bluuebunny/crossref_metadata_2025 huggingface dataset:
Basic concepts
Authors: Vaughan-Lee Michael
Published: November 2023

In 1902 William Burnside [5] wrote’A still undecided point in the theory of discontinuous groups is whether the order of a group may be not finite, while the order of every operation it contains is finite’. In modern terminology the most general form of the problem is ‘Can a finitely generated group be infinite while every element in the group has finite order?’. This question was answered in 1964 by Golod [10], who constructed finitely generated infinite p-groups.
Belief Revision
Authors: Gardenfors Peter , Rott Hans
Published: November 2023

The bird caught in the trap is white. C Now suppose that, as a matter of fact, the bird caught in the trap turns out to be black. This means that you want to add the fact ->C, i.e., the negation of C, to the database. But then the database becomes inconsistent. If you want to keep the database consistent—which is normally a sound methodology—you need to revise it. This means that some of the beliefs in the original database must be retracted. You don’t want to give up all of the beliefs since this would be an unnecessary loss of valuable information. So you have to choose between retracting A, B1, B1 -> B, or A A B C. When giving up a belief you have to decide which of the reasons for this belief to retain and which to retract (this is the backward direction).
The Complex Projective Line
Authors: Goldman William m.
Published: November 2023

This preliminary section discusses 1-dimensional complex geometry from the point of view adopted in this book. We begin with projective geometry, from which both complex elliptic and hyperbolic I-dimensional geometry derive. We base our treatment on the books of Cartan [24] and Coolidge [31]. For an excellent treatment of projective geometry in the real ca.5e, see Coxeter (34). A principal geometric object is a circle (which Cartan calls a “chain” in [24}) which is just a Euclidean circle or straight line. We find several algebraic ways of describing circles, which will be useful in the sequel. In particular we describe circles in terms of 2 x 2 Hermitian matrices. We shall make essential use of the null polarity (the unique object in projective geometry corresponding to the symplectic structure on ℂ) to identify anti-polarities with anti-involutions. Furthermore, elliptic and hyperbolic geometry are developed in terms of anti-polarities which are the projective counterpart of Hermitian forms.
Algebraic and Geometric Background
Authors: Goldman William m.
Published: November 2023

This chapter contains prerequisites for the main text. The previous chapter was meant to illustrate these ideas which are developed in greater generality here. After a fairly lengthy discussion of linear algebra in complex vector spaces (in particular real structures, Hermitian and symplectic structures), we review the analytic and differential-geometric background concerning Kähler manifolds. We emphasize symplectic and contact geometry. This chapter concludes with a discussion of “Heisenberg spaces” which model the boundary of complex hyperbolic space.
The Ball Model
Authors: Goldman William m.
Published: November 2023

Cartan’s generalization of the concurrence of the altitudes is discussed. More formulas are given in the third section of this chapter, including a discussion of orthogonal projections onto totally geodesic subspaces.
Automorphisms
Authors: Goldman William m.
Published: November 2023

This chapter divides into two separate sections. The first section discusses the symplectic geometry of Hn  C and constructs Hamiltonian potential functions for various 1-parameter groups of automorphisms.
Wave Mechanics
Authors: Hannabuss Keith
Published: November 2023

According to Planck and Einstein the energy and frequency of light are related by E = ђw. De Broglie observed that to be consistent with the theory of relativity the momentum p of a wave should be ђk where k is the wave vector of magnitude 2π /wavelength, perpendicular to the wave front. (This is because the special theory of relativity combines E and p and also ω and k into four-dimensional vectors, and linear relations between particular components force the same relations for all other components as well. This is explained in more detail in Section 17.1, which is independent of the rest of the book.)
Quadratic and linear potentials
Authors: Hannabuss Keith
Published: November 2023

Although the classical examples of harmonic oscillators such as springs or the simple pendulum are of limited use in the submicroscopic world of quantum mechanics, there are plenty of other applications that make the oscillator worth studying. Atoms in a crystal, for instance, oscillate about their mean positions and it is their vibrations that carry sound and heat through the material. Indeed, we know from classical theory that by using normal coordinates we may regard any system performing small oscillations about a point of stable equilibrium as a collection of harmonic oscillators. This extends even to the normal modes of vibration of a string or of the electromagnetic field. The harmonic oscillator thus provides the key to understanding how wave phenomena such as light can be quantized, and lies at the heart of Einstein’s idea of the photon and of Planck’s quantum.
The hydrogen atom
Authors: Hannabuss Keith
Published: November 2023

Whilst theoretical physicists struggled to understand the interactions between matter and radiation, new experiments were revealing that atoms had internal structure. In 1897 J.J. Thomson showed that cathode rays consisted of a stream of negatively charged particles much lighter than any known atom. These became known as electrons. It was the 1896 discovery and subsequent investigation of radioactivity which forced the startling realization that, far from being indivisible and indestructible as had been supposed, atoms can disintegrate or be shattered into smaller pieces.
Angular momentum
Authors: Hannabuss Keith
Published: November 2023

