bluuebunny/crossref_metadata_2025_split huggingface dataset:
State-space approximation
Authors: Shier Douglas R 
Published: November 2023

Abstract
The emphasis in the previous chapters has been on assessing the reliability of a binary system, whose components (nodes and/or edges) can be in either of two states (operating or failed). However, reliability is only one of a number of stochastic performance measures that might be of practical interest. For example, the number of node pairs that can communicate at a random instant might be more informative than simply whether or not all node pairs can communicate. Alternatively, we might be interested in the ‘fault tolerance’ of the system, measured by the expected number of disjoint paths joining two specified nodes. Since the exact calculation of these and other realistic performance measures is known to be #P-hard, there is reason to investigate methods for approximating such measures. While it might be thought that obtaining a good approximation to the performance of a network might be substantially easier than computing its exact value, this does not appear to be the case.
Some structure of groups of units
Authors: Clay James R 
Published: November 2023

Abstract
The intimate connection between the geneses of nearring theory and group theory provides fertile ground for harvesting interesting groups. Here, groups arise naturally in at least two ways within the field of nearrings with identity. First, there is the additive group of the nearring, and then there is the group of units of the nearring. As one studies any mathematical structure, one should always try to become familiar with the invariants of that structure. One such invariant for a nearring with identity is the group of units of that nearring. The groups of units are often particularly interesting for nearrings; it is a nice source for groups whose structure can be nicely described in classical group theoretic terms, for example, direct products, semidirect products, wreath products, and factor sets. The groups themselves are often rather complicated in structure, but yet not too complicated. This is a nice place to find the beauty of nearring theory. As well, it is a nice place to show how some rather classical group theoretic constructions arise in a natural setting.
Parallel Linear Algebra
Authors: Burrage Kevin 
Published: November 2023

Abstract
Perhaps one of the most crucial aspects in the development of parallel numerical methods for the solution of both initial value and boundary value problems is the incorporation of efficient parallel linear solution algorithms. These linear algebra aspects arise at the most fundamental of levels, when performing matrix-vector or matrix-matrix computations. They also arise when implicit methods are implemented, because the ensuing nonlinear equations are usually solved by a modified Newton technique which results in systems of linear equations. Thus a thorough understanding of the many facets associated with the solution of systems of equations is crucial to the reading of this monograph. Since only one chapter is devoted to these aspects, such a discussion cannot, by its very nature, be comprehensive and the reader should consult other books on this subject, such as Golub and van Loan (1989) and Dongarra et al. (1991) for a more thorough overview of numerical linear algebra.
Equationals
Authors: Chapman Jonathan , Rowbottom Frederick 
Published: November 2023

Abstract
Equationals are particular L′-formulae important for two reasons:
(i) they are preserved by a left-exact functor
(ii) a topos (with canonical structure) has equational axioms (see Chapter 7).
Some constructions on partial functions are introduced first, and used to interpret equationals categorically, allowing (i) to be shown.
Categories in a topos
Authors: Chapman Jonathan , Rowbottom Frederick 
Published: November 2023

Abstract
As Johnstone (1977, p. 47) says, a topos can be regarded as a ‘universe of discourse’, generalizing the category of sets. In particular, category theory can be developed relative to one. Two categorical approaches are well known:
(i) fibred categories (cf. Benabou (1985; in preparation), Celeyrette (1975), Grothendieck (1963), Johnstone (1983/84)
(ii) indexed categories (cf. Pare and Schumacher, and others (1978)).
Here we present a third: categories in a topos. While these could also be given in purely categorical terms, the presence of L′ allows them to be defined by simply writing down an indexed version of the usual definition of a category. Indices allow these structures to be large.
Two Major Theorems On The Primes
Authors: Rose H E 
Published: November 2023

Abstract
This chapter has a different character to the previous work; it consists entirely of the proofs of two important results—Dirichlet’s theorem and the prime number theorem (PNT). A preliminary discussion of these results is given in the introduction to Chapter 12. The individual methods used in these proofs are similar to those in the rest of this book, but difficulties may arise because of their length and complex structure. It is essential to have an overall view and not to get bogged down in details. As the first result has an easier derivation. its methods should be thoroughly understood before the second proof is tackled.
Elasticity and anelasticity: discrete viewpoint
Authors: Maugin Gerard A 
Published: November 2023

Abstract
The purpose of this chapter is to justify theoretically the somewhat formal contents of Chapter 3 on the basis of microscopic considerations. There is, of course, no methodological obligation to do so as the success of a phenomenological theory is determined by its efficiency in macroscopic (which, for many of us, means engineering) applications. Nonetheless, it is intellectually satisfying to find an agreement between continuous and discrete descriptions in certain limit conditions.
Fourier-transform solution of a Boussinesq problem for a hexagonally aeolotropic elastic half-space
Authors: Sneddon I N 
Published: November 2023

