bluuebunny/crossref_metadata_2025 huggingface dataset:
Dielectric polarization mechanism: potential importance for resonant interactions on biological systems
Authors: Schwan H P
Published: November 2023

Electrical properties are determined by the effects of electrical fields on mat¬ ter. Therefore much can be learned about field interactions from properties. If some interactions are localized, they may contribute but little to electrical properties, and bulk properties will then not reflect such specific interactions. An example is the cell membrane. The admittance of the membrane is determined by both its capacitance and its conductance. However, bulk properties as revealed by measurements with cell suspensions are not very sensitive to the membrane conductance. Yet it is the conductance, largely determined by the channels, which is directly related to ion exchange. Never-theless, a knowledge of the electrical properties of cellular compartments is revealing, as I shall demonstrate.
Possible resonance effects of ELF magnetic fields on ion channels
Authors: Sandblom John , Galt Sheila , Roos, Dan , Hamnerius Yngve
Published: November 2023

Considerable evidence has accumulated during recent years that ELF (extremely low-frequency) magnetic fields can interact with living tissues at the cellular level (Adey and Bawin 1982; Blackman etal. 1985a, b; McLeod et al. 1987; Smith et al. 1987). Existing data seem consistently to indicate the occurrence of regions of maximal absorption of energy, i.e. resonance effects, with respect to amplitude and frequencies of the magnetic fields. Examples of such systems are the calcium efflux from brain tissue (Adey and Bawin 1982; Blackman et al. 1985a, b) and the motility of diatoms (McLeod etal 1987; Smith etal. 1987) in which the responses to applied ELF signals show distinct peaks at certain frequencies.
Activation of T-lymphocyte growth in a low-frequency magnetic field
Authors: Brista V Britta , Mild Kjell Hansson , Mattsson, Mats-Olof , Lundgren Erik
Published: November 2023

An increasing number of reports indicate that the primary site for interaction between low-frequency electromagnetic fields and biological systems is at the cell membrane level (Adey 1988). Lectin-stimulated human lymphocytes have often been used to analyse biological effects of magnetic fields (for a recent review, see Cadossi et al. 1988) and, depending on the conditions, both stimulatory and inhibitory effects have been observed (Conti et al. 1986). T-lymphocytes represent an excellent assay system for such studies, since growth factor requirements are well defined, as well as parts of the signal transduction pathway.
Progress in developing insecticides from natural compounds
Authors: Khambay Bhupinder P S , O’connor Norval
Published: November 2023

Approximately one third of world food production is lost through damage caused by pests. The most efficient method of controlling insect pests relies on the use of insecticides (compounds which kill insects) many of which act on the insect nervous system. Although current commercial insecticides have limited persistence in the field, the public perception of insecticides as highly undesirable and environmentally unfriendly chemicals stems from the persistence of DDT, ironically, an insecticide which has probably given more benefit to mankind than any other chemical invention. A great deal of research is currently being directed towards finding alternatives to insecticides. However, the present limitations in efficiency and effectiveness of such approaches ensures that for the foreseeable future, insecticides will remain the most effective means of insect control in the field. Therefore the search for newer insecticides with even greater selectivity towards pests and activity against resistant insects will continue.
Metabolic signals in the rhizosphere: catabolism of calystegins and betaines
Authors: Goldmann Arlette , Message Brigitte , Lecoeur Loic , Delarue Marianne , Maille Monique , Tepfer David
Published: November 2023

Certain small secondary metabolites of plants are implicated in the establishment and maintenance of specific plant-bacterium relation ships. Some of these substances induce the transcription of bacterial genes implicated in the plant-bacterium interaction, e.g. virulence genes in the phytopathogen Agrobacterium tumefaciens (Stachel et al. 1985) and nodulation genes in the nitrogen-fixing symbiont Rhizobium (Firmin et al. 1986; Peters et al. 1986). In the former case, the inducing molecules are monocyclic phenols, such as acetosyringone, released from wounded tissues; in the latter, they are complex phenolic flavones or flavonoids from legume root exudates. These substances also serve as chemoattractants.
Digestibility-inhibiting substances from alfalfa
Authors: Massiot G , Lavaud C
Published: November 2023

The main sources of proteins for animal feed are cereals and soya. Only polygastric animals are able to partly degrade cellulose and to make use of non-cereal vegetable proteins. At the present time, soya-cake is mainly imported from the USA and Argentina, and in a quest for alternative and independent sources of proteins, Europe is trying to promote its own cultures of sunflower, rape, lupin, pea, and alfalfa.
Polyphenols–phytochemical chameleons
Authors: Haslam Edwin
Published: November 2023

