bluuebunny/crossref_metadata_2025_split huggingface dataset:
Foundations
Authors: Helemskii A YA 
Published: November 2023

Abstract
Strictly speaking, we shall only start on the subject of this book after we have introduced an additional structure – multiplication — into the objects of linear functional analysis — Banach spaces and some more general spaces; this is precisely what we shall talk about in the first definition of the first chapter. But first, in Chapter 0, it is necessary to indicate the stock of background material which is important: for us as a foundation.
Some of this material is widely known and is contained in standard textbooks but there is some which can be found only in specialized monographs and articles in journals. Therefore the amount of detail given in different: places in this chapter is very varied.
The polynomial Waring and Goldbach problems
Authors: Effinger Gove W , Hayes David R 
Published: November 2023

Abstract
From 1930 to 1932, Leonard Carlitz held a National Research Fellowship. He spent a substantial portion of his fellowship at Cambridge University, where he met Raymond Paley, a brilliant young English mathematician of about the same age as himself. In the decade just gone by, Hardy and Littlewood had captured the interest of the mathematical world with a remarkable series of papers on two classic problems in additive number theory—the Waring problem and the Goldbach problem. The new technique that they relentlessly focused on these problems was the circle method, first introduced by Hardy and Ramanujan in 1918 to derive an asymptotic expansion for the partition function.
Flatness Proper Ties
Authors: Yves Diers 
Published: November 2023

Abstract
Flatness properties are among the basic properties of Zariski categories. Up to now we have used the concept of flat morphism, but the first concept is that of flat object. An object A in A is flat if the endofunctor A ∐ (−) of A preserves monomorphisms. Then a morphism f: A→ B in A is flat if (B,f) is a flat object in A/ A, and an object A in A is absolutely flat if any morphism f: A→ B is flat in A. In an arbitrary Zariski category simple objects need not be absolutely flat, and therefore the two notions of von Neumann regular objects and absolutely flat objects are generally different. Some Zariski categories can have special flatness properties such as the following. Any object is flat, as in the category CAlg(k) of commutative algebras over a field k. Any object is absolutely flat, as in the category RegCRng of von Neumann regular commutative rings. Any simple object is flat, as in the category CRng of commutative rings. Any local flat epimorphism is an isomorphism, as in the category CAlg (A) of commutative algebra over a ring A. In an arbitrary Zariski category, a flat object A is faithfully (reflexively, properly) flat if the endofunctor A ∐ (−) reflects monomorphisms (isomorphisms, the terminal object). These three notions are generally different, but in some Zariski categories, such as CAlg (A), they coincide.
Proper maps and function space topologies
Authors: Du Plessis Andrew , Wall Terry 
Published: November 2023

Abstract
In this chapter we first collect together a number of topological facts concerning proper maps and function space topologies. Indeed, proper maps will appear frequently in this book, both as representatives of germs and in connection with global questions. Most of the results are taken from the literature, but the references are somewhat scattered and do not include all we need, so we give a unified treatment. We treat Sections 3.2-3.4 as reference sections for results of this kind needed in the rest of the volume.
The Flow of the Bingham Fluid with Friction
Authors: Ionescu Ioan R , Sofonea Mircea 
Published: November 2023

Abstract
This chapter deals with the study of some boundary-value problems describing the flow of the Bingham fluid with friction through a bounded domain Ω in ℝ. Existence and uniqueness results are given using elliptic variational inequality arguments. The blocking phenomenon is also studied and the link is given between the yield limit, the friction coefficient and the external forces for which the flow of the Bingham fluid is blocked. An iterative finite-element method for the approximation of the solution is presented and applied to wire-drawing processes.
Group partitions, affine spaces and translation groups
Authors: Batten L M , Brown J M N 
Published: November 2023

Abstract
Affine and projective geometries developed ‘classically’ as the study of invariants of certain groups of projective collineations. The equivalence of desarguesian projective and affine geometries to the well-known constructions from vector spaces over skew-fields was one of the first major results by way of a characterization. For more information on this, the reader is referred to Hilbert (1899), Veblen and Young (1910) and Dembowski (1968).
An embedding theorem for partial linear spaces
Authors: Blokhuis A , Calderbank A R , Metsch K , Seress A 
Published: November 2023

