bluuebunny/crossref_metadata_2025 huggingface dataset:
The impact of bereavement on children and young people’s welfare and development
Authors: Kelly Daniel
Published: November 2023

Give sorrow words: the grief that does not speak Whispers the o’er fraught heart and bids it break.Shakespeare, Macbeth (VII, ii)Helping children and families to cope with the impact of loss and bereavement is the focus of this chapter. There are particular issues for professionals to consider when seeking to support a child or family who are experiencing the threat or actuality of grief. Grief is usu- ally taken to mean the feelings and behaviours that are evoked in response to death. These may include sadness, numbness, anger, sleep disturbances, inability to concentrate, and fatigue (Hanus 1995). In children specific behaviours may be expected depending on age, personality, and life circumstances—as well as the nature of the relationship they had developed with the dead person.
Malignant pleural mesothelioma: clinical presentation, radiological evaluation and diagnosis
Authors: Peake M D , Entwisle J , Gray S G
Published: November 2023

It is difficult to appreciate now, when mesothelioma is increasing in frequency and has a relatively high profile, that it is only comparatively recently that it was unequivocally recognized as a distinct clinical entity. The first cases were probably reported by Joseph Lieutand as early as 1767 and the pathology was described in 1870 [2], although 16 years earlier Von Rokitanski had reported on a primary peritoneal ‘colloid tumour’ which was probably mesothelioma. The name ‘mesothelioma’ (i.e. from the mesothelium) was suggested by Klemperer and Rabin [4], who reported the unique features of these diffuse tumours of the pleura. Later, diagnostic criteria were proposed for malignant pleural mesothelioma (MPM) by Godwin and for the peritoneal variety by Winslow and Taylor [6]. Over the 20 years or so following these reports, MPM gradually became accepted as a tumour separate from bronchial carcinoma and metastatic disease .
Cytogenetic and molecular genetic changes in malignant mesothelioma
Authors: Testa D A Altomare J R
Published: November 2023

Malignant mesothelioma is characterized by a long latency, typically several decades, from the time of initial asbestos exposure to diagnosis [1], suggesting that multiple somatic genetic events contribute to the tumorigenic conversion of a mesothelial cell. Karyotypic analyses, which have revealed multiple clonal chromosomal alterations in most human mesothelioma specimens, provide supporting evidence for recurrent cytogenetic abnormalities in this highly aggressive neoplasm. Most of these recurrent changes involve deletions of discrete chromosomal regions, consistent with a recessive mechanism of oncogenesis. Loss and/or inactivation of tumour suppressor genes residing at these chromosomal regions is postulated to contribute to the neoplastic transformation of a mesothelial cell [2], and recent molecular genetic studies have implicated several tumour suppressor genes that are inactivated during the development and/or progression of malignant mesothelioma.
The role of surgery for diagnosis, staging, and symptom control in malignant pleural mesothelioma
Authors: Waller A E Martin-Ucar D A
Published: November 2023

Surgery in the management of malignant pleural mesothelioma (MPM) has largely been confined to obtaining tissue diagnosis or to effect symptom control by pleurodesis. Non-invasive image-guided methods of obtaining pleural tissues are reducing the need for surgical biopsy, and the increasing use of thoracoscopy under sedation by an interventional pulmonologist may also reduce surgical involvement. However, the increasing incidence of the disease together with reports of long-term survivors has resulted in a more aggressive surgical approach towards therapy. Palliative surgical debulking may have a role in symptom control beyond that of chemical pleurodesis in patients not suitable for radical therapy because their tumour is unresectable or they are inoperable and not fit for the procedure. In this chapter we focus on the reported experiences of authors in the use of surgery for the diagnosis, staging and symptomatic control in MPM.
Codeine
Authors: Hardy Janet R
Published: November 2023

Codeine (methylmorphine) is a naturally occurring derivative of an opium alkaloid. Along with morphine and thebaine, it is a true ‘opiate’, i.e. a natural product and not a synthetic derivative of opium as are many of the ‘opioids’ used in every-day practice. It is a relatively weak analgesic, used most commonly in mild to moderate pain, either alone or in combination with non-opioids, such as aspirin, paracetamol or non-steroidal anti-inflammatory drugs (NSAIDs). There has been considerable debate about the relative contribution of the parent compound and its metabolites to both the beneficial effects, i.e. pain relief, and the undesirable effects, such as constipation and nausea, but its major analgesic effect is thought to result from its partial biotransformation to morphine.
Tramadol
Authors: Davis Mellar P
Published: November 2023

Tramadol is a synthetic 4-phyenyl-piperdine analogue of codeine. It has been available in Germany since 1977 and in the United States since 1995. Tramadol is the most frequently used step II opioid worldwide and is marketed in over 100 countries. Over 50 million people have received tramadol. Tramadol has a unique multiple receptor agonist profile, which differs from other ‘step II’ opioids. Tramadol’s affinity for the mu opioid receptor (MOR) is 10-fold less than codeine, 100-fold less than dextropropoxyphene and 6,000-fold less than morphine. However, affinity for the MOR does not account for its relative analgesic potency, which is much greater.
Hydromorphone
Authors: Glare Paul
Published: November 2023

