bluuebunny/crossref_metadata_2025 huggingface dataset:
Methods and Calculi for Deduction
Authors: Bibel W , Eder E
Published: November 2023

Logic has been presented in David Israel’s Chapter as a language to formalize problems arising in subareas of intellectics (and of other fields, for that matter). In Davis’ Chapter, it is shown that logic also supplies a relationship (denoted by |=) among different statements (orformulas) in that language. Note that there are actually many logics in the literature. As a default, we meanfirst-order logic unless explicitly specified otherwise. The formulas related this way to the empty set of formulas (i.e.ϕ |= F) play a particularly important role. They are calledvalid formulas. It turns out that in many cases a problem can be reformulated as a logical formula to be proved valid. For this reason one often speaks of ‘theorem proving’ where in effect solving problems, as those just referred to, is the issue.
Classical vs Non-classical Logics (The Universality of Classical Logic)
Authors: Gabbay D M
Published: November 2023

This chapter addresses the problem of whether classical logic can be used as a universal system of logic and whether it can be applied, profitably and sensibly, in all areas where logic needs to be applied. More specifically, we focus on modal and temporal logics and ask whether the use of such special logics, as compared with the use of classical logic, is advantageous. We examine what we lose and what we gain if we use classical logic instead of specialized logics to describe and reason about the same (e.g. temporal) phenomena.
Introduction And Overview
Authors: Gabbay Dov M , Reynolds Mark A , Finger Marcelo
Published: November 2023

The sections below give an overview of the contents of this book. This volume, Volume 2 in the series, deals with the more applicable aspects of temporal logics. Volume 1 gave the basic concepts and methods and concentrated more on the expressive power of temporal languages, their axiomatization, their dimension and their decidability. Now we are ready to deal with some aspects of their applications. The first four chapters of the present volume continue with the more theoretical presentation, covering automata, branching time and labelled deduction. The rest of the book progresses in the direction of temporal databases, temporal execution and programming, actions and planning. For details, see the following sections of this chapter.
The Metatem Programming Language
Authors: Gabbay Dov M , Reynolds Mark A , Finger Marcelo
Published: November 2023

METATEM is really a paradigm for programming languages rather than one particular language. There are three basic principles:

The versions of METATEM described in [Barringer et al., 1989], [Finger et al., 1993], [Fisher and Barringer, 1991], [Fisher, 1993], [Reynolds, 1995], [Barringer et al., 1996) and [Reynolds, 1997) use the temporal languages PML and FMO with Until and Since.
Propositional quantifiers and fixed point operators
Authors: Gabbay Dov M , Hodkinson Ian , Reynolds Mark
Published: November 2023

In this chapter we investigate the two related topics of propositional quantifiers and fixed point operators. In sections 8.1-8.3 we look at languages in which there are formulae ∀xA and ∃xA where x behaves in A as a proposition. There are different semantics depending on what we mean by a ‘proposition’, i.e. what we let q range over. In any case we obtain such expressive languages that they are not directly useful for computation. In the rest of the chapter we look at some very useful sublanguages in which quantifiers of the form LFPqA are used to build formulae and in which their semantics are defined as the least fixed point of certain operators. As we will see, these fixed point languages allow a sort of inductive definition of new propositions.
Further expressive completeness results
Authors: Gabbay Dov M , Hodkinson Ian , Reynolds Mark
Published: November 2023

In this chapter we prove the same result as we did in the last. First we will examine the idea of gaps in the flow of time in some detail. Then we will introduce some new connectives to talk about such gaps and use the expressive completeness of the Stavi connectives to deduce expressive completeness results for these new connectives. We also present some axiomatizations of these connectives. Finally, we prove the expressive completeness of the Stavi connectives again but this time we do not use separation. Instead we present a more direct proof using games. Generalizations of such a proof may be useful in cases where separation is difficult to show.
Modal Logics
Authors: Chagrov Alexander , Zakharyaschev Michael
Published: November 2023

When discussing in Section 2.1 the meaning of intuitionistic connectives, we used in our language-a metalanguage with respect to ℒ-the undefined notion “proof’. Making the proof interpretation somewhat rougher, we can treat, for example, the intuitionistic formulap--→qVras the proposition
Canonical Formulas
Authors: Chagrov Alexander , Zakharyaschev Michael
Published: November 2023

In Sections 2.5 and 3.5 we characterized the geometry of Kripke frames validating some intuitionistic and modal formulas by imposing first order conditions on their accessibility relations. However, as was shown in Section 6.2, there exist formulas which have no first order equivalents. In this chapter we try another, purely frame-theoretic approach to the characterization problem which uses such notions as subframe, reduction, etc. Unfortunately, this approach is not universal either. But its limitation is of a different kind: it characterizes onlytransitivegeneral frames, but for every modal and intuitionistic formula. So all frames in this chapter are assumed to betransitive.
The Disjunction Property and Halldén Completeness
Authors: Chagrov Alexander , Zakharyaschev Michael
Published: November 2023