Natural polyphenols (syn. vegetable tannins) are complex higher plant secondary metabolites. According to earlier definitions they are water soluble, possess relative molecular masses in the range 500 to 3000, and besides giving the usual phenolic reactions, they have the ability to pre cipitate some alkaloids, gelatin, and other proteins, from solution. These complexation reactions are not only of intrinsic scientific interest as studies in molecular recognition but they have important and wide-ranging practical applications–in the manufacture of fashion leathers, in food stuffs and beverages, in herbal medicines, and in chemical defence and pigmentation in plants. Polyphenols are phytochemical chameleons. Their interactions with other molecular species is, on occasion, an important facet of the chemistry of plants and it also underlies man’s use of these materials in a number of practical spheres. In other situations these same interactions may well be undesirable if not totally unacceptable.
British gall-causing rust fungi
Authors: Preece* T f. , Hickt† A J
Published: November 2023

Although some fungal galls on cultivated plants have been the subject of much research (most of which has been aimed at preventing their occurrence) fungal galls on wild plants remain little studied. The literature on galls often includes long lists of rust fungi (Basidiomycotina: Ureclinales) but some of these fungi do not produce abnormal growth visible to the naked eye. It is suggested that visible swelling or thickening of plant organs is used to distinguish gall-causing rust fungi. After outlining the life history of a long-cycled rust the authors provide a list of principal British gall-causing rust fungi and their hosts.
Structure and systematics of eriophyid mites (Acari: Eriophyoidea) and their relationship to host plants
Authors: Boczek* Jan , Griffiths† D A
Published: November 2023

The eriophyid fauna is represented by 2400 species contained within six families, all of which are phytophagous and said to be monophagous to one species of plant. They possess a morphology unlike all other mites, with a minute cylindrical, worm-like or spindle-like body and two pairs of legs. Their habitat and effect on the plant ranges form leaf surface dwellers, with no detectable physical effect, through causers of leaf russeting, curling, edge-rolling, bud swelling, and brooming to producers of crinea and other complex galls. This paper discusses these phenomena and considers family ecology in relation to the gymnosperm and angiosperm hosts.
The population dynamics of the gall wasp Andricus quercuscalicis
Authors: Hails Rosemary S
Published: November 2023

The gall wasp Andricus quercuscalicis invaded Britain from the continent in the early 1960s. The life cycle involves both alternation of generations and alternation of host plants. This study draws on 8 years of population data and considers the factors that limit and regulate the distribution and abundance of A. quercuscalicis. This gall wasp, now abundant, appears to be resource-limited in the agamic generation due to competition for acorns in the ‘low years’ of the acorn cycle. Factors influencing the survivorship of the sexual generation are considered in detail. Although the sexual generation does not appear to be resource-limited, there is evidence of density-dependent mortality during gall establishment. This arises partly as a consequence of the oviposition pattern of the agamic females, because the distribution of eggs is highly aggregated between and within trees. As a result of density-dependent mortality, the distribution of mature galls is less highly clumped. Although the agamic knopper gall suffers only low rates of parasitism from a few species, several native parasitoids attack the sexual gall. The total percentage of parasitism is remarkably consistent from year to year even though the contribution from any one species fluctuates considerably.
Phytochemical investigation of candidate plants for the management of sickle cell anaemia
Authors: Adesanya S A , Sofowora A
Published: November 2023

Sickle cell anaemia (SCA) is a hereditary disease first described by Herrick in 1910. The genes of the patient code for the synthesis in cells of an abnormal haemoglobin HbS, which has /?6-valine instead of /?6-glutamic acid found in normal haemoglobin (HbA) (Murayama 1967). The resultant clinical manifestation of the disease is prominent in patients homozygous for the S gene (HbSS), while heterozygotes with other abnormal genes, such as SC, SThal, or SF, exhibit a milder form of the disease. People with HbAS, however, do not show the symptoms associated with SCA (Lawrence and Wallace 1974). SCA patients suffer characteristically from persistent ulcers, an enlarged spleen, and painful swelling of the digits and joints (Isaacs-Sodeye 1975).
Structural studies on new compounds from medicinal plants of Pakistan, Jordan, Sri Lanka, and Turkey
Authors: Rahman Atta-Ur- , Choudhary M I
Published: November 2023

Medicinal plants offer a vast resource of novel natural products, often with exciting activities and biological properties. The following chapter presents some representative examples of natural products isolated from medicinal plants of Pakistan, Jordan, Sri Lanka, and Turkey in our laboratories. Their structures were elucidated using modern mass spectroscopic and NMR techniques. Both lD (1H-NMR, C-NMR, DEPT, NOE, homodecoupling, etc.) and 2D (COSY-45°, NOESY, HOHAHA, heteroCOSY, 2D J-resolved, COLOC, etc.) NMR experiments as well as recently developed inverse NMR techniques (HMQC and HMBC) were utilized for determination of their structure.
Spatial and temporal control of cell division in plants
Authors: Doonan J H
Published: November 2023