Hydromorphone (HM) is a semi-synthetic derivative of morphine with a long history of successful use as an opioid analgesic, having been developed in 1922 by Knoll and used for cancer pain since 1932. It is almost pharmacologically identical to morphine, but has the advantages of high solubility in water and availability in a variety of dosage forms. HM is widely used in cancer pain management for opioid rotation.
Guidelines for referral in Europe
Authors: Menko Fred H
Published: November 2023

About 5 per cent of all cancer cases are due to high-penetrance, dominant mutations. A much larger proportion is caused by a combination of weaker susceptibility genes and/or environmental and lifestyle factors. A number of high-penetrance susceptibility genes have been identified and, recently, the clinical significance of genetic alterations in tumours has started to be appreciated.
Head and Neck Cancer
Authors: Hughes Ceri , Thomas Steven J
Published: November 2023

Head and neck cancer is a multi-step process that involves both environmental carcinogens and genetic susceptibility. Alcohol consumption and cigarette smoking account for disease development in the majority of cases of upper aerodigestive tract cancers in western and southern Europe and the US. Although it is probable that smoking and alcohol act independently as risk factors for upper aerodigestive tract cancers, they also act synergistically.
Leukaemia and Myeloma
Authors: Glare Paul
Published: November 2023

Acute leukaemia occurs in two main forms: either acute lymphoblastic leukaemia (ALL) or acute myeloid leukaemia (AML), within which there are several subtypes. In the past, eight subtypes of AML were recognized (FAB criteria), referred to as M0 to M7, the lower the code number the more undifferentiated. M1 (undifferentiated myeloblastic without maturation) and M2 (differentiated myeloblastic) are the commonest. The FAB classification system is being replaced by WHO criteria based on cytogenic and molecular aspects of the disease.
Melanoma
Authors: Hamilton Anne , Clark Katherine
Published: November 2023

Melanoma is one of the most common cancers. In the US, it accounts for 4.3 per cent of cancer incidence and 1.5 per cent of cancer mortality. The worldwide highest incidences of melanoma occur in Australia and New Zealand. In New South Wales (Australia), melanoma ranks second in incidence only to breast cancer in women, and prostate cancer in men. It accounts for 10 per cent of all new cancer cases, representing a lifetime risk of 1 in 29. The incidence in New South Wales is increasing in both men and women, although mortality is holding stable, accounting for 3 per cent of cancer deaths. The stable mortality rate is likely to be due to aggressive public awareness of the importance of reporting changing skin lesions and early detection programmes of the harmful effects of sun exposure.
Leptomeningeal Disease
Authors: Jackson Vicki , Nabati Lida
Published: November 2023

Leptomeningeal metastases are an important, yet relatively infrequent, complication of malignancy. Leptomeningeal metastases are found in 5 per cent of all patients with cancer, but are believed to be increasing in frequency, due to more successful treatment options for the underlying malignancy. Prolonged survival, coupled with improvements in neuroimaging, has increased the detection of leptomeningeal metastases.
Liver Metastases
Authors: Byrne Angela , Lee Michael J
Published: November 2023

Metastasis is the most common neoplasm affecting the adult liver, and the liver itself is the second most common site for malignant spread of disease after the lymph nodes. The dual blood supply and microvasculature of the liver contribute to this spread, as the fenestrations in the sinusoidal epithelium allow a foothold for tumour cells arriving via the bloodstream. The liver may be the site of metastasis from virtually any primary malignant neoplasm, but the most common primary sites are the colon, stomach, pancreas, breast, eye and lung. In children, the most common liver metastases are from neuroblastomas, Wilms tumours, or leukaemia (Table 27.1).
Malignant Bowel Obstruction
Authors: Mercadante Sebastiano
Published: November 2023

Bowel obstruction is a well-recognized complication in advanced cancer patients with abdominal or pelvic malignancy. Although it may develop at any time of the disease, it occurs more frequently at the advanced stage, with the highest incidence ranging from 5.5 to 42 per cent in ovarian carcinoma. Bowel obstruction ranges from 4.4 to 24 per cent in colorectal cancer.
Breathlessness
Authors: Alloway Lara , Keeley Vaughan , Higginson Irene
Published: November 2023

Breathlessness is a common and often multicausal symptom in patients with advanced cancer. The genesis and pathophysiology is poorly understood and it remains difficult to treat effectively. Studies show that breathlessness occurs in between 21–71 per cent of patients with cancer, with increasing prevalence and severity towards death. Hence breathlessness is often seen as a sign of impending death.
Weight Loss
Authors: Jatoi Aminah , Nguyen Phuong L
Published: November 2023

Studies clearly show that cancer patients and their families seek professional assessment of life expectancy and look for clues that might help in estimating it. Kirk and others recently observed that among a group of 72 cancer patients from Australia and Canada, nearly all sought information on prognosis.
Collection
Authors: Kaye Richard
Published: November 2023

