in thermal equilibrium, for instance, as already stated, neutral and charged dangling bonds, so that hopping or unactivated charge transfer can occur.
Super-Real Fields
Authors: Garth Dales H , Hugh Woodin W 
Published: November 2023

Abstract
Super-real fields are a class of large totally ordered fields. These fields are larger than the real line. They arise from quotients of the algebra of continuous functions on a compact space by a prime ideal, and generalize the well-known class of ultrapowers, and indeed the continuous ultrapowers. These fields are of interest in their own right and have many surprising applications, both in analysis and logic. The authors introduce some exciting new fields, including a natural generalization of the real line R, and resolve a number of open problems. The book is intended to be accessible to analysts and logicians. After an exposition of the general theory of ordered fields and a careful proof of some classic theorems, including Kaplansky's embedding theorems , the authors establish important new results in Banach algebra theory, non-standard analysis, an model theory.
The operational calculus and the field R
Authors: Garth Dales H , Hugh Woodin W 
Published: November 2023

Abstract
There have been two major themes in our work so far. The first, discussed in Chapter 4, was to study the relationships between various classes of real-closed η1 -fields, and in particular of super-real 171-fields. A diagram showing the relations that are almost immediately obvious was drawn on page 104.
Examples
Authors: Garth Dales H , Hugh Woodin W 
Published: November 2023

Abstract
So far, we have sought real-closed η1-fields K in particular classes of the classification scheme of Chapter 4 with the property that (with GCH), |K|=N2 and | Γ | = N1 (We explained in Chapter 5 that it is known for each ordered field K not satisfying this condition whether or not K# is normable.)
R as a hyper-real field
Authors: Garth Dales H , Hugh Woodin W 
Published: November 2023

Abstract
At the end of Chapter 6, we left open the question whether or not R, the unique real-closed, Cauchy complete η1-field of weight N1, is a hyper-real field, or even a super-real field. Our main result of the present chapter is that R is indeed a hyper-real field (in the theory ZFC + GCH).
Rigid fields and solid structures
Authors: Garth Dales H , Hugh Woodin W 
Published: November 2023

Abstract
The main work of this final chapter will be to show that there are super-real fields Kp of weight N1 for which the associated structures ℕ (P) and {0,1}N (P) are invariants of the field Kp. Thus any classification of such super-real fields must involve a prior classification of these structures. The basic method will also be used to show, in Theorem 11.49, that it is relatively consistent with ZFC + GCH that there is a prime ideal P with corresponding super-real Kp an ‘Ji-field of weight N1 such that P is both an exponential prime and a cut prime, but such that Kp is not even order-isomorphic to any super-real field of the form KQ, where Q is a prime z-ideal in some C(Ω).
Review of the genera of Mayflies of Panama, with a checklist of Panamanian and Costa Rican species (Ephemeroptera)
Authors: Flowers R Wills 
Published: November 2023

Abstract
The ancient insect order of Ephemeroptera, or mayflies, is a major component of the invertebrate fauna of freshwater habitats. They are found in lakes, ponds, and streams on all continents except Antarctica, as well as on many islands. The aquatic immature stages, or nymphs, play an important role in freshwater ecosystems by feeding on detritus and algae, and by serving as prey for fish and other aquatic animals. Adults are short-lived and frequently swarm at dusk or dawn. During swarming activities they are preyed upon heavily by dragonflies, birds, and bats. Although the importance of mayflies in temperate stream ecology is well documented, a relative lack of studies on tropical aquatic insects has meant that the importance of mayflies in tropical streams has sometimes been under-appreciated. Almost 5 months of field work in Panama (and many more in the United States) have convinced me that Panamanian and North American mayflies have comparable importance in their respective aquatic ecosystems. Figure 4.1 is a diagram of a mayfly adult, or imago, illustrating morphological terms used in this and other taxonomic papers. The genus depicted is North American but the terms apply generally. A nymph of the same genus is shown in Figs 4.2 and 4.3, also labelled. The life cycle of mayflies contains a flying but sexually immature subadult stage called a subimago which is unique to the Ephemeroptera. After a short time, usually within a day, the subimago moults to the fully mature adult or imago stage. Subimagos closely resemble imagos in appearance but can be distinguished by the cloudy appearance of their wings, the presence of a fringe of hair on the hind margins of the wings and, in males, the undeveloped condition of the genitalia. (In a few groups, the female never moults to the imago but completes her reproductive activities as a subimago.) Because the taxonomy of adult mayflies depends heavily on the structure of the male genitalia, female imagos and subimagos of either sex frequently cannot be identified. Nymphs can be identified most reliably when they are mature (almost ready to moult to the subimago stage) but generic identifications can usually be made on nymphs that are half grown or older.
Key to the genera of New World Apicotermitinae(Isoptera: Termitidae)
Authors: Fontes Luiz Roberto 
Published: November 2023

Abstract
The subfamily Apicotermitinae was first proposed by Grasse and Noirot (1954) and our present concept of the subfamily comes from the work of Sands (1972). The taxonomy of the New World Apicotermitinae is poorly known. Until 1976 38 species had been described, in the genera Speculitermes and Anoplotermes; the last species described, dates from 1959. Mathews (1977) concluded that Speculitermes does not occur in the New World and added two new genera, Ruptitermes and Grigiotermes, with five and one species, respectively. Fontes (1986) described Tetimatermes and Aparatermes, both monotypic. The five New World genera comprise a total of 41 species, and the generic assignment of about 30 species (now in Anoplotermes and Ruptitermes) should be re-evaluated. Three facts may have contributed strongly to the scarcity of taxonomic studies on the group. Termite taxonomy is based largely on the soldier caste, with alate and worker castes of the soldierless New World Apicotermitinae being less attractive to termite taxonomists. Most soldierless termites are small and have a subterranean habit, being found in galleries rather diffuse in the soil or inside mounds built by other termites; collection is thus more difficult. Finally, dissection of the worker digestive tube is fundamental for a solid taxonomic study of the group (Sands 1972; Mathews 1977; Fontes 1985, 1986) and the study of this structure is not always easy.