bluuebunny/crossref_metadata_2025_split huggingface dataset:
Sampling Theory and Wavelets
Authors: Fischer A 
Published: November 2023

Abstract
Over the past decade wavelets and wavelet techniques have become increasingly important in the more applied areas of mathematics. There seems to be hardly any field untouched by the recent preoccupation with these and related concepts. Their effectiveness in data compression makes them invaluable for the compression of auditory signals and images (Mallat 1989b; Wickerhauser 1991; Benedetto and Teolis 1993), their usefulness being further enhanced by their suitability for edge detection (Froment and Mallat 1992; Antoine et al. 1993). Wavelet and more general multilevel methods have been shown to be extremely efficient for the preconditioning of linear systems stemming from Galerkin approximations for elliptic problems (Dahmen and Kunoth 1992; Jaffard 1992).
Diagram Graphs
Authors: Pasini Antonio 
Published: November 2023

Abstract
Section 3.1.2, we represent generalized digons by drawing no edges in D. Then D(Γ) is just the simple graph obtained from the labelled graph 1) by dropping all labels. For instance, in all examples of Section 3.1.3 except (5) and (6.e) the diagram graph is a string. The diagram graph of a building of type Dnlooks like its Coxeter diagram (Section 3.1.3(5)). The diagram graph of the geometry of black and white triangles of Section 2.1.2(10) is a triangle, the same as its Coxeter diagram (Section 3.1.3(6.e)).
Parabolic Systems
Authors: Pasini Antonio 
Published: November 2023

Abstract
We also write Gi,jand Gi,jfor Gi,jand Q{i,j}, for short. Needless to say that, if C = g(Q0) (g E Q) is another chamber in the same orbit of Q containing C0 and if we substitute C for C0 in the above, then the subgroups Qi, Q J etc. should be replaced by their conjugates gQig-1, gGJg-1 etc.
Reduction of the ASDYM equation
Authors: Mason L J , Woodhouse N M J 
Published: November 2023

Abstract
In Chapters 5-7, we shall consider the classification of the integrable systems that arise as symmetry reductions of the anti-self-dual Yang-Mills (ASDYM) equation. In this chapter, we discuss general aspects of the reduction process. 1 We describe a framework for classification of the reduced equations, and we give examples of conformal reduction in the Abelian case to illustrate how some of the basic linear equations of mathematical physics arise from the ASD Maxwell equations. This is followed by a treatment of symmetry reduction in the non-Abelian case. We investigate the invariance of connections, define the associated Higgs fields and discuss their properties. Finally we look at other ‘hidden’ symmetries of the ASDYM equation, which do not arise from point transformations of space-time.
Reductions to one dimension
Authors: Mason L J , Woodhouse N M J 
Published: November 2023

Abstract
Amongst the reductions to one-dimensional systems are two central families of examples. The first, the integrable motions of symmetric tops found by Euler, Lagrange, and Kovalevskaya, are historically important for their part in stimulating the development of the subject. This is particularly true of Kovalevskaya’s example, which she discovered by requiring that the solutions to the equations of motion should have no movable critical points, that is, the location of singularities other than poles should not depend on the initial conditions.
Analytic Theory
Authors: Dwork Bernard 
Published: November 2023

Abstract
In this section we consider Ω a sufficiently large extension of ℚ complete under a valuation extending the p-adic valuation of ℚ. We think of A as a (possibly variable) element of ℚm and a ∈ HΩ, an element of Ωn lying on the hyperplane H. We have B = ℤ[λ] and the field K ( ⊂Ω) must contain ℚ(π, λ, a). We will insist that K be complete. We assume that the rational prime p satisfies the condition
Duality
Authors: Dwork Bernard 
Published: November 2023

Abstract
Let g∈R^, a ∈ H. Our object is to define a mapping with functorial properties of K˜a into W˜−a,−πs. The notation is that of § 16.2. Hypotheses (2.6) and (6.13) will not be used unless specifically indicated. The method used is that of Dwork (1964), §§ 6 and 9.
Triple Systems
Authors: Colbourn Charles J , Rosa Alexander 
Published: November 2023