In many of the systems studied in classical mechanics angular momentum is far more useful than ordinary linear momentum. For example, in the study of planetary orbits, or indeed any motion under a central force, the conservation of angular momentum plays a crucial role. We shall therefore turn our attention to the description of angular momentum in quantum mechanics.
Symmetry in quantum theory
Authors: Hannabuss Keith
Published: November 2023

Physical systems often have some kind of obvious symmetry, such as the rotational symmetry of the central force field about a nucleus. Mathemati cally this means that the system is invariant under the action of a symmetry group G. (The main ideas of group theory are reviewed in Appendix Al.) Such a physical symmetry must also be present in quantum theory in a way that is compatible with the other important structures, namely the vector spaces and inner products. The simplest way in which this can happen is for G to act on the inner product space 1i by unitary transformations, since these respect both the linear structure and the inner product.
Iterative perturbation theory
Authors: Hannabuss Keith
Published: November 2023

The Rayleigh-Schrodinger theory described in the preceding chapter is by no means the only approach to stationary perturbation theory, nor is it usually the most powerful. As one of many possible alternatives we shall now describe an iterative procedure for approximating stationary states, sometimes called Wigner-Brillouin perturbation theory, which resembles the Feynman-Dyson method of Section 11.3.
Symmetries of elementary particles
Authors: Hannabuss Keith
Published: November 2023

It will have become apparent over the last few chapters that the electrons, protons, and neutrons, which are the most prominent constituents of mat ter, are only some of the many particles that are now known. There are also neutrinos, which appear in some nuclear reactions, Yukawa’s mesons, which help bind the nucleus together, and then to every particle a corresponding antiparticle. With improved techniques for detecting particles in cosmic rays and the increasingly powerful particle accelerators built after the war more and more different kinds of subatomic particle were discovered. The various conservation laws found to hold during collisions between particles suggested that there must be some kind of symmetry principle linking different particles. For example, protons and neutrons belong to a class of particles called baryons, and during collisions the total number of baryons minus the total number of antibaryons is constant. A similar conservation law held for the class of leptons which included the lighter particles such as electrons and neutrinos. Scattering experiments at higher energies began to indicate that the proton has an internal structure suggesting that it might be composed of still smaller particles.
Linear Matrix Equations
Authors: Lancaster Peter , Rodman Leiba
Published: November 2023

In this chapter we present a self-contained account of some well-known facts concerning solutions of linear matrix equations. Our attention is restricted mainly to the Lyapunov and Stein equations: SA-BS=Γ, and S-BSA=Γ, respectively (see equations (5.2.3) and (5.2.4) below). In particular, their symmetric forms (when B = A*, Γ * = Γ) are important in the sequel. Conditions are developed which ensure the (suitably defined) “stability” of solution matrices S of these equations.
Geometric Theory for the Discrete Algebraic Riccati Equation
Authors: Lancaster Peter , Rodman Leiba
Published: November 2023

It is to be shown in Chapter 16 that, to solve the “linear-quadratic regulator” (or LQR) problem for a time-invariant differential system, it is necessary to solve an algebraic Riccati equation of the kind discussed in Part II of this book, equation (7.2.1) for example. The discrete analogue of the LQR problem requires the solution of a rather different algebraic equation for X: It is therefore tempting to describe this equation as a discrete algebraic Riccati equation (or DARE) and, when convenient, we shall do so. The geometric theory for the DARE turns out to be considerably more complicated than for the symmetric CARE. The identification of a main operator (whose invariant subspaces determine solutions of a DARE) is already a significant task when compared to analysis of CARE (see Proposition 12.2.2). Having done this, it is possible to obtain several conclusions for the DARE by a suitable transformation between equations of CARE and DARE types (see Lemma 12.3.2). In contrast to analysis of the CARE it is convenient to make use of techniques involving rational matrix functions at an early stage of the analysis.
Linear–Quadratic Regulator Problems
Authors: Lancaster Peter , Rodman Leiba
Published: November 2023

The “linear-quadratic regulator” (LQR) problem of optimal control has probably provided the greatest single stimulus for investigation of matrix Riccati equations in differential, difference, and algebraic forms. In this chapter the continuous and discrete LQR problems are to be outlined and then the solutions of these problems using Riccati equations are developed. Consistent with the spirit of this book attention is confined to time-invariant (i.e., constant coefficient) problems, even though significant parts of the theory are readily extended to linear time varying problems (see, for example, Brockett (1970), Kalman, Falb and Arbib (1969), or Russell (1979)). In the first four sections the LQR problem for time-invariant, continuous systems is described. We do not use the line of argument initiated by Kalman which involves the technique of dynamic programming. In view of our limited objectives a more direct line of argument seems appropriate even though it is rather delicate. This seems to originate with Brockett (1970), and has been refined by Hijab (1987). Here, we adapt the Brockett-Hijab development to our needs. This line of argument also has the great advantage that it is readily adapted to the discrete LQR problem. This is done in Sections 16.5 and 16.6.
The Total Least Squares Technique
Authors: Lancaster Peter , Rodman Leiba
Published: November 2023

