bluuebunny/crossref_metadata_2025 huggingface dataset:
An absolute wonder
Authors: Baggott Jim
Published: November 2023

Bohr’s theory of the atom did a fine job of explaining the absorption and em1ss10n spectra of one-electron atoms in terms of the quantum rules. Schrodinger’s wave mechanics did better in the sense that the rules of quantization were given a firm mathematical basis. However, problems still abounded. Experimental spectra revealed quite a number of problems for which wave mechanics (and matrix mechanics) appeared to have no solutions. In particular, some atomic emission lines predicted by the theory were seen to be split in the presence of a magnetic field into several quite distinct lines (a phenomenon known as the Zeeman effect). Neither wave mechanics nor matrix mechanics could explain this phenomenon without some further, largely ad hoc, assumptions. Worse still, when the spectra of atoms with two or more electrons were studied, certain predicted lines were found to be missing.
The schism
Authors: Baggott Jim
Published: November 2023

The strange behaviour of photons described in the last chapter immediately raises all sorts of difficult questions about the meaning of quantum theory. We might be encouraged to look for this meaning by going back to the theory’s mathematical formalism, perhaps by trying to find out how we might better interpret some of its elements. However, it is a central argument of this book that, no matter where we look, we are always led back to philosophy. At first sight, this might seem to be an odd thing to claim. After all, modem textbooks on quantum physics and chemistry rarely (if ever) discuss philosophy. We accept that the behaviour of photons is strange, but surely it is something that we can at least study experimentally—do we need philosophy in these circumstances? The answer is most certainly yes. Quantum theory directly challenges our understanding of the nature of matter and radiation, and the process of measurement at their most elementary levels, and we cannot go forward unless we adopt some kind of interpretation, some way of trying to make sense of it all. As we will see, this interpretation has to be based on some philosophical position.
A bolt from the blue
Authors: Baggott Jim
Published: November 2023

The confrontation between Einstein and Bohr over the interpretation of quantum theory has been painted in the past as a direct conflict between realism and positivism. However, more recent attempts to uncover the philosophical positions of both Einstein and Bohr have revealed that these were not so black and white. Einstein’s realism was conditioned by the strong empiricist influence in his own early experiences as a theorist and the growing wariness that led him eventually to reject Machian positivism. His was a realism born of a sense of necessity: a belief that a realist stance is the only one that leads to productive theorizing about the physical world. Bohr’s philosophy went through some quite marked changes, principally in response to Einstein’s challenges. The father of modem atomic theory could hardly subscribe to an uncompromising positivist position that rejected the reality of atoms. But the reality of the inner workings of those atoms was, Bohr contended, beyond the reach of a knowledge founded on complementary classical concepts of waves and particles. As Einstein’s challenges became deeper and more subtle, so Bohr’s position shifted to that of a distinctive anti-realism. Add to this a rhetoric in Bohr’s speeches and published writings that insisted on the logical inevitability of the Copenhagen interpretation, that insisted on its status as the only feasible interpretation, and that countenanced no other alternative, and you have dogma in the making. Heisenberg called it ‘Kopen hagener Geist der Quantentheorie’, the Copenhagen spirit of quantum theory which, he declared in 1930, ‘has directed the entire development of modem atomic physics’. Einstein frequently referred to the Copenhagen doctrine as ‘Talmudic’.
Pilot waves, potentials, and propensities
Authors: Baggott Jim
Published: November 2023

So, where do we go from here? It is apparent from the last two chapters that nature denies us the easy way out. The clear experimental demonstration of quantum entanglement rules out the idea of local hidden variables, one of the simpler solutions to the conceptual problems of quantum theory. For the time being at least, we are forced to live with the consequences of entanglement, non-locality, and ‘spooky’ action at a distance. This might make some of us uncomfortable, but there is no solace in the Copenhagen interpretation, which does not provide us with any answers and is still regarded by many to be no interpretation at all. And, lest we forget, there remain the problems of interpreting the meaning of quantum probability and the collapse of the wave function. Even those who adhere to the Copenhagen view tend to put aside or disregard the conceptual difficulties that these issues raise as they analyse the results from the latest particle-accelerator experiment. This is not a very satisfactory situation.
An irreversible act
Authors: Baggott Jim
Published: November 2023

If we are not persuaded of the approach to recovering causality in quantum physics through the de Broglie-Bohm theory (perhaps because, like Einstein, we think this route ‘too cheap’) or Popper’s reinterpretation of the meaning of probability, we must seek alternative solutions to the problems of quantum probability and the collapse of the wave function. Even if we choose to accept what quantum probability tells us concerning the fundamental indeterminism and acausality of the quantum world, we are still left to trouble over quantum measurement.
Many worlds, one universe
Authors: Baggott Jim
Published: November 2023

