bluuebunny/crossref_metadata_2025 huggingface dataset:
Geometric hyperplanes of embeddable Lie incidence geometries
Authors: Cooperstein B N , Shult E E
Published: November 2023

Very large subspaces play a key role in determining the structure of a space and in providing interesting examples of spaces not easily defined in other ways. A celebrated criterion, due to Teirlinck (1980), that a linear space be a projective space involves only the way certain geometric hyperplanes are distributed.
One diagram for many geometries
Authors: Fra A Del , GhinelJil D , Pasini A
Published: November 2023

The Intersection Property (IP) of Buekenhout (1981) will often be assumed in this paper. Several equivalent formulations are known for that property, (see Biliotti and Pasini 1982).
A problem on squares in a finite field and its application to geometry
Authors: Hirschfeld J W P , Szönyi T
Published: November 2023

The starting point of this work is the following lemma in Hirschfeld and SZOnyi (submitted): For q an odd prime power, let a be an element of GF(q2)\GF(q). Then there are precisely (q - l)/2 elements u in GF(q) for which a - u is a non-zero square in GF(q2).
The discriminant of a cubic curve
Authors: Kaneta H , Maruta T
Published: November 2023

Let K be an algebraically closed field of any characteristic. Denote by PG(n, K) the n-dimensional projective space over K. A cubic form in K[X, Y, Z] defines a cubic curve Vtf) in PG(2, K).
Applications of p-Adic Methods to Group Theory
Authors: Du Sautoy Marcus P F
Published: November 2023

In the late nineteenth century, Sophus Lie studied ‘transformation groups’ in an attempt to understand various geometries from more group-theoretic point of view. His pioneering work forged what has been known for nearly a century as the theory of Lie groups, i.e. topological groups with the underlying structure of a real manifold with respect to which the group operations are analytic. The importance of the theory of Lie groups can be judged by the diversity of its applications in topology, differential geometry and arithmetic. There have also been a host of parallel theories where the underlying real manifold is replaced by such structures as algebraic varieties, schemes and p-adic manifolds. It is the last of these which lies at the heart of this chapter. Such groups were encountered for the first time in 1907 in the writings of Hensel (17] on p-adic analytic functions. By 1936 they had appeared in work of Weil and Lutz on p-adic elliptic curves (see (50] and (29]).
Arithtnetical Sitnilarities
Authors: Klingen Norbert
Published: November 2023

This book deals with the characterization of extensions of number fields in terms of the decomposition of prime ideals, and with the group-theoretic questions arising from this number-theoretic problem. One special aspect of this question is the equality of Dedekind zeta functions of different number fields. This is an established problem which was solved for abelian extensions by class field theory, but which was only studied in detail in its general form from around 1970. The basis for the new results was a fruitful exchange between number theory and group theory. Some of the outstanidng results are based on the complete classification of all finite simple groups. This book reports on the great progress achieved in this period. It allows access to the new developments in this part of algebraic number theory and contains a unique blend of number theory and group theory. The results appear for the first time in a monograph and they partially extend the published literature.
Kronecker equivalence
Authors: Klingen Norbert
Published: November 2023

There is an old observation dating back to Fermat and Euler that for certain binary quadratic forms the prime numbers they represent are exactly given by certain congruence classes modulo some number m.
The internals of SHEEP
Authors: MacCallum M A H , Skea J E F , McLenaghan R G , McCrea J D
Published: November 2023

To make it possible to refer to RIE, for instance, whether a coordinate or a tetrad basis is in use, SHEEP allows the name of the tensor which the user types to be associated with more than one definition. Each definition is given as the specification of a “building function” associated with a different internal name for the tensor. Which building function is active usually depends on the context in which the calculations are being done. This concept is called tensor aliasing, and is mainly used for the more common tensors. For example, the building functions for the Riemann tensor in coordinates (RIEC) and in frames (RIEF) are different, yet (WMAKE RIE) will work correctly in both cases. It is useful to know when tensor aliasing will take place and how to obtain the internal name of a tensor from its alias, for those occasions where aliasing does not occur (for example in the writing of building functions and for inclusion of tensor components in FOIN formulae).
The Poincar é gauge theory
Authors: MacCallum M A H , Skea J E F , McLenaghan R G , McCrea J D
Published: November 2023

The Poincar é gauge theory (PGT) is a theory of gravitation in which spacetime is represented as a Riemann-Cartan manifold, i.e. a 4 dimensional differentiable manifold M with normal hyperbolic metric of sig nature (-, +, +, +) and a metric-compatible connection with nonzero torsion. For a detailed account of the theory the reader is referred to Hehl (1980) and Hehl et al. (1980). For the formulation of the PGT in terms of exterior differential forms see Trautman (1973, 1984), Schweizer et al. (1980), Kopczynski (1982), Wallner (1982, 1985), Goenner et al. (1984), Hehl et al. (1986), McCrea (1987) and Mielke (1987). Here we shall sketch briefly the main lines of the theory.
Fréchet modules over Stein algebras
Authors: Eschmeier Jörg , Putinar Mihai
Published: November 2023

