bluuebunny/crossref_metadata_2025_split huggingface dataset:
Constructive Approximation on the Sphere
Authors: Freeden W , Gervens T , Schreiner M 
Published: November 2023

Abstract
The subject of geomathematics focuses on the interpretation and classification of data from geoscientific and satellite sources, reducing information to a comprehensible form and allowing the testing of concepts. Sphere oriented mathematics plays an important part in this study and this book provides the necessary foundation for graduate students and researchers interested in any of the diverse topics of constructive approximation in this area. This book bridges the existing gap between monographs on special functions of mathematical physics and constructive approximation in Euclidean spaces. The primary objective is to provide readers with an understanding of aspects of approximation by spherical harmonics, such as spherical splines and wavelets, as well as indicating future directions of research. Scalar, vectorial, and tensorial methods are each considered in turn. The concentration on spherical splines and wavelets allows a double simplification; not only is the number of independent variables reduced resulting in a lower dimensional problem, but also radial basis function techniques become applicable. When applied to geomathematics this leads to new structures and methods by which sophisticated measurements and observations can be handled more efficiently, thus reducing time and costs.
Algorithms for Boolean Formula Evaluation and for Tree Contraction
Authors: Buss* Samuel R 
Published: November 2023

Abstract
Abstract
We present a new, simpler Alogtime algorithm for the Boolean sentence value problem (13SVP). Unlike prior work, this algorithm avoids the use of postfix-longer-operand-first formulas. We also show that tree-contraction can be made Alogtime uniform.
The Boolean sentence problem restricted to balanced sentences with only the connectives ⋀ and ⋁ is in online O(log(log n)) space. Hence every Alogtime predicate is deterministic log-time reducible to log(log n) space. This balanced and/or BSVP has logarithmic width, linear length, branching programs.
Stochastic geometry
Authors: Kingman J F C 
Published: November 2023

Abstract
So far we have considered random countable subsets of spaces S which have always been subsets of !Rd for some dimension d. The theory is, however, much more general, and applies to random structures which look quite different from the irregular array of isolated points depicted in Fig. 1.1. Suppose for instance that one looks through a microscope at a piece of paper. The view might roughly resemble Fig. 7.1, where the lines represent fi bres of the material. This could be modelled by representing the fibres as infinite straight lines, or in a more complex way allowing for thickness, finite length or departure from straightness. The lines could be regarded as lying in a plane, or in three dimensions if the thickness of the material justified it.
Thermodynamics of Two-Phase Systems
Authors: Gurtin Morton E 
Published: November 2023

Abstract
We consider an evolving interface, 𝓈 separating two phases, labelled 1 and 2, and write Ω1 (t) and Ω2(t) for the corresponding phase regions as discussed in Section 3.1. The normal N for, 𝓈 then coincides with the outward unit normal to ∂ Ω1. For themoment we will restrict attention to situations in which the body Ω = Ω1(t) ∪ Ω2(t) is all of ℝ2.
Universal Algebra
Authors: Meinke K , Tucker J V 
Published: November 2023

Abstract
This chapter is an introduction to the primary concepts, constructions and results about algebras, their isomorphism and axiomatization. As with other chapters in this Handbook, it is composed with the aims of teaching the mathematical theory and explaining its relevance to problems in computer science. Among areas of application we will consider are: abstract data types and their specification; syntax and semantics of programming languages; and synchronous concurrent algorithms and architectures. Some of these algebraic applications, and others such as asynchronous concurrent processes, are developed fully as the subject matter of chapters in later volumes of the Handbook.
Mathematical Induction
Authors: Walther Christoph 
Published: November 2023

Abstract
Proving statements of arithmetic usually requires induction. Statements like are well-known from basic mathematics courses and provide beginner’s exercises for applying the induction principle. If we prove such statements we often appeal to our ‘intuition’ and use our knowledge about arithmetic without being aware of each decision made during the search for a proof. Of course, this is not required as long as we are successful in proving theorems by induction. But if we intend to automate induction theorem proving our proof-strategic knowledge must be made explicit such that a computer can perform the right decisions when searching for a proof.
Higher Order Logic
Authors: Leivant Daniel 
Published: November 2023

Abstract
Higher order logics, long considered by many to be an esoteric subject, are increasingly recognized for their foundational importance and practical usefulness, notably in Theoretical Computer Science. In this chapter we try to present a survey of some issues and results, without any pretense of completeness. Our choice of topics is driven by an attempt to cover the foundational aspects of higher order logic, and also to briefly point to some areas of current and potential applications. The chapter falls into two parts. The first part, consisting of sections 1 through 4, is designed to bring forth the essential issues and facts of the topic. Section 1 is intended to motivate our interest in higher order logic, by presenting selected examples of the expressive power of second order logic, and contrasting them with the limitations of first order logic.
Defeasible Logic
Authors: Nute Donald 
Published: November 2023

