bluuebunny/crossref_metadata_2025 huggingface dataset:
Silent Fields
Authors: Lovegrove Roger
Published: November 2023

Since time immemorial mankind has taken it upon himself to wage war against nature -- against those species of birds and mammals which he believes conflict with his livelihood. This remarkable book is about that war of attrition against the native mammals and birds of England and Wales from the middle ages to the present day. There is widespread knowledge about the huge declines in popular species such as song birds, farmland birds, otters, and pine martens, however, there is less understanding about the deep-rooted causes of these losses, or about the complex relationship between mankind and these species. Roger Lovegrove has undertaken years of unique research: by searching through parish records of ‘vermin’ trapped, hunted, and killed over the generations, he has revealed an unprecedentedly accurate and detailed picture of the history of a nation’s wildlife, and of the often devastating impact and extinction that we have forced on our ecology. Consisting of species-by-species accounts, accompanied by beautiful, specially-commissioned illustrations, this book outlines the history - and often the future too - of a wealth of wildlife species, from badgers, bears and beavers, to wolves, kingfishers, the golden eagle and the humble house sparrow. The geographical scope is British, but the subject will be of interest to conservationists around the world because of the unique historical material that will be included. The topic has enormous relevance today, as public concern about the environment rises, and controversies rage about hunting, wildlife management and reintroduction of ancient species.
Introduction
Authors: Lovegrove Roger
Published: November 2023

This book charts the history of Man’s deliberate killing of terrestrial wildlife in Britain—specifically native birds and mammals—from about 450 years ago, up to the present. It is the story of his attempts to control, and at times to eliminate completely, species that he has deemed to be undesirable or unnecessary. The story that links past campaigns of vermin control to the modern practice of wildlife management (which is, in fact, control by any other name), is traceable from the very earliest organized records in the sixteenth century, through to present times. Thus we can follow the vicissitudes and effects of Man’s relationship with some of the most familiar species of wildlife with which he has shared this island since those times. There would only ever be one winner. Wildlife has suffered to an extreme extent, never more so than since the middle of the nineteenth century, when an onslaught on predatory species began with little or no regard for long-term consequences.
The social background to persecution
Authors: Lovegrove Roger
Published: November 2023

The implementation of the Tudor Acts in the mid sixteenth century not only introduced financial incentives for killing vermin, but also gave official sanction, moral emphasis, and structure to the less intensive and more haphazard war against many wild creatures that had in any case been prosecuted ad hoc over the earlier centuries since Man first settled the land. As this account will show, these Acts vastly increased the numbers of animals, birds, and even in some cases reptiles and amphibians, that were officially targeted in the name of agrarian protection. In some cases species were pursued, irrespective of the Acts, for reasons far removed from the stated agricultural considerations. Justification— should any have been needed—was readily found for example, in conflict with Man’s interests (Fox, Red Kite, Rook), fear (Adder), revulsion (Toad), or even prejudice and superstition.
Birds—individual species accounts
Authors: Lovegrove Roger
Published: November 2023

This chapter details the levels of persecution that individual species of birds listed in the Tudor Vermin Acts have endured over the centuries, up to recent times, and identifies the effect that this persecution has had on their status. In some cases, Man’s determination has successfully eradicated species (Sea Eagle, Goshawk) or has reduced them to the merest fragments of their former numbers and distribution (Red Kite, Chough). In other cases, intensive killing over great expanses of time has had virtually no effect (House Sparrow, Jay). One factor that stands out from examination of the historical record, as represented by the churchwardens’ accounts, is the difference between the number of birds on the Tudor lists (20-1) and the amount of control that was exercised against them, compared with that meted out to the smaller number of listed mammals (II). With the exception of a few geographical areas, the heavy emphasis was always on the mammals, as can be seen clearly in Appendix I.
Modern Control—Legal and Illegal
Authors: Lovegrove Roger
Published: November 2023

Until now I have dealt mainly with the persecution and control of animals that have for many centuries been classified simply as ‘vermin’. However, attitudes towards such species have changed with time and circumstance. This change has been increasingly reflected in a plethora of protective wildlife legislation enacted in the second half of the twentieth century. Much of it has been stimulated by the growing public concern about wildlife and the awareness of the disastrous impacts, both direct and indirect, that humans have had on many species.
A Modern Introduction to Quantum Field Theory
Authors: Maggiore Michele
Published: November 2023

The importance and the beauty of modern quantum field theory resides in the power and variety of its methods and ideas, which find application in domains as different as particle physics, cosmology, condensed matter, statistical mechanics and critical phenomena. This book introduces the reader to the modern developments, assuming no previous knowledge of quantum field theory. Along with standard topics like Feynman diagrams, the book discusses effective lagrangians, renormalization group equations, the path integral formulation, spontaneous symmetry breaking and non-abelian gauge theories. The inclusion of more advanced topics will also make this a most useful book for graduate students and researchers.
Introduction
Authors: Crespigny Lachlan De , Chervenak Frank
Published: November 2023