The concept of the collapse of the wave function was introduced into quantum theory by John von Neumann in the early 1930s and has since become an integral part of the theory’s orthodox interpretation. But if we were to ask ourselves what evidence we have that this collapse is a real physical phenomenon, we would have to admit that we have none. The notion of a collapse is necessary to explain how a quantum system initially present in a linear superposition state before the process of measurement is converted into a quantum system present in one, and only one, of the measurement eigenstates after the process has occurred. It was introduced into the theory because it is our experience that pointers point in only one direction at a time.
Introduction
Authors: Hodgkin Luke
Published: November 2023

M. de Montmort was working for some time on the History of Geometry. Every Science, every Art, should have its own. It gives great pleasure, which is also instructive, to see the path which the human spirit has taken, and (to speak geometrically) this kind of progression, whose intervals are at first extremely long, and afterwards naturally proceed by becoming always shorter.
Greeks, practical and theoretical
Authors: Hodgkin Luke
Published: November 2023

But, unlike Euclid, who attempts to prove musical propositions through mathematical theorems, Nicomachus seeks to show their validity by measurement of the lengths of strings. (Entry ‘Nicomachus of Gerasa’ in Dictionary of Scientic Biography) The leading Greek geometricians were all master carpenters. Euclid, the author of the Book of Principles, was a carpenter and known as such. The same was the case with Apollonius, the author of the book on Conic Sections, and Menelaus and others.
Planning the plantation enterprise
Authors: Evans Julian , Turnbull John W
Published: November 2023

Most of the previous two chapters, indeed most of this book, impinges on the subject of planning. Forest planning identifies activities and their timing to achieve the goals of forest management. It is at the foundation of any project, industrial, environmental, or social (rural development) forestry because it is all those processes and steps, which involve data collection, analysis, projections of supply and demand, estimates of equipment, manpower and training needs, and so on. Planning is primarily the responsibility of managers. It introduces order into any development to avoid haphazard and ill-conceived (unplanned) activities. Put simply, planning is the thinking behind the doing of a project to help it succeed.
Nutrition of tree crops
Authors: Evans Julian , Turnbull John W
Published: November 2023

Trees, like all plants, require supplies of certain chemical elements for growth. Elements needed in large quantities, called ‘macronutrients’, are nitrogen (N), phosphorus (P), potassium (K), calcium (Ca), magnesium (Mg), and sulfur (S). Elements needed in minute or trace amounts, ‘micronutrients’, are iron (Fe), copper (Cu), chlorine (Cl), manganese (Mn), boron (B), zinc (Zn), and molybdenum (Mo). Of course, in addition to these elements, which are mostly supplied from the soil, plants require carbon (C), hydrogen (H), and oxygen (O), the primary constituents of all organic matter, which are obtained from water and air. Atmospheric sources of nutrients in precipitation in general represent a tiny fraction of the requirements for growth.
Thinning
Authors: Evans Julian , Turnbull John W
Published: November 2023

Thinning is the operation that artificially reduces the number of trees growing in a stand. It is normally carried out several times and starts a few years after canopy closure. For example, in Kenya Pinus patulaplantations grown for saw logs are thinned three times during a 30-year rotation and the number of trees per hectare reduced from 1110 to 250 (Anon. 1996). In Nilambur, Kerala state, India, teak plantations are thinned six times during a 50–55-year rotation, which reduces the number of trees from 2500 ha-1 to 100–150 (Chundamannii 1998).
Protection—an introduction
Authors: Evans Julian , Turnbull John W
Published: November 2023

A planted forest of any kind: commercial, amenity, or village woodlot, is a considerable investment and an accumulating asset of raw material. Its protection is an essential part of silviculture. The nature of a plantation, its uniformity in age, species, and genetic make-up, together with the environmental conditions of the site it occupies, renders it more susceptible to some forms of damage, notably fire and climatic hazards. Whether this also applies to diseases and pests is considered in Chapter 24. Successful plantation forestry is only possible provided there is adequate protection. Managers accept there are risks associated with plantations but are becoming increasingly risk adverse.
Tree planting for ecosystem rehabilitation and restoration
Authors: Evans Julian , Turnbull John W
Published: November 2023

Globally, natural forest has been exploited, cleared, and has gradually declined in extent (Chapter 2). In some countries the area of forests has been decreasing for centuries, in others it is a recent occurrence. The rate of resource depletion has increased sharply in recent years in most tropical countries. Deforestation and/or forest degradation has resulted in losses of forest productivity in terms wood and non-wood products and environmental services. Biodiversity has been greatly reduced, especially in the species-rich tropical rain forests, and few forests can recover unaided. While some deforestation may be justified, the global community is concerned about the environmental consequences.
Extensions to the basic coalescent
Authors: Hein Jotun , Schierup Mikkel H , Wiuf Carsten
Published: November 2023

The basic coalescent process is based on the Wright–Fisher model of reproduction, assuming constant population size, random mating, and absence of selection. These are very strict conditions, which are rarely, if ever, met in nature. Fortunately, the coalescent framework can easily be extended to include simple deviations from these basic assumptions, resulting in a process that is believed to model the true mating pattern more closely. In what follows, we consider in turn how to deal with the following scenarios: fluctuating population size, population structure, and different kinds of selection. It should be stressed that it is relatively easy to combine these extensions in a single model if necessary.