In Chapter 2 we constructed, for each finite commuting tuple a ε L(E)n of regular operators on a Fréchet space E, an extension of the global ϑ (ℂn)- functional calculus of a to an algebra homomorphismϕ:σ(σ(a)→L(E), f↦f(a)), where σ (a) is the Taylor spectrum of a.
Finiteness theorems in analytic geometry
Authors: Eschmeier Jörg , Putinar Mihai
Published: November 2023

It is well known that a compact analytic manifold carries, besides the usual topological invariants (its Euler characteristic, the Betti numbers), some numerical invariants like the degree of the canonical divisor, the Hodge numbers, the arithmetic genus, and so on. A common property of all these invariants is that they coincide with the dimension of the cohomology spaces of certain analytic vector bundles or analytic sheaves. In this way, these invariants become accessible to algebraic and homological methods.
Multidimensional index theory
Authors: Eschmeier Jörg , Putinar Mihai
Published: November 2023

By far the most studied spectral invariant of a linear operator is the Fredholm index. This integer, associated with an operator with finite dimensional kernel and cokernel, has remarkable stability and functorial properties. The computation of the Fredholm index of concrete integrodifferential operators turns out to be the key to understanding the nature of the majority of analytic invariants encountered in modern global analysis. The celebrated Atiyah-Singer index theorem and its recent ramifications are the fundamental results in this direction.
A Formula for the Fourier Coefficients of Maass Cusp Forms
Authors: lwaniec Henryk
Published: November 2023

In his seminal paper [5] H. Maass extended the ghetto of classical cusp forms by automorphic forms which a.re not holomorphic but, instead, are eigenfunctions of the Laplace operator Δ. For a group with parabolic elements those Maass forms which decay exponentially to zero at every cusp are called cusp forms. The Maass cusp forms remain wrapped in a shroud of mystery; it is not even known today whether they exist for a generic group. However, for any congruence group the spectral resolution of abounds with Maass cusp forms. This is shown by a counting argument using Selberg’s trace formula, thus it is not constructive. Surprisingly enough, not a single Maass cusp form has ever been constructed for the modular group.
Galois Action on the Nilpotent Completion of the Fundamental Group of an Algebraic Curve
Authors: Oda Takayuki
Published: November 2023

This is a short report on our recent work on the Galois action on the nilpotent completion of the fundamental groups of algebraic curves ([14], [20], [21], [3]).
Units in Number Fields and Elliptic Curves
Authors: Lecacheux Odile
Published: November 2023

Determination of units in number fields is often the first stage when we study their arithmetic properties. It is indeed natural to be interested in number fields in which some units are obvious; let us give some examples.
Finite heights and rational points on surfaces
Authors: Tschinkel Yuri
Published: November 2023

In this note we study the distribution of rational points on algebraic surfaces. Geometry and combinatorics are used to establish upper bounds for the number of rational points of bounded height. Acknowledgments. I would like to thank Yu. I. Manin for many years of generous support and encouragement and the referee for very careful reading and many helpful remarks.
Linear recurrence relations for some generalized Pisot sequences
Authors: Boyd David W
Published: November 2023

Let r be a given real number. For arbitrary integers O < ao < a1, define the sequence of integers Er(a0,a1) by the nonlinear recurrence relation (1)
Discrepance et Diaphonie en Dimension Un
Authors: Faure Henri
Published: November 2023

Abstract Dans cette communication, nous présentons les derniers developpements concernant la discrépance quadratique T et la diaphonie F des deux familles de suites connues pour leurs faibles irregularites de distribution: suites ({na}) et suites de van der Corput.
On the v-adic independence of algebraic numbers
Authors: Roy Damien
Published: November 2023

We present here a conjecture which gives an arithmetic description of the v-adic rank of the finitely generated subgroups of Uv, without Galois hypothesis. Our conjecture implies Jaulent’s conjecture and, as we show in §3, it is a consequence of Schanuel’s conjecture.
Paulo Ribenboim: three aspects of his career
Authors: Viswanathan T M
Published: November 2023

This is a unique occasion bringing together a gathering of educators, scientists, professionals and leaders of the larger community. Before this august gathering, it is my privilege and honor to say a few words about the remarkable career of Paulo Ribenboim. His is a career dedicated to mathematics in its diverse manifestations. If I am asked to summarize his career, I would like to use a trio of phrases: Paulo’s global view of mathematics, his goal-oriented methodology, and his international commitment which took him to other centers of learning and research. I would like to say a few words about each one of these three aspects.
On polynomial size Frege proofs of certain combinatorial principles
Authors: Clote* Peter
Published: November 2023

Using a theorem of Barrington, we give a new recursion theoretic characterization of the class of ALOGT IM E computable functions and then introduce a corresponding free-variable equational calculus ALV  ′. The system ALV  ′, more elegant than an earlier system ALV, allows straightforward definitions of parity and other counting predicates, as well as the proof of correctness of these predicates. One thus easily obtains polynomial size Frege proofs for certain combinatorial principles such as the pigeonhole principle (S.R. Buss) and the equipartition principle (A. Goerdt).
Interpretability and fragments of arithmetic
Authors: jek Petr H á
Published: November 2023