It is amazing what little information is available about prenatal diagnosis in general pregnancy books designed for women. Prenatal diagnosis is either not included at all, or the information is very limited. Yet in most Western countries pregnant women have taken up prenatal testing with enthusiasm. Almost all women choose to have some prenatal testing, some women limit what they want to know about, and others want all the information they can possibly have on potential abnormalities.
Prenatal testing: 23 weeks until delivery
Authors: Crespigny Lachlan De , Chervenak Frank
Published: November 2023

Prenatal testing for abnormalities is carried out much less often from 23 weeks of pregnancy until delivery. At this stage, testing is aimed at identifying problems with your baby’s growth or following up a problem that was identified earlier on. The two main forms of prenatal testing that are done late in pregnancy are checking your baby’s heart rate, and an ultrasound examination. Occasionally amniocentesis and magnetic resonance imaging are performed.
Decisions after prenatal testing
Authors: Crespigny Lachlan De , Chervenak Frank
Published: November 2023

If an abnormality is detected, you have several options for your pregnancy. Before you make any decisions, you will need the best information possible, including professional advice. Your most important choice will be whether to continue with or end your pregnancy. If you decide to continue your pregnancy you will face other options. You may also be concerned about becoming pregnant again. When a problem with an unborn baby is detected, it is usually unexpected. About 3 per cent of all pregnancies will be affected by some fetal abnormality.
Some key ideas
Authors: Atkinson A C , Doney A N
Published: November 2023

Figure 2.1 is one schematic representation of an experiment. A single trial consists of measuring the values of the t response, or output, variables y  1, …, Y  t. These values are believed to depend upon the value of the m factors or explanatory variables u1 … um. However, the relationship is obscured by the presence of unobservable random errors ε  1, ... , ε  1,.
Criteria for a good experiment
Authors: Atkinson A C , Doney A N
Published: November 2023

The results of Chapter 5 illustrate that the variances of the estimated parameters in a linear model depend upon the experimental design, as does the variance of the predicted response. An ideal design would provide small values of both variances. However, as the results of Table 5.3 show, a design which is good for one property may be less good for another. Usually one or a few important properties are chosen and designs found which are optimum for these properties. In this chapter we first list some desirable properties of an experimental design. We then illustrate the dependence of the ellipsoidal confidence regions and of the variance of the predicted response on the design. Finally, the criteria of D-, G-, and V optimality are described, and examples of optimum designs are given for simple regression and quadratic regression.
Composite design criteria
Authors: Atkinson A C , Doney A N
Published: November 2023

An experimenter rarely has one purpose or model in mind when designing an experiment. For example, the results of a second-order response surface design will typically be used to test the terms in the model for significance, as well, perhaps, as being used to test for lack of fit. The significant terms will then be included in a model, the estimated response from which may be used for prediction at one or several points not necessarily within fll. As we have shown in previous chapters of this book, there are specific design criteria which are addressed to each of these tasks. However, a design which is optimum for one task may be exceptionally inefficient for another. One example is given in Table 11.2, where a comparison is made of several designs in terms of D-efficiency for the first-order model through the origin found appropriate for modelling the desorption of carbon monoxide.
Social and biological aspects of ethnicity
Authors: Chapman Malcolm
Published: November 2023

Today, most social anthropologists would feel qualified to contribute, if asked, to a discussion of ‘ethnicity’. Every social anthropologist has an interest in group-definition, in self-definition, in the definition of others, and so on—in all the phenomena which might, loosely considered, come under the heading of ‘ethnicity’. Virtually every anthropologist can provide ethnographic illustrations of these problems. This is no doubt partly because the topic has been fashionable over the last decade or so. It is also, however, because the phenomena in question are ubiquitous. Societies and cultures, however defined, are interested in boundaries. This means that all the work of all social anthropologists is potentially relevant to a paper concerning ‘ethnicity’. The field is almost limitless, and no definitive treatment is practically possible. Any selection of themes must, therefore, be arbitrary to some extent.
Some Tools for the Multivariate Analysis of Functional Data
Authors: Ramsay JO
Published: November 2023

One is often presented with data which are either known or appear to arise from some underlying smooth process. Repeated measurements data, for example, are usually described as arising from observing each experimental unit repeatedly at a sequence of times, and it can often be supposed that the passage of time produces a relatively smooth variation in the outcome measure, which of course may also be subject to other random influences as well.
History and population change
Authors: Pennington Renee , Harpending Henry
Published: November 2023