Abstract
Like all reasoning, defeasible reasoning involves inference. One makes an inference when one comes to have some belief on account of other beliefs that one has. The kind of relationship I intend by ‘on account of’ is one in which a person who makes an inference does or would put forward the beliefs on account of which she comes to have the new belief as reasons for accepting the new belief. This is very rough, but my main goal is not to explain inference. What I am concerned to do is to determine how the inferences made in defeasible reasoning, which I will call defeasible inferences, are different from other inferences..
Possibilistic Logic
Authors: Dubois D , Lang J , Prade H 
Published: November 2023

Abstract
Possibilistic logic is a logic of uncertainty tailored for reasoning under in-complete evidence and partially inconsistent knowledge. At the syntacticlevel it handles formulae of propositional or first-order logic to which are attached numbers between 0 and 1, or, more generally, elements in a to-tally ordered set. These weights are lower bounds on so-called degrees of necessity or degrees of possibility of the corresponding formulae. The de-gree of necessity (or certainty) of a formula expresses to what extent the available evidence entails the truth of this formula.
Temporal Logic
Authors: Gabbay Dov M , Hodkinson Ian , Reynolds Mark 
Published: November 2023

Abstract
This long awaited book gives a thorough account of the mathematical foundations of Temporal Logic, one of the most important areas of logic in computer science. The book, which consists of fifteen chapters, moves on from giving a solid introduction in semantical and axiomatic approaches to temporal logic to covering the central topics of predicate temporal logic, meta-languages, general theories of axiomatization, many dimensional systems, propositional quantifiers, expressive power, Henkin dimension, temporalization of other logics, and decidability results. Much of the research presented here is frontline in the new results and in the unifying methodology. This is an indispensable reference work for both the pure logician and the theoretical computer scientist.
Groups of prime exponent
Authors: Vaughan-Lee Michael 
Published: November 2023

Abstract
We let B(r, p) be the r generator Burnside group of exponent p, and we let R(r, p) = B(r, p)/K, where K is the intersection of all subgroups of finite index in B(r, p). Thus every finite r generator group of exponent p is a homomorphic image of R(r, p). Kostrikin’s solution of the restricted Burnside problem for prime exponent implies that if p is prime then R(r, p) is finite for r = 1, 2, … On the other hand, Adjan’s solution of the unrestricted Burnside problem implies that if p ≥665 then B(r, p) is infinite for r≥ 2.
Groups of prime-power exponent
Authors: Vaughan-Lee Michael 
Published: November 2023

Abstract
We consider groups of prime-power exponent q =pk&gt; 4 (with k &gt; 1). Adjan’s solution of the Burnside problem [l] tells us that if r≥2, q ≥665, and p &gt; 2 then B(r, q) is infinite. Zelmanov’s solution of the restricted Burnside problem for groups of prime-power exponent implies that L(r, q) is nilpotent, but Razmyslov’s Theorem tells us that L(r, q) has derived length at least 1 + [log2 r]. We look at the Lie rings of groups of exponent pk in §8.1. In §8.2 and §8.3 we look at some results in exponents 8 and 9.
Random Walks And Random Environments
Authors: Hughes Barry D 
Published: November 2023

Abstract
This is the first volume of a two-volume work devoted to probability theory in physics, physical chemistry and engineering. This volume provides an introduction to the problem of "random walk" and its applications. In its simplest form, the random walk describes the motion of an idealized drunkard and is a discrete analogue of the diffusion through a medium with traps, laser speckle and the conformations of polymers in dilute solution. Prior knowledge of probability theory is helpful, but not assumed.
Random Walks and Random Environments
Authors: Hughes Barry D 
Published: November 2023

Abstract
This is the second volume of a two-volume work devoted to probability theory in physical chemistry, and engineering. Rather than dealing explicitly with the idea of an ongoing random walk, each chaotic step taking place at fixed time intervals, this volume addresses models in which the disorder is frozen in space-random environments. The volume begins with a largely self-contained introduction to the geometry of random environments, emphasizing Bernoulli percolation models. The scope of the investigation then widens as we ask how structural disorder affects the transport process. The final chapters confront the interplay of two different forms of randomness; spatial randomness frozen into the environment and temporal randomness associated with the choices for next steps made by a random walker. The book ends with a discussion of "the ant in the labyrinth" problems. It is supported by an extensive bibliography and very little prior knowledge is assumed.
Time and Change for AI
Authors: Galton Antony 
Published: November 2023