Abstract
A solution of a basic Boussinesq problem relating to a hexagonally aeolotropic elastic half-space is derived by the use of two-dimensional Fourier transforms. An integral relation connecting the normal pressure on the bounding plane with the normal component of the displacement on that plane—analogous to Boussinesq’s relation in the isotropic case—is derived.
Asymptotic and other estimates for a semilinear elliptic equation in a cylinder
Authors: Flavin J N , Knops R J , Payne L E 
Published: November 2023

Abstract
We consider a semilinear elliptic equation in a cylinder of variable cross-section subject to zero conditions on the lateral boundaries. A second-order differential inequality is obtained for an L cross-sectional measure of the solution, where p is a positive integer. It is used to obtain an upper bound for the measure in terms of data, supposed specified on the plane ends of the cylinder (finite cylinder). A semi-infinite cylinder is then considered—the principal concern of the paper—and propositions are proved therefor; a global solution, when it exists, must decay at least exponentially in both cross-sectional and energy measures. These results, obtained without assuming that the solution tends to zero at large distances, depend crucially upon a lemma derived from the basic second-order differential inequality.
Linear dynamical stability in constrained thermoelasticity I. Deformation-temperature constraints
Authors: Chadwick P , Scott N H 
Published: November 2023

Abstract
Equations are derived governing an infinitesimal disturbance of a uniform equilibrium state Be of an unbounded body composed of a heat-conducting elastic material subject to a constraint linking the deformation and the temperature. No restriction is placed on the symmetry of the material and the freedom of choice of Be allows the presence of an arbitrary homogeneous prestrain. The stability of Be, in the context of linearized dynamics, is examined by studying the nature of plane-harmonic-wave solutions of the governing equations. It is found that, under very mild restrictions on the relevant material constants in Be, at least one of the four modes of wave propagation is always unstable, a conclusion which seriously undermines the legitimacy of the assumed type of constraint. The particular case of incompressibility at uniform temperature has been discussed by previous authors and is recapitulated here. Finally, an explanation of the inherent instability is provided by treating the constraint as a limit.
On the dynamical theory of rigid-viscoplastic materials
Authors: Naghdi P M , Srinivasa A R 
Published: November 2023

Abstract
This paper is concerned with the general constitutive aspects oi hnitely deforming rigid-viscoplastic materials. After a brief development of a partially active constraint appropriate for material response in a pre-plastic regime, quantitative results are presented in the context of basic formulation of spatial (or Eulerian) form of the various constitutive equations. This includes full discussion of the temporal continuity condition for the stress during transition from one type of material behaviour to another, the effect of internal constraints (which may be active only partially) on the stress response and the yield surface, as well as geometrical interpretation of the influence of the magnitude of the rate of deformation on the stress response. The nature of the latter rate effect is illustrated by a simple example utilizing a simplified constitutive equation for the stress.
The Basic Representation
Authors: Hoffman P N , Humphreys J F 
Published: November 2023

Abstract
The technicalities of these calculations have a certain appeal, but, on first reading, some may prefer to look at only what will be used later. This consists of the initial part of the chapter up to Theorem 6.2, the last two theorem statements, 6.11 and 6.12, together with the definitions preceding them and the examples after. The notes at the end refer to other methods of calculation, both in this book and in the literature.
Deeper Insertion, Evacuation and the Product Theorem
Authors: Hoffman P N , Humphreys J F 
Published: November 2023

Abstract
Since the algebra ΔQ is spanned by the Q-fuctions, the product Q μ Q v is a linear combination of the functions Q λ. Using the map och and Theorem 8.6, it can be proved that the coefficients involved are non-negative integers. The purpose of this chapter is to sketch a direct proof of this fact. But much more is done: the enumerative descriptions of these integers from Stembridge (1987, 1989) and Worley (1987) are given. This is the analogue of what is known as the Little-wood-Richardson rule for Schur functions, and for linear representations of S n or (certain) representations of GL(n, C).
The Lanczos algorithm for a pure imaginary Hermitian matrix
Authors: Lawson Charles L , Gupta Kajal K 
Published: November 2023

Abstract
Consider the application of the block Lanczos algorithm to a pure imaginary Hermitian matrix for the computation of a few of its extreme eigenvalues and eigenvectors. If the algorithm is started with a Q-block that is real, the various intermediate quantities that appear during execution of the algorithm will be either real or pure imaginary. An implementation taking this into account can reduce the number of arithmetic operations required per iteration of the Lanczos algorithm.
The multifrontal method in a parallel environment
Authors: Suff L S , Gould N I M , Lescrenier M , Reid J K 
Published: November 2023