Recall that a modal logicLhas the (modal disjunction propertyif, for everyn ≥ 1 and all formulas φ1, … ,φn, And a (modal or superintuitionistic) logicLis said to beHalldén completeif (15.1) holds for all φand ψcontaining no common variables
Correspondence between operational and denotational semantics: the full abstraction problem for PCF*
Authors: Ong C -H L
Published: November 2023

This chapter addresses a number of computationally relevant mathematical problems arising from the relationship between operational and denotational semantics of higher-type (or higher-order) sequential functional programming languages. We choose Scott’s language PCF (which stands for Programs for Computable Functions) as the vehicle for developing the leading ideas.
Cardinal Arithmetic
Authors: Shelah Saharon
Published: November 2023

I am always very enthusiastic about my last work, but since Dec 87 I am enthusiastic mainly about the work presented here. Let me try to share this with you, the reader. If we interpret “true” by “is provable in ZFC” (the usual axioms of set theory), as I do, then a large part of set theory which is done today does not deal directly with true theorems-it deals, rather, with a huge machinery for building counterexamples (forcing possible universes) or with “thin” universes (inner models). Very often the answer to “can this happen?” is “it depends”. Now, I believe that this phenomenon is inevitable, and expresses a deep phase of the development of set theory, which resulted in many fascinating theorems (and also in quite a few proofs of mine). However, there is still some uneasiness about it. A way to express it is to say that if Cantor would have risen from his grave today, he would not just have problems understanding the proofs of modern theorems-he would not understand what the theorems actually say. We do not try to fight this prejudice here, as it works in our favour.
Nw+l Has A Jonsson Algebra [Sh 355]
Authors: Shelah Saharon
Published: November 2023

We advance our knowledge on the cofinality of products of regular cardinals and give several applications; for example there is a Jonsson algebra on Nw+l and Nw+l -c.c. is not productive. This chapter introduces pp (using pcf’s) as our substitute to exponentiation and advances our understanding of pcf to have a considerable number of applications.
There Are Jonsson Algebras In Many Inaccessible Cardinals [Sh 365]
Authors: Shelah Saharon
Published: November 2023

Here we prove (in ZFC) that there is a Jonsson algebra on , λ if: , λ is an inaccessible not w-Mahlo or just, λ is an inaccessible (not necessarily strong limit) cardinal which has a stationary subset not reflecting in any inaccessible cardinals. We also prove this for many successor of singulars.
Random Walks In The Continuum Limit
Authors: Hughes Barry d.
Published: November 2023

A key issue in the theories of random processes and random systems, and perhaps the key issue so far as their relevance to physics and technology is concerned, is the resolution of the following question. What does randomness in the small conspire to produce in the large? We address this question for random walk processes, for which the answers are well understood, in the present chapter. The canonical application of random walk models is to the theory of Brownian movement.KKKKKKKKKKK M Y BI
Introduction To Volume 2
Authors: Hughes Barry D
Published: November 2023

In Volume 1 of this work, we gave a self-contained introduction to random walks and related processes. In these processes, ‘disorder’ is temporal in nature. Typically, a moving particle (the random walker) takes steps at fixed time intervals, and at each step a random direction is chosen, resulting in a chaotic trajectory. The present volume, in contrast, addresses models in which disorder is frozen in space. We describe such models as random environments.
An Introduction To Percolation Theory
Authors: Hughes Barry D
Published: November 2023

The basic ideas of percolation theory were anticipated in the early 1940s in the theory of polymer gelation (Flory 1941, Stockmayer 1944) and in the theory of branching processes (Good 1949). However, the genesis of percolation theory may be attributed justly to Broadbent (1954) in the published discussion of a paper by Hammersley and Morton (1954) on Monte Carlo methods. The early history of the subject is discussed by Hammersley (1983): Broadbent was at that time working at the British Coal Utilization Research Association on the design of gas masks for use in coal mines.
Transport And Conduction In Random Environments
Authors: Hughes Barry D
Published: November 2023

In Chapters 5-7 we examine a few of the many existing models of transport and conduction processes in random environments.
Algebraic Riccati Equations
Authors: Lancaster Peter , Rodman Leiba
Published: November 2023

This book provides a careful treatment of the theory of algebraic Riccati equations. It consists of four parts: the first part is a comprehensive account of necessary background material in matrix theory including careful accounts of recent developments involving indefinite scalar products and rational matrix functions. The second and third parts form the core of the book and concern the solutions of algebraic Riccati equations arising from continuous and discrete systems. The geometric theory and iterative analysis are both developed in detail. The last part of the book is an exciting collection of eight problem areas in which algebraic Riccati equations play a crucial role. These applications range from introductions to the classical linear quadratic regulator problems and the discrete Kalman filter to modern developments in HD*W*w control and total least squares methods.
Gemetric Theory the Real Case
Authors: Lancaster Peter , Rodman Leiba
Published: November 2023