The focus here is to provide means to simulate the distribution of the genealogy of a sample of genes and the distribution of the sample configuration. Further, it is our interest to point out some major differences between genealogies generated under the basic coalescent and under the scenarios discussed here. In Chapter 2 we learned how a sample configuration under neutrality can be generated in two steps: First simulate the genealogy, then add mutations to the genealogy. In the scenarios involving selection the genealogy and the sample configuration. can be simulated at the selected site. Subsequently, neutral (intra-allelic) mutations can be added to the genealogy in a second step, cto the procedure just mentioned above.
The coalescent with recombination
Authors: Hein Jotun , Schierup Mikkel H , Wiuf Carsten
Published: November 2023

Genetic recombination occurs in most organisms on earth, including euca- ryotes, bacteria, and viruses. Recombination occurs by quite different mechanisms in these three different types of organisms. In eucaryotes recom- bination is usually associated with sexual reproduction. Thus, it is generally believed that sexual reproduction exists because it facilitates genetic recom- bination. No generally accepted theory is available to explain why genetic recombination is so common, but in its favour are arguments that genetic recombination ensures that favourable variants are brought together in the same sequence (or, equivalently, that sequences are created which do not harbour any deleterious variants), and that recombination can maintain more variation which may enable survival over an evolutionary time scale.

The simple coalescence process, including the various extensions in the previous chapter assumes no recombination and this body of theory can therefore strictly speaking only be used on non-recombining sequences. In animals, only Y-chromosomes and perhaps mitochondrion satisfies this constraint, and it is therefore pertinent for practical analysis that recom- bination can be build into the process. Fortunately, this is possible as shown by Hudson in 1983 very shortly after the coalescent process was first formulated. However, recombination adds much more complexity than any of the extensions discussed in Chapter 4, mainly because no single ‘coalescent tree ‘ can describe a sample of recombining sequences. A graph is required to describe the ancestral process which complicates the math- ematical description considerably. However, the presence of recombination makes some estimators of evolutionary parameters more accurate than when applied on non-recombining sequences (see Chapter 6).
Getting parameters from data
Authors: Hein Jotun , Schierup Mikkel H , Wiuf Carsten
Published: November 2023

One strength of the coalescent approach is that it is data-oriented with emphasis on the sample of sequences that the investigator has collected. It aims at describing the processes that generated the data, retrospectively describing the sample in terms of possible previous events. In contrast, pre- coalescent population genetics is typically prospective: given the present what is the likely outcome of evolution? In the previous chapters we have shown how it is possible to simulate and predict quantities under the coalescent. In particular we have seen that it is possible to simulate data sets under various conditions and with different parameters, and that it is possible to calculate the probability of a data set for a fixed set of parameter values. This situation is depicted in Figure 6.1. The evolutionary parameters (collectively referred to as ψ ) can generate a variety of data where a given data set is just a single point in the possible space of data sets for a given ψ
Theory of Neural Information Processing Systems
Authors: Coolen A C C , Kühn R , Sollich P
Published: November 2023

Theory of Neural Information Processing Systems provides an explicit, coherent, and up-to-date account of the modern theory of neural information processing systems. It has been carefully developed for graduate students from any quantitative dsicipline, including mathematics, computer science, physics, engineering or biology, and has been thoroughly class-tested by the authors over a period of some 8 years. Exercises are presented throughout the text and notes on historical background and further reading guide the student into the literature. All mathematical details are included and appendices provide further background material, including probability theory, linear algebra and stochastic processes, making this textbook accessible to a wide audience.
Support vector machines for binary classification
Authors: Coolen A C C , Kühn R , Sollich P
Published: November 2023

Support vector machines (SVMs) carry out binary classifications. They involve a preprocessing stage which aims to transform data sets that are not linearly separable into ones that are. First, however, we will have to return to the properties of linearly separable problems, for reasons which will become clear. The preprocessing will be introduced afterwards.
Building blocks of Shannon’s information theory
Authors: Coolen A C C , Kühn R , Sollich P
Published: November 2023

In this chapter, we explore properties of entropy and of related measures of information theory, which will be useful for later applications of the framework. The chapter has the character of a compilation of key results (and proofs); it may thus also be taken as a reference.
Notes and suggestions for further reading
Authors: Coolen A C C , Kühn R , Sollich P
Published: November 2023

In carrying out dynamical studies such as those in the previous three chapters one always relies on general background knowledge of stochastic processes (at the microscopic level of description), and of non-linear dynamical systems (at the level of deterministic macroscopic observables); recommended general textbooks on these topics are the ones by van Kampen [79] and by Khalil [81], respectively.
Basics of equilibrium statistical mechanics
Authors: Coolen A C C , Kühn R , Sollich P
Published: November 2023