Abstract
We obtain the corollary that A(26, 8, 5) = 30, since Schellenberg (1975) has used a computer to prove that (B(5, 1) does not exist. We sketch a coding theoretic proof of this result. The partial linear space B(5, 1) is a symmetric group divisible design.
Generalized Reed-Solomon codes and normal rational curves: an improvement of results by Seroussi and Roth
Authors: Storme L , State J A Thas 
Published: November 2023

Abstract
In particular, we will consider k-arcs which are subsets of a normal rational curve, that is, the k-arcs which correspond to generalized Reed-Solomon codes and generalized doubly-extended Reed-Solomon codes (Seroussi and Roth 1986).
Coupling Constants for p-Adic Groups
Authors: Plymen R J 
Published: November 2023

Abstract
The work of Vaughan Jones has brought into prominence the theory of II1 factors, their traces and coupling constants. Factors of type II1 were discovered by Murray and von Neumann. They are weakly closed, star algebras of operators on a Hilbert space, with centre consisting of the scalars, and equipped with a finite, positive, trace functional. Such a factor N provides a scale by which to measure the relative dimension of the Hilbert space H on which it acts. We write this number as dimN(H). In this case there are no restrictions on the number. Indeed it may vary continuously from 0 to ∞. Jones varied this idea and looked at a pair of factors N ⊆ M considering the dimension of M relative to its subfactor N. This he defined as [M : N] = dim N (H)/ dimM(H), showing it to be independent of the Hilbert space. The importance of this idea became evident in the restrictions found on the index.
Iwasawa Theory, Factorizability and the Galois Module Structure of Units
Authors: Solomon David R 
Published: November 2023

Abstract
The aim of this paper is to present a new, p-adic approach to a certain problem concerning the structure of algebraic number fields. The problem is that of describing the group of units (more generally the S-units) of an extension field as a module for the Galois group. Our approach involves the application of Iwasawa's theory of Zp-extensions. The main module-theoretic tool will be the concept of factor equivalence. This is an equivalence relation between lattices acted upon by a finite abelian group G and is a weakening of (local) isomorphism as G-modules. The idea was first introduced in [19]. Much of the fundamental work is due to Fröhlich and throughout its development the emphasis has been on applications to questions of Galois module structure (see [19] and also, for example, [3]). Factor equivalence was first applied to the study of units in [10]. This paper, together with (9], are the main references for Sections 1 and 3 in which the basic ideas and results of factorizability and factor equivalence are explained. They should be consulted for further details and proofs of some results. (Our notation will differ somewhat from theirs however.
p-Adic Fourier Series
Authors: Woodcock C F 
Published: November 2023

Abstract
Throughout Z p and Q p will respectively denote the ring of p-adic integers and the field of p-adic numbers (for p prime). Thus Z p is compact and is the closure of Q p (indeed of N) in Q p . We denote by C P the completion of the algebraic closure of Q P with respect to the p-adic metric. Let V p denote the p-adic valuation of C p normalized so that V p (p) = 1.
Analytic functional calculus via integral representations
Authors: Eschmeier Jörg , Putinar Mihai 
Published: November 2023

Abstract
In a unital, commutative Banach algebra A there is a very natural notion of a joint spectrum for systems of elements in A. Let a = (a 1, …, a n) ∑ A n. Then the joint spectrum σ(a) of a is defined as the set of all n-tuples z ϵ ℂn for which the ideal generated by z 1 − a 1, …, z n − a n in A is proper, or equivalently, as the set σ (a) = â(ΔA), where In the fifties, Shilov (1953), Waelbroeck (1954), and Arens and Calderon (1955) showed how to construct an analytic functional calculus for finite systems of elements in A.
Spectral analysis on Bergman spaces
Authors: Eschmeier Jörg 
Published: November 2023