We investigate prominent fragments of first and second order arithmetic and show how they factorize with respect to interpretability.
Making infinite structures finite in models of second order Bounded Arithmetic
Authors: * SØren Riis
Published: November 2023

This also explains why in set-theory (unlike our case), the axiom of extensionality is not conservative over the other axioms.
Marked Poisson processes
Authors: Kingman J F C
Published: November 2023

It was noted in Section 1.2 that the Poisson distribution has a characteristic property in relation to the binomial distribution. If the random variable N has distribution p(µ) and if a second random variable M has a conditional distribution, given N, of the form B(N, p), then M and N - M are independent Poisson variables, with respective means pµ and (1- p )µ.
Phase Regions, Control Volumes, and Inflows
Authors: Gurtin Morton E
Published: November 2023

We consider an evolving interface 𝓈 separating two phases, labelled 1 and 2, and write Ω1  (t) and Ω 2 (t) for the corresponding phase regions, the subregions of the body occupied by phase 1 and phase 2.
Review of Single-Phase Thermodynamics
Authors: Gurtin Morton E
Published: November 2023

We assume that the body occupies a fixed region Ω in ℝ, and that the material is immobile, incapable of deformation, with heat conduction the sole transport mechanism. We base the theory on dynamical versions of the first two laws applied to arbitrary control volumes (subregions R of Ω). The first law, balance of energy, asserts that the internal energy of R change at a rate balanced by the heat flow into R and the power expended on R. The second law, growth of entropy, requires that the entropy of R change at a rate not less than the entropy flow into R. (14.1) For this single-phase theory there is no expense of power, since the bulk material is immobile, and since there is no phase interface.
Super-viscosity and spectral approximations of nonlinear conservation laws
Authors: Tadmor Eitan
Published: November 2023

Let PN stand for one of the standard spectral projections, such as Fourier, Chebyshev or Legendre. It is well known that such spectral projections, PNu , provide highly accurate approximations for sufficiently smooth u . This superior accuracy is destroyed if u contains discontinuities. Indeed, PNu produces 0(1) Gibbs oscillations in the local neighbourhoods of the discontinuities, and moreover, their global accuracy is deteriorated to first-order.
Waves in discrete fluids
Authors: Roe P L
Published: November 2023

We may describe as “discrete fluids”, sets of numbers that react with one another in a way that is supposed to imitate fluid behaviour. They possess conservation laws and wave-like properties, more-or-less resembling those of the continuum model. In the process of algorithm design, each property that matches is a success.
Computing steady incompressible flows past blunt bodies—A historical overview
Authors: Fornberg Bengt
Published: November 2023

There is a special fascination associated with problems which

Although there may be many more surprises left, and several technical details in the present models are extremely complex, the problem of determining the structure of steady incompressible flows past ‘simple’ blunt bodies (like a cylinder, a sphere, a flat plate perpendicular to free stream, arrays of such bodies etc.) can be said to fall in this category.
Simplified multi-dimensional flux limiter methods
Authors: LeVeque Randall J
Published: November 2023

The aim of this paper is to present a simplified framework for developing high resolution finite volume methods for multi-dimensional systems of conservation laws, such as the Euler equations of compressible flow. For simplicity, we consider the system

Ut + f(u)x + g(u)y = 0 (1.1)
On the eigensystems associated with numerical boundary schemes for hyperbolic equations
Authors: Zingg David W , Lomax Harvard
Published: November 2023

The linear convection equation is often used as a model equation in the study of numerical methods for hyperbolic partial differential equations. With periodic boundary conditions, the accuracy and stability of semidiscrete (spatial differences only) and fully-discrete approximations can be studied using Fourier analysis. The resulting matrix operator is circulant, the eigenvectors are the Fourier modes, and Fourier analysis is a simple means of obtaining the eigenvalues. For computations on a finite domain, entry changes can be required among the first few rows and the last few rows of the spatial operator matrix, depending on the interior difference operator. The difference approximations which provide the entries in these rows are called numerical boundary schemes (NBS’s).
Error estimates for adaptive cell vertex finite volume algorithms
Authors: Mackenzie J A , Mayers D F , Mayfield A J
Published: November 2023

Fundamental to the success of adaptive mesh generation – and adaptive methods in general – is the use of reliable and efficient error estimators. A reliable error estimator is one which can bound above and below the norm of the error. An efficient error estimator is one which does not dramatically over or underestimate the error.
SFDN-α-GMRES and SQN-α-GMRES methods for fast high resolution N-S simulations
Authors: Qin N , Xu X , Richards B E
Published: November 2023

The existence of strong shock waves, thin shear layers and their interaction in hypersonic flows requires the use of a high resolution scheme for an accurate numerical simulation. Through an extensive study (6] of different flux formulae on their capabilities of capturing both shock waves and shear layers, the Osher flux difference splitting scheme has been found to be satisfactory. However, high resolution schemes usually involve more complicated formulation and thus longer computation time per iteration as compared to the simpler central differencing scheme. Therefore, the acceleration of the convergence for high resolution schemes becomes an increasingly important issue.
First Order Logic
Authors: Davis Martin
Published: November 2023