Notice that AXo = (AA+)B and, as AA+ is just the orthogonal projector onto Im A, Xo is the minimum norm solution of the consistent system AX = (AA+)B obtained by projecting Im B onto Im A. Thus, in this process, the subspace Im A plays the pivotal role and the “right-hand side” matrix B is “adjusted” to produce a solvable system. In many applications inconsistent systems arise in an attempt to model consistent equations which are corrupted by observation, modelling, or computational errors. The argument given above can be criticized in this context for holding The best least squares solution of linear systems remains a very important and widely useful technique after a 200-year history. The total least squares idea can be traced back for about 100 years, but has come into prominence more recently with investigations of numerical techniques
Canonical Factorization
Authors: Lancaster Peter , Rodman Leiba
Published: November 2023

The concept of canonical factorization plays a crucial role in numerous applications, and therefore has been thoroughly studied, especially in recent years. The conclusion of this chapter and its main objective concern canonical factorizations of rational matrix functions W(λ.) with respect to the imaginary axis.
Customer requirements and specification
Authors: Ince D C
Published: November 2023

To examine the problems that occur with natural language based documents. To outline what makes a good specification. To detail a simple procedure for requirements analysis and system specification. To show how mathematics is a good medium for specification. The aim of this chapter is to examine some of the faults found in customer statements of requirements and software specifications written in natural language. The purpose in doing this is twofold. First, the document given to staff who produce the software specification is the customer statement of requirements. It is important that such staff realize the nature of such documents. Second, the inadequacies of natural language as a specification medium are most manifest in statements of requirements and software specifications. Before attempting to describe the use of mathematics in system specification, it will be useful to describe the faults that it should eliminate.
The Z schema calculus
Authors: Ince D C
Published: November 2023

To describe how Z schemas can be used as objects in formal specifications. To introduce the schema calculus. To show the Z schema calculus being used in some small examples. Schemas are a convenient way of organizing the description of specifications. They have a form that replicates a pattern found throughout the discrete mathematics described in the early parts of this book.
Lexical-domain object-feature logic
Authors: Sandewall Erik
Published: November 2023

We now proceed along the lines defined in Chapter 4, subsection 4.1.2 and introduce a lexical object domain alongside, but distinct from, the value domains for the features. This extension allows the logic to refer to object domains in the O component of scenario descriptions. I will refer to the resulting logic as lexical-domain object-feature logic, or LFL. Section 5.4 will outline how a terminological language can be defined on top of the LFL semantics, and therefore indicates a bridge to KL-ONE-type languages.

LFL does not contain a notion of time, so it can only be used for describing static or momentary phenomena. However, within LFL we define a concept of state which will be used extensively to repreSCDt the ‘snapshots’ or momentary states in later chapters.
Temporal feature logic for discrete time domains
Authors: Sandewall Erik
Published: November 2023

Earlier chapters have defined IDS developments whose structure is the five tuple 〈B, M, R, A, 〉. They have also defined the operation of chronicle completion where a scenario description is given, and where it is sufficient to first identify the set of developments that satisfy the given description, then to extract the set of weakened models of the form 〈M, R〉while throwing away the rest of the information, and then to use the set of weakened models as the set of intended conclusions from the given scenario description. In this way, one will only obtain conclusions about feature-values and changes of feature-values at various points in time, but not conclusions about, for example, the starting times and ending times of actions.
Intended models for chronicles in 𝒦-IA
Authors: Sandewall Erik
Published: November 2023

By the definitions in chapter 2, subsection 2.3.1, a chronicle in 𝒦-LA is a tuple 〈 𝒦, 0, 〈IA, LAW 〉, SCD, OBS 〉. Some of the previous chapters have defined the syntax of formulae which may occur in LAW, SCD, and OBS. Other chapters have defined an underlying semantics in terms of the ego-world game and the trajectory concepts. We are now ready to establish the connection between those two backgrounds, and to define the intended set of models for a given chronicle in terms of the underlying semantics. In this context we shall also introduce a number of auxiliary concepts, including syntactical constraints on the formulae in the premise partitions LAW, SCD, and OBS. Similarly we introduce some subsidiary model-theoretic concepts, such as the classical and intended models restricted to a finite time interval, which will be used in the subsequent proofs.
Model Theory
Authors: Manzano María
Published: November 2023