Abstract
The multifrontal solution of symmetric and positive-definite finite element problems may be represented by an assembly tree. The leaves correspond to the elements themselves and each interior node corresponds to the substructure consisting of all the elements corresponding to its descendants. The overall matrix may be assembled and factorized by performing merge and elimination operations at each node. These operations may be performed in any order, subject to the restriction that each node must wait for the completion of all operations at its children. This allows parallel execution of the operations at any two nodes that are not such that either is a descendant of the other.
Some further topics
Authors: Amberg Bernhard , Franciosi Silvana , Giovanni Francesco De 
Published: November 2023

Abstract
Which normal subgroups does a factorized group have? In particular, are there normal subgroups of G = AB contained in or containing one of the two factors A and B? The examples in Section 6.1 show that, if the group G = AB ≠ 1 is the product of two abelian groups, then one of the factors need not necessarily contain a non-trivial normal subgroup of G. On the other hand, Lemma 2.1.4 proves that such a normal subgroup exists if the group G is finite. In the first part of this section we are concerned with extensions of this fact to certain infinite groups.
The influence of analogue machines in the 1930s: the Manchester and Cambridge differential analysers
Authors: Croarken Mary 
Published: November 2023

Abstract
In contrast to the growth in popularity of desk calculating machines during the late 1920s and the 1930s which Comrie helped to promote, the use of mathematical instruments by British scientists did not increase on anything like the same scale. Planimeters, integraphs, and harmonic analysers continued to be manufactured, but the mathematical laboratories set up within university departments during the late 1920s and early 1930s were, in general, equipped with desk calculators and not mathematical instruments.
Essentials of Logic Programming
Authors: Hogger Christopher John 
Published: November 2023

Abstract
Logic programming has developed into a broad discipline within computing science. Besides its basic role as a declarative programming language, it is also contributing significantly to such fields as artificial intelligence, new-generation computing, software engineering and deductive databases. This new book presents the fundamentals of logic programming from both practical and theoretical viewpoints. It covers various extensions of the formalism, its relationship to Prolog, its formal semantics and its applications to program analysis and transformation. The text is illustrated with numerous diagrams. There are two distinguishing features of the book designed to make it adaptable to various forms of usage and accessible to various audiences. The material is organized into sixty modular themes, permitting many kinds of course to be based upon it; and it includes nearly seventy pages of detailed answers to all of the exercises posed in the themes.
Literature sources
Authors: Hogger Christopher John 
Published: November 2023

Abstract
The following sources of material relating to logic programming are certainly not exhaustive, but will provide a good introduction and pointers to other works.
Journal of Logic Programming New Generation Computing Logic and Computation Artificial Intelligence
Machine Intelligence Knowledge Engineering Review
Journal of Automated Reasoning Journal of the ACM Communications of the ACM
Journal of Theoretical Computer Science Journal of Symbolic Logic
Journal of Logic and Computation
Problem solving and logical implication
Authors: Hogger Christopher John 
Published: November 2023

Abstract
Our overall approach in any problem-solving exercise will be to supply as input some set S of sentences expressing our assumptions about the problem domain, and to require the problem solver to yield as output some sentence s expressing a conclusion about the problem domain. Our minimal requirement of the relationship between S and s is that the following shall hold: if S correctly expresses the assumptions then s correctly expresses the conclusion.
SLD-resolution
Authors: Hogger Christopher John 
Published: November 2023

Abstract
An un satisfiable set of input clauses will typically afford numerous ways of deriving the empty clause by resolution: there may be many ways of choosing parent clauses, while for each choice of parents there may be many ways of resolving them according to the various literals available for resolving upon. The history of research into resolution proof procedures (coupling the resolution principle with certain strategies) has been largely concerned with determining how to restrict these choices-in the interests of efficiency-without sacrificing completeness. In this context, note that for our purposes it is not sufficient merely to be assured that the empty clause be derivable-we usually want to derive it in every way that yields some distinct new answer to the problem.
Partial orders and lattices
Authors: Hogger Christopher John 
Published: November 2023

Abstract
Presently we shall want to examine the relationships between the various Hmodels of a definite program. The usual framework in which we investigate such matters is the theory of lattices, which are just particular kinds of partial order.
A (weak) partial order over a set S is any subset’(‘ of SxS having these properties:
The relation ( is termed ‘weak’ owing to its reflexivity, in contrast to a ‘strict’ partial order ‘&lt;‘ which has to be irreflexive, asymmetric and transitive. Clausalform definitions of these basic properties of order relations can be found in the answers to Question 1 of Exercises 41.
Denotational semantics for def”mite programs
Authors: Hogger Christopher John 
Published: November 2023