Rather than explaining the ideas and methods of equilibrium statistical mechanics in an abstract setting, we illustrate them directly in the context of neural network models. In Section 16.1 we defined our basic model for the operation of recurrent networks with binary units.
The discovery of long-term potentiation
Authors: Lomo Terje
Published: November 2023

This paper describes circumstances around the discovery of long-term potentiation (LTP). In 1966, I had just begun independent work for the degree of Dr medicinae (PhD) in Per Andersen’s laboratory in Oslo after an eighteen-month apprenticeship with him. Studying the effects of activating the perforant path to dentate granule cells in the hippocampus of anaesthetized rabbits, I observed that brief trains of stimuli resulted in increased efficiency of transmission at the perforant path-granule cell synapses that could last for hours. In 1968, Tim Bliss came to Per Andersen’s laboratory to learn about the hippocampus and field potential recording for studies of possible memory mechanisms. The two of us then followed up my preliminary results from 1966 and did the experiments that resulted in a paper that is now properly considered to be the basic reference for the discovery of LTP.
Kainate receptors and the induction of mossy fibre long-term potentiation
Authors: Bartolotto Zuner A , Lauri Sari , Isaac John T R , Collingridge Graham L
Published: November 2023

There is intense interest in understanding the molecular mechanisms involved in long-term potentiation (LTP) in the hippocampus. Significant progress in our understanding of LTP has followed from studies of glutamate receptors, of which there are four main subtypes (a:-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA), N-methyl-D-aspartate (NMDA), mGlu and kainate). This article summarizes the evidence that the kainate sub-type of glutamate receptor is an important trigger for the induction of LTP at mossy fibre synapses in the CA3 region of the hippocampus. The pharmacology of the first selective kainate receptor antagonists, in particular the GLUKs subunit selective antagonist LY382884, is described.
Silent synapses: what are they telling us about long-term potentiation?
Authors: Kullmann Dimitri M
Published: November 2023

At several cortical synapses glutamate release events can be mediated exclusively by NMDA receptors, with no detectable contribution from AMPA receptors. This observation was originally made by comparing the trial-to-trial variability of the two components of synaptic signals evoked in hippocampal neurons, and was subsequently confirmed by recording apparently pure NMDA receptor-mediated EPSCs with stimulation of small numbers of axons. It has come to be known as the ’silent synapse’ phenomenon, and is widely assumed to be caused by the absence of functional AMPA receptors, which can, however, be recruited into the postsynapic density by long-term potentiation (LTP) induction.
Structural changes at dendritic spine synapses during long-term potentiation
Authors: Harris Kristen M , Fiala John C , Ostroff Linnaea
Published: November 2023

Two key hypotheses about the structural basis of long-term potentiation (LTP) are evaluated in light of new findings from immature rat hippocampal slices. First, it is shown why dendritic spines do not split during LTP. Instead a small number of spine-like dendritic protrusions may emerge to enhance connectivity with potentiated axons. These ’same dendrite multiple synapse boutons’ provide less than a 3% increase in connectivity and do not account for all of LTP or memory, as they do not accumulate during maturation. Second, polyribosomes in dendritic spines served to identify which of the existing synapses enlarged to sustain more than a 30% increase in synaptic strength.
Introduction
Authors: Etingof Pavel , Latour Frédéric
Published: November 2023

The quantum dynamical Yang–Baxter equation (QDYBE) was first considered by physicists Gervais and Neveu, and later studied systematically by Felder. It is an equation with respect to a (meromorphic) function R : 𝔥* → End𝔥 (V ⊗ V ), where h is a commutative finite dimensional Lie algebra over C, and V is a semisimple 𝔥-module.
Intertwiners, Fusion and Exchange Operators for 𝔘q(𝔤)
Authors: Etingof Pavel , Latour Frédéric
Published: November 2023

In this section, we will let q be a nonzero complex number which is not a root of unity. We could also let q = eℏ/2, where n is a formal parameter. Let 𝔤 be a semisimple Lie algebra. We can define intertwining operators and the fusion operator for 𝔘 q (𝔤) in the same way as we did for g. The fusion operator JWV (λ) : W ⊗ V → W ⊗ V will then satisfy the following.
The literature of the astrolabe to 1450
Authors: Lorch Richard
Published: November 2023