The task of providing a mathematical basis for logical reasoning was already clearly posed by Leibniz in the 17th century. However, it was not until the work of Boole two hundred years later that any substantial progress was made. Boole’s work set the stage for the rapid development of modern logic, but in itself the logic of Boole suffered from a crippling defect from which presentations of formal logic had been suffering from the time of Aristotle.
General Patterns in Nonmonotonic Reasoning
Authors: Makinson David
Published: November 2023

In little more than a decade, a number of different approaches to nonmonotonic reasoning have been devised. Each of them proposes a framework for ‘jumping to conclusions’, that is, for tentatively inferring from given information rather more than is deductively implied. They are nonmonotonic in the sense that increasing the amount of information available as premises may sometimes lead to loss of some of the conclusions that can be drawn.
Circumscription
Authors: Lifschitz Vladimir
Published: November 2023

The idea of circumscription can be explained by a simple example. We would like to represent information about the locations of blocks in a blocks world, using the ‘default’:

Normally, a block is on the table. (1.1)
Brancing time
Authors: Gabbay Dov M , Reynolds Mark A , Finger Marcelo
Published: November 2023

In this chapter we shall consider logics and languages that are appropriate for describing events in branching time. Much of the motivation for considering time to be branching comes from the idea of using different branches to represent different possible histories of some part of the world. Thus, we are really looking at logics which combine temporal aspects with features of a modal logic of possibility and necessity.
Metatem In Intensive Care
Authors: Gabbay Dov M , Reynolds Mark A , Finger Marcelo
Published: November 2023

In these days with complex systems designed to cope with anything from exchanging stocks and shares to dispatching ambulances, it becomes increasingly more important to make sure that the design is adequate. Of course, it is not possible to be perfectly sure about the adequacy of a design. However, there are ways of attempting to be more certain and two of the most satisfactory are reasoned justification and testing. This chapter is about both.
Incompleteness
Authors: Chagrov Alexander , Zakharyaschev Michael
Published: November 2023

In the preceding chapter we saw that many standard superintuitionistic and normal modal logics are Kripke complete, even finitely approximable and so decidable. Many of them turned out to be canonical and hence strongly Kripke complete, with their canonical frames satisfying good first order properties. Now we are facing the natural question: isn’t it possible to extend these completeness results to all logics in Extlnt and NExtK? To present examples of incomplete (in one sense or another) logics in these classes and elucidate to some extent the origin of the incompleteness is the main aim of this chapter.
Relational Semantics
Authors: Chagrov Alexander , Zakharyaschev Michael
Published: November 2023

Having solved the completeness problem, the algebraic semantics, introduced in the previous chapter, deprives us, however, of that transparent interpretation of logical connectives which made it possible to construct models for formulas by analyzing step by step their subformulas and adding new points, if necessary. In other words, we have lost that thread which connected the structure of formulas with the “geometry” of their models. Fortunately, this is not that case when “gaining in force we lose in distance”. In this chapter we define a more general concept of frame, combining in itself the merits of both algebras and Kripke frames.
A Plain TEX Primer
Authors: Clark Malcolm
Published: November 2023

This primer is an introduction to TeX and provides the reader with sufficient information to get started with the majority of tasks which he or she may wish to tackle. It explains why TeX approaches its subject in the way it does, and provides the "context' into which it fits. Plain TeX is the common starting point for TeX users and can be extended or modified to suit individual needs. With the aid of this book, scientists and researchers preparing their own books and papers, or technical typists, used to the conventions and jargon of their field, will find little difficulty in adopting TeX's approach.
Percolation Thresholds
Authors: Hughes Barry D
Published: November 2023

For several two-dimensional lattices, the percolation thresholds are known exactly. Exact values of bond thresholds are discussed in §3.1, and site thresholds in §3.2. No exact rigorous values are currently available for percolation thresholds of three-dimensional lattices. We discuss bounds, conjectures and empirical formulae in §3.3, and the numerical estimation of thresholds in §3.4. For most lattices of real interest, very accurate estimates of bond and site thresholds are available. For the most part, the discussion is restricted to Bernoulli percolation models, though a few remarks on directed problems are included in §3.3 and §3.4.
Alternative formulations of quantum theory
Authors: Hannabuss Keith
Published: November 2023

The mathematical description of quantum theory rests on the idea of states and observables. However, the dynamical description of these two described in Section 6.4 is quite different.
Stationary perturbation theory
Authors: Hannabuss Keith
Published: November 2023

For most physically interesting systems it is not possible to find simple closed formulae for the energy levels and wave functions. Generally the best that one can do is to find numerical approximations and iterative schemes. Since Schrodinger’s equation is a differential equation there are many standard numerical methods that can supply approximate solutions, but there are also various special techniques tailored to this particular situation, which we shall describe over the next chapters.
A Comparison of Notions of Negation as Failure
Authors: Schlipf John S
Published: November 2023