Abstract
Triple systems are among the simplest combinatorial designs, and are a natural generalization of graphs. They have connections with geometry, algebra, group theory, finite fields, and cyclotomy; they have applications in coding theory, cryptography, computer science, and statistics. Triple systems provide in many cases the prototype for deep results in combinatorial design theory; this design theory is permeated by problems that were first understood in the context of triple systems and then generalized. Such a rich set of connections has made the study of triple systems an extensive, but sometimes disjointed, field of combinatorics. This book attempts to survey current knowledge on the subject, to gather together common themes, and to provide an accurate portrait of the huge variety of problems and results. Representative samples of the major styles of proof technique are included, as is a comprehensive bibliography.
Varieties and complexity
Authors: Evens Leonard 
Published: November 2023

Abstract
We shall use some basic facts about the prime ideal spectrum of a commutative ring. Good sources for this material are Bourbaki (1972) and Atiyah and MacDonald (1969). The latter text summarizes most of the relevant facts in exercises. In what follows, unless otherwise asserted, k is a field of characteristic p and G is a finite group.
Categories of Commutative Algebras
Authors: Diers Yves 
Published: November 2023

Abstract
This book studies the universal constructions and properties in categories of commutative algebras, bringing out the specific properties that make commutative algebra and algebraic geometry work. Two new universal constructions are presented and used here for the first time. The author shows that the concepts and constructions arising in commutative algebra and algebraic geometry are not bound so tightly to the absolute universe of rings, but possess a universality that is independent of them and can be interpreted in various categories of discourse. This brings new flexibility to classical commutative algebra and affords the possibility of extending the domain of validity and the application of the vast number of results obtained in classical commutative algebra.
The Geometry of Topological Stability
Authors: Du Plessis Andrew , Wall Terry 
Published: November 2023

Abstract
The aim of this book is to give necessary and sufficient conditions for aCoo map to be C0-stable; the aim is achieved in a wide range of dimensions via a detailed study of the geometry and topology of many classes of "generic" singularities. The methods developed for examining the topology and geometry use results from many areas of mathematics - geometric topology, stratification theory, algebraic topology, algebraic geometry, commutative algebra... - and further progress will doubtless be made from the application of deeper results from these areas. Conversely, it is to be hoped that the description of the behaviour of generic singularities will also have interesting consequences for these areas of mathematics, which are those with most interaction with singularity theory. The book describes original research; essentially none of its results has previously appeared elsewhere, either in scientific articles or in books.
Functional and Numerical Methods in Viscoplasticity
Authors: Ionescu Ioan R , Sofonea Mircea 
Published: November 2023

Abstract
This book presents some mathematical methods used in the study of initial and boundary problems for Bingham fluids and rate-depedent viscoplasticity. Existence and uniqueness results are presented and the behaviour of the solution with respect to the data is also studied. For some problems, the numerical approximation of the solution is also given and numerical results are presented. Elliptic variational inequalities, convex functions, monotone operators, semigroups of operators, and nonlinear evolution equations are used as mathematical instruments. The book presents a sudy of some problems of viscoplasticity using various and different mathematical methods, the mathematical results are interpreted from a mathematical point of view, and the theory is developed to deal with numerical results from possible applications in industry and technology.
Connections, Definite Forms, and Four-manifolds
Authors: Petrie Ted , Randall John 
Published: November 2023

Abstract
The central theme of this book is the study of self-dual connections on four-manifolds. The authors have adopted a topologists' perspective and so have included many of the explicit calculations using the Atiyah-Singer index theorem as well as presenting arguments couched in terms of equivariant topology. The authors' aim is to present moduli space techniques applied to four-manifolds and to study vector bundles over four-manifolds whose structure group is SO(3). Results covered include Donaldson's proof that the only positive definite forms occur as intersection forms and the results of Fintushel and Stern which show that the integral homology cobordism group of integral homology three-spheres has elements of infinite order. Little previous knowledge of differential geometry is assumed and so postgraduate students and research workers will find this both an accessible and complete introduction to an area that is currently one of the most active in mathematical research.
Algebraic Computing in General Relativity
Authors: MacCallum M A H , Skea J E F , McLenaghan R G , McCrea J D 
Published: November 2023