The generation of body form in plants occurs without substantial cell migrations. The relative immobility of plant cells has consequences for the manner in which morphogenesis may occur. In animals, cells can move subsequent to their formation, but during plant growth additional cells have to be produced at a given position (where they are required) within the body of the plant. Subsequent cell enlargement (usually directed elongation) and further cell divisions may allow some flexibility in formation of the final morphology. The molecular basis of cell proliferation in plants is poorly understood, but a reasonable surmise might be that cell division and cell elongation are downstream targets of those factors which generate pattern. Based on this surmise, it has been our purpose to develop molecular markers with which we can follow the location and progress of cell division within multicellular plant organs and thereby gain some insight into how cell division might be regulated during morphogenesis.
Role of the CTRl kinase in ethylene signal transduction inArabidopsis
Authors: Pallin J B , Woeste K E , Kieber J J
Published: November 2023

The simple olefin ethylene has been known to have dramatic effects on plants since the early part of this century when the various effects of illuminating gas on pea seedling development were first described (Neljubow 1901). Since then, ethylene has been shown to influence a diverse array of plant growth and developmental processes, including germination, leaf and floral senescence, abscission, epinasty, stress responses, and fruit ripening (Abeles et al. 1992). The biosynthetic pathway for ethylene has been elucidated and genes encoding the two key enzymes, ACC synthase and ACC oxidase, have been cloned from a number of plant species (reviewed in Kende 1993).
Introduction
Authors: Srinivasan Mandyam V , Venkatesh Svetha
Published: November 2023

Vision is, without doubt, our sense par excellence. That the eye and the visual pathways could have evolved simply as a result of natural selection was a concept that taxed even Darwin’s imagination as he espoused his trail-blazing theory of evolution in The origin of species (Darwin 1859). It is no surprise, then, that the task of developing artificial systems that ‘see’ and ‘perceive’ the world in the way we do, is not a trivial one.
Interface areas in small fish
Authors: Harrison I J
Published: November 2023

Morphometric relationships between selected body tissues and body mass are analysed for small gobies (Teleostei: Gobiodei). These species show large body surface areas relative to mass, which might be advantageous for facultative cutaneous respiration but potentially disadvantageous for osmoregulation and locomotion. Large body surface areas per unit mass and correlated drag forces could account for ‘transient’ modes of swimming in small fish. Some species show large mass-specific development of gill area and, in this respect, are thought to be paedomorphic. Gill development in miniature teleosts must be constrained ultimately by pharyngobranchial space and a compromise must be reached between gills and skin in respiratory and osmoregulatory roles.
Speciation in small mammals
Authors: Searle J B
Published: November 2023

There are more species of small mammal (less than 1 kg) than species of large mammal, with the rodents, bats, and insectivores particularly speciose. Small mammals show greater differentiation into species at both the local and the regional level. Species of small mammal tend to occupy smaller geographic ranges than large species so that, within a geographic region the size of North America, it is common to find examples of several to many parapatric species of small mammal (often congeneric), each with essentially the same ecological needs. When species of small mammal do have large ranges, they are often subdivided into many parapatric subspecies.
The psychology of human-smalI vertebrate interactions
Authors: Mcbride Anne
Published: November 2023

Humans develop a variety of relationships with animals. At one end of the range, where the animal serves a special psychological function for the human, strong attachment bonds may develop. Contrastingly, the human may simply interact with the animal, treating it as an object devoid of individuality per se. In this latter case the relationship is between the human and some distinct aspect of the species or breed which is divorced from the individual animal’s character. The animal provides a means by which humans can make a statement about themselves or provides some form of intellectual stimulation and/or social facilitation.
Fruit aroma precursors with special reference to phenolics
Authors: Crouzet J , Sakho M , Chassagne D
Published: November 2023

Odorous compounds present in food reach the olfactory mucosa receptors in two different ways. The first is by directly sniffing volatile molecules into the nose, where they interact with the receptors producing the sensation known as odour. The second is where volatile substances released from food in the mouth reach the olfactory epithelium by a retronasal route, producing the sensation known as aroma. The combined sensations of odour, aroma, and taste give the overall ‘flavour’ of a food.
Introduction
Authors: Cartledge Bryan
Published: November 2023

If he could have understood them, Thomas Linacre would have been well satisfied with the first series of lectures on the environment which bear his name, As he lived and died long before the basic laws of science had been established and formulated, he would find the lectures largely incomprehensible. But as a classical scholar and grammarian who was also a physician (his task of ministering to the physical needs of, among others, Henry VIII and Cardinal Wolsey can have been no sinecure), Linacre doubtless had a good understanding of the interdependent relationships between the various areas of human knowledge, even within the relatively narrow frontiers which that knowledge had reached in his lifetime. Since Linacre’s death nearly five centuries ago, those frontiers have expanded exponentially and their advance is still accelerating: but the interdependence, which Linacre would have recognized and which these lectures demonstrate so well, remains.
The environment: problems and prospects
Authors: Southwood Richard
Published: November 2023