Logic languages are free from the ambiguities of natural languages, and are therefore specially suited for use in computing. Model theory is the branch of mathematical logic which concerns the relationship between mathematical structures and logic languages, and has become increasingly important in areas such as computing, philosophy and linguistics. As the reasoning process takes place at a very abstract level, model theory applies to a wide variety of structures. It is also possible to define new structures and classify existing ones by establishing links between them. These links can be very useful since they allow us to transfer our knowledge between related structures. This book provides a clear and readable introduction to the subject, and is suitable for both mathematicians and students from outside the subject. It includes some historically relevant information before each major topic is introduced, making it a useful reference for non-experts. The motivation of the subject is constantly explained, and proofs are also explained in detail.
Basic notions: universal algebra
Authors: Manzano María
Published: November 2023

We start by introducing the notion of structure, defining it as a triple formed by a nonempty set, called the universe, and a series of relations and functions defined over the universe of the structure. Some of these structures are well-known structures in mathematics; for example, they are groups, rings, orders, or Peano structures.
Hypothetical reasoning with intuitionistic logic
Authors: Bonner Anthony J
Published: November 2023

This chapter addresses a limitation of most deductive database systems: they cannot reason hypothetically. Although they reason effectively about the world as it is, they are poor at tasks such as planning and design, where one must explore the consequences of hypothetical actions and possibilities. To address this limitation, this chapter presents a logic-programming language in which a user can create hypotheses and draw inferences from them. Two types of hypothetical operations are considered: the insertion of tuples into a database, and the creation of new constant symbols. These two operations are interesting, not only because they extend the capabilities of database systems, but also because they fit neatly into a well-established logical framework, namely intuitionistic logic. This chapter presents the proof theory for the logic, outlines its intuitionistic model theory, and summarizes results on its complexity and on its ability to express database queries. Our results establish a strong link between two previously unrelated, but well-developed areas: intuitionistic logic and computational complexity. This, in turn, leads to a strong link with classical second-order logic. Furthermore, unlike many expressibility results in the literature, our results do not depend on the artificial assumption that the data domain is linearly ordered.
Logic Without Model Theory
Authors: Kowalski Robert
Published: November 2023

Arguably, model theory serves two main functions: (1) to explain the relationship between language and experience, and (2) to specify the notion of logical consequence. In this chapter I shall propose the notion of ‘knowledge assimilation’, the assimilation of new information into a knowledge base, as an alternative understanding of the way in which a knowledge base formulated in logic relates to externally generated input sentences that describe experience. I shall argue that the notion of logical consequence can also be understood within a knowledge assimilation framework, in terms of sentences that must hold no matter what stream of input sentences might arise in the future.
The Transmission of Truth and the Transitivity of Deduction*
Authors: Tennant Neil
Published: November 2023

Frege assigned to logic the task of ‘discovering the laws of truth’ Logical proofs preserve truth from their premisses to their conclusions. Logic is also said to be a matter of form, not content. I intend in this essay to stay with considerations of just truth and logical form, in order to, address the question of the transitivity of deduction.
Logical Constants as Punctuation Marks*
Authors: Došxen Kosta
Published: November 2023

This chapter presents a proof-theoretical approach to the question ‘What is a logical constant?’ The approach starts with the assumption that logic is the science of formal deductions, and that basic formal deductions are structural deductions, i.e. deductions independent of any constant of the language to which the premises and conclusions belong. Logical constants, on which the remaining formal deductions are dependent, may be said to serve as ‘punctuation marks’ for some structural features of deductions. This punctuation function, exhibited in equivalences which amount to analyses of logical constants, is taken as a criterion for being a logical constant. The chapter presents an account of philosophical analysis which covers the proposed analyses of logical constants. Some related assumptions concerning logic are also considered. In particular, since a logical system is completely determined by its structural deductions, alternative logical systems arise by changing structural deductions while having constants with the same punctuation function. Some other approaches to the question ‘What is a logical constant?’, grammatical, model-theoretical, and proof- theoretical, are briefly considered.
Finitary Inductively Presented Logics*
Authors: Feferman Solomon
Published: November 2023

A notion of finitary inductively presented (f.i.p.) logic is proposed here, which includes all syntactically described logics (formal systems) met in practice. A f.i.p. theory FS0 is set up which is universal for all f.i.p. logics; though formulated as a theory of functions and classes of expressions, FS0 is a conservative extension of PRA. The aims of this work are (i) conceptual, (ii) pedagogical and (iii) practical. The system FSo serves under (i) and (ii) as a theoretical framework for the formalization of metamathematics. The general approach may be used under (iii) for the computer implementation of logics. In all cases, the work aims to make the details manageable in a natural and direct way.
Field Measurement
Authors: Kangshen Shen , Crossley John N , Lun Anthony W -C
Published: November 2023

The Greek historian Herodotus (5th century BC) said that the civilization of Egypt was merely a gift of the Nile. Each year this river floods the land and leaves rich soil behind. Egyptian geometry is said by Herodotus to have originated in the need, created by this annual flooding, to redetermine the boundaries of the lands owned by the farmers.
Excess and Deficit
Authors: Kangshen Shen , Crossley John N , Lun Anthony W -C
Published: November 2023

The 20 problems of this Chapter discuss the solution of linear equations by using the Rule of Double False Position.