Abstract
Based on lectures given at a summer school on computer algebra, the book provides a didactic description of the facilities available in three computor algebra systems - MAPLE, REDUCE and SHEEP - for performing calculations in the algebra-intensive field of general relativity. With MAPLE and REDUCE, two widespread great-purpose systems, the reader is shown how to use currently available packages to perform calculations with respect to tetrads, co-ordinate systems, and Poincare` gauge theory. The section on SHEEP and Stensor, being the first published book on these systems, explains how to use these systems to tackle a wide range of calculations with respect to tackle a wide range of calculations in general relativity, including the manipulation of indicial formulae. For the researcher in general relativity, the book therefore promises a wide overview of the facilities available in computer algebra to lessen the burden of the lengthy, error-prone calculations involved in their research.
The Additive Divisor Problem and Exponential Sums
Authors: Jutila M 
Published: November 2023

Abstract
involving the divisor function d(n) and some functions f and g satisfying certain regularity conditions. Because it is easier to work with smoothed sums, we equip the outer sum in Weyl’s method - taken over squares of short sums - with a suitable weight function η ( n), which .is a smoothed version of the characteristic function of the interval of summation.
The Notion of a Shimura Variety
Authors: Murty V Kumar 
Published: November 2023

Abstract
The purpose of this note is to introduce the number theorist to Shimura varieties. These are a class of algebraic varieties associated to certain reductive algebraic groups, and studied extensively by G. Shimura over a period of many years. They embody deep arithmetic and geometric information. In recent years, Deligne has added some new insights and provided an intrinsic formulation. In this note, we shall introduce the terminology and give some examples. In particular, we barely scratch the surface of the theory, and we shall not discuss the deeper aspects such as canonical models, cohomology and L-functions. The reader interested in a more thorough discussion as well as references to the literature is advised to consult the article of Milne [Mi].
Class groups of exponent two in real quadratic fields
Authors: Louboutin S , Mollin R A , Williams H C 
Published: November 2023

Abstract
Moreover the solution in [10] provided applications to conjectures in the literature; viz., one of Chow la [l], one of Yokoi [15], one of Mollin [7], and three of Mollin-Williams [8,9]. Therefore this paper completes the task of determining all real quadratic fields of ERO-type having class group Cx of exponent eK ≤2, (with one possible exceptional value ruled out by the GRH). The next section provides notation and preliminary results needed to provide the proof of the ma.in result. A few remarks on our tables are given in Section 4.
Introduction
Authors: Reutenauer Christophe 
Published: November 2023

Abstract
The aim of this preliminary chapter is to show that the Lie algebra of Lie polynomials, which is introduced in Chapter 1 and which is the subject of this book, is indeed the free Lie algebra. Apart from some elementary universal constructions, two results are required: the Poincare-Birkhoff-Witt theorem (actually only its consequence, that a Lie algebra is embedded in its enveloping algebra), and the fact that the free Lie algebra is a free module. The first result will not be proved here, as it is included in many textbooks. The second one is proved in Section 0.3.
Scalar Spherical Harmonics
Authors: Freeden W , Gervens T , Schreiner M 
Published: November 2023