Sir Richard Southwood, FRS, Vice-Chancellor of Oxford University and Linacre Professor of Zoology; is one of Britain’s foremost environmentalists. After nine years as a Lecturer in Zoology at Imperial College London and three as Reader in Insect Ecology at the University of London, Sir Richard was in 1967 appointed University Professor of Zoology and Applied Entomology while also heading that Department at Imperial College and directing the Field Station of the College. In 1974 he became Chairman of the Division of Life Sciences at Imperial College and in the same year was appointed to membership of the Royal Commission on Environmental Pollution (RCEP); he was Chairman of the Commission from 1981 to 1986. Meanwhile, in 1979, Sir Richard had moved to Oxford on his appointment to the Linacre Professorship of Zoology and his election to a Fellowship at Merton College. He has been a member of the National Radiological Protection Board since 1980 and its Chairman since 1985. He was installed as Vice-Chancellor of the University in October, 1989. He is the author of numerous books and papers on insects and ecology. Sir Richard’s acceptance of Linacre’s invitation to deliver the inaugural Linacre Lecture gave the series the most auspicious possible start.
The environment: a political view
Authors: Heseltine Michael
Published: November 2023

The Rt. Hon. Michael Heseltine, MP, was elected to Parliament as Conservative member in 1966 and has held a seat ever since. He took his degree in Philosophy, Politics, and Economics at Oxford and entered politics from a background in business and publishing. In 1970 he became Parliamentary Under-Secretary of State at the Department of the Environment and following the defeat of the Conservative Party in the general election of October 1974 held the positions of Opposition Spokesman on Industry (until 1976) and the Environment (1976-1979). When the Conservatives under Mrs Thatcher were returned to office in 1979, Michael Heseltine returned to the Department of the Environment as Secretary of State; in 1983 he was appointed Secretary of State for Defence.
The dilemma of the Amazon rain forests: biological reserve or exploitable resource?
Authors: Prance Ghillean T
Published: November 2023

Professor Ghillean (lain) Prance was appointed Director of the Royal Botanic Gardens, Kew in 1988, after spending 25 years in the United States. He is one of the world’s foremost experts on the Amazon rainforests. After graduation and the award of a doctorate at Oxford University, Iain Prance went to New York on what was intended to be a temporary appointment at the New York Botanical Gardens; in the event, he stayed on to become, in 1968, Curator of Amazonian Botany. He was subsequently appointed Director of Research at the New York Botanical Gardens and then Director of its Institute of Economic Botany. He held Visiting Professorships at the City University of New York and at Yale University. He was Leader of the United States Amazonian Exploration Program for 20 years and visited the region on numerous occasions. He is the author of several books on botany and Amazonia.
Health, environment, and tropical development
Authors: Bradley David
Published: November 2023

Nowhere has the environment so great and obvious an effect on health as in less developed countries, nor are there any countries where greater environmental changes are taking place as a result of the search, whether successful or otherwise, for socioeconomic development. These environmental changes are in turn reflected in changes of health.
Changing diseases in changing environments
Authors: May Robert
Published: November 2023

Death from infectious disease was a much more commonplace thing in Victorian Britain than it is today. Most readers of this book will be able to cast their minds back several generations in their own family history to recall how the large families of Victorian times typically lost several children before adulthood. Likewise, children often lost parents-not least that symbol of the Victorian Age, Prince Albert-to infectious diseases. Such events run through the literature of that age: Beth in Little Women, the eponymous and obnoxiously saintly Little Lord Fauntleroy, the Lady of the Camellias.
Operational principles of brushless servomotors
Authors: Uchiyama Shunichi
Published: November 2023

A brushless servomotor has been developed by using interdisciplinary mechatronics engineering. A mechanical switching device (commutator) is replaced by electronic circuits and controllers, resulting in a maintenance-free and high-performance servo drive. This chapter also describes various other kinds of technologies used in servomotor drive development. The brushless servomotor is an a.c. motor in all respects and is in fact called the a.c. servomotor. Combined with a dedicated control device, the performance of the brushless servomotor is found to be equal to or superior to the performance of the high-performance d.c. servomotor.
Brushless servomotor control
Authors: Dote Yasuhiko
Published: November 2023

‘To control’ is defined as ‘to manipulate an object so as to serve a certain purpose (so as to make it work as desired).’ In our case, the motor is called the controlled system, the physical quantities (voltage, current, frequency, torque, angular velocity, and angle) are called the controlled variables, the required manipulations are called the manipulated variables (armature current, and frequency), and the instruction to be given is called the control reference.
Measurement and evaluation of brushless servomotors
Authors: Ishimine Hitoshi
Published: November 2023

Servomotors are used for automatic controllers, especially for servo-mechanisms. They control the stopping position and the rotational speed. Therefore, users demand that servomotors rotate evenly over a wide range of speed without being influenced by the load, and that they follow up the command signals and respond quickly. The topics explained in this chapter are measurement and evaluation of the items to be considered in satisfying the users’ demands.
Introduction
Authors: Vas Peter
Published: November 2023