Using the geometric methods developed in Chapter 7 we now study symmetric Riccati equations of the form (7.2.1) for which the coefficient matrices A, C, D are assumed to be real and, accordingly, only real solutions X are sought. The theory will parallel that of Chapter 7 and so, when the real case does not differ significantly from the complex case already investigated, proofs may be omitted or merely outlined. However, for some purposes it will be necessary to call on the analysis of real matrix pairs carried out in Section 2.7 and Chapter 3.
Perturbation Theory for Discrete Algebraic Riccati Equations
Authors: Lancaster Peter , Rodman Leiba
Published: November 2023

Taking advantage of the geometric theory for the discrete algebraic Riccati equation developed in Chapter 12, as well as the comparison theorems of Chapter 13, we can now study the behaviour of hermitian solutions of discrete algebraic Riccati equations under small perturbations of the coefficients of these equations. The emphasis is on the behaviour of extremal (minimal and maximal) solutions. Their behaviour as functions of the coefficients is studied here as well. The material of this chapter is, of course, the analogue of that in Chapter 11 and is developed here for the DARE of equation (12.2.1) rather than the CARE of equation (7.2.1).
Discrete Algebraic Riccati Equations and Matrix Pencils
Authors: Lancaster Peter , Rodman Leiba
Published: November 2023

The use of the matrix T makes it necessary, of course, to assume that A is invertible. This assumption can be avoided by relating the DARE to a J-unitary pencil (see Section 2.9) of the form rather than the pencil λI −T. When A is not invertible this pencil has an eigenvalue at infinity, a phenomenon which cannot arise in a classical eigenvalue problem. There are other advantages in the matrix pencil technique which will be mentioned in the sequel. Some of the basic ideas and results are described in this chapter but, in the authors’ view, the theory cannot be described as complete, and is still a developing area of research.
Parameter Optimization Algorithms
Authors: Bishop Christopher M
Published: November 2023

In previous chapters, the problem of learning in neural networks has been formulated in terms of the minimization of an error function E. This error is a function of the adaptive parameters (weights and biases) in the network, which we can conveniently group together into a single W-dimensional weight vector w with components. In Chapter 4 it was shown that, for a multi-layer perceptron, the derivatives of an error function with respect to the network parameters can be obtained in a computationally efficient way using back-propagation. We shall see that the use of such gradient information is of central importance in finding algorithms for network training which are sufficiently fast to be of practical use for large-scale applications.
Pre-Processing And Feature Extraction
Authors: Bishop Christopher M
Published: November 2023

Since neural networks can perform essentially arbitrary non-linear functional mappings between sets of variables, a single neural network could, in principle, be used to map the raw input data directly onto the required final output values. In practice, for all but the simplest problems, such an approach will generally give poor results for a number of reasons which we shall discuss below. For most applications it is necessary first to transform the data into some new representation before training a neural network. To some extent, the general-purpose nature of a neural network mapping means that less emphasis has to be placed on careful optimization of this pre-processing than would be the case with simple linear techniques, for instance. Nevertheless, in many practical applications the choice of pre-processing will be one of the most significant factors in determining the performance of the final system.
Formal Bases for Dataflow Analysis of Logic Programs
Authors: Debray Saumya K
Published: November 2023

Compile-time dataflow analysis finds a variety of applications, such as compile-time optimization, program parallelization, testing, program transformation and specialization, and program verification. This chapter gives a broad overview of the field of dataflow analysis of logic programs. Starting with a general discussion of abstract interpretation, a formal framework that underlies much of the work on static program analysis, it discusses some of the wide variety of frameworks that have been proposed for the analysis of logic programs, considers the relationship between complexity and precision of analysis, and examines some specific analyses that have been proposed in the literature.
Modular Termination Proofs for Logic and Pure PROLOG Programs
Authors: Apt Krzysztof R , Pedreschi Dino
Published: November 2023

We provide a uniform and simplified presentation of the methods of Bezem (1993) (first published as (Bezem 1989)) and of Apt and Pedreschi (1993) (first published as (Apt and Pedreschi 1990)) for proving termination of logic and PROLOG programs. Then we show how these methods can be refined so that they can be used in a modular way.
Interior point methods
Authors: Roos Cornelis , Vial Jean-Philippe
Published: November 2023

The interest in interior point methods for linear programming emerged from Karmarkar’s contribution in 1984. This field has soon become one of the most active in the area of mathematical programming. It introduced new ideas and techniques that now have received their own place among the basic tools in optimization. In this chapter we intend to provide an introduction to the theory of interior point methods.
Diagrams and the Concept of Logical System
Authors: Barwise Jon , Hammer* Eric
Published: November 2023

This volume is devoted to an interesting and important question: what is a logical system? The question is interesting because a good answer could do much to systematize and unify a bewildering logical landscape; it is important because if an answer were widely accepted, it could help guide research in logic in the years to come. In attempting to answer this question, there are various approaches that could be taken. One would be to look at the things people have called logical systems and try to develop a natural framework which would encompass most or many of these, and then explore the consequences of the framework, seeing what else falls under the framework and what the consequences of the general notion happen to be. This was basically the approach taken, for example, in Barwise [1], one of the early attempts to develop such a framework.
Structure, Consequence Relation and Logic
Authors: Crocco G , Fariñas del Cerro L
Published: November 2023