Abstract
The general aim of a denotational semantics in the logic programming context is to attribute to each predicate symbol p in a program P some well-defined relation r. The chosen relation then represents the meaning of pin P-it is what p is considered to denote in this program.
Ideally we want to definer for pin the least redundant way, that is, to define the minimal r sufficient for the task. Moreover, we prefer this smallest r to be uniquely minimal, so that the meaning given to p shall be unambiguous. For the case where P is definite these requirements are met by the minimal model MM(P) which, for all n, attributes to the n-ary predicate symbols in P the smallest respective n-ary relations in Hn which jointly determine a model. Every other model would redundantly enlarge the relations’ extensions, thereby rendering them ‘more defined’ than necessary.
The SLD finite failure set
Authors: Hogger Christopher John 
Published: November 2023

Abstract
In this Theme we introduce the notion of a finite failure set. Relative to a given program P and a given inference system, this set comprises exactly those ground atoms q for which the query ?q finitely fails. We shall restrict our attention throughout to the case where Pis definite and the inference system is SLD.
Once we know what the finite failure set is relative to SLD inference, we shall also be able to say something about the execution by SLDNF of queries containing fail calls-subject, of course, to the assumption that the chosen computation rule is safe. We shall not say anything in this Theme about the more general situation where fail calls may occur also in clause bodies, for the position then is significantly more complicated.
Reduction
Authors: Hankin Chris 
Published: November 2023

Abstract
Convertibility is a symmetric relation and therefore does not correspond very closely to our intuitions about computing with terms. In this chapter we study a new relation on terms which better fits our intuitions. Having introduced the basic concepts, we present the Church-Rosser Theorem; this is a central theorem in the ,\-calculus and we study it in some detail. The other key theorem is the Standardisation Theorem; before presenting this we require the notion of a residual and a definition of head normal forms. We also show how constants may be added to the calculus and establish conditions under which the Church-Rosser property is preserved.
Further Reading
Authors: Hankin Chris 
Published: November 2023

Abstract
We have given a Computer Science perspective on the material covered in this book. Many of the fundamental results have been produced by logicians. Our inspiration in writing this book has been Barendregt’s encyclopaedic tome [5]. Most of the basic material presented here is treated in much more detail in [5] and the interested reader is urged to consult it. The classical presentation of the A-calculi is Church’s 1941 report [10]. One of the earliest textbooks in the field was Hindley, Lercher and Seldin’s Introduction to Combinatory Logic; while this is no longer available, [17] is a much-expanded treatment of the same material. The latter is written from a mathematical logician’s perspective, so it is short on comutational intuitions, but it is nonetheless a useful reference, particularly for material on typed calculi.
Logic, Computers, Turing, and von Neumannt
Authors: Robinson J A 
Published: November 2023

Abstract
The two outstanding figures in the history of computer science are Alan Turing and John von Neumann, and they shared the view that logic was the key to understanding and automating computation. In particular, it was Turing who gave us in the mid-1930s the fundamental analysis, and the logical definition, of the concept of ‘computability by machine’ and who discovered the surprising and beautiful basic fact that there exist universal machines which by suitable programming can be made to perform any computation whatsoever. This theoretical work of Turing’s had direct practical influence on the designs of the first modern general-purpose electronic digital computers in the mid-1940s. Von Neumann also had a prominent role in the emergence of these first machines, whose logical design has changed remarkably little in its general features during the almost fifty years since it was first formulated. The conventional wisdom is that von Neumann is primarily responsible for this design, which is accordingly known as the ‘von Neumann architecture’. Without detracting from von Neumann’s enormous importance, we maintain that this attribution somewhat distorts reality. The birth of the general-purpose computer, and with it computer science, owes far more to Turing than is usually acknowledged. Turing’s contribution was both direct (arising from his own activities in the 1940s) and indirect (because of his little-known but powerful intellectual influence on von Neumann, starting from the mid-l930s).
Utilizing Structure Information in Concept Formation
Authors: Handa K , Nishikimi M , Matsubara H 
Published: November 2023

Abstract
Inductive learning is a quickly growing area of machine learning, and the methodology of concept formation is to realize the task of inductive learning incrementally and without supervision. We have proposed a concept formation system CAFE, that creates a concept hierarchy from structured instances. The system uses a new classification algorithm mutual induction and an evaluation function known as concept-predictability. Our theory is that a system that deals with structures can not only expand possible domains of learning but also use structure information of instances as a domain theory, enabling accurate and fast learning. Such a system can even learn to neglect attributes that do not affect classification, provided appropriate structure information is given. We have evaluated CAFE in two domains (artificial and natural), and the results have proved our theory.