It is the purpose of the present book to describe various alternating current (a.c.) and direct current (d.c.) electrical machines and variable-speed drives, including some of the most recently introduced modern drives, and also to present a general theory which is applicable during steady-state and transient operation. For this purpose a very detailed physical and mathematical analysis is presented which relies mainly on space-vector theory but the relationship to other theories, including the matrix theory of the generalized machine theory, has been emphasized throughout the book. The book can be used without any prior knowledge of space-vector theory or other theories. To make the book self-contained, the fundamental principles of the various alternating current electrical machines and drives are also discussed; thus it can be used for complete and self-contained courses at different levels. Furthermore it can be used by researchers and other academics and members of the industry, and it has been one of the main intentions to develop the theory and equations in a user-oriented form. Thus, in many parts, the equations are given in their final (state-variable or analytical) forms, which can be directly used for computer simulations or for hand calculations. These also include the small-signal equations, which enable stability analysis to be performed.
Core Losses
Authors: Miller TJE , Rabinovici R
Published: November 2023

After copper losses, core losses are generally the second largest component of power loss or inefficiency in the brushless motor, although their significance may become overriding at very high speeds. They arise from the variation of magnetic flux-density throughout the core, particularly the stator core. This variation incurs hysteresis and eddy-current losses, (Chapter 16). Briefly summarizing, the hysteresis loss results from the “unwillingness” of the steel to change its magnetic state, and as the flux-density varies cyclically the magnetic state describes a locus in the B/H diagram: the energy loss per cyde is proportional to the enclosed area, so the average power loss due to hysteresis is proportional to the frequency of the variation in the magnetic field. Eddy-current loss is also caused by variations in flux-density, which induce current to flow in the stator steel at the same frequency as the variation in the magnetic field. The EMF which drives these currents is proportional to the peak magnetic field and to the frequency of variation, but the power loss is proportional to the square of the EMF and therefore also varies with the square of the peak flux-density and the frequency. Eddy-current losses can be reduced by using thinner lamination steels.
Cooling
Authors: Miller TJE
Published: November 2023

Heat transfer is as important as electromagnetic and mechanical design. The analysis of heat transfer and fluid flow in motors is actually more complex, more nonlinear, and more difficult than the electromagnetic behaviour. It is often dealt with by means of simplified equivalent circuits, and rarely receives the detailed analysis lavished on electromagnetic aspects. Perhaps there is some justification for using approximate methods for heat transfer, when exact methods are pursued for electromagnetic design. The electromagnetic design determines the geometry of laminations which are cut to fine tolerances. Their geometry and thickness, together with their material properties and the design of the windings, determine whether or not the motor will deliver the required torque. They also determine the precise voltages and currents that will be experienced by the power semiconductors in the controller.
Introduction
Authors: Vas Peter
Published: November 2023

In the present book, artificial-intelligence-based electrical machines and variable-speed drives are discussed. For this purpose, various static and adaptive fuzzy logic systems, unsupervised and supervised artificial neural networks, fuzzy-neural networks, and genetic-algorithm-assisted systems are considered. Artificial intelligence (AI) is used for various purposes, including simulation (in the steady state and transient state), identification, estimation, control, design, condition monitoring, and diagnosis. Great emphasis is laid on presenting detailed description of the various techniques. For this purpose and also to make the book self-contained, the fundamentals of the different AI-based techniques, which are also referred to as soft-computing techniques in the literature, are also discussed in detail and many worked-out examples are given. The book contains the most up-to-date and modern developments in the field.
Fuzzy-neural systems
Authors: Vas Peter
Published: November 2023

In Section 4.5 the main features of adaptive fuzzy-neural systems were discussed. It follows that a fuzzy-neural network has a structure resulting from the combination of a fuzzy system and a neural network. It is the goal of this network to perform a required non-linear mapping from input to output spaces by using a neural network integrated with a fuzzy system (fuzzy-neural network) whose parameters are adjusted to improve performance by using a learning algorithm. Usually the design methods are hybrid design methods, originating from both fuzzy system and neural system concepts. Some of the main features are: Main aspects of neural-fuzzy system integration: the most useful features of the two system should be combined; combination should be performed in such a way that resulting integrated system should be most efficient.
Artificial-intelligence-based steady-state and transient analysis of d.c. machines, estimators, control
Authors: Vas Peter
Published: November 2023