Traditionally logic is defined using set theoretical concepts since historically, the main application of formal logic was mathematical concepts. Systems alternative to classical logic were proposed very early on. However, the new application of logic to computer science requires us to express concepts very different from those handled by the standard set operations.
General Logics and Logical Frameworks
Authors: Martí-Oliet Narciso , Meseguer José
Published: November 2023

This chapter summarizes a theory of general logics first introduced in [39], in which different aspects, or components, of a logic such as its entailment relation, its proof theory, and its model theory are axiomatized. For the model-theoretic component, the theory of institutions of Goguen and Burstall [24] is adopted. Combinations of several such aspects of a logic are also supported by the theory. Special importance is given to the notion of mapping between logics that preserves the logical structure of some aspect, such as the entailment relation, or the satisfaction relation for the models. Such maps play for logics a role analogous to that played by group homomorphisms for groups. The notion of a logical framework, understood as a logic :  ℱ in which many other logics can be represented, is then expressed in terms of appropriate representation maps ℒ →  ℱ. The particular logical framework provided by rewriting logic [40] is introduced and discussed, and some of its good properties for representing logics and for reflecting aspects of its own metatheory are explained.
The Emperor’s New Clothes: Some Recurring Problems in the Formal Analysis of Counterfactuals
Authors: Hansson Sven Ove
Published: November 2023

Three major formal approaches to counterfactual conditionals are analysed: the derivability approach (Chisholm, Goodman, Mackie), the worldselection approach (Stalnaker, Lewis), and the belief revision approach (Harper, Levi, Gardenfors). The three approaches are shown to be essentially interchangeable from the point of view of formal logic. Furthermore, they are shown to have three important limitations in common, namely non-deductiveness, circularity, and shift ability. It is argued that despite these limitations, logical analysis can contribute to philosophical understanding of counterfactual conditionals.
Early Analysis
Authors: Russ Steve
Published: November 2023

By the end of the eighteenth century the algebraic and infinitesimal methods that had been used to solve the geometry problems of the seventeenth century had proved so successful in a wide range of physical problems that, under the general heading ‘analysis’, they had become the dominant part of mathematics. The intuitive concepts of space, time, and motion, long associated with geometry and mechanics, were losing ground to the more formal manipulation of functions and equations by the methods of calculus. It was perhaps inevitable after the advent of analytic geometry that these developments should lead, during the eighteenth century, to analytical or ‘rational’ mechanics. In the Preface to his Méchanique analytique (1788) Lagrange wrote:
Vibrational studies of short- and intermediate-range order in glasses
Authors: Galeener Frank L
Published: November 2023

While the diffraction of X-rays, neutrons, or electrons gives definitive information about the structure of crystalline solids, such measurements give much less information about the structure of amorphous (a-) solids. This points to the need for many different experimental probes of structure, including EXAFS, NMR, vibrational spectroscopy, visible and electron microscopy.
John Napier, Baron of Merchiston
Authors: Coolidge Julian Lowell , Gray Jeremy
Published: November 2023

We must, I think, accept as a fact that most of the contributions to mathematics made by men whom I class as great amateurs may be beautiful or attractive or ingenious, but seldom indeed are they what we may call practically useful. Perhaps Leonardo’s studies of war machines, or better his work in hydraulics, perhaps Pietro’s studies of perspective or Durer’s invention of descriptive geometry, should not be condemned as unpractical, but the general statement remains true. But now we come to a glaring exception, in the work of the theologically contentious Scot whose name appears above.
Blaise Pascal
Authors: Coolidge Julian Lowell , Gray Jeremy
Published: November 2023

Every writer who deals extensively with the history of mathematics pays considerable attention to the famous theologian, philosopher, and master of French style whose name appears above. He was born in 1623, and died in 1662. His originality and ability were remarkable; had he confined his attention to mathematics he might have enriched the subject with many remarkable discoveries. But after his early youth he devoted most of his small measure of strength to theological questions, and his contributions to philosophical thought, and to fixing :French prose outweigh in importance what he has done for pure science.
Non-Euclidean geometry and revolutions in mathematics
Authors: Zheng Yuxin
Published: November 2023

Non-Euclidean geometry has occupied a very important position in the discussion about revolutions in mathematics, as the two opposite sides have both used it as a typical case for their views. In Section 9.1, I shall first briefly analyse the discussion so far, and then make my own position clear. In Section 9.2, I shall argue for the revolutionary nature of non-Euclidean geometry, and on this basis, a further analysis of revolutions in mathematics will be given. In Section 9.3, I shall discuss the significance of non-Euclidean geometry and its bearing on problems of the nature of mathematical truth and modes of thought. I shall then present a theory of types of mathematical truth and ‘the harmonious principle of the counter-way thinking’.
A restoration that failed: Paul Finsler’s theory of sets
Authors: Breger Herbert
Published: November 2023

If we are to talk of ‘restoration’, we must first clarify what we mean by ‘revolution’. I have to confess that I use the notion of a mathematical revolution only with a certain hesitation. There is an apparent and striking contrast between the high emotional value of this notion (just drop the word and you’ll provoke a fierce debate) and its lack of precision if applied to mathematics. Nevertheless, I believe that this notion could be given a meaning which is both interesting and applicable to mathematics. I have to confine myself to some tentative remarks, and further inquiry will be necessary anyway.
The Fregean revolution in Logic
Authors: Gillies Donald
Published: November 2023