In the astrolabe, a flat circular plate (the rete) carrying a representation of the ecliptic and some of the stars, is rotated against another circular plate (the plate), on which the horizon and parallels to the horizon (the almucantars) are marked. The instrument may thus imitate the rotation of the celestial sphere against the horizon co-ordinates and, in particular, the Sun and the stars can be seen moving over the altitude circles. Normally, there are other markings on the plates, such as the division of the ecliptic on the rete and unequal-hour lines on the plate. (An ‘unequal’ or ‘seasonal’ hour (there were other terms for this) was one-twelfth of the daylight hours or night hours; they were commonly used for civil purposes in preference to ‘equal’ or ‘astronomical’ hours.) Any method of flattening the sphere onto the plane will do, if it is sufficiently even, but usually a stereographic projection is used — from the south pole for the northern parts of the celestial sphere (northern projection) and from the north pole for the southern regions (southern projection). One reason for this choice is to facilitate the work of the instrument-maker, for in stereographic projection, circles on the sphere are transformed into circles (or straight lines) on the plane. On the back of the instrument, there is an alidade or rule with sights, with which the altitude of the Sun and the stars may be measured on a scale on the rim of the instrument, which is sus- pended so as to hang vertically. Altitudes form the link between the sky and the astrolabe. In general, writings on the astrolabe may be classified according to the following three types: those on the construction of the instrument; those on its use; and those on the theory of stereographic projection.
From brass to text: the European astrolabe in literature and print
Authors: Turner A J
Published: November 2023

The first and most important [instrument] encountered is once again, the astrolabe; perhaps this has not been sufficiently noted, for concerning it, the number of works published in all the countries of Europe from the sixteenth to the eighteenth centuries, is prodigious. And in these it is described as being useful not only for astronomical and nautical observations, but also for [surveying] operations in the field. It would be virtually impossible to give a bibliography of it which would always remain incomplete.
Astrological scales on the National Maritime Museum astrolabes
Authors: Ackermann Silke
Published: November 2023

Then he [the barber] put his hand in his leather bag and took out an astrolabe with seven plates inlaid with silver and, going into the courtyard, held the instrument up to the sun’s rays and looked for some time. Then he said to me, ‘O my lord, eight degrees and six minutes have elapsed of this day, which is Friday, the eighteenth of Safar, in the six hundred and fifty-third year of Hijra and the seven thousand three hundred and twentieth year of the Alexander era, and the planet now in the ascendant, according to the mathematical calculations of the astrolabe, is Mars, which is in conjunction with Mercury, a conjunction that is favorable for cutting hair. I can also see that you are intending to meet another person and for that the time is inauspicious and ill-advised.
Mixed volumes and extremum problems
Authors: Webster Roger
Published: November 2023

The first three sections introduce volume for convex sets, establish its properties and show how it can be calculated, while the remaining ones discuss the theory of mixed volumes, surface area, and two of geometry ‘s most famous extremum problems.
Solutions to exercises
Authors: Webster Roger
Published: November 2023

1. (i) A+ (B + C) ={a+ (b + c):aeA,beB,ceC)

={(a+ b) + c:aeA,beB,ceC)
Matrices And Atlases
Authors: Dunn J Michael , Hardegree Gary M
Published: November 2023

We have introduced the notion of matrices in Chapter 5. Before introducing abstract notions, as matrix product and matrix homomorphisms, we devote this section to an overview of several logically important matrices. This also gives us a chance to familiarize the reader with the abstract notions, which will be formally defined later, on concrete examples. After outlining some basics, we present the Lukasiewicz (and Kleene) matrices, the G Ö del matrices and the Sugihara matrices. We furnish examples of submatrices, matrix isomorphism and-homomorphism, product and preservation of tautologies. We conclude this section with a quick look at infinite generalizations and different philosophical interpretations.
Fundamental facts and concepts
Authors: Diestel Reinhard
Published: November 2023

This chapter gives an introduction to those facts and concepts that are fundamental to the theory of simplicial decompositions. We begin with a short section on terminology and notation, whose main purpose is to introduce simplicial decompositions in a formal way. There will also be a few other definitions, which may not actually be used until somewhere later in the book. They are included for completeness only and will be recalled when they are needed.
Separating simplices and the existence of prime decompositions
Authors: Diestel Reinhard
Published: November 2023

Does every graph admit a simplicial decomposition into primes? And if not, which graphs do? It is not difficult to guess from the second of these questions that the answer to the first must be ‘no’—which, on the face of it, may not even seem very surprising. After all, it is a big step from observing that a particular graph contains a separating simplex, i.e. is not itself prime, to finding a set of prime induced subgraphs, complete with well-ordering, that satisfies such specific conditions as (S1)–(S3).
Simplicial minors and the existence of prime decompositions
Authors: Diestel Reinhard
Published: November 2023

In this chapter we shall pursue further, and to some extent round off, the problem of the existence of simplicial tree-decompositions of countable graphs into primes. Our first existence theorem, Theorem 3.1 of Chapter 2, has already given us some insight into the structure of a countable graph not admitting a prime decomposition; recall that such a graph G contains a separating simplex S with an inaccessible side C, where in addition S is essentially attached to another component C′ of G\S. The phrase ‘essentially attached’ here means that the sub simplex S [ C′] of S need not cover S entirely, but is still large enough not to possess a prime extension into C.
Applications of simplicial decompositions
Authors: Diestel Reinhard
Published: November 2023

This chapter is different in aim and character from the previous chapters. Rather than exploring further the theory of simplicial decompositions, we give a brief overview of their applications, in a self-contained yet fairly concise. form. We shall omit all proofs (except where a proof follows directly from results described earlier in this book); instead, detailed references will be given.
Order and lattices
Authors: John P. Cleave
Published: November 2023

