bluuebunny/crossref_metadata_2025_split huggingface dataset:
Reduce as an algebraic programming language
Authors: MacCallum Malcolm A H , Wright Francis J 
Published: November 2023

Abstract
A Reduce “program” is not a well-defined object like a Pascal or FORTRAN program, but is just a body of code intended to perform a particular task. It will usually be a collection of procedures (equivalent to procedures, functions and subroutines in other languages), control structures, let-rules and variable assignments. Often these will be read or loaded from a file, and then the “program” will be run by invoking a procedure, which may itself call other procedures. Alternatively, the “program” may run as it is being read just as it would if the statements were entered one-by-one from the keyboard.
Programming 1n (R)Lisp
Authors: MacCallum Malcolm A H , Wright Francis J 
Published: November 2023

Abstract
In this very brief introduction to Lisp, we will try to avoid features very specific to CULisp (Cambridge Lisp), which we ourselves use, but we will sometimes mention differences between Lisps. There are many good (and some bad) books on Lisp: one we have found useful is Winston and Horn (1988) though this is based on Common Lisp (older editions used Maclisp). Cambridge Lisp’s built in commands are in lower case, though names in either case are allowed (and there is in fact an upper case version also). However, we will follow our usual conventions and put Lisp commands in upper case here for clarity.
Advanced topics
Authors: MacCallum Advanced topics [CT] Malcolm A H , Wright Francis J 
Published: November 2023

Abstract
The first part of this chapter builds on chapters 5 and 6 to intro duce algebraic use of symbolic mode via a case study in the development of a simple new Reduce facility. It then discusses the use of matrices as local rather than global objects and uses some symbolic procedures to provide complete (but inelegant) support for local matrices. The second part presents an example of using Reduce to generate FORTRAN 77 code for use in numerical computations, in which a Chebyshev-economized polynomial approximation is generated in Horner or nested form suitable for efficient numerical evaluation. Finally, a few remaining facilities are listed that have not been discussed in detail.
Differentiation: The Amplitwist Concept
Authors: Needham Tristan 
Published: November 2023

Abstract
To know the graph of an ordinary real function is to know the function completely, and so to understand curves is to understand real functions. The key insight of differential calculus is that if we take a common or garden curve, place it under a microscope and examine it using lenses of greater and greater magnifying power, each little piece looks like a straight line.When produced, these infinitesimal pieces of straight line are the tangents to the curve, and their directions describe the local behaviour of the curve. Thinking of the curve as the graph of f(x), these directions are in tum described by the derivative, f′ (x).Despite the fact that we cannot draw the graph of a complex function, in this chapter we shall see how it is still possible to describe the local behaviour of a complex mapping by means of a complex analogue of the ordinary derivative—the “amplitwist”.
Diagonalization and Self-Reference
Authors: Smullyan Raymond M 
Published: November 2023

Abstract
The main purpose of this book is to present a unified treatment of fixed points as they occur in Gödel's incompleteness proofs, recursion theory, combinatory logic, semantics, and metamathematics. The book provides a survey of introductory material and a summary of recent research. The first chapters are of an introductory nature and consist mainly of exercises with solutions given to most of them.
Polygons and area
Authors: Huxley M N 
Published: November 2023

Abstract
Given a simple closed curve, what is the area inside it? This is the problem of quadrature, important in the history of mathematics. At first to find the area meant to construct a square of equal area; later it meant to find a real number, the ratio of the area of the curve to the area of a unit square. To find a real number can mean one of four things.
Analysis on Symmetric Cones
Authors: Faraut Jacques , Korányi Adam 
Published: November 2023

Abstract
The present book is the first to treat analysis on symmetric cones in a systematic way. It starts by describing, with the simplest available proofs, the Jordan algebra approach to the geometric and algebraic foundations of the theory due to M. Koecher and his school. In subsequent parts it discusses harmonic analysis and special functions associated to symmetric cones; it also tries these results together with the study of holomorphic functions on bounded symmetric domains of tube type. It contains a number of new results and new proofs of old results.
The Gamma Function Of A Symmetric Cone
Authors: Faraut Jacques , Korányi Adam 
Published: November 2023

Abstract
This chapter begins the serious study of analysis on symmetric cones. In terms of the generalized determinant and minors we introduce Δs, a kind of generalized power function. With the aid of this we define and evaluate the generalized gamma and beta functions associated with the cone. This then leads to identities involving the Laplace transformation of the generalized power function and to differential identities. In Sections 2 and 3 we then discuss the theory of the analytic continuation of the generalized Riesz integrals and some of their applications.
Complex Jordan Algebras
Authors: Faraut Jacques , Korányi Adam 
Published: November 2023