The collection axioms are the arithmetic analogue of Fraenkel’s collection principle in set theory. Fraenkel’s principle says that if f is a function (defined by a first-order formula) whose domain is a set x, then the range of f can be ‘collected’ together as a subset of some set y.
Optimization in ℝn
Authors: Pinch Enid R
Published: November 2023

Before examining then n-variable case it will be instructive to look at the familiar problem of finding the maxima and minima of a function of one variable. This is not as straightforward as one might at first think and the difficulties encountered here are of a similar type to those found in the more technically complex theories of optimization in ℝnthe calculus of variations and modern optimal control.
Differentiable manifolds
Authors: Willmore T J
Published: November 2023

Differentiable manifolds and their geometry appear naturally in the study of diverse areas of mathematics, including Lie group theory, homogeneous spaces, probability theory, differential equations, the theory of functions of a single complex variable and of several complex variables, algebraic geometry, classical mechanics, relativity theory, and the theory of elementary particles of physics. Riemannian geometry is a special geometry associated with differentiable manifolds and has many applications to physics. It is also a natural meeting place for several branches of mathematics.
Riemannian manifolds
Authors: Willmore T J
Published: November 2023

Let M be a differentiable manifold. We say that M carries a pseudo Riemannian metric if there is a differentiable field g = (gm} , m ∈ M, of non-degenerate symmetric bilinear forms gm on the tangent spaces Mm of M. This makes the tangent space into an inner product space. Let Y, Z be differentiable vector fields defined over an open set U of M. By asserting that g is differentiable we mean that the function g( Y, Z) is differentiable. Often we will write < Y, Z> instead of g( Y, Z). If in addition the forms gm are positive definite we call the metric Riemannian. A differentiable manifold with a (pseudo-)Riemannian metric is called a (pseudo-)Riemannian manifold.
Maximum principles and decoupling for positive solutions of reaction-diffusion systems
Authors: Hernández Jesús
Published: November 2023

Reaction-diffusion systems have been intensively studied during recent years; see (Smaller 1983), where many references can be found. In particular, existence and multiplicity of solutions for the corresponding elliptic systems have been considered, mostly for the case of positive solutions. Indeed, for many systems arising in applications, they are the only physically meaningful solutions (concentrations, populations, etc).
Approaches for calculating network reliability
Authors: Shier Douglas R
Published: November 2023

This chapter provides a survey of several general approaches for calculating the reliability of probabilistic networks. Throughout the remainder of this book, a specific network model and performance measure will be emphasized. Namely, it is supposed that G = (N, E) is a directed network, having a distinguished source node s and distinguished destination node t. The nodes of G are assumed to be perfect, whereas the edges k ∈ E are assumed to fail in a statistically independent fashion with known probabilities q = 1 − P of particular concern here will be the two-terminal reliability measure R(G), the probability that there is a path of operative edges from s to t in G. This paradigm not only serves to illustrate the essential features of the approaches discussed in this chapter, but it also features prominently in the algebraic methods that form the core of the remaining chapters.
Nearrings
Authors: Clay James R
Published: November 2023

Nearrings arise naturally in various ways, but most nearrings studied today arise as the endomorphisms of a group or cogroup object of a category. These nearrings are rings if the group object is also a cogroup object. During the first half of the twentieth century, nearfields were formalized and applications to sharply transitive groups and to foundations of geometry were utilized. Planar nearrings grew out of the geometric success of the planar nearfields and have found numerous applications to various branches of mathematics as well as to coding theory, cryptography, the design of statistical experiments, families of mutually orthogonal Latin squares and constructing planes with circles having radius and centre even though there is no metric involved. Even though nearrings may lack the extra symmetry of a ring, there is often a very sophisticated elegance in their structure. It has recently been observed that there is an abundance of symmetry in finite cirucular planar nearrings, which disappear if the nearring is a ring.
Order And Stability - A General Framework
Authors: Burrage Kevin
Published: November 2023

Chapter 2 attempted to give an overview and present a general structure in which many classes of differential equation methods can be studied. This third chapter continues the review of sequential methods and describes in more detail the properties of the numerical methods introduced in Chapter 2. This will be done from the framework of a very general class of methods known as multivalue methods. These properties can then easily be particularized to various classes of methods such as linear multistep and Runge-Kutta methods by understanding how these classes of methods fit into the multivalue framework. This is a very natural approach and one that has not really been attempted before, simply because not all the theoretical tools had been sufficiently developed. Recent developments now allow a systematic treatment of multivalue methods. However, it is important not to lose sight of the historical developments which have nearly always involved a movement from the particular (linear multistep and Runge-Kutta methods) to the general (multivalue methods).
Waveform Relaxation Techniques
Authors: Burrage Kevin
Published: November 2023