In the present chapter, first, the Al-based steady-state and transient analysis of d.c. machines is discussed. For this purpose ANNs and fuzzy-neural networks are used. This is followed by describing AI-based drives, e.g. d.c. drives with ANN speed estimators, d.c. drives with fuzzy controllers, d.c. drives with fuzzy-neural estimators, d.c. drives with neuro controllers (including combined controllers, e.g. where instead of using a separate speed and current controller, a single, ANN-based combined controller is used).Traditionally mathematical model-based analysis techniques have always been used for the steady-state and transient analysis of electrical machines and drives. There are many techniques, but they mainly differ in their complexity and the many assumptions used. In general, when generalized machine theory is used for transient analysis of a d.c. machine, the stator and rotor differential equations, together with the equation of motion, are used for simulation purposes. In a d.c. drive these equations are complemented by the equations governing the controllers and the converter. Thus, in general, a system of first-order non-linear differential equations is obtained, which can be solved by using a numerical technique (e.g. Runge-Kutta technique). However, it is also possible to perform the simulations by using neural networks, or fuzzy-neural networks, which do not require a mathematical model [Vas, 1998]. Such a system is not restricted by the many assumptions used in conventional electrical machine theories.
The organization of the book
Authors: d’Invemo Ray
Published: November 2023

There is little doubt that relativity theory captures the imagination. Nor is it surprising: the anti-intuitive properties of special relativity, the bizarre characteristics of black holes, the exciting prospect of gravitational wave detection and with it the advent of gravitational wave astronomy, and the sheer scope and nature of cosmology and its posing of ultimate questions; these and other issues combine to excite the minds of the inquisitive. Yet, if we are to look at these issues meaningfully, then we really require both physical insight and a sound mathematical foundation. The aim of this book is to help provide these. The book grew out of some notes I wrote in the mid-1970s to accompany a UK course on general relativity. Originally, the course was a third-year undergraduate option aimed at mathematicians and physicists. It subsequently grew to include M.Sc. students and some first-year Ph.D. students. Consequently, the notes, and with it the book, are pitched principally at the undergraduate level, but they contain sufficient depth and coverage to interest many students at the first-year graduate level. To help fulfil this dual purpose, I have indicated the more advanced sections (level-two material) by a grey shaded bar alongside the appropriate section. Level-one material is essential to the understanding of the book, whereas level two is enrichment material included for the more advanced student. To help put a bit more light and shade into the book, the more important equations and results are given in tint panels.
The K-calculus
Authors: d’Invemo Ray
Published: November 2023

Before we start, we should be clear what we are about. The essential activity of mathematical physics, or theoretical physics, is that of modelling or model building. The activity consists of constructing a mathematical model which we hope in some way captures the essentials of the phenomena we are investigating. I think we should never fail to be surprised that this turns out to be such a productive activity. After all, the first thing you notice about the world we inhabit is that it is an extremely complex place. The fact that so much of this rich structure can be captured by what are, in essence, a set of simple formulae is to me quite astonishing. Just think how simple Newton’s universal law of gravitation is; and yet it encompasses a whole spectrum of phenomena from a falling apple to the shape of a globular cluster of stars. As Einstein said, ‘The most incomprehensible thing about the world is that it is comprehensible.’
Integration, variation, and symmetry
Authors: d’Invemo Ray
Published: November 2023

Then, with certain modifications, we can combine tensor densities in much the same way as we do tensors. One exception, which follows from (7.1), is that the product of two tensor densities of weight W1 and W2is a tensor density of weight W1 + W2.
The energy-momentum tensor
Authors: d’Invemo Ray
Published: November 2023

Our programmer for this chapter is to look at the three most important energy—momentum tensors in general relativity, namely, the energy—momentum tensors for incoherent matter or dust, a perfect fluid, and the electromagnetic field. In passing, we shall encounter a tensor formulation of Maxwell’s equations governing the electromagnetic field. Again, our treatment will not be exhaustive or complete, but will be sufficient for generating the explicit expressions for the three tensors, and these expressions will be essentially all that we require in future chapters. We shall also look more carefully at the Newtonian limit and discuss the calculation for determining the coupling constant.
The structure of the field equations
Authors: d’Invemo Ray
Published: November 2023

1. The field equations are differential equations for determining the metric tensor gabfrom a given energy-momentum tensor Tab.Here, we are reading the equations from right to left. This is a Machian way of viewing the equations since one specifies a matter distribution and then solves the equations to ascertain the resulting geometry. It is also a natural way of looking at the Einstein-Maxwell equations, namely, what geometry corresponds to a given Maxwell tensor? The most important case of the equations is when Tab= 0, in which case we are concerned with finding vacuum solutions.
Experimental tests of general relativity
Authors: d’Invemo Ray
Published: November 2023