In this chapter I argue that Frege’s work in logic initiated a revolution in the subject. Indeed, the phrase ‘the Fregean revolution in logic’ can be used in much the same sense as ‘the Copernican revolution in astronomy’, the point being that Copernicus began the revolution, but did not complete it The Copernican revolution begins with the publication of Copernicus’s De revolutionibus in 1543. This work initiated a series of fundamental changes in the subject, but the revolutionary period did not really end until the publication of the Principia in 1687 and the establishment of the Newtonian synthesis. In an exactly parallel fashion, the Fregean revolution begins with the publication in 1879 of the Begriffsschrift. Opinions may differ as lo when the revolutionary period in logic ended, but I would see the publication of Gödel’s incompleteness theorems in 1931 as forming a natural terminus. Jean van Heijenoort, in editing his justly famous collection From Frege to Giidel. A source book in mathematical logic, 1879-1931, recognized that we have here a natural period in the history of logic. This he describes, not indeed as a revolution, but as ‘a great epoch in the history of logic’ (Heijenoort 1967, p. vi).
Simultaneous static and dynamic light scattering: application to polymer structure analysis
Authors: Schmidt Manfred
Published: November 2023

Light scattering is one of the most widely applied methods for the determination of molecular weights. Moreover, the light scattered by a polymer solution contains information about the static and the dynamic properties of the molecules, all of which are important for polymer characterization. In the elastic or static scattering experiment the excess scattering intensity of the solution compared with that of the pure solvent is measured. Here we assume that the scattered light exhibits the same wavelength as the primary light source and accordingly, only static or time-averaged quantities are measured. In reality the scattering particles move randomly in solution, owing to Brownian motion. Since they can be regarded as local transmitters, the scattered light exhibits a Doppler shift, the magnitude of which depends on the velocity and on the direction of motion of the individual particle. A typical scattering volume contains many of these particles, moving with different velocities in different directions. Consequently the observed pectrum of the scattered light is symmetrically broadened. This spectrum S(ω) is principally measured by inelastic or dynamic light scattering, which leads to the dynamical properties of the molecules in solution, such as the translational diffusion coefficient.
A World Made
Authors: Macintosh Wilson Alistair
Published: November 2023

The first great mathematician to arise on the shores of the Aegean was Pythagoras (frontispiece), son of Mnesarchus, born in the modern Pythagoreion on the island of Samos probably around 580 BC. Pythagoras was first the pupil of Pherecydes of Syros, who introduced the idea of reincarnation into Greece, probably from India. It was believed by his followers, that Pythagoras could remember some of his more recent previous lives, and the wisdom attained in them. Pythagoras next studied under Thales at Miletus, who encouraged him to go to Thebes, where he could be initiated into the Mysteries by the priests of Amon-Re. According to legend, Pythagoras spent twenty-two years in Egypt completely penetrating the Mysteries, and a further ten years in Babylon studying the arithmetic and geometry of the Babylonians.
The philosopher’s
Authors: Macintosh Wilson Alistair
Published: November 2023

In Chapter 2, we described how the ancient Egyptians were forced to resurvey their fields every year by the annual flooding of the Nile. We recall that the Pharaoh’s engineers carried out this process by breaking the fields into triangular plots. The study of triangles was therefore called by the Greeks ‘geometrid’ from their words geos (Earth, land) and metres (measure). The facts of geometry were, as described earlier, first obtained by measurement. We measure that the angles of a triangle add up roughly to 180°, that the area of a triangle is equal to half its base times its height, and so on. Measurement depends finally upon the eye. But the eye can be deceived.
The Elements Of Euclid
Authors: Macintosh Wilson Alistair
Published: November 2023

The person who, more than any other, helped to bring shape and form out of the confusion of the geometrical ‘proofs’ existing at his time, was Eucleides of Alexandria (c.330-c.275 BC). In his great work the Elements (of geometry), Euclid drew together the derivations of the Pythagoreans and many others into a unified whole. The Elements provided a model for all succeeding mathematical works. It represents the beginning of modern mathematics.
An Island Interlude
Authors: Macintosh Wilson Alistair
Published: November 2023

Of all the islands of the Cyclades, Opalos is the most remote and the most beautiful. This is the land of the peaceful King Thallos. Do not think to find it on the map, stranger, for it is far too small to be shown. But the friendly dolphins know their way there, down the highways of the fishes. The island is mountainous and well wooded, but near its centre lie flat and verdant pastures. Here graze the abundant herds of fat cattle that are the pride of the Opalans, and the basis of their fame.
The German mathematical community
Authors: Schuering Gert
Published: November 2023