Historical changes in Herero mortality and fertility documented in previous chapters show that the health of this population has improved remarkably in the last century. In this chapter, we use these findings to address important issues in Herero history. We also discuss how improvements in survivorship and reproductive performance correspond to changes in population growth rates, social structure, and individual reproductive success.
Asymptotics
Authors: Lindsey J K
Published: November 2023

If exact analytic results for the likelihood function of some model are difficult to obtain or are complex to calculate, it is often useful to have available approximations. Indeed, this was precisely what we did for the likelihood function of continuous distributions in Section 3.2.1, for the approximate likelihood based on the standard error in Section 3.5.2, for model selection in Section 3.6.1, and for profile likelihoods in Section 3.6.3. Numerical approximations are very important in statistics. Some of the common techniques, with which the reader should be familiar, are outlined in Appendix D. In this chapter, we shall be concerned with deriving some of the more commonly used analytic approximations. Often n independent observations are made, in a random sample, assuming the same parametric statistical model. In such situations, it may be interesting to study what would happen if we could imagine observing a much larger sample or perhaps the whole theoretically infinite population. Many statisticians go further and claim that maximum likelihood estimation is premised on the viewpoint according to which the data collection process can accrue information in a way that can lead, in the limit, to all parameters in a given model becoming known. As we saw in Chapter 1, this, in fact, makes little sense from a modelling perspective, except perhaps when production and measurement error models are involved. However, it is the major assumption underlying the original derivation of many of the classical results to be exposed in this chapter.
Jellyfish, Polyps and Worms?
Authors: Southwood T R E
Published: November 2023

The continents of the earth move. The crust (lithosphere) consists today of seven large tectonic plates and a number of smaller ones. Several of them have continents attached to their ‘backs’, and shuffle across the globe, moved by the deeper convection currents of the liquid rock in the middle layer, the mantle. When the plates move away from each other in the deep ocean, liquid rock (magma) flows upwards and solidifies to form ridges. In some other places the plates may scrape past each other, causing fault lines (such as the San Andreas Fault). When they collide directly, one passes below the other, a process known as subduction. If this happens where the plates are ‘carrying’ continents then these buckle and rise to form mountains (for example, the Himalayas). Most volcanic activity occurs around the edges of the plates, but some submarine mountains and volcanic islands arise towards the middle of plates. These are due to hot spots, which are generated in particular stationary sites in the mantle. As the plates move across a hot spot a chain of volcanoes are successively ‘punched ‘ through it; only one end of the chain is active — where the plate is currently over the hot spot. The Hawaiian Islands and the older line of submarine mountains, known as the Emperor Seamounts (see map p. 176), that stretch up to the Kamchatka Peninsula, are a spectacular example of the effects of a hot spot and show how the Pacific plate has moved over the past 75 million years.
A Sparse Start
Authors: Southwood T R E
Published: November 2023

The supercontinent Pangaea remained intact throughout this period and various small land masses that now constitute South-East Asia moved to join the eastern corner of Laurasia. Although Pangaea stretched from near one pole to near the other it seems that there was no land that was actually over a pole and there is no evidence of continental ice sheets. The ocean currents will have flowed freely, particularly in the enormous Panthalassic (Palaeopacific) Ocean, bringing warm water to colder latitudes. The Tethys Ocean existed as a deep bight, at tropical level, to the eastern side of Pangaea. The sea rose from its low level at the end of the Permian, so that along the margins of the Tethys Ocean there were often luxuriant tropical swamp forests. The period was probably a relatively warm one, gradually becoming hotter; away from the oceans conditions were often very arid and there is evidence of the evaporation of inland seas in the large deposits of rock salt, gypsum, and anhydrite formed at this time. Animal and plant life seems to have been relatively sparse when the period began.
Today’s World Dawns
Authors: Southwood T R E
Published: November 2023

This period which brings us right up to the present, is often referred to nowadays as the Cenozoic. The first part of it, the Tertiary, is by far the longest component, generally being taken as extending until 1.81 million years ago. It has itself been divided into a number of periods: Palaeocene (to 55 Mya), Eocene (to 33.7 Mya), Oligocene (to 23.5 Mya), Miocene (to 5.2 Mya), and Pliocene (to 1.64 Mya). The majority of the second part, the Quaternary (1.64 Mya–10,000 years ago), is generally known as the Pleistocene.
Humans: The Great Modifiers
Authors: Southwood T R E
Published: November 2023

All organisms have an impact on their environment. Some, ranging from coral polyps forming reefs to beavers forming dams, have a very real effect on the physical environment. But the impact of Homo sapiens since the ‘Great Leap Forward’, 50–40,000 years ago, has been more varied and has become increasingly extensive; it is, however, the key to our success—;our ability to exist in vast numbers and to live in virtually every corner of the globe. The Neanderthals existed for over 300,000 years, many times longer than modern man has yet achieved, but they never extended beyond southern Europe and South-west Asia (Neanderland); their range was limited, even when allowing for the ice sheets.
Eating well and feeling good
Authors: Graham Philip
Published: November 2023