Abstract
Outside physics and philosophy one seldom reasons much about time and change in the abstract, but on the other hand reasoning about particular times and changes—dates, processes, events, and so on—is all-pervasive both in the specialist sciences and in everyday life. No account of reasoning can properly be called complete if it does not say something about how we reason about change; and if, as in Al, the aim is to simulate or duplicate human reasoning computationally, then the account of change required must be both extensive and detailed. In this section we survey six areas pertaining to Al in which a need for temporal reasoning has been felt, introducing some of the key issues arising in these areas; in later sections we examine these issues in greater detail.
The Discrete Kalman Filter
Authors: Lancaster Peter , Rodman Leiba 
Published: November 2023

Abstract
One of the more important motivations for the study of algebraic Riccati equations was recognized in the early 1960s after publication of the works of Kalman (1960a) and Kalman and Bucy (1961) on filtering and prediction problems of discrete and continuous types, respectively. A full development of the theory behind these processes is beyond the scope of this book. However, this chapter is devoted to an intuitive development of the ideas behind discrete Kalman filtering and, in Section 17.5, an account of the basic convergence theorem for the Riccati difference equation. This may be all that the reader needs to know about the problem, or it may lead the way to more thorough treatments such as the careful mathematical development of Catlin (1989) or the graduate engineering text of Anderson and Moore (1979).
Structured Stability Radius
Authors: Lancaster Peter , Rodman Leiba 
Published: November 2023

Abstract
In applications, Ω is considered a “good” set, and a matrix X having all its eigenvalues in O is considered a “good” matrix. For example, if n is the open left half-plane, then a “good” matrix means that the matrix is c-stable. In general, r(A; B, C, Ω) can be interpreted informally as the “distance” from a given “good” matrix A to the set of “bad” matrices, where the distance is measured by the size of additive perturbation of the form BDC, with fixed B and C and variable D. The term structured refers to this particular structure of admissible perturbations.
Commercial software development
Authors: Ince D C 
Published: November 2023

Abstract
To describe how modern software projects are managed and organized. To describe some problems currently encountered in software development. To describe some misconceptions about the use of mathematics on a software project. Many readers of this book will be familiar with programming only as a software development activity. This chapter provides an introduction to a number of the more important software development activities and places the rest of the book firmly in the context of an engineering approach to software. Producing a major software system with a large number of staff, each of whom will have a wide range of competence and skills, is one of the most complex activities the human race currently undertakes.
Inert and inhabited dynamical systems
Authors: Sandewall Erik 
Published: November 2023

Abstract
This book addresses the knowledge repreSCDtation and reasoning about inert and inhabited dynamical systems, where the agent(s) inhabiting the system are characterized by their ability to perform actions. A system is then defined in a quite general fashion as a collection of objects which have individual properties as well as relationships between each other. Color, weight, and velocity are examples of properties; adjacency, support, and mutual visibility are examples of relationships. The property assignments and relationships that hold in the system at a point in time constitute its state. A part of the state may be designated as the system’s input at the preSCDt time.
Neural Networks for Pattern Recognition
Authors: Bishop Christopher M 
Published: November 2023

Abstract
This book provides the first comprehensive treatment of feed-forward neural networks from the perspective of statistical pattern recognition. After introducing the basic concepts of pattern recognition, the book describes techniques for modelling probability density functions, and discusses the properties and relative merits of the multi-layer perceptron and radial basis function network models. It also motivates the use of various forms of error functions, and reviews the principal algorithms for error function minimization. As well as providing a detailed discussion of learning and generalization in neural networks, the book also covers the important topics of data processing, feature extraction, and prior knowledge. The book concludes with an extensive treatment of Bayesian techniques and their applications to neural networks.
Learning And Generalization
Authors: Bishop Christopher M 
Published: November 2023

Abstract
As we have emphasized in several other chapters, the goal of network training is not to learn an exact representation of the training data itself, but rather to build a statistical model of the process which generates the data. This is important if the network is to exhibit good generalization, that is, to make good predictions for new inputs. In Section 1.5, we introduced the simple analogy of curve fitting using polynomials, and showed that a polynomial with too few coefficients gives poor predictions for new data, i.e. poor generalization, since the polynomial function has too little flexibility. Conversely, a polynomial with too many coefficients also gives poor generalization since it fits too much of the noise on the training data. The number of coefficients in the polynomial controls the effective flexibility, or complexity, of the model.
General introduction
Authors: Manzano María 
Published: November 2023

Abstract
Model Theory is the branch of mathematical logic which concerns the relations between mathematical structures and formal languages. The abstract scheme of Model Theory is as follows: we have a language Land a class of objects ℳ which are structures, and between those two types of realities we have a bridge—the notion of truth. Such an arrangement, apparently so simple, provides great flexibility and reach to Model Theory.
First order languages: semantics
Authors: Manzano María 
Published: November 2023