Abstract
Among the examples on which the techniques developed throughout our book can be tested, there is a privileged one: the class of tuples of analytic Toeplitz operators acting on Bergman spaces over bounded pseudoconvex domains in ℂn. This is for two reasons: first because of the maturity of the function theory on Bergman spaces, and second because of the recent advances in the spectral theory of single Toeplitz operators on one-variable Bergman spaces. To be more specific, the fundamental L 2-estimates for the a-operator proved by Hormander (1965) permit the solution of basic division and interpolation problems in spaces of analytic functions with control on the L 2-growth at the boundary (see for instance Mityagin and Henkin 1971; Skoda 1972; Ohsawa 1988). On the other hand, the spectral picture of Toeplitz operators acting on one-dimensional Bergman spaces is well developed (see Axler 1988).
Transcendental Numbers and Functions of Several Variables
Authors: Waldschmidt Michel 
Published: November 2023

Abstract
We start by two density problems: one was raised by Sansuc and deals with algebraic number fields, the other is a question of Mazur and deals with abelian varieties. While the first has just been completely solved by D.Roy, only partial answers have been obtained so far for the second. In both cases the main tool is the theorem of the algebraic subgroup. We show tha.t this theorem enables one to recover Baker’s result on linear combinations of logarithms of algebraic numbers in at least four different ways. Another consequence, once more due to R. Roy, concerns matrices whose entries are linear combinations of logarithms of algebraic numbers.
Response
Authors: Ribenboim Paulo 
Published: November 2023

Abstract
I am very happy with all my friends who are here, and who have come to Kingston to hear many outstanding speakers, and perhaps also a little bit to comfort me as I approach my retirement. So I will begin with a warning: I am not yet retiring! In fact, I will only do so two years from now. I hope not everyone here is saddened by that news! Looking back to all my years of mathematical activity, I see little merit in what I have done. I will explain why.
General principles of MPT
Authors: Grenander Ulf 
Published: November 2023

Abstract
The regular structures introduced in Part I, configuration spaces, image algebras, patterns, are qualitative in nature. For example, a configuration is either regular or not. In Chapters 7-11 we shall relax the regularities, allowing them to be gradual as measured by their probability of appearing in the ensemble we are observing. Expressed otherwise, we shall measure the degree of regularity or irregularity, see the morphogenetic device in Section 4.3.9.3. This metric approach, metric pattern theory, or MPT, leads us to introduce probability measures on spaces that contain and may be larger than the regular structures; see Note 7.A.
Deformation mechanisms
Authors: Grenander Ulf 
Published: November 2023

Abstract
If all images in a pattern were presented in their pure form to the observer the task of pattern analysis would be drastically simplified compared to what is usually the case: the observed images are degraded versions of the pure ones. It would be unrealistic to sidestep this issue and we must therefore study pattern deformations in some detail. Let us start with some generalities.
Applications of Hall sets
Authors: Reutenauer Christophe 
Published: November 2023

Abstract
We begin by introducing Lyndon words and the Lyndon basis of the free Lie algebra; this is a particular Hall set, with special properties, such as triangularity of the change of basis. The dual basis of the Poincare-BirkhoffWitt basis associated to a Hall basis may be computed recursively, by using the shuffle product; this is done in Section 5.2. In the next section a special Hali basis is constructed, which is compatible with the derived series of the free Lie algebra. The special properties of Lyndon words, with respect to the alphabetical order, are also true for Hall words once the appropriate order on words is defined: to obtain it, one factorizes each word, and then orders sequences of Hall words alphabetically (Section 5.4). In the final section, we show how Hali sets lead to the construction of variable-length codes, with various synchronization properties.
Open induction, Tennenbaum phenomena, and complexity theory
Authors: Kaye Richard 
Published: November 2023

Abstract
This paper collects together several ideas concerning weak systems of arithmetic related to the theory !Open of Shepherdson (1964, 1965) and the theory I E 1 of Wilmers (1985), and describes some of the author’s investigations in this area over the last few years. Its two main themes are encapsulated by the following questions: in what way do these theories relate to the computational complexity of natural problems? And: how might one go about proving independence results in this realm? To set the scene and to discuss these questions in more detail we must first give some definitions.
Integer Parts of Real Closed Exponential Fields
Authors: Ressayrc J -P 
Published: November 2023