As in algebraic systems, the subsystems (closed sets) of logic are ordered by the relation of inclusion and in Chapter 3, §3.10, this relation was represented by ‘lattice diagrams’. This itself is sufficient reason for developing a theory about this ordering. But, more importantly, the logical consequence of a logic itself defines an order relation, implication (Definition 3.8), which has familiar properties (Example 3.4(ii)). The notion of logical equivalence is defined in terms of this relation.
Quasi-Boolean algebras and empirical continuity
Authors: John P. Cleave
Published: November 2023

A class of lattices called quasi-Boolean algebras (QBA’s) is examined in this chapter. These lattices include Boolean algebras, but the relation between the two classes is stronger than mere inclusion, as is shown in §7.5. The main reason for studying QBA’s is that they are structures underlying Korner’s theory of inexactness and empirical continuity (§§7.7, 7.8) and his three-valued logic of inexactness discussed in Chapter 8.
Structure of G-manifolds
Authors: Kawakubo Katsuo
Published: November 2023

In this chapter, we elucidate the structure of G-manifolds for G, a compact Lie group, building on the foundation of the previous chapters. This chapter together with Chapter 5 constitutes the principal part of the book.
A Census of Finite Generalized Quadrangles
Authors: Payne Stanley E
Published: November 2023

A construction is given for each known isomorphism class of finite generalized quadrangles. Generalized quadrangles, as a special case of generalized polygons, were introduced by J. Tits in 1959 [26]. There he gave what are considered to be the classical exmples. As special cases of other types of geometries, these classical examples appeared elsewhere, most notably among the partial geometries of R. C. Bose [3]. The first nonclassical examples were also found by J. Tits in the mid-1960s and first appeared in P. Dembowski [5]. All these examples had parameters (s,t)of the form (q,q),, ,(q,q), or (q,q), where qis an arbitrary prime power. independently by M. Hall, Jr. [9]. Shortly afterwards, S. E. Payne [17] gave an abstractly more general construction which was shown in [18] to produce a new family for qany power of 2. More recently, starting with a construction of W. M. Kantor [10], several new families with parameters have been discovered, often with restrictions on the prime power q.Although the point-line dual of a GQ with parameters (s,t)is a GQ with parameters (t,s), implying that one could assume thats isnever larger than t,we often find it interesting to mention both a GQ and its point-line dual. In any case, each finite GQ known to us is isomorphic to at least one of the constructions given below or to its point-line dual.
Representation Theory of Chambersysterns of Affine Type
Authors: Ott Udo
Published: November 2023

For more than ten years geometry has been in an important period dominated by ideas developed in the course of laying the foundation for Lie geometries. Recent work on certain classification problems for geometries of spherical type point to the significance of representation theory for the ana1ysis of these geometries. The general method of using Hecke algebras provides the appropriate tool for studying certain aspects of the subject.The question arises whether the Hecke algebra will continue to be useful in problems involving chambersystems of affine type. The purpose of this summary is to give a report on the program to find a workable description of the finite dimensional irreducible representations of the affine Hecke algebras.Remarkably enough, at this early stage representation theory enables us to introduce the notion of dimension for affine chambersystems.
The geometry of trilinear forms
Authors: Aschbacher”‘ Michael
Published: November 2023

All of us at this conference are familar with projective geometry on a vector space Vover a field F,and the refinements of projective geometry induced by a bilinear form on V.This note discusses the analogous geometries induced by trilinear forms on V.There does not seem to be much in the literature on this subject. In [4], Cohen and Helminck determine all alternating trilinear forms of dimension at most 7 over fields of cohomological dimension at most 1. In (1], [2], [3] there is some discussion of alternating and symmetric trilinear forms. There is of course an extensive literature on Lie algebras and Jordan algebras which is of some relevance. In the case of bilinear forms, the study of alternating forms is easier than the study of symmetric forms. The same seems to be true of trilinear forms. Nevertheless I will restrict my discussion to symmetric trilinear forms, as I have done more work with symmetric forms than alternating forms. However much of the discussion carries over to alternating forms.
Planar Graphs
Authors: Read Ronald C , Wilson Robin J
Published: November 2023

A graph G is planar if it can be drawn in the plane or on the surface of a sphere so that no two edges meet, except at a vertex at which both are incident. Such a drawing partitions the set of points of the plane or sphere not lying on G into faces; for example, the following drawing has 6 faces.