There are two prevalent myths about the teens and their attitudes to food, appetite, and appearance. One is that they are all overweight because they are so inert and watch television or videos the whole time; the other that they are all on the verge of anorexia. Because this is a time of rapid growth, the calorie needs of those in their teens are indeed greater than at other times of life. Teenagers do eat more food. Most have an appetite that is somewhere between healthy and ravenous. Further, as we shall see, many teenagers, especially girls, are distressed about their appearance and are trying to do something about it. They are either embarking on a diet, actually dieting, or have just given up on a diet. But in fact about four in every five of them are a perfectly healthy weight, neither overnor underweight and, contrary to media reports, most are in no danger either of anorexia or obesity.
Leisure and work
Authors: Graham Philip
Published: November 2023

During the last hundred years, leisure and, to a lesser extent school, have replaced work in the way young people in their teens spend their time. But, having given them so much leisure time, the adult world has failed to provide for it, complaining about the way the young spend it, but largely leaving them powerless to do anything about it themselves. Of course, the young do fill their time especially if, in their mid and late teens, they are completely dedicated to working for public examinations. But this leaves most of those in their early teens and many of those in their late teens with a time vacuum, often filled, as we shall see, only with empty boredom.
Joining up the teens again
Authors: Graham Philip
Published: November 2023

In previous chapters we have seen how young people of teen age, quite contrary to the popular view, are mostly reasonably well-behaved, cheerful, equable, and studious. They find much to enjoy in their lives, especially their friendships, their leisure activities, and their family life. In support of this conclusion, a report from the Future Foundation, based on a survey of 500 representative 13–18-year-olds in the spring of 2002, concludes ‘Most teenagers express broad satisfaction with their lives. The majority choose to describe their lives as happy, fun, and carefree. Much of this satisfaction stems from their lives outside of school, where they are enjoying growing freedoms The majority express satisfaction with their family life and enjoy a supportive relationship with their parents Astonishingly, a third of teenagers claim they have not argued at all with their parents in the past year ‘. So this is not a time of life that parents should anticipate with the fear and trembling that some of the media and indeed some professionals seem to encourage. Those in their teens who, as children, got by reasonably well can be expected to continue to do so. Some will have difficulties, but many of those who do will have been troubled since their earlier years. The teen years are not a cure for troubled behaviour; nor do they, as a general rule, cause trouble. Most parents and young people themselves can look forward to the teens as an enjoyable and rewarding time of life.
Early ideas on the origin of life
Authors: Fenchel Tom
Published: November 2023

According to the Judeo-Christian tradition, the world and all living things originated in a singular event of creation. Today, all enlightened people in the western world consider Genesis as a myth without physical reality (so-called creationists in USA are excluded from the category of enlightened persons). But in earlier centuries the Church insisted on a literal interpretation of the biblical tradition, and its resistance to the theory of evolution continuing up until recent times exemplifies this.
Myotonic dystrophy: a multisystemic disorder
Authors: Harper Peter S
Published: November 2023

Myotonic dystrophy is one of the most variable of all disorders, a factor that has profound implications for its management. The details of this variability and its consequences are reflected in the specific chapters of this book, but in this introductory chapter an overview of the principal clinical aspects is given, particularly to help the clinician only partly familiar with myotonic dystrophy, who may have encountered it through a particular manifestation and wishes to gain a clearer picture of the overall features of the disorder. The chapter is also written for research scientists, who, as the emphasis progressively shifts towards therapeutic initiatives, need to know the key clinical problems that basic research is aimed at eventually overcoming. Those wishing for more detailed information will need to consult other sources, such as the author’s monograph (Harper 2001).
Paediatric cardiology for the primary care physician
Authors: Franklin Rodney , Slavik Zdenek
Published: November 2023

Over 90% of cardiac pathology in the paediatric population in the developed world is congenital in origin, in that it is present at birth, even if undetected until older; in contrast, adult heart disease is largely classified as being acquired. In less developed countries, rheumatic fever is still prevalent.
Dermatology
Authors: Goodyear Helen
Published: November 2023

This chapter looks at commonly occurring skin disorders in children and their treatment.The skin often gives valuable information leading to diagnosis with both acutely sick children, e.g. meningococcal disease and chronic conditions, e.g. neurofibromatosis. The skin signs of these conditions have been mentioned in the relevant chapters. History and examination give the clues to skin disorders and as well as asking general questions some specific ones are useful

History

Length of time -When did it start? Does it come and go? Are there crops of lesions?
Speech and language disorders and hearing problems
Authors: Luscombe Maria , Harding Celia , Bannon Michael
Published: November 2023