When logic programming was generalized to allow negative subgoals, difficulties immediately arose concerning the meaning of negation as failure in the context of these subgoals. Various semantics have been proposed, each attempting to capture natural intuitions about negation as failure and to preserve other intuitive properties. We discuss several such semantics for normal logic programs here: the minimal model semantics, the perfect model semantics for stratified programs, the two- and three-valued program completion semantics, and the stable and well-founded semantics. We contrast them in various ways: we present some examples and intuitions that might be used to justify them, discuss which violate or preserve certain properties of more classical logics and which allow modular programming, and present some results about expressive powers and computational complexity.
Commonsense Entailment: A Conditional Logic for Some Generics
Authors: * Nicholas Asher
Published: November 2023

Lions eat zebras, Quakers are pacifists, or birds fly are examples of generic statements. I believe that such statements should be represented logically as quantified conditionals and thus that the study of generic statements can reveal something of interest about the logical properties of conditionals that we find expressed in natural languages. One indication that this view may be right is that generic statements behave like quantified conditionals. They license certain patterns of inference that look much like those supported by some conditionals. Like almost all forms of conditionals, generics support an inference of weakening of the consequent: lions eat zebras implies lions eat zebras or kangaroos.
Conditional Action
Authors: Segerberg Krister
Published: November 2023

Normally one would expect the As to be pairwise inconsistent and jointly exhaustive, but there is no need to require that this be the case. In a situation where several As obtain, the claim of (§) amounts to the claim that all the corresponding Bs hold. If none of the As obtains, then the claim is vacuous and hence considered to be trivially true.

In a similar way there is a concept of action by cases in dynamic logic. The corresponding concept is a 2n-ary operator (operating on n programs and n propositions to form a new program):
Conditional Implications and Non-monotonic Consequence
Authors: Gabbay Dov M
Published: November 2023

The study of non-monotonic reasoning through properties of its consequence relation was first proposed by Gabbay [5]. Let L be a language and let |˜ a relation between sets of well-formed formulas (wffs) Δ and single wffs A, of the form Δ|˜A. Gabbay proposed three minimal conditions on a relation ˜ to be considered as a non-monotonic logic. These are as follows.
Millet and Rice
Authors: Kangshen Shen , Crossley John N , Lun Anthony W -C
Published: November 2023

The reader may find it convenient to refer to Section 0.2 on Metrological Systems, in the Introduction, p. 6, in particular the units of length, p. 6, capacity, p. 9, and weight, p. 9. The subsections there provide the conversions between the various units used throughout Chapter 2.
Short Width
Authors: Kangshen Shen , Crossley John N , Lun Anthony W -C
Published: November 2023

This Chapter exhibits calculations working backwards to find a side or diameter, etc., from a known area or volume. For example, to find a side of a rectangle whose area and other side are known, to find the side of a square whose area is known, to find the side of a cube of known volume, to find the circumference of a circle whose area is known or to find the diameter of a sphere whose volume is known. These five kinds of problems were collected into one Chapter. The original inspiration for the development of the numerical solution of equations of high degree is closely related to these backwards computations.
Fair Levies
Authors: Kangshen Shen , Crossley John N , Lun Anthony W -C
Published: November 2023

Travelling problems about the relationship between distance, velocity and time. Some include motion in the same direction, with variations in the starting time and meeting point (Problems 12-14).
From CPA to nonlinearity and mesostructures in condensed matter
Authors: Krumhansl James A
Published: November 2023

During the years 1966-72, Roger Elliott, Paul Leath, and I collaborated on the theory of randomly disordered systems (cf. Elliott et al. 1974). This collaboration laid the groundwork for much of my own research over the past 17 years, the subject of which is summarized in the chapter title. The workhorse of many theoretical studies in condensed matter, of both electronic properties and atom dynamics (phonons), for the past three decades has been the method of thermodynamic Green’s functions. Elliott and several of his students developed much of its earliest application to the lattice dynamics of crystals with defects in a series of papers in the early-1960s. The especially persuasive features of the Green’s function method were: (1) the procedure was systematic; (2) experimental quantities could be extracted directly from the Green’s function. Much experimental work on localized and resonant defect modes was stimulated thereby.
Study of tin in amorphous germanium
Authors: Taguena-Martinez J , Barrio, R A , Chambouleyron I
Published: November 2023

For multiple-band solar cells and other optoelectronic devices, the absorption edge of the semiconducting layers must be adjusted to some optimum value. This can be done by alloying both elemental semiconductors (amorphous silicon and amorphous germanium) with other elements. The energy gap can be widened by adding carbon or nitrogen (Tawada et al. 1982) and narrowed by introducing tin (Mahan et al. 1984). However, preserving good optoelectronic properties in these alloys is not an easy problem. In particular, tin in amorphous germanium induces new electronic states in the pseudogap (Chambouleyron et al. 1988; Chambouleyron and Marques 1989).
Frothy disputes-the evolution of the structure of two-dimensional froth
Authors: Weaire D
Published: November 2023