The standard application of initial value problem codes such as VODE (Brown and Hindmarsh (1989)) or STRIDE (Butcher et al. (1979)) can become inefficient for large systems of equations where different state variables have widely differing time rates. This is due to the fact that the same method and stepsize scheme is used in an attempt to represent accurately all components to a specified vector of tolerances. Various approaches have been proposed to overcome this drawback, based on partitioning (Hairer (1981)) and multirate (Skelboe (1989)) techniques. The idea here is to decompose the system into subsystems with similar time rates which can then be treated by possibly different methods and time-step strategies, more or less independently of one another. Of course the difficulty here is in knowing (automatically) how to couple the components and the nature of the coupling (perhaps variable) between the subsystems.
Discrete Waveform Methods
Authors: Burrage Kevin
Published: November 2023

The previous chapter dealt with the issue of convergence rates for continuous waveform algorithms when applied to either linear or nonlinear problems. Techniques for choosing appropriate splittings were formulated based on estimating the coupling between components or subsystems by an analysis of the one-sided and two-sided Lipschitz constants associated with the splitting.
Implementation Of Waveform Algorithms
Authors: Burrage Kevin
Published: November 2023

The previous two chapters have focused on both waveform and discretized waveform algorithms. It has been shown that convergence results can be obtained for general splittings based on one-sided (L  1) and two-sided (L  2) Lipschitz constants, and that there is a remarkable similarity between these results for both the continuous and the discretized case.
Partial function theory, L′
Authors: Chapman Jonathan , Rowbottom Frederick
Published: November 2023

L’ is a conservative extension of the (canonical) local set theory L for a topos S (described in Section 2.12), to include symbols for partial functions in S. Beeson (1980/81, 1985, pp. 97—9), has (independently) considered a comparable first-order theory. Taking on board partial function symbols presents problems like those considered by Scott (1979), where he discusses a formulation of intuitionistic logic taking into account partially defined elements. L’ will be contrasted with this formulation. For more information on Scott’s approach, see Grayson (1978) where the set theory is developed in an abstract setting; Fourman and Scott (1979) for interpretation over a complete Heyting algebra; Fourman (1977) for the interpretation in an arbitrary topos. While Scott’s system has partial function symbols via descriptions, its interpretation in a topos is relatively complicated.
Topoi in a topos
Authors: Chapman Jonathan , Rowbottom Frederick
Published: November 2023

There are two aims in this chapter:

(a) to introduce topoi in S. These are categories in S with the usual canonical structure (terminal object, pullbacks, subobject classifier and powers), satisfying indexed versions of the standard topos axioms expressed in L′.
Wavelets and Spline Interpolation
Authors: Chui Charles K
Published: November 2023

Abstract. This is an introductory tutorial of wavelets from a spline theorist’s point of view. The concept of integral wavelet transform (IWT) for time-frequency localization is discussed, and a comparison of compactly supported orthonormal wavelets, spline wavelets, and biorthogonal wavelets is given. When spline wavelets are being used, interpolatory splines are readily available for orthogonal wavelet decompositions, yielding the IWT at dyadic locations without performing any integration. In addition, since the dual spline wavelets are used as wavelet window functions, linear-phase filtering is accomplished.
Preliminaries
Authors: Ellis Graham
Published: November 2023

There are many occurrences in mathematics of sets whose objects can, in some natural way, be added and multiplied. For instance we have the integers ℤ, the even integers 2ℤ, the rational numbers Q, the real numbers ℝ, and the complex numbers ℂ. Not all of the occurrences are as sets of numbers.
Error codes
Authors: Ellis Graham
Published: November 2023

In this chapter we study some applications of finite fields to coding theory. This is a theory concerned with the efficient transmission of digital information, and is essential for the proper functioning of electronic equipment such as computers and compact disk players. To explain the basic ideas behind the theory we begin by looking at a simple code used every-day by bookshops when ordering books. All modern books can be identified by their International Standard Book Number. For instance, the ISBN of A First Course In Abstract Algebra by J. B. Fraleigh is 0-201-16847-2.
Ruler and compass constructions
Authors: Ellis Graham
Published: November 2023

The last three chapters have been concerned primarily with finite fields. In this chapter we turn our attention to infinite fields and in particular to subfields of the real numbers ℝ. Our interest in such fields is derived from a construction problem in Euclidean geometry. Many geometric constructions can be performed using only a pencil, compass, and unmarked ruler. For instance, suppose we wish to bisect an angle θ, as in Fig. 5.1. This can be done, using our limited tools, as follows. Firstly use the compass to draw a segment of a circle cutting the sides of the angle at points A and B say. Then draw two circles of equal radius centred at A and B; these two circles intersect at points C and D, say, as in Fig. 5.2. The line CD bisects θ.
Pappus’ theorem and Desargues’ theorem
Authors: Ellis Graham
Published: November 2023