A graph G is outerplanar if G can be drawn in the plane so that all the vertices lie on the boundary of the exterior face. Euler’s formula states that, if a connected planar graph G has n vertices and e edges, then any drawing of G in the plane or on the sphere has/ faces, where n −e +f = 2.
Problems for investigation
Authors: Gofman Judita
Published: November 2023

Even at a very early age, investigating a pattern of numbers or shapes can lead to intriguing discoveries (no matter how small) and may raise a number of challenging questions. Therefore investigative work seems to provide a suitable introduction to the art of problem solving. What should one investigate? And how? This chapter contains a selection of problems, based on some popular types of investigation, such as: iterating a certain procedure and analysing the results; search for patterns; looking for exceptions, or special cases in a pattern; generalizing given problems; studying converse problems.
The Calculus of Variations
Authors: Collins Peter J
Published: November 2023

It is to Queen Dido of Carthage, in the ninth century b.c., that the oldest problem in the Calculus of Variations has been attributed. The ancient Greeks certainly formulated variational problems. Most of the more celebrated analysts of the last three centuries have made substantial contributions to the mathematical theory and, in particular, the names of Bernoulli, Newton, Leibnitz, de l’Hôpital, Euler, Lagrange, Legendre, Dirichlet, Riemann, Jacobi, Weierstrass and Hilbert are attached to important phenomena or results. Nowadays, the Calculus of Variations not only has numerous applications in rigorous pure analysis and in physical applied mathematics (notably in classical and quantum mechanics and potential theory), but it is also a basic tool in operations research and control theory. We shall in this chapter use the notation f ∈ C  m(A) to indicate that f is a real-valued function, defined and m-times continuously differentiable on A, where A ⊆ ℝn and m, n are positive integers.
Introduction
Authors: Grandine Thomas A
Published: November 2023

The projects in this book are intended to accomplish several things. The first is to present numerical computations in a context in which they might actually occur. Thus, the students, under the guise of completing various tasks for a fictitious company, gain insight into the role that numerical methods play in science and industry. The projects are all constructed so that the solutions have physical meaning for the particular problem which must be solved. In addition, the problems occasionally require two or more numerical methods in order to obtain the solution. This means that the projects are occasionally unpredictable: a student never knows exactly when a numerical method discussed earlier in the course is going to be required to solve a current problem. This global view of the subject makes it possible for the student to realize that real-world problems are never as straightforward as many textbooks would have you believe. Thus, an appreciation for the relevancy of the material is enhanced.
The setup
Authors: Grandine Thomas A
Published: November 2023

As a recent graduate of the Binary Institute of Technology, one of the leading institutions of science and engineering in the world, you have just entered the job market. After locating the college placement office on the campus BIT map, you have wandered in to begin your search for an exciting and challenging career. The people there have scheduled several interviews for you, and you have begun your job search by talking to representatives of several big companies. After careful consideration of the dozen or more job offers which are currently in front of you, you have decided to accept the job with the Applied Computational Mathematics and Engineering Company. ACME is a huge international corporation with many very diverse interests. Some of these are computers, energy, construction, pharmaceuticals, chemicals, mineral exploration, and oceanography.
Project 3
Authors: Grandine Thomas A
Published: November 2023

One division of ACME, the Heuristic Algorithm and Copious Kilobyte Exchange Regulatory agency, is currently designing a package of subroutines for one of ACME’s new computer systems. The system, Super-powered Laserized Industrial Development Engine for Rapid, Useful, Logarithmic Encryption, is intended primarily as a supercomputer for numerical computation. The SLIDE RULE should be a revolutionary new tool with which difficult numerical problems might be solved. The HACKER agency is short-handed at the moment, and they are going to need help to complete the programming of the subroutine package. Since SOLVE is not terribly busy at present, many of its consultants are being assigned to HACKER to finish the job. Since you are relatively new to ACME, you have drawn this particular task as your current project. Your individual task is a relatively straightforward one. Your job is to write a subroutine which solves quadratic equations.
Project 10
Authors: Grandine Thomas A
Published: November 2023

The Superconductor Hotshot Operational Research Team, a division of ACME, has been producing an electronic device, called the Fortified Utility Switching Engine, for the Bureaucratic, Large, Overblown, Washington Network, a branch of the federal government. The SHORT FUSE has been manufactured under strict specifications, which SHORT has supposedly upheld. Recently, however, some of the BLOWN FUSEs have begun to fail, and BLOWN is preparing to cancel its contract with ACME, claiming that the SHORT FUSEs have not been manufactured to specifications. Naturally, SOLVE has been called in to investigate this matter. Since you have much expertise in this area, you have been selected by Biro Kratt as the individual responsible for discovering just what is going on and who is to blame. The successful completion of this project may well allow SHORT to retain its multimillion-dollar contract with BLOWN. A personal salary increase may also be in the offing if you are successful.
Project 15
Authors: Grandine Thomas A
Published: November 2023