A former Trinity College Dublin scientist described the state of physics in his period (the late seventeenth century) as ‘an heap of froathy disputes’. The phrase is very apt for our subject. Ordinary froth or foam commends itself as an apparently very simple disordered system, yet its properties have proved difficult to pin down conclusively. In particular, it coarsens with time, and the asymptotic form of this evolution has been a subject of debate, if not dispute, for the last 10 years. At the present point, we are approaching a somewhat anticlimactic conclusion, which returns to the original point of view of Cyril Stanley Smith, who first analysed the problem around 1950.
Percolation models of electrical, mechanical, and superconducting breakdown
Authors: Leath P L
Published: November 2023

I was first introduced to the concept of the percolation transition by Roger Elliott at Oxford as we studied the phonon spectra of disordered systems and the properties of diluted magnets. At about the percolation threshold the spikes in the spectra, which correspond to isolated defects, defect pairs, and clusters, merge together to form spectral bands for the percolating species, and we spent some time looking at these effects in disordered systems. Since those days, percolation concepts and theory have really become ubiquitous and a substantial portion of my work (other than that on excitations in disordered systems) has been with percolation problems. Recently, we have begun applying percolation concepts to the breakdown of electrical, mechanical, and superconducting properties of materials (Duxbury et al. 1986, 1987; Duxbury and Leath 1987; Leath and Tang 1989; Xia and Leath 1989), and the work I report here was done in collaboration with these co-authors.
Anisotropy of Kondo systems arising from mixing
Authors: Levy Peter M , Zhang Shufeng
Published: November 2023

In the 1950s and 1960s Roger Elliott studied the magnetic properties of rare-earth metals. The model he used to explain their thermodynamic and transport behaviour consisted of local f electrons subjected to a crystalline electric field, and conduction electrons that interact with the local electrons through the Coulomb interaction. By considering the aspherical (multipolar) parts of this interaction, Roger was able to account for ‘the curious temperature dependence of the resistivity of some rare-earth metals’ (Elliott 1954).
Superparamagnetism in antiferromagnetic particles is a surface phenomenon
Authors: Blackman J A , Trohidou Kalliopi
Published: November 2023

The study of magnetism in small particles developed in the 1940s and 1950s in the field of rock magnetism largely through the work of Neel, and it is in this context that superparamagnetism was first introduced. Both ferro- and antiferromagnetic particles can exhibit superpara¬ magnetism. Below the bulk critical temperature but above the blocking temperature one can regard the particle as having a net spin which is free to rotate. The superparamagnetism is the paramagnetism of this assemblage of giant spins. For an antiferromagnetic particle the numbers of spins on each sublattice are generally unequal. The number of uncompensated spins determines the net moment of the particle in this case, as was first discussed by Neel (1961).
Wetting between curved substrates
Authors: Swift Michael , Yeomans Julia
Published: November 2023

The wetting transition for planar geometries is now well understood (see Dietrich 1988 for a review). Wetting on curved substrates, however, has only received attention much more recently. The initial work on wetting outside a single sphere or cylinder has shown many new and interesting features (Levison et al. 1985; Brochard 1986; Gelfand and Lipowsky 1987; Holyst and Poniewierski 1987; Indekeu et al. 1988). Here we give an account of results obtained by extending these ideas to a substrate which comprises concentric spheres or cylinders.
Non-separable anisotropic pair potentials: two-dimensional liquid crystals and orientational glasses
Authors: Holdsworth P C W , Gingras, M J P , Bergersen B
Published: November 2023

Realistic pair potentials for anisotropic systems (VN5) are non-separable in molecular and intermolecular orientations. That is, the pairwise interaction depends, not only on the orientation of the axis of anisotropy, ni and ni of molecules i and j and the distance between the molecules lri), but also on the direction of the intermolecular vector.
Plato
Authors: Coolidge Julian Lowell , Gray Jeremy
Published: November 2023

Whoever has written about the early history of mathematics has not failed to mention Plato, and usually in terms of praise. But the question of just how much he contributed to mathematical science is not easy to answer, and the anterior question of just how much mathematics he actually knew is still more difficult. There was plenty of mathematics to be known in his time.
William, Viscount Brouncker
Authors: Coolidge Julian Lowell , Gray Jeremy
Published: November 2023

William, second Viscount Brouncker, held a more exalted position in the world’s eye than any other great amateur mathematician. He inherited his Irish peerage from his father, for whom it had been created, and who stood high in Court favour. William fully maintained the family loyalty to the throne. He was long intimate with Pepys, and held exalted, if not perhaps arduous, positions both in the Treasury and the Admiralty. But his great public service consisted in being one of a small number of scientific enthusiasts who founded the Royal Society. He not only helped to found it, but was the first President, from 1662 to 1677.
Guillaume L’Hospital, Marquis De Sainte-Mesme
Authors: Coolidge Julian Lowell , Gray Jeremy
Published: November 2023

Guillaume Franqois L’Hospital, Marquis de Sainte-Mesme, Comte d’Entremont, Seigneur d’Ouques, etc., was born in 1661 and died in 1704. He was a shining example of a man of the highest social distinction whose love of learning drove him to devote much of his short life to scientific writing. There were, as we shall see, certain inexactitudes n his mathematics, but they were nothing compared to the vagaries in the spelling of his name: ’He is also known as the Marquis de !’Hospital. The family also spelled the name Lhospital and, somewhat later l’Hopital.’
Dynamic light scattering and linear viscoelasticity of polymers in solution and in the bulk
Authors: Wang C H
Published: November 2023