In its simplest form this works as follows.
Right-angled Triangles
Authors: Kangshen Shen , Crossley John N , Lun Anthony W -C
Published: November 2023

This chapter could have been called “Pythagoras’ theorem” if it had been written in the West.
Commensurable spin structures and their excitations
Authors: Mackintosh A R , Jensen J
Published: November 2023

The standard model of rare-earth magnetism was constructed during the 1950s and early 1960s, and Roger Elliott was one of its major architects. One of the first coherent descriptions of the theory is to be found in his classic discussion of the magnetic structures of the heavy rare-earth metals by means of the molecular-field approximation (Elliott 1961). With his colleagues, he also gave in the following year an account of the magnetic excitations (Cooper et al. 1962). In these, as in other early theoretical treatments of rare-earth magnetism, most of the results were obtained by analytical means, and the problems caused by the incommensurability of the lattice and magnetic periodicities were either ignored or treated by perturbation theory. In this chapter we shall adopt a mean-field method which is closely related to those used earlier, but differing from them in two important respects. There is convincing experimental evidence that the periodicity of magnetic structures such as the helix in the rare earths (and particularly in holmium which we shall be considering in some detail) tends to ‘lock in’ to some rational multiple of the lattice periodicity.
Helical spin systems: a progress report
Authors: Harris A B
Published: November 2023

The introduction of models to describe helical spin systems in rare-earth metals was initiated by the pioneering work of Roger Elliott (1961), to whom this volume is dedicated. The purpose of this chapter is to review some recent theoretical developments in this general area. We note that this topic of research has had continuing impetus from both experiment and theory. One family of experiments concerns the nature of magnetism in the metallic rare earths and this work is reviewed elsewhere in this volume. Also, we point out the existence of helical magnetic insulators of the chemical form TX2, where T represents a transition metal, such as Co or Ni and X is typically Br or I. The magnetic structure and some properties of such materials are well established (Adam et al. 1980; Day and Ziebeck 1980; Kuindersma et al. 1981). Furthermore, a recent experimental programme (Endoh et al. 1988), stimulated by the need to understand the high-temperature superconductors, had focused on the lanthanum cuprate materials, which display both quantum effects in the pure materials (Chakravarty et al. 1988, 1989) and helical spin correlations (Shirane et al. 1989) in the doped materials.
Dressed particles in the Hubbard chain
Authors: Kawakami Norio , Okiji Ayao
Published: November 2023

The Hubbard model has been studied for a long time as a simplified model for electron correlation problems such as the metal-insulator transition, itinerant magnetism, and so on. Moreover, the discovery of high 7;, superconductors has again raised an important question about the strong correlation problem near the metal-insulator transition, including low-dimensional quantum fluctuations (Anderson 1987). In recent works, we have precisely studied various thermodynamic properties of the one-dimensional Hubbard model (Kawakami et al. 1989; Usuki et al. 1989) and clarified the underlying physics near the Mott insulator in terms of the dressed particles of the Bethe ansatz method (Kawakami and Okiji 1989a, b). In this brief report, we present the exact calculation for the dressed particles in the Hubbard chain near the Mott insulator.
Pietro Dei Franceschi
Authors: Coolidge Julian Lowell , Gray Jeremy
Published: November 2023

The problem of representing three-dimensional objects accurately on a flat surface would seem naturally to be one that would attract the attention of both the mathematicians and the artists, and that at an early date. As a matter of fact both categories of persons left it severely alone until a surprisingly late time. The geometers may have thought it too simple to exercise their skill, the artists found it too mathematical to suit either their taste or their capacity.
Jan De Witt
Authors: Coolidge Julian Lowell , Gray Jeremy
Published: November 2023

Most of the men whom I have classified as amateurs in mathematics gave the remainder of their professional lives to quiet intellectual pursuits. Perhaps it would not be quite accurate to say this of Leonardo da Vinci, who gave some attention to waging war, but even in his case the balance of intellectual activity went to affairs of the mind, quiet pursuits of the studio or of the study. This, however, is far from being true of that great patriot, the Grand Pensionary of Holland and West Friesland, to whom I now turn.
Johann Heinrich Hudde
Authors: Coolidge Julian Lowell , Gray Jeremy
Published: November 2023

It is greatly to the credit of van Schooten that two of his pupils who attained high position in public life should have spent part of their leisure in mathematical study and produced work worthy of comment. do not know the name of any other teacher who produced two such pupils, and both remained loyal to their master, which has not always been the case. One of these pupils was De Witt whom we have just considered, the other was the man whose name stands above. He began as a student of jurisprudence and certainly retained an interest in that branch all of his life.
Buffon
Authors: Coolidge Julian Lowell , Gray Jeremy
Published: November 2023