Identifying and working with children who have a range of communication needs in the early years population is a challenging and complex task. Speech language and communication difficulties may present in isolation or in conjunction with a range of other developmental difficulties. Similarly, the cause of these difficulties can be attributed to a range of factors within the individual themselves, or social, emotional, or environmental factors. Primary care workers such as health visitors and GPs have a vital role in identifying which children may require further intervention.
Adolescence and primary care
Authors: Jacobson Lionel , Owen Diane
Published: November 2023

It’s not that he doesn’t listen … sometimes he doesn’t fully comprehend that he’s talking in a way you can’t understand … it would help if they talked to teenagers. (Female teenager)Please listen to us, we’re people too you know. (Male teenager)Adolescent patients can be forthright and give frank opinions on the care they receive from primary care, and the above quotes may represent a distillation of some of the issues that will become more apparent throughout this chapter. Young people can be very sensitive to nuances of care and care provision, and this chapter will feature other teenage voices and their comments, because we contend that communication skills may be just as important as clinical skills when providing primary care for teenagers.
Isotopes And Delivery Systems For Brachytherapy
Authors: Flynn Anthony
Published: November 2023

The aim of this chapter is to consider which radioactive materials might be suitable as brachytherapy sources, to describe some practical brachytherapy sources, and to consider how these sources may be applied to the patient in a controlled and safe way. It is assumed that the reader has some familiarity with the basics of radioactivity and the emissions from radioactive substances. Radioactive sources for brachytherapy are now available with many radionuclides and in various shapes and sizes, and there is no such thing as an ‘ideal’ brachytherapy source. Different sources have different applications depending on their emission type and radiation energy and how they are constructed.
Prostate Cancer: Permanent Seed Brachytherapy And High Dose-Rate Afterloading Brachytherapy
Authors: Ash Dan , Hoskin Peter
Published: November 2023

Permanent seed implantation for prostate cancer is essentially for patients with localized disease who have a high probability of cure. There are no specific symptoms caused by localized prostate cancer and many patients present with symptoms of benign prostatic hypertrophy, which is investigated by performing a PSA. There is also an increasing group of asymptomatic patients who request PSA for screening. A raised PSA is an indication for transrectal ultrasound and biopsy to confirm the diagnosis.
Astrolabes At Greenwich
Authors: Cleempoel Koenraad Van
Published: November 2023

The astrolabe is one of the most intriguing of all early scientific instruments. Invented by the Greeks, the design and construction of the astrolabe remained largely unchanged for hundreds of years as it passed through the Arabic, Indian, Persian, and Medieval European cultures. The astrolabe was the starting-point for the design of many other types of calculating and observing instruments in the Middle Ages and the Renaissance. With 53 astrolabes, the National Maritime Museum at Greenwich houses one of the largest collections in the world. This number presents a fair balance between the Eastern (30) and the Western (23) instruments, with some exceptionally fine highlights in each group. This beautifully-produced large format book catalogues the astrolabes in the National Maritime Museum collection, and includes accompanying essays written by world experts in their fields. Published in series with 'Globes at Greenwich' and 'Sundials at Greenwich', this prestigious catalogue will appeal to collectors of such scientific instruments as well as academic historians of science.
Optimal Control and the Calculus of Variations
Authors: Pinch Enid R
Published: November 2023

Optimal Control is a modern development of the calculus of variations and classical optimization theory. For this reason, this introduction to the theory of Optimal Control starts by considering the problem of minimizing a function of many variables. It moves from there, via an exposition of the calculus of variations, to the main subject which is the optimal control of systems governed by ordinary differential equations. This approach should enable the student to see the essential unity of the three important areas of mathematics, and also allow Optimal Control and the Pontryagin Maximum Principle to be placed in a proper context. A good knowledge of analysis, algebra, and methods, similar to that of a diligent British undergraduate at the start of the final year, is assumed. All the theorems are carefully proved, and there are many worked examples and exercises for the student. Although this book is written for the undergraduate mathematician, engineers and scientists with a taste for mathematics will find it a useful text.
Tensors and differential forms
Authors: Willmore T J
Published: November 2023

In this chapter we associate new vector spaces to given vector spaces. We have already seen that corresponding to a given vector space V we have another vector space V*, namely the dual vector space consisting of linear maps of V into the field ℝ. Moreover, the reader will have met already the sum V ⊕W of two vector spaces V and W, consisting of pairs ( v, w) of V x W with the usual operations acting separately on each component.
Blowup for some reactive-Euler induction models
Authors: Bebernes J , Bressan Alberto
Published: November 2023