Abstract
In later chapters we will study complex tube domains over symmetric cones. These are domains in the complexifications of Euclidean Jordan algebras. The first two sections of the present chapter discuss the relevant definitions and basic facts, including some properties of the structure group of a complexified Euclidean Jordan algebra which will be needed later. The subsequent sections will not be needed later in this book; however, they contain basic background information. Section 3 gives a generalization of the Jordan canonical form of matrices, which is valid in any complex Jordan algebra. In Section 4 we prove that the class of Euclidean Jordan algebras coincides with the class of formally real Jordan algebras. In Section 5 we prove that the complexifications of Euclidean Jordan algebras exhaust the seemingly larger class of complex semi-simple Jordan algebras.
Water Waves: Relating Modern Theory to Advanced Engineering Applications
Authors: Rahman Matiur 
Published: November 2023

Abstract
The purpose of this book is to present a self contained introduction to the mathematical and physical aspects of the theory of water waves. The book is aimed at undergraduate and graduate levels for engineers, physical scientists and mathematicians. Each chapter is concluded with practical problems expressed as exercises and accompanied by ample references for further studies. The book consists of ten chapters arranged into three parts: Part I: Basic Fluid Mechanics and Solutions Techniques which cover chapters 1-3. Part II: Water Waves covering chapters 4-7. Part III Advanced Water Waves which covers chapters 8-10. Parts I and II are elementary in nature; whereas Part III is more advanced. The first three chapters give the derivations of the fundamental mathematical equations. Chapter 2 outlines appropriate differential equations to describe the physical phenomena, and Chapter 3 reviews solution techniques of some simplified partial differential equations. Chapter 4 gives the developmental of wave equations, including the essential boundary conditons and describes small amplitude wave theory. Chapter 5 deals with finite amplitude wave theory and Chapter 6 outlines the study of tidal dynamics in shallow water. For random wave case, the deterministic methods described in previous chapters do not hold good. Therefore, chapter 7 is clearly devoted to wave statistics and wave energy spectrum. The application of wave theory is demonstrated in Chapter 8. Chapter 9 examines the nonlinear long waves in shallow water from a mathematical view point. The book concludes with Chapter 10 which illustrates the inverse scattering technique to solve solitary wave problem.
Computational Methods in Linear Prediction for Band-Limited Signals Based on Past Samples
Authors: Mugler D H 
Published: November 2023

Abstract
An accurate prediction of the “next” value of a signal from its past samples is an important problem for many applications. Linear prediction coding, (Elias 1955; Rabiner and Schafer 1993), even predicts values several steps ahead of the last data sample. For the transmission of a block of signal samples, the LPC method is to record the first several samples and then use a linear prediction formula to estimate the values of the rest of the samples in the block (Meyer 1994, p. 33).
Almost Sure Sampling Restoration of Band-Limited Stochastic Signals
Authors: Pogany T 
Published: November 2023

Abstract
The origin of sampling principles for stochastic signals is not exactly known. Work of Kotel’nikov (1933) in this area was first made known to Western mathematicians by Kolmogorov, who mentioned it in a brief manner at the end of his talk at the Symposium on Information Theory at MIT, held on September 10−12, 1956 (Kolmogorov 1956). This involves the well-known sampling series, usually attributed to Whittaker, Kotel’nikov and Shannon in the Western literature, but often caned the Kotel’nikov formula in Eastern Europe and the former Soviet Union countries.
The Structure of Groups of Prime Power Order
Authors: Leedharn-Green C R , McKay S 
Published: November 2023

Abstract
The coclass project (1980-1994) provided a new and powerful way to classify finite p-groups. This monograph gives a coherent account of the thinking from which the philosophy that lead to this classification developed. The authors provide a careful summary and explanation of the many and difficult original research papers on the coclass conjecture and the structure theorem, thus elucidating the background research for those new to the area as well as for experienced researchers. The classification philosophy has lead to many new and challenging problems. Amongst those considered are problems about pro-p-groups, the Grigorchuk group, the Nottingham group as well as linear pro-p-groups. Throughout the book the authors have used a wide range of algebraic techniques and have developed from first principles, or from basic and well known results, the cohomology of groups, spectral sequences, and representation theory. This comprehensive and long-awaited survey of the recent and current research on the structure of finite p-groups will be an important reference for all group theorists.
Biordered sets
Authors: Higgins Peter M 
Published: November 2023

Abstract
In Section 1.5 the notion of the biordered set of a semigroupS was introduced, along with the associated idea of a sandwich set of an ordered pair of idempotents,S(e,f). That an element may always be drawn fromS(e,f) in caseS is regular was used implicitly in Theorem 1.4.17, and sandwich sets were also used to describe those regular semigroups in which the natural partial order is compatible with multiplication (Theorem 1.5.10 and Corollary 1.5.11).
Initial concepts and first results
Authors: Helemskii A YA 
Published: November 2023