In Chapter 2 we saw that any field K gives rise to a projective plane PG(2, K). One very natural question to ask is: do all projective planes arise from a field in this way? In the present chapter we show that the answer is no. We do this by first proving that a classical theorem of Euclidean geometry, namely Pappus‘ theorem, holds in the projective plane PG(2, K) for all fields K, and then by exhibiting a projective plane in which Pappus‘ theorem does not hold. Another theorem of Euclidean geometry which may or may not hold in a given projective plane is Desargues‘ theorem. A famous result of projective geometry states that in any finite projective plane Pappus‘ theorem is implied by Desargues‘ theorem.
Solution of polynomials by radicals: Galois groups
Authors: Ellis Graham
Published: November 2023

In this chapter we consider the problem of finding formulae for the roots of polynomials over ℚ. Nice formulae, involving only the four field operations +, − , × , / and the extraction of nth roots, exist for all such polynomials of degree 4 or less.
Patterns of dots and partitions of integers
Authors: Cofman Judita
Published: November 2023

Since antiquity patterns of dots have played an important role in the theory of numbers. The followers of Pythagoras (around 540 BC) represented certain integers by sets of dots arranged in the shape of polygons or polyhedra; such integers are nowadays called figurate numbers.
Do it with groups
Authors: Cofman Judita
Published: November 2023

The theory of groups is an important branch of modern algebra, with various applications in mathematics and in physics. The notion of a group is based on that of a binary operation on a set. A binary operation on a non-empty set S is a rule which associates to every ordered pair (a, b) of (not necessarily distinct) elements a, b of S a unique element of S.
Chapter II
Authors: Cofman Judita
Published: November 2023

In order to find a method for solving this problem let us experiment by dividing the heaps of pebbles in two different ways, following the given rules, and compare the corresponding sums.
Chapter IV
Authors: Cofman Judita
Published: November 2023

Suppose that a light ray emerging from P meets m1 at R, then m2 at S, and after that passes through Q. In order to find R and S we analyse the sketch drawn in Fig. 2.23(a).
Chapter VII
Authors: Cofman Judita
Published: November 2023

Drop a perpendicular from Ponto the x-axis, and denote its foot by P’ (Fig. 2.35). Triangles OP2 A, OP1A, and OPP; are similar (they are all right-angles triangles and share the angle L P  2OA).
Chapter IX
Authors: Cofman Judita
Published: November 2023

Let n be an arbitrary integer. ⊕ is a binary operation on ℤn = {O, 1, ... , n - 1} because i ⊕ j ∈ ℤn for any i,j ∈ ℤn, It is easy to verify that ℤn (⊕) satisfies all group axioms:.
Chapter X
Authors: Cofman Judita
Published: November 2023

We shall give two proofs of the formula

Proof 1 is based on the method called the principle of inclusion and exclusion.
MFE In 1-D: Second-Order Equations
Authors: Baines M J
Published: November 2023

The MFE method has most often been used on second-order PDE’s involving two space derivatives of u. Indeed, the method was introduced specifically for problems involving convection and diffusion with steep moving fronts in the solution (see Chapter 2, Sections 2.7 and 2.8) (Miller and Miller 1981, Gelinas et al. 1981, Djomehri 1983). Although in diffusion problems we cannot expect any link with the approximate method of characteristics of Chapter 4 the MFE method is still a method of trajectories and we need to understand the properties of the nodal speeds. To do this we make a special study of the linear heat equation
Diophantine Equations
Authors: Rose H E
Published: November 2023

Diophantus worked in Alexandria probably in the middle of the third century AD (some authors suggest early in the second century AD). His six or seven surviving books show that he had a highly developed understanding of many number theoretical problems. These mainly involved the solution of equations in positive integers or positive rational numbers although his methods of working suggest that he was aware of negative numbers. He was one of the first to introduce symbolic notation into mathematics; for example.
Nonlinear acoustic surface waves in crystals
Authors: Maugin Gerard A
Published: November 2023

In general, surface waves represent time-varying and spatially nonuniform perturbations. The spatial variation in the field amplitude is markedly confined to the vicinity of the limiting surface of a body and practically vanishes outside this relatively narrow zone. They are examples of the so-called inhomogeneous waves. The treatment of surface waves is one of the simplest-but not necessarily easy-dynamic problems concerning a body with finite extension along one of its dimensions. The boundary conditions must be considered such that, at least in principle, any field theory and the resulting continuous field equations exhibit some surface wave phenomenon.
The second-order deformation of an incompressible isotropic slab under torsion
Authors: Lindsay K A
Published: November 2023