The Board of Engineers for Aqueous Voluminous Edifices and Restraints, the civil engineering division of ACME, is currently working on the design for a dam to be constructed in the Oscillating Gorge on the Interpolant River, not far from the town of Runge’s Mill. Recently, however, an environmentalist group, the Demagogues Against Mutilating Nature, have begun to protest against the construction of the Oscillating Gorge Dam. The DAMN outcry ‘Stop the damn dam’ has been so successful, in fact, that ACME has been served with a court injunction preventing the start of the actual construction. In order for BEAVER to continue work on its dam, ACME is going to have to get DAMN satisfied. The environmental impact of the dam is a complex issue, especially because the flow rate of the Interpolant River is so variable. One of the problems in answering the DAMN concerns is that no one is really quite sure what the hydrostatic pressure behind the dam is going to be as a function of the height of the water. Because the flow rate is so variable, the dam is going to have to be built in order to withstand greatly varying pressures. In order for the engineers to submit an acceptable design, it is going to be necessary to know just what those pressures are. This is where you come in. You are going to have to determine the hydrostatic pressure. Biro Kratt has assigned you to this project because of your reputation for integrity, knowing that DAMN will abide by your findings.
Project 18
Authors: Grandine Thomas A
Published: November 2023

ACME is conducting an important experiment aboard the space shuttle Discovery on its historic mission to the Asteroid Belt between Mars and Jupiter. Because of the importance of these experiments, you have been ordered to go along to assist. While you have been assigned several other important computations to perform during the six month flight, you have also been assigned the task of assisting the navigator during the mission. In particular, it will be your job to help the navigator avoid the asteroids. There will be one part of the journey that will be especially tricky for the pilot to steer. Three rather large asteroids will be in the vicinity of Discovery within a particular ten-hour period of time. You are going to have to compute and plot the trajectories of these three asteroids during that ten-hour period.
Project 19
Authors: Grandine Thomas A
Published: November 2023

The city of Cyborg has a problem. It has just been invaded by malfunctionis equipmentatis, a species of insect which likes to nest inside high-tech electrical equipment. Unfortunately, this peculiar nesting habit is wreaking havoc throughout Cyborg, since the bugs are causing equipment failures everywhere. In order to combat this infestation, the Cyborg city council has asked Quellers United Against Surviving Hexapods, a local exterminating company, to submit a bid for spraying to eliminate the pests. Simultaneously, it has hired the National Unit for Insecticide Spraying to Aid a Nice, Clean Environment, a division of ACME, to study the situation. Assuming that QUASH gets the contract to spray to eliminate the pests, it will be the job of NUISANCE to determine the effects of the spraying. For some reason, you have been assigned to this project. Your briefing papers are deliberately vague, and it is not at all clear just how your presence is going to be helpful. However, ACME has flown you to Cyborg to join the team from NUISANCE, so you have taken your camera along to take pictures of butterflies and birds as it is very unlikely that there will be much else for you to do there. After stopping at a bookstore to buy a butterfly book, you decide to spend the day at the park.
Project 20
Authors: Grandine Thomas A
Published: November 2023

The Telephone Operators Union for Calling Home is unhappy about the quality of the telephone lines in one of their main districts. As it turns out, a subsidiary of ACME, the Reprehensible Enterprise for Auditory Communication and Hearing, a local telephone company, is responsible for maintaining the phone lines in that district. In response to the complaints from TOUCH, REACH has ordered new fiber optic cables to install to replace the worn out copper wires still in service. Another division of ACME, the Organization for Using Telephones, manufactures optic fibers, and they will be supplying the new materials for REACH. Optic fiber manufacture is a tricky business, though, and because REACH is determined to improve the quality of its phone lines, they are insisting on using high quality optic fibers. In order for OUT to be able to produce fibers of this quality, there is one engineering difficulty that is going to have to be ironed out. This involves a computation to determine just how fast the silicon rods should be fed into the furnace to produce the desired optic fibers. It will be your job to help the people at REACH, OUT, and TOUCH. Someone there has specifically asked for you, since by now you have an ACME-wide reputation for doing an excellent job.
Project 21
Authors: Grandine Thomas A
Published: November 2023

The Big Remote Army Supply Station, a military installation of great importance to the defense of much of the western world, has just been penetrated by an agent working for the Spaceage Proliferation of Industrial Espionage Society. The security people working at BRASS have discovered that the agent, working from the inside, managed to secure blueprints for an important new jet. Fortunately, the SPIES agent has not yet had an opportunity to deliver the plans, so there is still a chance of capturing him before he reports his findings. By working with BRASS, American Intelligence has learned that the agent is currently hiding in a small boat moored some distance offshore. Blackford Oakes, the man that American Intelligence has sent to recapture the agent, is quite capable and daring, and he intends to seize the boat by parachuting onto it under cover of darkness.
Documentation
Authors: Grandine Thomas A
Published: November 2023

The following pages contain excerpts from the NAG FORTRAN Workstation Library documentation. More complete documentation may be found in the NAG FORTRAN Workstation Library Manuals. Before using any of these routines, please refer to the appropriate Appendix of the NAG FORTRAN Workstation Library Manuals to determine the interpretation of bold italicized terms and other implementation dependent details. In particular, the routine name may be precision dependent. Thus, in certain implementations, the last letter of the routine name may be different, and real may be interpreted as DOUBLE PRECISION. The pages that follow have been reprinted by permission of NAG, Ltd. The copyright of the following pages remains the property of NAG, Ltd.