Abstract
The subject of this book is a kind of synthesis. In the well-known textbook by Rickart it is said jokingly, but not without justification, that the head of the theory is in algebra and the feet in analysis [64, vi]. To characterize the present chapter such a comparison could be extended. Here our subject is presented as a new-born baby and so it has a disproportionately large head and small feet: in fact the reader will see that at the beginning of the account algebra is somewhat dominant compared with analysis. In the second chapter — as is customary with the growth of a body — the proportion begins to even out and there appear the first significant results based on an equally balanced interaction between the two “basic” disciplines — theorems on spectra and on the structure of polynormed skew fields. This, in its turn, will lay the foundation for the central results of the general theory contained in Chapter IV.
Commutative and star Banach algebras
Authors: Helemskii A YA 
Published: November 2023

Abstract
shall speak of results that historically form the core of our subject and reflect that interplay of analysis and algebra which is characteristic of it. Here we shall describe, for the most part, the achievements of the “classical period” of Banach algebras (approximately 1939-1953). The results, as a rule, refer to two classes of algebras: (I) commutative and (II) those having some intrinsic symmetry the so-called star algebras. Accordingly, two closely-related theories are given (the second depends on the first). In each of them there is a climax — when there appears a construction for making “something concrete and tangible”, within the given class, from a given (abstract) algebra: in the first case this is a function algebra, in the second it is an operator algebra. The constructed algebra contains extensive information about the original algebra and, under certain additional assumptions, it is an isometrically isomorphic copy of it.
Borel’s Methods of Summability
Authors: Shawyer Bruce , Watson Bruce 
Published: November 2023

Abstract
Summability methods are transformations that map sequences (or functions) to sequences (or functions). A prime requirement for a "good" summability method is that it preserves convergence. Unless it is the identity transformation, it will do more: it will transform some divergent sequences to convergent sequences. An important type of theorem is called a Tauberian theorem. Here, we know that a sequence is summable. The sequence satisfies a further property that implies convergence. Borel's methods are fundamental to a whole class of sequences to function methods. The transformation gives a function that is usually analytic in a large part of the complex plane, leading to a method for analytic continuation. These methods, dated from the beginning of the 20th century, have recently found applications in some problems in theoretical physics.
Relations with the family of circle methods
Authors: Shawyer Bruce , Watson Bruce 
Published: November 2023

Abstract
In this chapter, we give a survey of the family of circle methods, as de- veloped by Meyer−König in [185]. These methods are related to Borel’s methods in that, under certain order conditions on the sequence {sn}, they are essentially equivalent. We shall begin with Knopp’s version of Euler’s method, as first developed by Knopp in 1922 [151], [152]. We shall then survey the Taylor methods, defined by Hardy and Littlewood in 1916 [113]. Included in the survey is Valiron’s method, given by Hardy and Littlewood in [113]. In order to assist in getting the relationships amongst these methods, Meyer−König introduced a new method in [185].
Algebraic Varieties
Authors: Yves Diers 
Published: November 2023

Abstract
The Zariski category RedCAlg ( k) of reduced commutative algebras over an algebraically closed field k is the most appropriate for the study of algebraic varieties over k. What are the special features of this Zariski category that make classical algebraic geometry work? It is a locally neotherian Zariski category whose initial object is simple and algebraically closed, and in which any object is reduced. We use here the notion of locally neotherian categories introduced by Gabriel and Ulmer [16) and that of algebraically closed objects introduced by Fakir [14) in any locally finitely presentable category. We prove that classical algebraic geometry can be performed on any Zariski category satisfying these properties.
Calculations of instability loci
Authors: Du Plessis Andrew , Wall Terry 
Published: November 2023

Abstract
The theory developed in Sections 9.5, 9.6, 10.2, and 10.3 shows how analysis of certain (positive) instability ideals leads to the identification of civilized submanifolds of jet space and thus, by Sections 9.2-9.4, to sufficient conditions for topological stabilityThe algorithms described in Sections 10.4-10.6 give an essentially mechanical way to compute positive instability ideals. They provide surprisingly fast computations of these ideals, given the numbers and degrees of the variables involved. None the less, all but the simplest of these computations seem to be beyond direct calculation by hand. We have used electronic computers (SUN 4, DEC 3100) furnished with computer algebra software (MAPLE) instead. This raises the question of check ability of the results obtained. In fact these results are checkable, and without too much effort. We return to the situation and notation of Section 10.4.
The Computational Complexity of Differential and Integral Equations
Authors: Werschulz Arthur G 
Published: November 2023