The theory of elasticity has been traditionally divided into problems associated with linear theory and those involving the general theory. The method of successive approximations seeks to bridge this division by expressing general solutions in terms of the ‘small‘ parameter of linear theory although in practice advancement beyond linear theory is often only technically feasible if the linear solution is either mathematically elementary or the problem enjoys a strong degree of symmetry. Questions concerning existence and uniqueness of solutions have been addressed by Signorini (1) and Stoppelli (2, 3) under suitable conditions of differentiability. For many problems in linear elasticity, the method of successive approximations has no relevance since linear theory encapsulates all the essential features of a realistic solution. However, there are some problems involving either torsion or shear in which linear theory appears inadequate in the sense that some component of the linear solution is zero whereas reality suggests otherwise. In such problems, the theory of successive approximations has a valuable role to play in the determination of such components of the leading solution. Second-or higher-order theories must be derived directly from general theory: they cannot be derived from linear theory as it is already approximate. In particular, higher-order theories differentiate between reference and deformed coordinates (unlike linear elasticity) and for this reason it is convenient to work with reference coordinates. One consequence of this decision is that the appropriate stress tensor may no longer be symmetric although in this application, symmetry does prevail. Further details are available in Green and Adkins (4)
Finite-amplitude waves in deformed Mooney-Rivlin materials
Authors: Boulanger Ph. , Hayes M
Published: November 2023

In a previous paper (3), Currie and Hayes showed that two linearly polarized finite-amplitude shear waves, polarized in directions orthogonal to each other and to the direction of propagation n, may propagate along any direction in a Mooney-Rivlin material which is maintained in a state of arbitrary static finite homogeneous deformation.
Closure of an arc crack in an isotropic homogeneous material due to uniaxial loading
Authors: Chao† R , Laws N
Published: November 2023

In this paper we consider the problem of an arc crack in an infinite isotropic elastic solid under uniaxial loading at infinity. The major analysis is undertaken with the help of complex-variable methods. A point of particular concern is that existing analyses do not properly account for partial crack closure due to load orientation. A proper solution is given for partially closed cracks. This solution is compared with the standard open-crack solution of Muskhelishvili (1). For most purposes the classical solution is adequate†but there are significant differences.
Deformations of an elastic, internally constrained material part 2: nonhomogeneous deformations
Authors: Beatty Millard F , Hayes Michael A
Published: November 2023

This is a sequel to part 1 in which a theory describing the nonlinear mechanical response of a class of homogeneous, isotropic elastic materials subject to finite deformations and characterized by Bell’s constraint tr V = 3 was presented. Although Bell discovered this constraint within the context of experimental work in finite-strain plasticity, in part 1 it was examined for homogeneous deformations in the context of finite elasticity. Here the emphasis is on non-homogeneous, finite deformations for isotropic, homogeneous, elastic Bell-constrained bodies. Six families of solutions are presented. They include the bending and stretching of a rectangular block; the straightening of a cylindrical sector into a rectangular block; the bending with axial stretch of one circular cylindrical wedge into a similar wedge; the inflation, bending, extension, and azimuthal shearing of an annular wedge; the radial deformation of a spherical shell and membrane—including inflation, compression, and eversion; and, finally, the equibiaxial stretch and sinusoidal shear of a block.
Representation Groups for the Symmetric Group
Authors: Hoffman P N , Humphreys J F
Published: November 2023

In this chapter, we shall determine the Schur multiplier of the symmetric group S  n, and give presentations for it representation groups. To find an upper bound for M(S  n), we shall present a portion of Schur’s method to calculate M(G) starting from a presentation of G. For this, two basic results in group theory, Theorems 2.1 and 2.3 below, are quoted without proof. Alternatively, there is a direct approach to this upper bound which uses the twisted group algebra and the existence of a projective representation for any given cocycle; for a treatment, see Jozefiak (1989), pp. 198-200. The first quoted result consists of some consequences of the classification theorem for finitely generated abelian groups.
Representations of Objects in 𝒢
Authors: Hoffman P N , Humphreys J F
Published: November 2023

In this chapter, we shall discuss the representation theory of an object (G,z, σ) in 𝒢. To avoid unnecessary repetition, the word “representation” will be used to mean “linear representation” as defined in Chapter 1. We shall restrict attention to representations over the complex numbers. Character theory can then be used in many proofs. This is a suitable point, therefore, for a short digression recalling the main results of character theory. The following six paragraphs, labelled (Di), will each conclude with a statement of a property of characters labelled (Ci). The reader should consult Huppert (1967) for proofs of the non-obvious facts below. The references given in parentheses are to that book.
The Q-functions
Authors: Hoffman P N , Humphreys J F
Published: November 2023

In this chapter, we shall define the Q-functions. These symmetric functions were introduced by Schur. It will be convenient 10 use a different defini1ion. Schur’s defining formula will appear in Chapter 9. First we give some basic facts about symmetric functions.
The Irreducible Negative Representations of
Authors: Hoffman P N , Humphreys J F
Published: November 2023

The character calculations and Q-functions of the last two chapters can now be combined to obtain the main results on the irreducible projective representations of S  n and A  n.
Reduction, Branching and Degree Formulae
Authors: Hoffman P N , Humphreys J F
Published: November 2023

The relationship between combinatorics and linear representations of the symmetric group has proved to be of mutual benefit to both. Much recent progress on the projective representation theory of the symmetric group depends on a combinatorial framework which allows one to develop a similar relationship. The main idea is that of a shifted diagram, which we introduce next. The reduction formula and branching rule are then interpreted combinatorially using diagrams. Finally, the degrees of the irreducible projective representations of S  n are calculated and related to the idea of a standard shifted tableau.
Rounding errors in algebraic processes¬ in level-index arithmetic
Authors: Olver F W J
Published: November 2023