There certainly never was a man belonging to that class which I have called amateur mathematicians who had a wider interest in all science, especially descriptive science, than George-Louis Leclerc, Comte de Buffon. His monumental Histoire naturelle is overwhelming in size and the variety of topics treated, but he had besides a very real interest in theoretical mathematics. He was especially preoccupied with what one might call the metaphysical aspect of the subject. The discovery of the infinitesimal calculus had raised a number of very puzzling questions as to the real meaning of the various concepts involved.
Bernhard Bolzano
Authors: Coolidge Julian Lowell , Gray Jeremy
Published: November 2023

The distinguished Czech writer whose name stands above bears, from the point of view of this book, a certain resemblance to Blaise Pascal. Both were deeply interested in religion and philosophy, both were involved in controversy and suffered for the faith that was in them. Both did such brilliant mathematical work that they might well be classed as professionals. But I have included Pascal with the amateurs because he was more famous as a philosopher and a writer of beautiful French prose than as a mathematician, and I take up Bolzano because t seems to me interesting that a man who was a remarkable pulpit orator, only removed from his chair for his political opinions, should have thought so far into the deepest problems of a science which he never taught in a professional capacity.
Appendix (1992): revolutions reconsidered
Authors: Mehrtens Herbert
Published: November 2023

Thomas Kuhn’s terms ‘paradigm’ and ‘scientific community’ have made their way into the standard vocabulary of science. ‘Revolutions’ appear to be somewhat outmoded, and the ‘disciplinary matrix’ with its elements is no longer called by this name, but is nevertheless commonly in use in analyses of the science and their history. The debate on the relative importance of ‘internal’ and ‘external’ factors in the development of science has faded away, and various forms of constructivism and contextualism now dominate advanced historical and theoretical work.
Dynamic light scattering from polymers in solution and in bulk
Authors: Fytas George , Patkowski Adam
Published: November 2023

Of the various light scattering techniques, DLS is the most widely applied in studying diffusional polymer dynamics in solution, as described extensively elsewhere in this volume. On the other hand, FPI is less frequently used to record the depolarized Rayleigh and polarized Brillouin spectrum. Depolarized dynamic light scattering (DDLS) can yield important information on the rotational diffusion coefficient and on internal dynamics of macromolecules composed of optically anisotropic monomer units. DDLS experiments, however, are very rare,121 mainly because of experimental difficulties due to the very low intensity of the depolarized component of scattered light and the short decay times of the correlation functions. The polarized Brillouin spectrum (BS) of isotropic materials is mainly due to local density fluctuations and can measure the relaxation of the longitudinal modulus of viscoelastic fluids at GHz frequencies not easily accessible to other experimental techniques.
Critical dynamics of binary liquid mixtures and simple fluids studied using dynamic light scattering
Authors: Štěpánek Petr
Published: November 2023

Many systems of various kinds undergo phase transitions described by a critical point characterized by critical values of the relevant variables of the system. For the purpose of this chapter, the two kinds of phase transitions to be considered are the vapour-liquid phase transition typically described by a temperature–pressure diagram; the one-phase-two-phase transition of a binary mixture described by a temperature—composition diagram, an example (based on refs 1 and 2) of which is shown in Fig. 14.1.
The Pyramid Builders
Authors: Macintosh Wilson Alistair
Published: November 2023

Whilst Europe had been held firmly in the grip of the ice, the northern part of Africa was enjoying a mild tropical climate. The grassy plains and lush savannahs supported abundant herds of game, and following these herds many tribes of nomadic hunters. At the end of the Ice Age the rainfall decreased, and the region began to dry out, becoming in the end the world’s greatest desert, the Sahara. The nomadic tribes were forced into the fertile valley of the one great river, the Nile.
The Contribution Of Islam
Authors: Macintosh Wilson Alistair
Published: November 2023

On 8 June AD 632 Mohammed, the Prophet of Allah, died at Medina in present-day Saudi Arabia. The last of the prophets had gone to his reward. Addressing Mohammed’s followers, Abu Bakr, his father-in-law, said: ‘People, let him amongst you who served Mohammed know that Mohammed is dead, but let him who served God continue in his service, for Mohammed’s God lives and never dies.’ The succession was decided between Abu Bakr, Umar and Mohammed’s cousin Ali, the choice finally falling on Abu Bakr, who became the first Khalifa (deputy). We know him as the first Caliph.
Introduction
Authors: Mott Sir Nevill
Published: November 2023

Before the appearance of quantum mechanics we had little understanding of why some solids, such as the metals, were good conductors of electricity and others were not. The Hall effect gave a measure of the number of free electrons in a metal, the Hall constant R8 being, according to theories then available, equal to 1/nec, n being the number of electrons per unit volume, e the electronic charge, and c the speed of light. From the experimental values of this quantity it appeared that the number of free electrons in a metal was of the same order as the number of atoms. In insulators, on the other hand, all electrons seemed to be stuck; none were free to move. This could not be explained, nor could many other properties of solids.
Non-standard structures for super-real fields and the gap theorem
Authors: Garth Dales H , Hugh Woodin W
Published: November 2023