In the nineteenth century, German mathematics reached its peak. During this period, under German influence, mathematics (and especially pure mathematics) became a modern scientific discipline. German mathematicians took over from the French as the international leaders. They carried forward the programme of rigorization which had emerged in France after the revolution. Between 1800 and 1820 there was only one really important mathematician in Germany—Carl Friedrich Gauss—and young mathematicians used to go to Paris for more advanced studies. But only ten years later, the situation had changed drastically. You can get an impression of this change from the list of important contemporary mathematicians which Georg Simon Ohm drew up in 1838.
Ordered fields
Authors: Garth Dales H , Hugh Woodin W
Published: November 2023

In the previous chapter, we gave a certain development for ordered sets and ordered groups. In this chapter, we shall add another layer of structure, and we shall discuss ordered fields. In many ways, our development will follow the earlier story, but naturally at a few points we shall have to work a little harder to take into account all the structures that must be preserved in our embedding and isomorphism theorems.
Completions of ordered groups and fields
Authors: Garth Dales H , Hugh Woodin W
Published: November 2023

There is an extensive, and rather technical, theory of various types of completions of ordered groups and fields. (In the literature, the groups are not necessarily either totally ordered or abelian.) We sketch here the aspects of the theory that we shall be concerned with, defining what we shall call the Cauchy completion of an ordered group, to be constructed by using ‘Cauchy pregaps’.
Normability and universality
Authors: Garth Dales H , Hugh Woodin W
Published: November 2023

One of our motives for beginning our investigations of super-real fields was a certain normability question. Let us explain this question.
Biogeography of the Panamanian region, from an insect perspective
Authors: Kimsey Lynn Siri
Published: November 2023

Tracing the biogeography of organisms in a specific region is a complex and difficult exercise. However, it can provide considerable insight into the evolutionary events that shaped the taxa involved. There are many problems inherent in the study of historical aspects of distributions and biotic associations. Principal among these are insufficient or inaccurate data about phylogenetic relationships among taxa, and a serious lack of accurate distribution records. It is not unusual for generic, subfamily, or family geographic limits to be underestimated by hundreds or even thousands of miles in tropical groups, due to incomplete collecting. Another difficulty arises when relating palaeogeography to present distributions. Determining the continental areas that remained above water is very important to the biologist, but geologists are much more concerned with locating true continental margins. As a result, continental areas that were not submerged are rarely indicated in palaeo geographic maps, and this information is often difficult to find summarized in any form (Coney 1982; Owen 1983; but see Barron 1987).
Guide to the Springtails of Panama and Costa Rica (Collembola)
Authors: Palacios-vargas Jose G
Published: November 2023

Springtails are small arthropods, traditionally considered to be members of the class Insecta and the subclass Apterygota. Many authors now believe that they are better placed either with the class Entognatha, together with the orders Diplura and Protura (see diagram of the Hexapoda, p. xii), or as a separate class, Collembola. Springtails are most commonly found in such humid habitats as moist ground, forest litter, moss and bark of trees, nests of social insects, and nests of some birds and mammals. They exist in great diversity in caves and caverns, where their populations can become very large (Palacios-Vargas 1983a; Hoffmann et al. 1986; Christiansen and Reddell 1986). Generally, species that live in arid areas (Palacios-Vargas 1988) are covered by scales or bristles that protect them from desiccation. Springtails are common on epiphytes (Palacios-Vargas 1981), and in freshwater and marine littoral regions (Christiansen and Bellinger 1988), and are among the surface inhabitants of freshwater bodies (epineuston, see Rapoport and Sanchez 1963; Palacios-Vargas and Vazquez 1988). They can be found from sea-level to more than 7000 m, under permanent ice.
Dry season strategies of two Panamanian butterfly species, Anartia fatima (Nymphalinae) and Pierella luna luna (Satyrinae) (Lepidoptera: Nymphalidae)
Authors: Aiello Annette
Published: November 2023

Tropical Lepidoptera of seasonally dry forest are faced with the challenge of surviving a dry period each year, when larval food plants may die back, and adult food sources and water may be in short supply. These Lepidoptera must rely on various physiological and/or behavioural strategies to persist until the onset of the wet season. In Panama, a number of species, of several families (e.g. Megalopygidae, Limacodidae, Hesperiidae, Noctuidae), prepare a pupal cocoon in which they may diapause as final instar larvae (personal observation) and then pupate the following wet season. Others, such as certain giant silk moths (Saturniidae: Hemileucinae), may pass the dry season as pupae and emerge as adults during the initial rains of a future wet season (Janzen 1982). Certain butterflies, such.as Celaenorrhinus fritzgaertneri (Hesperiidae) (DeVries 1987) and Eurema daira (Pieridae) (Opler, in DeVries 198 7), pass the dry season as adults in reproductive diapause. In Australia, E. herla and E. laeta also enter reproductive diapause, while three other Eurema species breed continuously, expanding and contracting their geographical distributions as larval food plant availability fluctuates (Jones and Rienks 1987). The present paper examines the dry season strategies of two Panamanian nymphalid butterflies, one of which passes the dry season in pupal diapause and the other of which persists in humid areas (dry season refugia), until the onset of the rains makes range re-expansion possible once more. The two nymphalid butterflies, Anartia fatima (Fab., 1793) (Nym phalinae) (Fig. 3 7.1, top) of disturbed areas, and Pierella luna luna (Fab., 1793) (Satyrinae) (Fig. 37.1, bottom), a forest floor inhabitant, are both common on Barro Colorado Island (BCI), Panama. Each is discussed separately, including methods and results, followed by a brief, general discussion, including comments on fluctuations of lepidopteran parasitoids.
Pantophthalmidae of Central America and Panama (Diptera)
Authors: Val Francisca C
Published: November 2023