Abstract
This paper is an extended abstract: the detailed proofs an being prepared for future publication. We define real exponential fields as ordered fields with a function 2x satisfying a set E of four basic axioms. We show that every real closed exponential field in this sense possesses an “integer part”, that is a discrete subring Z such that z+ is closed under 2x, and every element x of the field has an “integer part” ⌊ x ⌋ ∈ Z, such that ⌊ x ⌋ ≤ x &lt;: ⌊ x ⌋ + 1. By using such integer parts, we show that Th(ℝ, 2x) is equivalent to E + Th(ℝ, 21/(H-x3); and we deduce the model completeness of Th(ℝ,2x) from the model completeness ofTh(ℝR,21/(l+x2 )by an argument which differs from Wilkie’s original proof.
Completely random measures
Authors: Kingman J F C 
Published: November 2023

Abstract
It has also the very special property that the random summands on the right of (8.2) are independent random variables. This suggests the concept of a completely random measure on S. This is a random function ct&gt; from the collection of measurable subsets of S into [O, oo] such that, for any collection of disjoint measurable sets A1, A2, A3, ••• , the random variables ct&gt;(Ai) are independent, and The count function of a Poisson process is a completely random measure, but with the additional property that its values are integers. Without this additional condition, a much richer variety of completely random measures can be constructed, but it turns out they all come, in a sense to be made precise, from Poisson processes.
Basins of attraction and the time-dependent approach to obtaining steady-state numerical solutions
Authors: Yee H C 
Published: November 2023

Abstract
The symbiotic relationship between the strong dependence on initial data and the permissibility of spurious stable and unstable asymptotic numerical solutions for commonly used numerical algorithms in computational fluid dynamics (CFD) is illustrated for nonlinear model ordinary differential equations (ODEs) and partial differential equations (PDEs) with known analytic solutions. This is an attempt to understand the global asymptotic behavior of finite difference methods for highly nonlinear and stiff differential equations (DEs). With the aid of a parallel Connection Machine (CM2), the complex behavior and sometimes fractal like structure of the associated numerical basins of attraction of the commonly used time and spatial discretizations are revealed and compared. Here a basin of attraction is a domain of a set of initial conditions whose solution curves (trajectories) all approach the same asymptotic state. Also ¼’e use the term “spurious asymptotic numerical solutions” to mean asymptotic solutions that satisfy the discretized counterparts but do not satisfy the underlying ODEs or PDEs (e.g., nonphysical solutions, nonconvergent solutions or divergent solutions). Asymptotic solutions here include steady-state solutions, periodic solutions, limit cycles, chaos and strange attractors. The results of this investigation can be used as an explanation of the possible causes of error, and slow convergence and nonconvergence of steady-state numerical solutions when using the time-dependent approach for nonlinear hyperbolic or parabolic PDEs.
A general upwind formulation for compressible flows on multi-element meshes
Authors: Dervieux Alain , Fézoui Loula , Leclercq Marie-Pierre , Stoufflet Bruno 
Published: November 2023

Abstract
In the past few years much effort has been devoted to the design of numerical methods applying on unstructured meshes, in order to obtain more complicated methods that can be more easily used, due to mesh generality. This work has been concentrated on mono-element meshes (only one type of element) and particularly on triangles with P1 or Po degrees of freedom. Now, there are strong motivations for considering different elements and multi-element meshes in two possible directions. Firstly, combining triangles and quadrangles can be advantageous in particular for the capture of boundary layers. Secondly, considering higher-order elements is a door to higher-order accuracy in general geometries. For this purpose we start from a Lagrange- Galerkin formulation (Lagrange interpolation, Galerkin variational formulation) and consider upwind extensions. Many upwind methods applying on unstructured meshes are related to Lagrange-Galerkin finite element discretisations. One class of methods, that conserves the finite element philosophy, is the so-called SUPG or Galerkin Least-Square formulation, which has been successfully applied to solve 3-D problems [l]. Recently, distributive schemes ensuring a maximum principle and preserving a linear solution of the advective equation have been studied by several teams (among others [12]). The extension to systems is performed through a multiwave decomposition. Another kind of method, initiated by INRIA and Dassault Aviation, relies on an interpretation of a Galerkin formulation as a Finite Volume centered approximation applied on a dual mesh [2], [3], [4], where the central differences integration is replaced by a Riemann solver [5]. This methodology, which is nowadays widely used, has proved to be reliable as an industrial tool to solve aerodynamic flow problems [6].
Surface grid generation with a linkage to geometric generation
Authors: Suzuki Masahiro 
Published: November 2023