The evolution of thermal explosions in gaseous systems depends on the interaction between chemical heat release, conductive thermal losses, and the effects of compressibility. The latter factor can accelerate reaction rates in constant volume systems where compression heating plays a role (Bebernes and Bressan 1982; Kassoy and Poland 1983; Bebernes and Kassoy 1988). In unconfined systems however, the conversion of some thermal energy to kinetic energy may retard the appearance of thermal runaway. Systems in which conductive losses are unimportant will inevitably explode, perhaps faster than diffusive systems. In this sense it is important to be able to predict which physical processes control the evolution of an exothermic reaction in a specific gaseous system. In this paper, we present the results of our recent studies which provide a rational basis for deciding the correct induction model for the given physical system and analyze these models mathematically (Kassoy et al. 1989a, b; Bebernes and Kassoy 1989; Bressan, in press;).
Excitability behaviour of myelinated axon models
Authors: Bell Jonathan
Published: November 2023

One of the more quantitative areas of biology is celluar neurobiology. The reason for this is that there are relatively well developed experimental techniques and good experimental data which are necessary for the development of models. Also, we can rely theoretically on the conservation principles. A particular subarea of this field is axonology where we consider the excitability behaviour of axonal processes associated with single nerve cells under various stimulation conditions. An important, yet specialized, such process is the myelinated axon in higher animals.
Topological methods for the study of travelling wave solutions of reaction-diffusion systems
Authors: Gardner R A
Published: November 2023

Another important issue is to determine which of the waves supported by a particular system are stable, since these are the only waves that will be physically observable. It is also of interest to be able to identify the unstable waves, since this may indicate the presence of other stable states.
Construction of projective planes
Authors: Ellis Graham
Published: November 2023

In this chapter we turn our attention to rings with only a finite number of elements, and in particular to finite fields. (Recall that a field is a commutative ring with identity 1≠0 in which each non-zero element has a multiplicative inverse.) Finite fields play an important role in many branches of mathematics. We begin by showing how the existence of certain finite fields leads, via projective geometry, to the solution of a particular problem in combinatorial mathematics. We then go on to investigate the existence of finite fields. Several of the concepts that we introduce in connection with finite fields will be of use when we later turn our attention to infinite fields. For this reason we give definitions in more generality than at first glance seems necessary.
Cryptography
Authors: Ellis Graham
Published: November 2023

In this chapter we consider some recent developments in cryptography. To explain the basic ideas behind this subject let us consider the situation of an international bank, with branch offices in many of the principal cities of the world, whose head office needs weekly confidential reports from the branches. These reports are sent by fax, and to ensure confidentiality have to be disguised. The problem then is to design a secret code, called a cryptosystem, which will resist any codebreaking attempts by the bank‘s competitors. The report or message that is to be sent to head office is called plaintext, and the disguised message is called ciphertext. The plaintext and ciphertext are written in some alphabet which we assume to consist of the usual letters A–Z together with possibly punctuation marks, numerals, blanks, and any other symbols used in writing the reports. The process of converting plaintext to ciphertext is called enciphering, and the reverse process is called deciphering.
A glimpse of higher-dimensional spaces: hypercubes, lattice paths, and related number patterns
Authors: Cofman Judita
Published: November 2023

The classical geometries of dimensions two and three, the elementary properties of which are taught at school, were first described systematically by Euclid, about 300 BC, in his famous book the Elements. For this reason these geometries are called euclidean geometries of dimensions two and three respectively.
Chapter V
Authors: Cofman Judita
Published: November 2023

Suppose that a≡b (mod m). This means If m divides a - b then a - b = ms for some integer s. Suppose that when bis divided by m the remainder is r, that is, b =mt’+ r for some integer t’.
Chapter VI
Authors: Cofman Judita
Published: November 2023

Next find in S′ the summand containing Y  n—1. • Suppose that Y  n—1= Y  ik. In S′ interchange Yik and Y;n_ ; this transforms S′ into S″.
Algebraic Topics
Authors: Rose H E
Published: November 2023

In this chapter we introduce three topics with an algebraic flavour which will be useful later: algebraic numbers and integers, primitive roots, and characters. Although not closely connected it will be convenient to consider them now. Algebraic number fields will not be treated in detail: a good introduction can be found in Stewart and Tall (1979). We shall give the basic definitions and some examples of particular number fields. Algebraic number theory can be studied in two ways. First. as a subject in its own right emphasizing the algebraic aspect, but it is not our purpose to do this. Secondly, some problems relating to the rational numbers are best treated in this more general context.
Continued Fractions
Authors: Rose H E
Published: November 2023

Some number theoretic properties of the real numbers will be considered in this chapter and its sequel. We begin by asking how closely a rational number aIb can approximate to a real number a assuming some restriction on the size of b: that is. given a, can integers a and b be found to satisfy for a suitably chosen monotone increasing function f ? This is the basic question in Diophantine approximation theory.
Partitions
Authors: Rose H E
Published: November 2023