In this chapter, we shall consider the experimental status of general relativity. We shall see that the status is very different from that of special relativity, which has been subjected to a welter of different tests. Indeed, there are very few theories whose experimental footing has been so well established. In contrast, there are very few tests of the general theory. The main reason for this small number is that the gravitational fields experienced in our locality are very weak and their effects are not significantly different from the corresponding Newtonian ones. The extent to which the tests we have are actually tests of the particular set of field equations of general relativity as opposed to much weaker statements like the principle of equivalence is also arguable. The first tests of the theory were the three so-called ‘classical tests’ of general relativity, namely, the precession of the perihelion of Mercury, the bending of light, and the gravitational red shift. These tests have been augmented more recently by a fourth classical test, the delay of a light signal in a gravitational field.
Charged black holes
Authors: d’Invemo Ray
Published: November 2023

the Reissner-Nordstrom solution for a charged mass point. The importance of this solution is that its structure is in many ways similar to that of the more complicated Kerr solution describing rotating black holes which we shall meet in the next chapter. The approach we adopt is to look for a static, asymptotically flat, spherically symmetric solution of the Einstein-Maxwell field equations.
Rotating black holes
Authors: d’Invemo Ray
Published: November 2023

In this chapter, we shall investigate the Kerr solution which describes rotating black holes. It turns out to be a rather long process to solve Einstein’s vacuum equations directly for the Kerr solution. We shall, instead, describe a ‘trick’ of Newman and Janis for obtaining the Kerr solution from the Schwarzschild solution. This same trick can then be applied to the Reissner-Nordstrnm solution to obtain the Kerr-Newman solution, the most general solution for a charged rotating black hole. In order to discuss this approach, we start by introducing the very important idea of a null tetrad.
Plane gravitational waves
Authors: d’Invemo Ray
Published: November 2023

Our consideration of gravitational radiation or gravitational waves (gravity waves for short) starts from the pioneering work of Einstein and is based on the linearized form of the field equations. In this approximation, we shall see that plane wave solutions lead to the result that gravitational waves are transverse and possess two polarization states. Put another way, the gravitational field has two radiation degrees of freedom. In the linearized approximation of the field equations, general relativity is recast as a Lorentz-covariant theory. Considerable caution has to be exercised in doing this because there are associated with it a number of serious difficulties and limitations (the details of which are beyond the brief of this book), but nonetheless it does throw some important light on the general theory.
Radiation from an isolated source
Authors: d’Invemo Ray
Published: November 2023

The extent to which the results of the linearized theory can be trusted is not clear. The non-linearity of the gravitational field is one of its most characteristic properties, and it is likely that at least some of the crucial properties of the field should show themselves through the non-linear terms. Indeed, we have met exact solutions of the Einstein vacuum field equations corresponding to plane gravitational waves and we have seen that superposition of them leads to the creation of intrinsic singularities. This result is certainly absent in the linear case, so clearly there are differences. However, even these solutions are global vacuum solutions abstracted away from sources and as such are physically unrealistic, even if they may give us important information about how waves behave in asymptotic regions. What we would really like to do is to be able to investigate gravitational waves from bounded isolated sources, since then we would be in a position to discuss energy transfer and it is this which determines whether or not gravitational waves behave in the same way as other forms of radiation. Such a model system consists of an isolated bounded source (preferably possessing as much symmetry as possible, so that the field equations are easier to handle) which has been quiescent for a semi-infinite period, then radiates for a finite time, and afterwards becomes quiescent again. If the resulting waves are real physical waves, in that they carry energy, then we might expect the source to lose mass (and possibly other multipole moments may change) in the process.
How matrices arise
Authors: Barnett Stephen
Published: November 2023

In this chapter we describe a few of the very many areas of applications in which matrices are used, the choice of topics being deliberately diverse.
Eigenvalues and eigenvectors
Authors: Barnett Stephen
Published: November 2023

The underlying problem in much of the theory discussed so far in this book is that of solving sets of linear algebraic equations. To be able to deal with other applications, such as solution of sets of linear differential equations, we need the ideas of this chapter. Indeed, these are essential for much further development of matrices.
Polynomials, stability, and matrix equations
Authors: Barnett Stephen
Published: November 2023

In Problem 4.8 it was seen how when the Laplace transform is applied to a set of constant-coefficient linear differential equations then the solution involves the characteristic polynomial of the system matrix. Readers familiar with the Laplace transform will be aware that any nth order linear differential equation can be transformed into a problem involving an nth degree polynomial; the same applies to linear difference equations when the z-transform is used (Ogata, 1987). In this chapter we show how properties of polynomials can be investigated using matrix techniques. In particular, it will be seen that the gaussian elimination procedure once again proves useful.
Polynomial and rational matrices
Authors: Barnett Stephen
Published: November 2023

11.15 which describe a certain simple dynamical model. Suppose that the initial conditions for 01, 81, 02, 82 are all zero. Applying the Laplace transform to these equations then produces The 2 x 2 matrix A(s) on the left in (12.2) is an example of a polynomial matrix, whose elements are themselves polynomials. As for a scalar polynomial, A(s) can be written in terms of powers of s:
Miscellaneous topics
Authors: Barnett Stephen
Published: November 2023