Abstract
It has been well recognized that setting grids on the surface is the most time-consuming task in grid generation process and it is a bottle-neck of the Computational Fluid Dynamics (CFD) analysis. This is attributed to a gap between geometric generation and surface grid generation. The purpose of this paper is to present an approach to close this gap. A simple diagnosis of surface grid quality is also proposed.
Grid convergence for adaptive methods
Authors: Warren Gary P , Anderson W Kyle , Thomas James L , Krist Sherrie L 
Published: November 2023

Abstract
Adaptive-grid methods for computational fluid dynamics have gained popularity in recent years due to their potential to provide highly accurate solutions with relatively few grid points. This gain in popularity owes in large part to the difficulty in modeling complex three-dimensional geometries with globally-refined “structured” grids. By using adaptive-grid techniques, it is generally felt that important flow field features, such as shock waves, can be resolved with a high degree of accuracy because of the flexibility to distribute grid points in regions of interest. In addition, since the point distribution enables a large number of points to be concentrated in limited areas, the memory and computational times can be minimized.
Body capturing using adaptive cartesian grids
Authors: Falle S A E G , Giddings J R 
Published: November 2023

Abstract
In recent years there has been considerable interest in using adaptive cartesian grids to compute complex flows (e.g. Berger & Collela 1989; Berger & Leveque 1990; Quirk, J.J. 1990). Such methods are extremely effective for the interior part of the flow, but they suffer from the disadvantage that they do not represent solid surfaces as accurately as body fitted grids. This difficulty can in part be overcome by using a polygonal representation of the body surface (Leveque 1988, Quirk 1992), but it is then impossible to avoid the presence of extremely small cells which lead to very small time steps when using explicit schemes. For inviscid problems this time step restriction can be avoided by allowing waves to pass through more than one cell in a time step (Leveque 1988, Berger & Leveque 1990), merging the small cells with neighbouring large ones (Quirk 1992) or using sub time stepping in the small cells. However, it is not easy to extend these ideas to viscous problems or to more than two dimensions, and it is therefore worth exploring alternative approaches.
Calculation of multiple solutions for the two-dimensional Navier-Stokes equations
Authors: Sobey I J , Mullin T 
Published: November 2023

Abstract
As is the case for many nonlinear sytems of equations, the Navier-Stokes equations may not have a unique solution. There are a great number of papers dealing with bifurcation theory and its application to nonlinear systems yet the study of multiple solutions to the Navier-Stokes equations is only in its infancy [see Benjamin (1978)]. An increasingly important tool in studying such flow fields is computational fluid mechanics. In using CFD to study the innermost structure of fluid flow it has to be recognised that one is attempting to distinguish very fine structural details of flow fields. In addition, many phenomena of interest are inherently unsteady, so it is necessary to use time marching algorithms in order to compute such flows. At present it is difficult to be sure that existing CFD algorithms have the resolution to be used in this way.
Absorbing boundary conditions for acoustic and elastic waves
Authors: Renaut Rosemary A 
Published: November 2023

Abstract
In this paper I review the use of approximate one-way wave equations (OWWES) obtained from rational approximations to as absorbing boundary conditions for acoustic and elastic waves. In particular, I will present a procedure which allows for very easy implementation of high- order boundary conditions for acoustic waves. Similar techniques applied to the elastic wave equation confirm that an Ansatz of Engquist and Majda [2] about the form of a low order boundary condition is correct.
A 2D multiblock method for viscous and inviscid flow computations
Authors: Mensink C , Deconinck H 
Published: November 2023

Abstract
Based on a finite volume discretization of the compressible Euler and Navier-Stokes equations, a multiblock method has been developed in which non overlapping gridblocks are connected in a fully conservative way. The gridblocks may contain different gridline densities with either continuous or discontinuous gridline connections at the block boundaries.