There are many relationships between subsets of the set of partitions of an integer n. The most famous, due to Euler, states that the number of partitions of n with odd parts equals the number of partitions of n with distinct parts. In the example above the first three partitions have distinct parts. whilst the first, fourth, and seventh partitions are the only ones with exclusively odd parts. A number of other properties of this type will be discussed in this chapter.
Elliptic Curves: Basic Theory
Authors: Rose H E
Published: November 2023

Most of the older theory of Diophantine equations is an ad hoc collection of individual methods without general applicability. Some constructions can be used in a number of cases, for example the infinite descent method (Chapter 6) or Skolem’s method (Chapter 14), but others apply only to single equations; examples include the congruence arguments used to show that particular Mordell equations are insoluble (also Chapter 14). Beginning with the work of Poincare and using the methods of algebraic geometry. a more organized and substantial theory has been developed during this century which applies to a wide range of equations defined over fields.
Computational aspects of the Jordan canonical form
Authors: Beelen Theo , Dooren Paul Van
Published: November 2023

In this paper we discuss algorithmic aspects of the computation of the Jordan canonical form. Inspired by Golub and Wilkinson (1976) on the computation of the Jordan canonical form, an O(n) algorithm was developed by Beelen and Van Dooren (1988) for computing the Kronecker structure of an arbitrary pencil AB - A. Here we show how the ideas of this algorithm lead to a special algorithm for reconstructing the Jordan structure of the standard eigenvalue problem Al - A.
Analysis of the Cholesky decomposition of a semi-definite matrix
Authors: Higham Nicholas J
Published: November 2023

Perturbation theory is developed for the Cholesky decomposition of an n x n symmetric positive semi-definite matrix A of rank r. The matrix W = A ;A12 is found to play a key role in the perturbation bounds, where A11 and A12 are r x rand r x (n - r) submatrices of A respectively.
Pluripotential Theory
Authors: Klimek Maciej
Published: November 2023

Pluripotential theory is a recently developed non-linear complex counterpart of classical potential theory. Its main area of application is multidimensional complex analysis. The central part of the pluripotential theory is occupied by maximal plurisubharmonic functions and the generalized complex Monge-Ampère operator. The interplay between these two notions provides the focal point of this monograph, which contains an up-to-date account of the developments from the large volume of recent work in this area. The substantial proportion of this monograph devoted to classical properties of subharmonic and plurisubharmonic functions makes the pluripotential theory available for the first time to a wide audience of analysts.
Generalized Characteristic Equation And Existence Of Positive Solutions
Authors: Györi I , Ladas G
Published: November 2023

Our aim in this chapter is to introduce a generalized characteristic equation for non-autonomous delay differential equations and then utilize it to obtain sufficient conditions for the oscillation of all solutions. Furthermore, we utilize the generalized characteristic equation to obtain some powerful comparison results and to demonstrate the existence of positive solutions for a wide class of linear delay equations with variable coefficients and variable delays.
Oscillations Of Neutral Differential Equations
Authors: Györi I , Ladas G
Published: November 2023

A neutral delay differential equation is a differential equation in which the highest-order derivative of the unknown function appears in the equation both with and without delays.
Oscillations Of Integrodifferential Equations
Authors: Györi I , Ladas G
Published: November 2023

The main result in this section is the following necessary and sufficient condition for the existence of a solution of eqn (9.3.1) which is positive for t>0.
Applications Of Oscillation Theory To The Asymptotic Behaviour Of Solutions
Authors: Györi I , Ladas G
Published: November 2023

Our aim in this chapter is to show that sometimes it is possible to investigate the global asymptotic behaviour of all solutions of a differential or a difference equation by investigating separately the oscillatory and the non-oscillatory solutions. We shall demonstrate this technique by applying it in Section 11.1-11.3 to some equations in mathematical biology and in Section 11.4 to a non-autonomous linear difference equation.
The Nautical Almanac Office as a computing centre and the founding of the Scientific Computing Service
Authors: Croarken Mary
Published: November 2023

Thefundamental purpose of HM Nautical Almanac Office was to calculate and publish accurate ephemerides to aid navigation and to assist astronomers. These ephemerides were published annually as the Nautical almanac. Comrie’s principle responsibilities as Superintendent of the NAO were the supervision and improvement of the publication of the Nautical almanac. As part of this work Comrie undertook a major revision of the Nautical almanac, incorporated in the 19 31 Nautical almanac which had remained more or less unaltered since 1834. He rearranged, rewrote, and enlarged it to make it both more useful and easier to read. Comrie’s mechanization of the computing methods used to prepare the Nautical almanac (described in Chapter 3) introduced other revolutionary changes for the NAO.
The creation of a national computing centre
Authors: Croarken Mary
Published: November 2023