Let U be a free ultrafilter on ℕ, and let ℝ ℕ/U be the corresponding ultrapower. As we remarked in Chapter 4, ℝ ℕ/U is of the form Kp for a certain valuation prime z-ideal P = Jp in C(βℕ). From the point of view of model theory, ℝ ℕ/U has a special importance: it is the underlying field of a non-standard model of analysis. Thus ℝ ℕ/U is a real-closed η1-field of cardinality ,, but, further than this, much of the structure of ℝ can be ‘transferred’ to ℝ ℕ/U; ℝ ℕ /U with this additional structure is what is termed a ‘non-standard model of analysis’. (See Chapter 10 for a brief resume of model theory.) We shall show that a (in general, weaker) version of this additional structure exists for an arbitrary super-real field K p. This structure will allow us to obtain additional information about super-real fields, and in particular about the structure of their gaps.
A History Of Ornithology In Mexico And Northern Central America
Authors: Howell G , Steve N , Webb Sophie
Published: November 2023

The history of ornithology in Middle America justifies a book in itself and here we provide only a brief outline of the subject. The early development of ornithological exploration is best understood within the frame of world history. Thus little, if anything, was achieved while Middle America remained under Spanish rule, science being anathema to the prevalent religious fervor of the conquistadors. Mexican independence, however, dating from 1821, made it possible for all Europeans and Americans to settle in or visit Mexico and send home whatever they wanted. During the same year, the dissolution of the Viceroyalty of Guatemala into its five provinces (which then became the five Central American countries) opened Central America to foreigners.
Birding In Mexico And Northern Central America
Authors: Howell G , Steve N , Webb Sophie
Published: November 2023

Rather than providing a list of specific localities where one can expect to find various species, we consider it more useful to provide some information on how to look for birds. A major problem with giving specific sites in the region is that, even within parks, habitat alteration and ‘development’ are so frequent and rapid that reliance on directions, even recent ones, can be frustrating when a new road has been built, a forested area cleared for cattle pasture, etc.
Taxonomy
Authors: Howell G , Steve N , Webb Sophie
Published: November 2023

The purpose of taxonomy (the science of classification) is to describe and name divisions of living organisms and to establish relationships between them. Most people are aware of the major division of living things into two kingdoms—plants and animals. Birds are a group at the level called a class within the Animal Kingdom and members of the Class Aves are characterized by having feathers. Divisions within the Class Aves bring us to the level of species. A group of similar species forms a genus. Every known species possesses a unique name based on a binomial system based upon Latin, an internationally accepted common language. The specific name comprises the genus name (first letter capitalized), followed by the specific name (all lower case).
Ecological diversity and host plant relationships of Treehoppers in a lowland tropical rainforest
Authors: Loye Jenella E
Published: November 2023

Membracids are a diverse and abundant component of the insect fauna of the tropical forest understorey. Like the well-known aphid faunas of the temperate regions, they are phloem-feeders and are able to bypass a number of plant defences which function against chewing herbivores (Dixon 19 85; Slansky and Rodriguez 1987). Membracids are thought to have originated in the tropics (Funkhouser 1951); however, while the ecological importance of aphid parasitism is well documented, that of their primarily tropical counterparts, the membracids, is virtually unknown (Wood 1986). This oversight may be due in part to their highly cryptic and relatively sessile nature. However, using light-traps, Wolda (1979, 1982, personal communication) has collected data on the seasonal abundance of 91 species on Barro Colorado Island in Panama, thus providing an excellent reference point from which to begin an ecological examination of this fauna. No major survey of specific host plant relations has ever been undertaken for the tropical membracids; consequently, we do not have enough information to address such a fundamental question as whether there is any relationship between membracid phylogeny and the taxa of hosts they exploit. However, Wood and Guttman (1982) demonstrated the powerful evolutionary effect that host switching has had on the biology of the temperate Enchenopa binotata complex. The limited life history data available for tropical membracids has recently been enriched by Wood (1986) who listed data for 126 Costa Rican and some Panamanian membracids (see also Ekkens 1972, Haviland 1925; Hinton 1977; Wood and Olmsted 1984), and implicated ant predation as the selective force in treehopper presocial behaviour. The family Membracidae has a diversity of life histories and a sessile nature, which makes them the ideal insect group for relating life history patterns to nutritional quality and availability of the host plant.
(Homoptera: Psylloidea)
Authors: Burckhardt Daniel , Brown Robert G
Published: November 2023