Abstract
The restriction to the unit sphere Ω of any homogeneous harmonic polynomial of degree nis called a spherical harmonic of order n.It turns out that any spherical harmonic is an eigenfunction of the Beltrami operator. On the sphere, spherical harmonics are the analogues of the exponential functions for Fourier analysis. They were introduced in the 1780s to study gravitational theory (cf. P.S. DE LAPLACE (1785), A.M. LEGENDRE (1785)). Early books on the theory of potentials and spherical harmonics are due to E. HEINE (1878) and F. NEUMANN (1887). Indeed, spherical harmonics are essential for the analysis of any phenomena with spherical symmetry, e.g. celestial mechanics, terrestrial magnetism, earthquakes, solar corona etc. The use of spherical harmonics in all geosciences for the purpose of representing fields is a well established technique. A great incentive came from the fact that global geomagnetic data became available in the first half of the last century (cf. C.F. GAUSS (1839)).
Green’s Functions With Respect To Iterated Beltrami Operators
Authors: Freeden W , Gervens T , Schreiner M 
Published: November 2023

Abstract
A fundamental question when approximating a function on the sphere by its truncated Fourier expansion (orthogonal expansion) in terms of spherical harmonics is the existence of a manageable error term. An adequate answer is the construction of integral formulae that will now be presented. It will be shown that the error term between a function and its truncated Fourier series expansion is explicitly available in integral form provided that sufficient smoothness is imposed on the function under consideration.
Spherical Radial Basis Functions
Authors: Freeden W , Gervens T , Schreiner M 
Published: November 2023

Abstract
In this chapter we deal with spherical radial basis functions, i.e. kernel functions depending only on the (spherical) distance between unit vectors. The importance of our considerations lies in the development of general Sobolev spaces ℋ and (invariant) pseudodifferential operators Λ in which it is possible that (i) the radial basis function is recognized as axisymmetric reproducing kernel function of ℋ and (ii) the kernel admits a Legendre expansion determined by the symbol {Λ^(n)} of a pseudodifferential operator Λ. Criteria are given for measuring the space-frequency localization of (radial basis) functions on the sphere. The trade off between space localization on the sphere and frequency localization in terms of spherical harmonics is described in form of an ‘uncertainty principle’.
Tensor Spherical Harmonics
Authors: Freeden W , Gervens T , Schreiner M 
Published: November 2023

Abstract
Many problems arising in geomathematics are of tensorial nature and spherical geometry. An important tool in dealing with such problems is the theory of tensor spherical harmonics. We present in this book a theory of tensor spherical harmonics generalizing in canonical way our approach to vector spherical harmonics. A striking point is that the tensor spherical harmonics are generated from the scalar ones by use of certain operators mapping scalar functions to tensor fields. As a matter of fact, these formulations (being as always independent of any choice of spherical coordinates) offer the possibility of extending all essential results known for scalar spherical harmonics to the tensorial case, including the definition of a tensorial Beltrami operator, the addition theorem, and tensorial versions of the Funk-Hecke formula. Furthermore, our appoach allows a straightforward transition of scalar approximation methods to the tensorial framework.
Provably Total Functions in Bounded Arithmetic Theories R, U and V
Authors: † Samuel R Buss* 
Published: November 2023

Abstract
Abstract
The outline of this paper is as follows: in section 2, we introduce the computational complexity classes using witness oracles and prove several fundamental closure properties for them. In section 3, we briefly review the fragments of Bounded Arithmetic needed and prove that various complexity classes of functions can be defined in these theories. In section 4, we review the witness predicate and prove the witnessing lemma and various corollaries for the first-order systems. Section 5 is a translation of the results of section 4 to the second-order systems. The reader who is interested primarily in first order-systems may safely omit all the sections that pertain to second-order objects and second order-systems (sections 2.2, 3.3 and 5). However, the reader interested in second-order systems must read the entire paper since we frequently omit proofs in the second-order case.
An Equivalence between Second Order Bounded Domain Bounded Arithmetic and First Order Bounded Arithmetic
Authors: Razborov Alexander A 
Published: November 2023

Abstract
But Bounded Arithmetic also gives an opportunity to directly interpret second order objects in a first order language. The antagonism “second order vs. first order” translates via this interpretation to “arbitrary integers vs. those “small” integers x for which f(x) exists” where f is a rapidly growing function whose existence is not provable in Bounded Arithmetic.
Feasible interpretability
Authors: Verbrugge* Rineke 
Published: November 2023