Within a year of the Admiralty Computing Service becoming operational Todd, Sadler, and A. Erdelyi, an Admiralty scientific consultant during the war, realized that the degree of centralized computation they could offer within the Admiralty did not go far enough. The ACS did not operate on a large enough scale to run a fully equipped computing service. It was not economically feasible to install punched card machines or a differential analyser for example. In some cases, therefore, computing efficiency was sacrificed because the most suitable type of equipment was not available to the ACS. Those responsible for the ACS, Todd and Sadler, were of the opinion that only centralization at the national level would achieve the economies of scale necessary to provide a fully equipped service.
Computing machine developments at Cambridge and Manchester
Authors: Croarken Mary
Published: November 2023

In Britain in the late 1940s there were three main centres which became heavily, and successfully, involved in the development of electronic stored program computers. These three centres were the NPL Mathematics Division, Cambridge University, and Manchester University. The computer research at the NPL has already been discussed and was part of the work which the Mathematics Division carried out as part of its role as a national computing centre. At Cambridge and Manchester the situation was very different. At Cambridge the existing Mathematical Laboratory was used as a vehicle for computing machinery development. At Manchester the computing centre developed around the research interests of the engineers and mathematicians based at the university.
Classifying clauses
Authors: Hogger Christopher John
Published: November 2023

Clauses may be classified according to the number of positive and negative literals they contain.

A definite clause contains exactly one positive literal and zero or more negative literals.

Example— happy(chris) or ,eating(chris, apple_crumble)

A positive unit clause is a definite clause containing no negative literals.

Example—happy(chris)

A negative unit clause is a negative clause with exactly one negative literal.

Example— ,desirable(pop_music)

A unit clause is either a positive unit clause or a negative unit clause, as in the last two examples.

A negative clause contains zero or more negative literals and no positive literals.

Example— ,happy(chris) or ,eating(chris, sheep’s_brains)
Elements of proof theory
Authors: Hogger Christopher John
Published: November 2023

Whereas model theory considers the assignment of meaning to sentences, proof theory considers the generation of sentences from other sentences. Later on we shall see that proof theory yields a precise framework in which to articulate the computational features of the logic programming formalism, whilst model theory yields precise information about the formalism’s semantics.
Resolution in logic programming
Authors: Hogger Christopher John
Published: November 2023

We shall now start bringing together various ideas from the preceding Themes in order to explain how resolution is typically adapted for the purpose of logic programming.
Search strategy
Authors: Hogger Christopher John
Published: November 2023

Given any program P and any query Q, the choice of some computation rule determines a unique SLD-tree rooted at Q. This tree represents all the SLD computations that can be derived using that computation rule. In general, different computation rules applied to a given input set {P, Q} will determine different SLD-trees, although-as observed previously-all those trees will agree upon the computed answer set.

A typical interpreter implements some fixed computation rule, although there are some interpreters which allow the user to choose a rule from a range of alternatives. A common way of specifying one’s own computation rule without considering the interpreter is to define that rule via a meta-program M interposed between the interpreter and the object program {P, Q); the interpreter then executes M using its own rule, and this action in turn drives the execution of the object program in accordance with the defined rule. Whichever such arrangement is made, however, we always know that some unique SLD-tree has to be incrementally constructed by the interpreter in order that it may search for answers.
Adequacy of the SLD paradigm
Authors: Hogger Christopher John
Published: November 2023

In previous Themes we have described the basic workings of a computational formalism founded upon the following principles:

The scope of the present course permits only a brief consideration of these issues; moreover, we must leave many other important issues wholly unaddressed.

A definite-clause program determines, for each m-ary predicate symbol p appearing in it, some relation Rp which is a subset of um where H is the Herbrand domain of the language. Now consider any function f mapping un to

H where n>O. Clearly every such function f can be trivially represented by a corresponding (n+1)-ary relation Rp satisfying
The lattice of models for a definite program
Authors: Hogger Christopher John
Published: November 2023

First, since we shall deal here only with (H-)models and (H-)interpretations, the prefix 'H-' will henceforth be omitted but assumed by default. We begin by recalling that a model is just a particular set of ground atoms deemed to be true. Our main interest is in the question of whether a given model makes more atoms true than it needs to in order to satisfy a given definite program—equivalently, whether that model includes any smaller models.
Fix point interpretation of the minimal model
Authors: Hogger Christopher John
Published: November 2023

The process by which the method in Theme 45 generates each interpretation Ik+l from its predecessor lk can be cast as the application of a function Tp:

This function, which is a total mapping from the powerset of B(P) to itself, is specific to the given program P (hence the subscript P in its name) and is defined as follows:

Clearly this definition just formalizes our earlier informal account of how one interpretation is obtained from another.

Given any function f defined on a partially-ordered set [S, ], it is of primary interest to know whether or not that function is monotonic and/or continuous. It is monotonic if and only if for all ueS and veS, f(u) f(v) whenever u v and it is continuous if and only if