The adult Panamanian psyllids were recently revised by Brown (1985) who recorded 137 species assigned to 33 genera, and also by Brown and Hodkinson (1988). The present paper provides an identification key for the last larval instar of 28 species in 15 genera, including material from Panama and other parts of tropical America. The psyllid larvae have received generally less attention than the adults, even though they often provide more significant characters than the latter. This applies to separation of species, e.g. Cacopsylla pyricola (Forster) and notata (Flor) (Burckhardt and Hodkinson 19 86), as well as to higher classification (White and Hodkinson 1985). Therefore, despite the small number of species represented by larvae, it seem useful to publish a provisional key. The material examined for the present study, listed in Appendix 19.1, is deposited in the following institutions and collections: BMNH: British Museum (Natural History), London; IDH: I.D. Hodkinson collection, Liverpool Polytechnic, Liverpool, UK; MHNG: Museum d’Histoire naturelle, Geneva, Switzerland; U CD: University of California, Davis, California, USA; USN M: United States National Museum of Natural History.
(Gelastocoridae,
Gerridae, Mesoveliidae, Saldidae, Veliidae)
Authors: Polhemus John T , Manzano Maria del Rosario
Published: November 2023

Species of the suborder Heteroptera constitute a major part of the obligatory marine insect fauna of the world. This paper treats the Heteroptera species known to occur in near shore or littoral marine habitats of the Eastern Tropical Pacific, the ‘Panamic Province’ and adjacent regions, reaching from the Sea of Cortez, Mexico in the north to Guayaquil Bay, Ecuador in the south along the west coast of the Americas (see Ekman 1953, p. 38), but excluding the Galapagos Islands which have a distinct endemic fauna. The only truly pelagic insects, those that have permanently colonized the open ocean, belong to the heteropteran genus Halobates, and although not dealt with further here are admirably treated by Herring (1961). Of the seven families of Heteroptera with obligatory marine species, only Hermatobatidae and Omaniidae have yet to be found in the Eastern Tropical Pacific. The former family is known from the Caribbean and Hawaii, so may occur in the Panamic Province; the latter seems confined to the Inda-Pacific region. The families known to occur in the Panamic Province are Gelastocoridae, Gerridae, Mesoveliidae, Saldidae, and Veliidae; a checklist is given below. Each of these five families also have freshwater inhabiting species, and some of these species are euryhaline thus occasionally invading the marine habitat; one such species is Mesovelia mulsanti White which regularly turns up as single specimens in samples from mangrove estuaries and bays. The species treated here are those that have been deemed to be obligatorily marine associated; however this is as yet a quite subjective judgment due to our insufficient knowledge of their ecology and habitat preferences. Every diligent survey of a tropical marine habitat reveals new taxa and important new information; it was just such an effort by the second author that brought to light the new taxa described herein and much of the associated ecological data.
The neuropteroid orders of Central America (Neuroptera and Megaloptera)
Authors: Henry Charles S , Penny, Normand. , Adams Phillip A
Published: November 2023

Imagine that you are a student in a course on insect identification, and you are presented by your instructor with an ‘unknown’ to classify, merely to order. It has extremely long, knobbed antennae, like a butterfly; perhaps it is a lepidopteran. Yetits wings are membranous, narrow, and strong, and it has legs that are spiny and obviously modified for seizing small insect prey items during flight; these are characteristics of a dragonfly, order Odonata. But yellowish-white markings on the rather fat abdomen, together with a narrow waist, give the specimen a wasp-like appearance: it could be in the Hymenoptera, or maybe a good wasp-mimicking fly (order Diptera). Examine the compound eyes: each is extremely large, as one expects of an odonate, but also divided by a deep sulcus into an upper and lower half, as in certain male mayflies-is the insect an aberrant ephemeropteran? Finally, you decide that your instructor has glued together the parts of many insects, to fool you. In fact, however, you have just been introduced to the peculiar, fascinating order of insects known as Neuroptera, and you are looking at a member of one of its most curious families, the Ascalaphidae or owlflies (Fig. 28.1).
Stingless Bees: A guide to Panamanian and Mesoamerican species and their nests (Hymenoptera: Apidae: Meliponinae)
Authors: Roubik David W
Published: November 2023

Research on the perennial bee colonies of tropical forests is somewhat impaired by a lack of taxonomic guides and universally accepted nomenclature. The stingless honey-making bees (Meliponinae) are arguably the most abundant bees on earth and certainly the bees most often seen in the tropics, but few specialists can identify them. Comprehensive guides will probably not be available for use by non-specialists until much more field work and museum research is completed. In the interim, dozens of species already in major collections have not been described. A clear delineation of supraspecific groups, to which undescribed species can readily be assigned, is of value for field workers who encounter such undescribed taxa. The present work is a guide that will allow researchers to distinguish among the stingless bees of Panama and also the natural nests occupied by colonies, which are encountered in the field. Further, to allow determination of the subgenus or genus of the stingless bees of Mesoamerica and Mexico in general, a checklist (p. 506) of unique or easily observed traits for each is included. The key to Panamanian species is to some extent artificial because characters of only relative value are included, such as bee size and colour. The more detailed information which involves traits found in few groups or unique to some, is summarized in tabular form (a ‘quick key’ to genera and subgenera) and in a diagram of phylogenetic relationships among the Neotropical Meliponinae.