Abstract
In the previous chapter, we studied structures independently of the first order language. Nonetheless, if we wish to penetrate the sanctuary of Model Theory, we need a formal language. The language we shall use is a first order language with equality. The objects of such a language are symbols and sequences of symbols. More precisely, we shall have logical symbols, variables, relation symbols, and function symbols. Further to saying which symbols constitute the alphabet of the language, we will have to make explicit which are the allowed combinations of symbols: how one forms the terms and the formulas of the language. The formation rules of such expressions will be of recursive nature, and they will provide us with a decision procedure for checking whether or not a certain sequence of symbols of the alphabet is a formula or a term.
Completeness of first order logic
Authors: Manzano María 
Published: November 2023

Abstract
In the previous chapter we saw that in order to speak of a structure or a class of structures it is convenient to introduce a formal language appropriate to each case. Among the formulas of the language, we shall usually be interested in determining which ones are true in the structure (or class of structures), and even though we rely on the semantic notion of truth, it is often difficult to establish the truth of a formula by recourse solely to the direct verification of the truth conditions. Much more difficult, however, is to determine if a formula is a consequence of a set of formulas.
Basic notions: model theory
Authors: Manzano María 
Published: November 2023

Abstract
In the first chapter we studied structures and some relations between them, such as isomorphism and embedding, without using a formal language. In the second chapter we introduced the formal first order language in which we can speak of structures. We also defined the fundamental semantic notions. By using such notions we were able to assert, in some cases, that a certain formula is logically valid: i.e. that it is true in all possible interpretations of the symbols contained in it. In the third chapter we proved that the notion of consequence corresponds exactly to that of deducibility. Those concepts and theorems, although very important, are not, however, the fundamental topics of Model Theory which lie precisely in the middle ground between algebra and logic.
A computational view of interior point methods
Authors: Gondzio Jacek , Terlaky Tamás 
Published: November 2023

Abstract
Many issues that are crucial for an efficient implementation of an interior point algorithm are addressed in this chapter. To start with, a prototype primaldual algorithm is presented. Next, many tricks that make it efficient in practice are discussed in detail. Those include: preprocessing techniques, initialization approaches, methods for computing search directions (and the underlying linear algebra techniques), centering strategies and methods of stepsize selection.
Rectangular Arrays
Authors: Kangshen Shen , Crossley John N , Lun Anthony W -C 
Published: November 2023

Abstract
The 18 problems of this Chapter deal with systems of linear equations. Except for Problem 13, they all involve determinate systems. The technique employed is remarkably modern. The coefficients are laid out in an array and then the coefficient matrix of the array is reduced to triangular form using elementary matrix operations. Negative numbers are used in this Chapter and accordingly the rules for operating with negative quantities are presented.
Sea Island Mathematical Manual
Authors: Kangshen Shen , Crossley John N , Lun Anthony W -C 
Published: November 2023

Abstract
This manual consists of nine Problems and was written by Liu Hui in 263 AD as a continuation of his commentary on Chapter 9, Gougu, of the Nine Chapters. During the Tang Dynasty (618-907 AD), these Problems were separated from the Nine Chapters and made into a separately recognized mathematical work, entitled the Sea Island Mathematical Manual. As Liu Hui put it in his Preface to his Running Commentary on the Nine Chapters (p. 54): “I have written the Rule of Double Differences with some comments, so as to facilitate our search for the original meanings.
Denis Diderot
Authors: Coolidge Julian Lowell , Gray Jeremy 
Published: November 2023

Abstract
Few persons think of this intellectually omnivorous encyclopaedist as a mathematician, and he certainly was not a mathematician of the first rank. But he was a man of a keen and inquiring mind, who in his earlier years was really interested in mathematics, especially in their applications; yet his discussion of the current theories of mathematical probability, which I personally have not seen, show an equal interest in the philosophy of the subject.
William George Horner
Authors: Coolidge Julian Lowell , Gray Jeremy 
Published: November 2023

Abstract
I Should perhaps begin with an apology for including this man in my list of distinguished amateurs who have contributed to mathematical science. A great mathematician he certainly was not. A man distinguished in public life he was not, a master in an altogether undistinguished boys’ school. The contribution to mathematics for which he is generally known, Homer’s method for the solution of numerical equations, was, as we shall see, discovered sixteen years earlier by Paolo Ruffini, and six centuries earlier by Ch’in Chiu-Shao.
Anthyphairetic Ratio Theory
Authors: Fowler D H 
Published: November 2023

Abstract
In response to the opening question of my dialogue, which was couched in the terms of Elements V Definition 3, my slaveboy develops a process of repeated reciprocal subtraction which is then used to generate a definition of ratio as a sequence of repetition numbers (see S13 and Bi4, i.e. the 13th speech, by Socrates, and the 14th, by the boy). As my Socrates says (Sis), and as I have already illustrated in Section 1.2(d), this is not the only possible way of defining ratio or proportion, even within the context of early Greek mathematics; so, to distinguish it, I shall often refer to this as ‘the anthyphairetic ratio’, and call the underlying subtraction process ‘anthyphairesis’.