Abstract
This book is concerned with a central question in numerical analysis: the approximate solution of differential or integral equations by algorithms using incomplete information. This situation often arises for equations of the form Lu=f, where f is some function defined on a domain and L is a differential operator. The function f may not be given exactly-we might only know its value at a finite number of points in the domain. Consequently the best that can be hoped for is to solve the equation to within a given accuracy at minimal cost or complexity. The author develops the theory of the complexity of the solutions to differential and integral equations and discusses the relationship between the worst-case setting and other (sometimes more tractable) related settings such as the average case, probabilistic, asymptotic, and randomized settings. Furthermore, he studies to what extent standard algorithms (such as finite element methods for elliptic problems) are optimal. This approach is discussed in depth in the context of two-point boundary value problems, linear elliptic partial differential equations, integral equations, ordinary differential equations, and ill-posed problems. As a result, this volume should appeal to mathematicians and numerical analysts working on the approximate solution of differential and integral equations as well as to complexity theorists addressing related questions in this area.
Dynamic Processes for Rate-Type Elastic-Visco Plastic Materials
Authors: Ionescu Ioan R , Sofonea Mircea 
Published: November 2023

Abstract
This chapter deals with dynamic problems for semilinear rate-type constitutive materials. The existence and uniqueness of the solution is given using arguments of linear continuous semigroups in Hilbert spaces. In the viscoelastic case an energy bound of the solution is given and it is proved that linear elasticity is a proper asymptotic theory for viscoelastic materials. An approach to perfect plasticity is also studied, by a passage to the limit. The case of rate-type materials involving internal state variables is also discussed and some monotony and fixed point methods in the study of dynamic problems are presented. Finally the evolution of the perturbations of homogeneous simple shear is analysed and the link with strain localization is given.
Elliptic Operators With Variable Coefficients
Authors: Robinson Derek W 
Published: November 2023

Abstract
The previous chapters were devoted to the analysis of strongly elliptic op erators associated with general representations of a Lie group. These oper ators are natural generalizations of the usual elliptic differential operators on Rd with constant coefficients and next we consider similar analogues of elliptic operators with variable coefficients. But extension of the class of operators is only possible by restriction of the representations.
A non-degenerate generalized quadrangle with lines of size four is finite
Authors: Brouwer A E 
Published: November 2023

Abstract
Proof. Each point is incident with the same number of lines, t say, where our aim is to show that t is finite. The hypothesis implies that there are two disjoint lines, L and M say. Consider the 16-set γ that is the union of four lines meeting both L and M.
Geometric hyperplanes of embeddable Lie incidence geometries
Authors: Cooperstein B N , Shult E E 
Published: November 2023

Abstract
Very large subspaces play a key role in determining the structure of a space and in providing interesting examples of spaces not easily defined in other ways. A celebrated criterion, due to Teirlinck (1980), that a linear space be a projective space involves only the way certain geometric hyperplanes are distributed.
A problem on squares in a finite field and its application to geometry
Authors: Hirschfeld J W P , Szönyi T 
Published: November 2023

Abstract
The starting point of this work is the following lemma in Hirschfeld and SZOnyi (submitted): For q an odd prime power, let a be an element of GF(q2)\GF(q). Then there are precisely (q - l)/2 elements u in GF(q) for which a - u is a non-zero square in GF(q2).
Applications of p-Adic Methods to Group Theory
Authors: Du Sautoy Marcus P F 
Published: November 2023

Abstract
In the late nineteenth century, Sophus Lie studied ‘transformation groups’ in an attempt to understand various geometries from more group-theoretic point of view. His pioneering work forged what has been known for nearly a century as the theory of Lie groups, i.e. topological groups with the underlying structure of a real manifold with respect to which the group operations are analytic. The importance of the theory of Lie groups can be judged by the diversity of its applications in topology, differential geometry and arithmetic. There have also been a host of parallel theories where the underlying real manifold is replaced by such structures as algebraic varieties, schemes and p-adic manifolds. It is the last of these which lies at the heart of this chapter. Such groups were encountered for the first time in 1907 in the writings of Hensel (17] on p-adic analytic functions. By 1936 they had appeared in work of Weil and Lutz on p-adic elliptic curves (see (50] and (29]).
Arithtnetical Sitnilarities
Authors: Klingen Norbert 
Published: November 2023

Abstract
This book deals with the characterization of extensions of number fields in terms of the decomposition of prime ideals, and with the group-theoretic questions arising from this number-theoretic problem. One special aspect of this question is the equality of Dedekind zeta functions of different number fields. This is an established problem which was solved for abelian extensions by class field theory, but which was only studied in detail in its general form from around 1970. The basis for the new results was a fruitful exchange between number theory and group theory. Some of the outstanidng results are based on the complete classification of all finite simple groups. This book reports on the great progress achieved in this period. It allows access to the new developments in this part of algebraic number theory and contains a unique blend of number theory and group theory. The results appear for the first time in a monograph and they partially extend the published literature.