The Pantophthalmidae is a small family of Diptera found exclusively in Neotropical forests. These flies are relatively rare in collections; and very scanty materials have been added since the revision by Val (1976). The 20 species, accepted as valid, are placed in two genera: Opetiops, with one species, known only from South America, and Pantophthalmus, with 19 species (Val 1976), ranging from Mexico to Argentina. Eleven species of Pantophthalmus are known to occur in Central America. Very little is known about the biology of the Pantophthalmidae. Even for the best studied species P. pictus (Andrade 1930) and P. tabaninus (Greene and Urich 1931; Bartholomew and Lighton 1986) there is no agreement about the feeding habits of the imago and larvae. The larvae live in galleries in trunks of dead or living trees. Andrade (1930) believed that the larvae were xylophagous while Thorpe (1934) had the opinion that they fed on fermenting sap. Greene and Urich (1931) believed that adults do not feed, while Thorpe (1934) argued that because the adults have mouthparts and a well-developed digestive system, they probably do feed. First instar larvae of P. tabaninus use orifices that are already present in trunks of trees and excavate their galleries using these orifices as the starting point, while in P. pictus the larvae begin excavation of their galleries in the absence of existing openings in the trunks. The larvae dig horizontal galleries in the trunks of various types of trees. P. pictus is found in live trees (Fieberg 1906; Andrade 1930), and P. tabaninus in decaying or fallen trees, but never in healthy ones (Greene and Urich 1931).
An analysis of interactive webs of a scale-insect community, their host plants, and natural enemies
Authors: Itioka Takao
Published: November 2023

Competition and predation have both been considered as important factors in determining the community structure of animals, but their relative importance is controversial (Connell 1983; Schoener 1983; Sih et al. 1985). In herbivorous insects, predation has been generally considered more important than competition (Hairston et al. 1960; Lawton and Strong 1981; Connell 1983; Schoener 1983; Lawton and Hassell 1984; Strong et al. 1984; Sih et al. 1985). However, there are a few exceptions (reviewed in Schoener 1983; Strong et al. 1984), and the relative importance of these factors differs depending on environmental conditions, trophic positions, and taxa (Connell 1983; Schoener 1983; Colwell 1984; Sih et al. 1985). Furthermore, it has been suggested that the direct influence of host plants on herbivorous insects (Crawley 1983; Denno and McClure 1983; Coley et al. 1985; Rhoades 1985; Mattson et al. 1988; Schultz 1988) and indirect influences through natural enemies (Price et al. 1980) may also be strong factors, and that within-plant heterogeneity can affect the survival and reproduction of herbivorous insects (Crawley 1983; Schultz 1983; Whitham et al. 1984).
From rocks to theories: techniques of preparation and methods of analysis
Authors: Janvier Philippe
Published: November 2023

The series of reconstructions reviewed in Chapter 1 is the result of a long process of study that begins with the discovery of a fossil and may end with the elucidation of its relationships with extant animals. Additional information, on how, where, and when an animal lived may be obtained from its anatomy or from the rock in which it is preserved. Other fossils, associated with it, or the nature of the sediment can provide such information. Conversely, the fossils can generate theories about the rocks, that is, hypotheses on the age of the beds or the palaeogeography. The purpose of this chapter is to illustrate this process of discovery as applied to early vertebrates. The methods and techniques are generally the same as for younger fossil vertebrate groups or even for any fossil, but some are particular to material of this type.
Interrelationships of the major craniate taxa: current phylogenetic theories and controversies
Authors: Janvier Philippe
Published: November 2023

The major taxa described in the preceding chapter are all supposed to be clades, with perhaps one exception, the thelodonts, which are regarded by some palaeontologists as an ensemble of generalized craniates or vertebrates. However, the relationships between these taxa remain the subject of sometimes heated discussion, even if such higher clades as the gnathostomes or osteichthyans are now relatively well corroborated.
Petrology of the Solomon Islands Younger Volcanic Suite
Authors: Stanton R L
Published: November 2023

Before proceeding to examine the behaviour of the ore elements - the principal ore-forming cations - in the spectrum of Solomon Islands younger lavas, it is necessary to consider briefly the more important petrological and petrochemical features and the geographical distribution of the rock types involved.
Copper
Authors: Stanton R L
Published: November 2023