Measurements of viscoelastic properties of polymers in solution and in the bulk provide information abo’ut the nature and rates of configurational rearrangements of macromolecules. A knowledge of the overall translational and rotational motion of the macromolecules and their segmental motion is important in elucidating the dynamics and the structure of the macromolecules in the liquid state. Dynamic light scattering has been shown to be a sensitive technique for the measurement of molecular configurational rearrangements and segmental motion of flexible polymer chains.
Dynamic light scattering from polymer gels
Authors: Geissler Erik
Published: November 2023

The two principal features that distinguish dynamic light scattering in a gel from that in a solution are the appearance of a permanent elastic modulus G that persists even when the sampling frequency tends to zero, and the existence of static polymer superstructures that partially heterodyne the scattered light. The theory underlying the most commonly encountered form of dynamic light scattering in polymer gels was proposed in 1973 by Tanaka et al. As in light scattering from ordinary binary fluids, the gel is considered to be a uniform continuum subject to spontaneous thermal fluctuations that modify the dielectric permittivity and hence scatter light. As with fluids, swollen gels exhibit fluctuations in the overall density involving the simultaneous compression of network and solvent, as well as osmotic deformations in which polymer and solvent move in opposition to each other while the total sample volume remains approximately constant. In a light scattering experiment, since both the incident and scattered beams consist of plane waves, the matching perturbation in the medium that causes the scattering must also be of plane wave type. In the scheme of Tanaka et al., the modes in the gel are described by a displacement u of the polymer network that obeys an equation of motion.
The Divine Archimedes
Authors: Macintosh Wilson Alistair
Published: November 2023

Archimedes, son of Pheidias the astronomer, the greatest mathematician of ancient times, was born at Syracuse in Sicily in 287 BC (Fig. 13.1). As a young man, Archimedes was sent to Alexandria to study under the successors of Euclid. Whilst at Alexandria, he formed friendships with Conon of Samos and Eratosthenes of Cyrene, which lasted throughout their lives. He usually sent his discoveries to his two friends, before publishing them. Another friend to whom he dedicated several of his works, was Conon’s pupil Dositheus of Pelusium.
Quasi-amorphous semiconductors
Authors: Mott Sir Nevill
Published: November 2023

These materials have been extensively studied recently. They have large unit cells, the number of atoms in a unit cell being as large as 1000. Boron and boron-rich compounds are typical. They appear to show hopping conduction at low temperatures, following the Mott law (σ= σ exp{ −(T0/T)1/14}) rather than that expected if the Coulomb gap is important. Figure 10.1 (from Golkova and Tadzkiev 1986; see also Golkova 1991) shows the conductivity and thermopower, with hopping at low temperatures and activated conduction at higher temperatures, for GdB66. A full description of their properties is given by Golkova (1989).
High-temperature superconductors
Authors: Mott Sir Nevill
Published: November 2023

Since, as in other superconductors, the current carriers are bosons, in the case of the p-type materials paired holes, to understand many of their properties we need to consider the behaviour of bosons in a non-crystalline environment. In this chapter we concentrate on this aspect of the problem presented by these materials. First, however, we give a brief outline of a theory of their behaviour, which at the time of writing remains controversial. This theory is based on the assumption first made by Shafroth (1955) and in greater detail by Alexandrov and Ranninger (1981a,b) that superconductors could exist in which the carriers are bosons, and the critical temperature is that at which the boson gas becomes non-degenerate.
Ordered sets and ordered groups
Authors: Garth Dales H , Hugh Woodin W
Published: November 2023

The fundamental notion that will inform our work is that of order: we shall be concerned with ordered sets, ordered groups, and ordered fields, and so, in due course, we shall specify how various algebraic operations interact with order structures. We shall begin, however, by recalling the precise definitions of various orders themselves and by giving some elementary properties of ordered sets. The most important early definition is Definition 1.7, where we introduce α 1- β1-, and η 1-sets. In Definition 1.8, we shall introduce an ordered set Q which is both a β -set and an η -set, and we shall show in Theorem 1.15 that Q is the only such set: every β 1- η 1-set is order-isomorphic to Q.
Outline Of The Species Accounts
Authors: Howell G , Steve N , Webb Sophie
Published: November 2023

With the publication of the sixth edition of the American Ornithologists’ Union (AOU) checklist of North American birds (1983), a taxonomic and nomenclatural base was established for the species of North and Middle America. In some cases our opinions differ from those of the AOU, including the placement of species within genera or families, usually based on our own field and museum studies. Where our views concerning a species’ taxonomic status differ from those of the AOU, this may be stated at the end of the relevant species’ account.
Glossary
Authors: Howell G , Steve N , Webb Sophie
Published: November 2023

alar bar: pale diagonal bar on outer coverts of upper wing, that is, a short carpal bar. allopatric: having separate (breeding) ranges; usually refers to closely related or similar forms. See pp. 61–4. alternate (alt): the plumage attained by many species before or during the breeding season, though not necessarily by breeding adults; equivalent to ‘summer’, breeding, or nuptial plumage. See basic; see also pp. 65–7.
Earwigs of Panama (Dermaptera)
Authors: Brindle Alan , Arias Diomedes Quintero
Published: November 2023