In this chapter we bring together some further material which is of interest for applications. By necessity we shall have to use a rather terser style than in the rest of the book, since many of the topics we discuss have been the subject of entire texts in their own right. To emphasize the reference nature of this chapter, the exercises are collected together at the end.
Optimal control problems
Authors: Hocking Leslie M
Published: November 2023

All vehicles require controls if they are to function in a desired manner. These controls may, for example, steer the vehicle, accelerate it, or stop it. We can therefore think of the vehicle in two parts: the engine, body, and seats, and the controls: accelerator, brake and steering wheel. The controls may be activated by a driver in the vehicle or remotely by radio signals from outside. It is also possible for the controls to be worked automatically by a feedback device. There are two ways in which controls may be needed by a moving system. They are needed to move the system from an original state to a desired one, but they may also be needed for continuous operation in order to counter deviations from a desired path. For example, a ship may be set on a straight course, but without constant applications of touches on the rudder it will tend to wander from the desired bearing. This is because the system is unstable and unavoidable minute disturbances will produce a large drift from the correct course unless controls are applied.
Further Examples
Authors: Hocking Leslie M
Published: November 2023

The theory developed in Chapter 4 was illustrated there by some simple examples. Now we can apply it to problems of a more complex nature. We have already considered the problem of positioning an object by means of a controlling force. Now let us suppose that as well as controlling the rate of change of the velocity of the object, we are also able to control its velocity directly.
The basic Pontryagin maximum principle
Authors: Hocking Leslie M
Published: November 2023

In this chapter we state the Pontryagin maximum principle (PMP) in its simplest form and use it to solve some simple examples. Extensions to a less restricted class of problems are discussed in Chapter 7, but the proof of the PMP is postponed to Chapter 9. Before giving the complete statement of the PMP, and in order to see clearly how the principle is applied, we look first at a very simple problem in detail and go through the steps required in using the PMP to obtain a solution. A system in unstable equilibrium is one in which any deviation from equilibrium increases if the system is left to itself. The application of a control aims to reduce the deviation to zero, but at some cost depending on the size of the control that has to be employed. Suppose the state of the system is given by a single state variable x1, with x1 = 0 in equilibrium.
Extensions to the PMP
Authors: Hocking Leslie M
Published: November 2023

The basic form of the PMP can be extended to apply to more general targets than the single point so far assumed. We can also include the effect ofa terminal cost, and we can make a simple amendment of the principle to allow non-autonomous problems to be treated. It often happens that we do not need to specify the final state of the system completely. It may be sufficient, for example, that one component only of the state vector must reach a specified value, while the other components are free to take any values consistent with the solution of the state equations. In that case, we lose information about the solution of the state equations, and this lack must be supplied from another source. If not, we would end with an undetermined problem. The extra conditions come from a constraint on the co-state vector at the terminal time. These conditions are stated and applied here, but, in accordance with our procedure, the reason for their validity is postponed until Chapter 9, where we give an outline proof of the PMP and its extensions.
Introduction and an example
Authors: Pretzel Oliver
Published: November 2023

Before attempting to construct an example of a finite field, we should discuss why there is any need for fields other than the binary field B. After all, practically all computation is done in binary. So why make life harder by working over other fields? There are, however, several good reasons why a knowledge of finite fields is indispensable in the study of error-correcting codes, and I shall list three of the more obvious ones here.
The structure of finite fields
Authors: Pretzel Oliver
Published: November 2023

Now that you have seen a method of constructing finite fields, we turn to the task of analysing their structure. In this chapter we establish four fundamental results. These results are all related to a prime number, called the characteristic of the field, that determines its arithmetical properties. As the results are analytical in nature, their proofs are not applied directly, like the proofs involving Euclid’s algorithm. Rather, the characteristic is implicitly used by many algorithms. You can use the algorithms without understanding the theory, but you will not be able to design or modify them.
Primitive elements
Authors: Pretzel Oliver
Published: November 2023

You will recall that in our example of GF(16) we introduced ‘logarithms’ for non-zero field elements that could be used like conventional logarithms to convert multiplication into addition. This is certainly of practical significance, since addition modulo 15 is easily implemented on a chip, while polynomial multiplication followed by division with remainder (the method used to define multiplication) is both more complicated and slower. On the other hand, the existence of such logarithms is closely linked to a remarkable property possessed by finite fields that is of great theoretical importance. If logarithms exist, then every non-zero element of the field is an integer power of the element with a logarithm 1. In the case of GF(16) every non-zero element is a power of the element we have denoted by 2.
BCH codes as subcodes of Hamming codes
Authors: Pretzel Oliver
Published: November 2023

How do you modify a Hamming code to correct two errors? In other words, how can you increase its minimum distance from 3 to 5? You will either have to lengthen the code words or eliminate some of them from your code. Correcting two errors in a long word may not be much better than correcting one error in a short one. So we adopt the second approach. That is, we shall try to produce a double error-correcting subcode of the Hamming code by removing some code words to make the new code sparser.