Abstract
Abstract
In PA, or even in 1.Δ.o + EXP, we can define the concept of feasible interpretability. Informally stated, U feasibly interprets V iff: for some interpretation, U proves the interpretations of all axioms of V by proofs with Giidel numbers of length polynomial in the length of the Gödel numbers of those axioms.
Stochastic models for random sets of points
Authors: Kingman J F C 
Published: November 2023

Abstract
Figure 1.1 might represent the positions of visible stars in a patch of the sky, the positions (seen from above) of trees in an area of woodland, or those of certain archaeological sites. There is no clear pattern, the points are haphazardly distributed with no obvious regularity or trends in density. Similar situations can arise in three dimensions or in one, or in more complicated geometries. If we look at the whole sky, for example, the stars appear to be distributed over the surface of a sphere. Poisson processes are models of such phenomena, which use the theory of probability to describe this sort of highly random behaviour. Their characteristic feature is a property of statistical independence.
Poisson processes in general spaces
Authors: Kingman J F C 
Published: November 2023

Abstract
The state space S in which the points of a Poisson process sit is usually Euclidean space of some dimension d, or more generally (Chapter 7) a manifold which is locally equivalent to Rd. The theory does not, however, make use of the special properties of Euclidean space, but only needs a reasonable family of subsets to be used as test sets to count the random points. That is, we need sets for which the count function The natural way to do this is to suppose that S is a measurable space.
Deduction Systems Based on Resolution
Authors: Eisinger Norbert , Ohlbach Hans Jürgen 
Published: November 2023

Abstract
Statements about the real world or about Active or abstract worlds are often interrelated in that some of them follow from others. For example, given the statements: ‘Every cat eats fish’ ‘Garfield is a cat’ ‘Garfield eats fish’ one would agree that the third statement follows from the other two. Whenever we assume the first and the second statement to be true (in our considered world), we also have to accept the truth of the third statement.
Logical Features of Horn Clauses
Authors: Hodges Wilfrid 
Published: November 2023

Abstract
Horn clause logic is a part of first-order logic. It was first isolated by J. C. C. McKinsey (1943), who was working on decision problems. Between 1956 and 1970, Anatoliī Mal’tsev published a series of papers in which he showed that Horn clauses form the right setting for a large part of universal algebra—including the theory of presentations and initial models. Algebraic specification lies within this part of universal algebra.
Logical Basis for the Automation of Reasoning: Case Studies
Authors: Was Larry , Veroff Robert 
Published: November 2023

Abstract
With the availability of computers in the late 1950s, researchers began to entertain the possibility of automating reasoning. Immediately, two distinctly different approaches were considered as the possible basis for that automation. In one approach, the intention was to study and then emulate people; in the other, the plan was to rely on logic. In this chapter, we focus mainly on the latter, for logic has proved to provide an excellent basis for the automation of reasoning.
Handbook of Logic in Computer Science
Authors: Spurr Jane 
Published: November 2023

Abstract
The Handbook of Logic in Computer Science is a multi-volume work covering all major areas of application of logic to theoretical computer science. The Handbook comprises six volumes. Each volume contains five or six chapters giving an in-depth overview of one of the major topics in the field. It is the result of many years of co-operative effort by some of the most eminent frontline researchers in the area. It will no doubt be the standard reference work in logic and theoretical computer science for years to come - essential reading for all those interested in theoretical computer science and logic.
Designing a Theorem Prover
Authors: Paulson Lawrence C 
Published: November 2023

Abstract
Because many different forms of logic are applicable to computer science, a common question is — How do I write a theorem prover? This question can be answered with general advice. For instance, first do enough paper proofs to show that automation of your logic is both necessary and feasible. The question can also be answered with a survey of existing provers, as will be done in this chapter. But automatic theorem proving involves a combination of theoretical and coding skills that is best illustrated by a case study. So this chapter presents a toy theorem prover, called Folderol, highlighting the key design issues. Code fragments are discussed in the text; a full program listing appears at the end of the chapter.