The Dermaptera, or earwigs, is a small order of about 1900 species worldwide, of which about 450 are Neotropical. The Neotropical earwig fauna is not yet adequately known; it is likely to be very rich in species, having close affinities with the dermapterans of South Africa (genus Esphalmenus Burr, 1909, Pygidicranidae) and West Africa (genus Forcipula Bolivar, 1898, Labiduridae). Of the eight families of Dermaptera now recognized (Sakai 1982), two families (Apachyidae and Chelisochidae) are absent from the Neotropical region. The Holarctic region has a poor Dermaptera fauna (for example, only 26 species are known for the whole USSR; Bei-Bienko 1967); the number of species becomes even smaller in northern Mexico. Earwigs seem to prefer warm or hot moist tropical forests, particularly the tropical and subtropical forests of South America. Central America should prove to have a large Dermaptera fauna also. The ectoparasitic and wingless oriental Arixeniina and north African Hemimerina (two genera, ectoparasitic on murid rats: Hemimerus Walker, 18 71 and Araeomerus Maa, 19 74) are often considered separate suborders, distinct from true earwigs. Usually the latter can be recognized easily by the forceps at the end of the abdomen (Fig. 12.1). Whilst some other insects may have abdominal cerci, there is seldom any difficulty in recognizing an earwig as such. Some textbooks use the term ‘cerci’ for the forceps of earwigs, but it seems preferable to use ‘forceps’ because, in all adult and almost all immature earwigs, the forceps are composed of two unsegmented branches, which are not segmented as are normal cerci. The immatures of few earwigs have very long, segmented cerci (Diplatyidae), or partially segmented forceps (a few African Karschiellini, Pygidicranidae).
(Homoptera: Cicadoidea)
Authors: Wolda Henk , Ramos J A
Published: November 2023

Cicadas are among those insects which play an important part in everyday life in Panama, and unlike that of the domestic cockroaches, houseflies, and mosquitos the role of cicadas is a rather pleasant one. The ‘Cocorrón de la Semana Santa’ (Quesada gigas) announces with its loud whistle the advent of Easter and the dusk chorus of the ‘Totorrin’ (Fidicina mannifera) is widely used by the Panamanian farmer as a signal for the end of the workday in the field. Yet little is known about the cicada fauna of Panama. Young (1972, 1974, 1980a, b, c, 1982, 1984) has devoted a series of papers to the cicadas in Costa Rica with information about their seasonality and habitat selection, but that information is not necessarily valid for the cicadas in Panama. Many insect species in the tropics tend to have a rather restricted distribution so that one may expect the species in Panama to be different, and those that are shared by the two countries may occur in different habitats and thus may have different life history characteristics.
Reproductive behaviour and ecology of Urania (Lepidoptera: Uraniidae) moths and of their larval food plants, Omphalea spp. (Euphorbiaceae)
Authors: Smith Neal G
Published: November 2023

Scientific and popular interest concerning day-flying moths of the subfamily Uranilnae (Uraniidae) is the result of their handsome appearance (e.g. Urania Fabricius spp. in the neotropics, and Chrysiridia spp. of east Africa and Madagascar) and their spectacular, periodic migrations (Williams 19 58; Skutch 1970; Valerio 1966; Young 1970; Odendaal and Ehrlich 1985, Smith 1972, 1982, 1983a,b). Here I will address broader aspects of the only New World genus, Urania, and its larval foodplants, species of the euphorbiaceous genus Omphalea. The known natural history, although scanty, is scarcely as bad as is implied by the above quotes. According to Seitz and Gaede (1930), six species and several ‘forms’ of Urania have been described. Three are shown in Fig. 38.1 and the ranges of all are shown in Fig. 38.2. These ranges can be misleading because Urania species, unless on migration, tend to occur in pockets of relatively wet or aseasonal forest. Population levels of resident adults fluctuate widely and may be completely absent from apparently suitable habitat for a year or more. During years of mass migrations, uranias may be seen throughout all the areas shaded in Fig. 38.2. There are scattered sightings from Texas and Florida in the United States (Kendall 1978).
Communal infant care in marmosets and tamarins: relation to energetics, ecology, and social organization
Authors: Tardif Suzette D , Harrison, Mary L , Simek Mary A
Published: November 2023

The need for helpers in infant care has been hypothesized as shaping the mating system and social structure in callitrichid primates. Recent field studies suggest that substantial variation may exist in mating patterns and social structure both within and between callitrichid species. Disagreements remain as to whether the modal mating system is monogamy or polyandry. However, the inability of a single adult to raise multiple offspring of a relatively high total litter weight by herself is frequently cited as causally related to both monogamy (Hershkovitz 1977; Leutenegger 1980) and polyandry (Garber et al. 1984; Terborgh and Goldizen 1985; Sussman and Garber 1987).