With iron, copper is ubiquitous among the sulphides of volcanic-associated exhalative ores. It is also by far the dominant non-ferrous sulphide element of the subvolcanic porphyry copper deposits, and of the feeder vein systems that underlie many exhalative deposits. The overwhelmingly dominant mineral is chalcopyrite (CuFeS2), but this may be associated with small quantities of bomite (Cu5FeS4) in porphyry and Cyprus-type ores, and occasionally by traces of cubanite (CuFe2S3) and valeriite (Cu3Fe4S7). Any covellite (CuS) or chalcocite (Cu2S) in these ores is usually secondary. As noted in Chapter 2, copper - chiefly as chalcopyrite - may dominate exhalative deposits ranging from those of basalt to rhyolite and bimodal associations. It is characteristically the principal non-ferrous metal of basalt-associated Cyprustype ores; in deposits of andesitic to rhyolitic association it is mostly commonly overshadowed by zinc and then lead.
Strontium
Authors: Stanton R L
Published: November 2023

Although strontium occurs between its two closely related alkaline-earth elements calcium and barium in Group Ila of the Periodic Table, and although calcium compounds are common and sometimes abundant components of exhalative ores, strontium is conspicuous by its absence — at least in anything other than trace quantities - in deposits of this kind.
Titanium
Authors: Stanton R L
Published: November 2023

Strontium has been considered among the present group of elements (Chapter 10) because, in spite of its close chemical similarity to barium (a commonly abundant component of exhalative ores) and its substantially greater incidence than barium as a trace element in volcanic rocks, it is virtually absent from exhalative ore deposits. Barium (and calcium) are abundant components of many orebodies of the volcanic regime. It seemed, therefore, that the conspicuous absence of the closely related alkaline-earth element strontium might well provide a clue to the identity of some important fractionating process - and hence an indication of mechanisms of derivation and transport of the materials of ores overall.
Chromium
Authors: Stanton R L
Published: November 2023

Like titanium and vanadium, its close neighbours in series 4 of the periodic table of the elements, chromium is essentially absent from exhalative ores and their associated chemical sediments of the volcanic regime. Although chromium has long been recognized as a significant component of the troilite phase of iron meteorites, it has not been found as other than minute traces in the iron sulphides of volcanogenic orebodies. Further eloquent evidence for its essential absence from exhalative ores lies in its extremely low incidence in what are well-recognized chromium acceptors among associated oxides and silicates. Thus, in spite of its propensity for entering the spinel structure (see chromite and related spinels), chromium is not found in the magnetite of accompanying iron oxide-rich exhalites and their weathering products.
Manganese
Authors: Stanton R L
Published: November 2023

Manganese is a commonly prominent, but erratically occurring, component of exhalative ores. It may appear (usually as complex mixed oxides, but also as silicate and carbonate and as a component of some sulphides) as the dominating element of exhalative sediments, and a number of important manganese ore deposits are of this nature. It also occurs, as a constituent of iron manganeserich exhalites, as an associate of, but separate from, some base metal sulphide ores; and in other instances constitutes an important component of the sulphide orebody itself.
Iron
Authors: Stanton R L
Published: November 2023

From the quantitative point of view iron is by far the most important exhalative sulphide metal. Many exhalative deposits contain little sulphide other than that of iron: as pyrite, pyrrhotite, or both. Most Cyprus-type deposits are dominated by pyrite, with chalcopyrite and sphalerite appearing as no more than subordinate components. The Archaean deposits of Canada, the felsic-associated exhalative deposits of the Appalachians, the Caledonides, the Urals, and the Eastern Highlands of Australia, and many others, contain pyrite and/or pyrrhotite as their principal sulphide. In some cases, such as Mt Isa in Queensland, deposits may be most accurately described as large sulphide iron formations containing sufficient ‘impurities’ of chalcopyrite, sphalerite, and galena to constitute base-metal orebodies.
Cobalt
Authors: Stanton R L
Published: November 2023

Cobalt is virtually ubiquitous as a trace to very minor constituent of exhalative sulphide ores, but rarely if ever appears as a major component. Its average level of abundance in such deposits is difficult to estimate but is probably no more than about 0.05 per cent. The cobalt may occur as a major element of sulpharsenides and related minerals, which themselves occur in very small amount, or as a trace to minor element of the more common and abundant sulphides such as pyrite, pyrrhotite, and chalcopyrite.
Petrogenesis: 1: The lavas
Authors: Stanton R L
Published: November 2023

In this chapter we consider the derivation and mode of development of the spectrum of lava types that constitute the Solomon Islands Younger Volcanic Suite. By implication this may also cast a little light on the genesis of lavas of other island arcs, particularly those of dominantly intra-oceanic affiliation. The writer is, however, well aware of the enormous effort - field, petrographic, geochemical, and experimental - already devoted to the problem of island-arc lava generation by .a long line of distinguished investigators, and is more than conscious that any contribution this chapter may make is likely to be modest - and even more likely to be judged simpleminded. Apart, however, from several minor forays by the author (Stanton 1967, 1978; Stanton and Ramsay 1980), there seems to have been no comprehensive attempt to use the geochemical behaviour of the ore elements to elucidate mechanisms of lava evolution, and this chapter is offered as an initial contribution. In doing this we consider first whether the three principal lava groups are in fact a single consanguineous series, then (very briefly) their likely derivation, and finally the ways in which the variety of lava compositions may have been induced.