The level-index number system represents numbers in a computer by their repeated logarithms. Its chief advantage is closure in finite¬ precision arithmetic, thereby eradicating the problems of overflow and underflow. This talk indicates how a Wilkinson-type running error analysis can be carried out in the new system.
Experiences with some software engineering practices in numerical software
Authors: Jacobs D A H , Markham G
Published: November 2023

The reliability of numerical mathematical software depends not only on the underlying methods but also on the software processes by which these methods are realized in an executable programming language,i.e. the techniques used for the construction of code and its accurate documentation.
Oscillations Of Linear Scalar Delay Equations
Authors: Györi I , Ladas G
Published: November 2023

In this chapter we present some of the most basic results in the theory of oscillations of linear delay differential equations with constant and variable coefficients and with constant delays. We begin with a detailed description of the concept of oscillation.
Oscillations Of Systems Of Delay Equations
Authors: Györi I , Ladas G
Published: November 2023

This chapter deals with the oscillation of all solutions of systems of delay differential equations. Section 5.1 gives a powerful necessary and sufficient condition for the oscillation of all solutions of a linear autonomous system. Section 5.2 utilizes this result to obtain explicit conditions for the oscillation of linear autonomous equations. Section 5.3 deals with the oscillation of linear, non-autonomous equations. Section 5.4 provides sufficient conditions for the oscillation of all solutions of a non-linear system of delay logistic equations.
Miscellaneous Topics
Authors: Györi I , Ladas G
Published: November 2023

Sections 12.1 and 12.2 contain some simple but interesting results on the non-existence of slowly oscillating periodic solutions. Section 12.3 deals with necessary and sufficient conditions for all solutions of a neutral equation with periodic coefficients to oscillate. In Section 12.4 we obtain a result on the growth of rapidly oscillating solutions of some linear equations.
The mechanization of computation at the Nautical Almanac Office
Authors: Croarken Mary
Published: November 2023

During the 1910s and 1920s scientists were, in general, slow to adopt desk calculating machines for their work. Small computing laboratories had been set up by Pearson and Whittaker but in most other institutions routine computations were carried out using logarithmic tables. As outlined in the previous chapter the British Nautical Almanac Office (NAO) at Greenwich was no exception.
The alleged virtues
Authors: Hogger Christopher John
Published: November 2023

Many arguments have been advanced in favour of logic programming. The principal argument is that it enables one to express knowledge explicitly in a machine-independent manner, making programs more compact, flexible and intelligible. The thesis that the representation and derivation of knowledge is what computing is all about is not, at present, conceded by the majority of programmers, and even those who do concede it do not necessarily see logic programming as the natural way of realizing it. However this may be, the main strands of the thesis are as follows.

Logic programming can be regarded as the corner-stone of knowledge based programming. The expressiveness of logic enables one to formulate (encode) assumptions about the problem domain in a direct, implementation¬ independent manner. Conversely, one can readily decode such a formulation in order to recover its underlying assumptions. Furthermore, the conclusions computed from the formulation are exactly its logical consequences, and so are directly relatable to the assumptions.
Clausal-form logic
Authors: Hogger Christopher John
Published: November 2023

Clausal form is one of the many normal forms of first-order logic and is the sublanguage in which pure logic programs are conventionally written. The common feature of all normal forms is that they make the structure of sentences more regular. Whatever sentences we might initially construct in arbitrary first order logic in the course of formulating some problem, those sentences can always be converted into new clausal-form sentences without any loss of expressiveness. We define a sentence to be in clausal form if and only if it takes the form < matrix> where the universal-prefix is a string of universal quantifiers, the matrix is a quantifier-free conjunction of formulas and each of those formulas is a disjunction of one or more literals.
Herbrand procedures
Authors: Hogger Christopher John
Published: November 2023

In the early days of automated theorem proving much use was made of the principles discussed in the last Theme: replace the given clause-set by its ground instantiation; then seek a contradiction. The formal justification for this approach relies upon a profound and highly important result in proof theory known as Herbrand’s Theorem. There are many ways of expressing and specializing this theorem, but the specialization of it which follows is perhaps the one best-suited to our present context:
Applying and composing substitutions
Authors: Hogger Christopher John
Published: November 2023

When resolution is used for clausal-form predicate logic, the task of constructing a resolvent generally requires substituting certain terms for variables in the literals which the resolvent inherits from its parents. Later on we shall say exactly how this is done, but in the meantime it will be useful first to make precise what we mean by ‘substitutions’ and then to consider some of their properties.
Resolution versus Herbrand procedures
Authors: Hogger Christopher John
Published: November 2023

It is instructive to see what would be involved in using a Herbrand procedure in order to solve the ‘grandparent’ problem presented in the last Theme:

According to the Herbrand Theorem, the ground instantiation is contradictory (inconsistent) if and only if it includes some finite, contradictory subset. One such subset consists of the four clauses shown above in bold face. It is trivial to derive
The occur-check
Authors: Hogger Christopher John
Published: November 2023

The unification algorithm presented in the previous Theme includes in its comparison cycle the following test: else if either of e1 and e2 is a variable which occurs strictly within the other then issue “failure” and tem1inate This test is called the occur-check and its purpose is to disallow self-referential bindings such as X/f(X). Here is a simple example in which that binding would arise in the unifier if the occur-check were to be omitted:

The binding X/f(X) effectively assigns to X the infinite term f(f(L)), whereas all expressions in our language are presumed to be syntactically finite. In particular, although the Herbrand domain might well be an infinite set of terms, the terms themselves are presumed to be finite.
Pruning the search using ‘cut’
Authors: Hogger Christopher John
Published: November 2023

The cut (denoted in most Prolog dialects by either ! or/) is a control device which caters for dynamic curtailment (or pruning) of the search process. For ease of implementation, and to provide for simple user-control over its activation, a cut is both expressed in the program text and scheduled for execution just like any other call. Executing a cut prevents some part of the tree from being searched-we say that it prunes the tree. This is how it works. Suppose a call to A invokes a clause of the form

This program will always produce correct answers no matter how it is queried. For instance, Figure 38.1 shows the SLD-tree obtained by querying which of 3 and 2 is the least. The leftmost computation gives the unique and correct solution Z/2. The rightmost computation correctly fails but is redundant, since we know that if the query
Herbrand interpretations and models
Authors: Hogger Christopher John
Published: November 2023

The theory of Herbrand interpretations and models (abbreviated respectively to ‘H-interpretations’ and ‘H-models’) provides a foundation for defining and analysing the semantics of logic programs. In particular, it provides information about the satisfiability of any logic program in the domain over which it computes. Some analyses of the logic programming formalism must of necessity consider non-Herbrand interpretations, but these lie beyond our present scope. Thus the only domain we shall consider here is the Herbrand domain. The first important fact to note is that the satisfiability properties of the program in this domain are the same as the satisfiability properties of its ground instantiation.
Minimal models and logical consequence
Authors: Hogger Christopher John
Published: November 2023

There is a simple but important connection between any definite program P, its minimal model MM(P) and each of its ground atomic logical consequences q, as follows:

Thus MM(P) is exactly the set of all ground atoms which are implied by P. We shall see later that this is just one of several ways of giving significance to a program’s minimal model. The proof of the above relationship makes use of the so-called model intersection property:
Minimal models and derlvability
Authors: Hogger Christopher John
Published: November 2023

We saw in the last Theme that the minimal model MM(P) of a definite program P comprises just the ground atomic logical consequences of P: An immediate outcome of this is that MM(P) also characterizes the ground atomic queries ?q which are solvable using SLD-resolution, since
On the Construction of Unifying Terms Modulo a Set of Substitutions
Authors: Langet S
Published: November 2023

The aim of this paper is to provide a mathematical problem which is of interest for getting practicable methods in the field of inductive program synthesis. The problem we have in mind is obviously a dualism to the unification problem in some equational theory. We consider two terms t 1, t2 and two possibly different substitutions b 1, b2 for each of them. The problem is to find a unique term t for both terms such that t and t I as well as t and t2are unifiable with respect to the underlying equational theory by using b1 or b2as a unifier. The problem is trivially decidable in free-term algebra. It is undecidable in the general case. Moreover, even if the underlying equational theory is decidable, then the problem we have in mind may be undecidable, too. Finally, we derive sufficient pre conditions for proving its decidability.
Interactive Induction
Authors: † W Buntinet , Stirling D
Published: November 2023

A variety of artificial intelligence induction systems are being success fully used for knowledge acquisition. In some of these systems, knowl edge acquisition is not an automatic procesii hut rather an interactive process between expert/user and system, with induction serving as the focus. We refer to this generic approach as interactive induction. In this paper we examine some case studies, and discuss the approach and software facilities required to support it. Key features for success are the methods and man-machine environment employed to elicit prior, subjective information from an expert (in order to augment the knowl edge implicit in the training data), together with the expert’s acceptance and validation of the knowledge induced.
Design of Knowledge Processing Systems—Principles and Practice
Authors: Ohsuga S
Published: November 2023

In this paper we discuss some ideas for making intelligent computer systems really useful and a system developed based on the idea. Key issues ill designing such a system are the knowledge representation language and system management. The issues relate closely to the manner of solving problems. The analysis of problem-solving processes by human beings suggests to us that a model-based method must he adopted as a new generic method of problem-solving by computers. The method involves operations to build and modify the model as well as capabilities for model analysis and evaluations. The knowledge representation language must he designed so as to be suitable for rep resenting both the model itself and the model building-analysis-manipu lation process. The system must also have the system management capability to define the best scope of knowledge relevant to solve each domain-specific problem and to maintain the system consistency. In this paper we discuss a general view for the design philosophy of such an intelligent system and an implementation.