bluuebunny/crossref_metadata_2025_split huggingface dataset:
The internals of SHEEP
Authors: MacCallum M A H , Skea J E F , McLenaghan R G , McCrea J D 
Published: November 2023

Abstract
To make it possible to refer to RIE, for instance, whether a coordinate or a tetrad basis is in use, SHEEP allows the name of the tensor which the user types to be associated with more than one definition. Each definition is given as the specification of a “building function” associated with a different internal name for the tensor. Which building function is active usually depends on the context in which the calculations are being done. This concept is called tensor aliasing, and is mainly used for the more common tensors. For example, the building functions for the Riemann tensor in coordinates (RIEC) and in frames (RIEF) are different, yet (WMAKE RIE) will work correctly in both cases. It is useful to know when tensor aliasing will take place and how to obtain the internal name of a tensor from its alias, for those occasions where aliasing does not occur (for example in the writing of building functions and for inclusion of tensor components in FOIN formulae).
The Poincar é gauge theory
Authors: MacCallum M A H , Skea J E F , McLenaghan R G , McCrea J D 
Published: November 2023

Abstract
The Poincar é gauge theory (PGT) is a theory of gravitation in which spacetime is represented as a Riemann-Cartan manifold, i.e. a 4 dimensional differentiable manifold M with normal hyperbolic metric of sig nature (-, +, +, +) and a metric-compatible connection with nonzero torsion. For a detailed account of the theory the reader is referred to Hehl (1980) and Hehl et al. (1980). For the formulation of the PGT in terms of exterior differential forms see Trautman (1973, 1984), Schweizer et al. (1980), Kopczynski (1982), Wallner (1982, 1985), Goenner et al. (1984), Hehl et al. (1986), McCrea (1987) and Mielke (1987). Here we shall sketch briefly the main lines of the theory.
Fréchet modules over Stein algebras
Authors: Eschmeier Jörg , Putinar Mihai 
Published: November 2023

Abstract
In Chapter 2 we constructed, for each finite commuting tuple a ε L(E)n of regular operators on a Fréchet space E, an extension of the global ϑ (ℂn)- functional calculus of a to an algebra homomorphismϕ:σ(σ(a)→L(E), f↦f(a)), where σ (a) is the Taylor spectrum of a.
Finiteness theorems in analytic geometry
Authors: Eschmeier Jörg , Putinar Mihai 
Published: November 2023

Abstract
It is well known that a compact analytic manifold carries, besides the usual topological invariants (its Euler characteristic, the Betti numbers), some numerical invariants like the degree of the canonical divisor, the Hodge numbers, the arithmetic genus, and so on. A common property of all these invariants is that they coincide with the dimension of the cohomology spaces of certain analytic vector bundles or analytic sheaves. In this way, these invariants become accessible to algebraic and homological methods.
Multidimensional index theory
Authors: Eschmeier Jörg , Putinar Mihai 
Published: November 2023

Abstract
By far the most studied spectral invariant of a linear operator is the Fredholm index. This integer, associated with an operator with finite dimensional kernel and cokernel, has remarkable stability and functorial properties. The computation of the Fredholm index of concrete integrodifferential operators turns out to be the key to understanding the nature of the majority of analytic invariants encountered in modern global analysis. The celebrated Atiyah-Singer index theorem and its recent ramifications are the fundamental results in this direction.
A Formula for the Fourier Coefficients of Maass Cusp Forms
Authors: lwaniec Henryk 
Published: November 2023

Abstract
In his seminal paper [5] H. Maass extended the ghetto of classical cusp forms by automorphic forms which a.re not holomorphic but, instead, are eigenfunctions of the Laplace operator Δ. For a group with parabolic elements those Maass forms which decay exponentially to zero at every cusp are called cusp forms. The Maass cusp forms remain wrapped in a shroud of mystery; it is not even known today whether they exist for a generic group. However, for any congruence group the spectral resolution of abounds with Maass cusp forms. This is shown by a counting argument using Selberg’s trace formula, thus it is not constructive. Surprisingly enough, not a single Maass cusp form has ever been constructed for the modular group.
Finite heights and rational points on surfaces
Authors: Tschinkel Yuri 
Published: November 2023

Abstract
In this note we study the distribution of rational points on algebraic surfaces. Geometry and combinatorics are used to establish upper bounds for the number of rational points of bounded height. Acknowledgments. I would like to thank Yu. I. Manin for many years of generous support and encouragement and the referee for very careful reading and many helpful remarks.
Paulo Ribenboim: three aspects of his career
Authors: Viswanathan T M 
Published: November 2023

Abstract
This is a unique occasion bringing together a gathering of educators, scientists, professionals and leaders of the larger community. Before this august gathering, it is my privilege and honor to say a few words about the remarkable career of Paulo Ribenboim. His is a career dedicated to mathematics in its diverse manifestations. If I am asked to summarize his career, I would like to use a trio of phrases: Paulo’s global view of mathematics, his goal-oriented methodology, and his international commitment which took him to other centers of learning and research. I would like to say a few words about each one of these three aspects.
On polynomial size Frege proofs of certain combinatorial principles
Authors: Clote* Peter 
Published: November 2023

Abstract
Using a theorem of Barrington, we give a new recursion theoretic characterization of the class of ALOGT IM E computable functions and then introduce a corresponding free-variable equational calculus ALV ′. The system ALV ′, more elegant than an earlier system ALV, allows straightforward definitions of parity and other counting predicates, as well as the proof of correctness of these predicates. One thus easily obtains polynomial size Frege proofs for certain combinatorial principles such as the pigeonhole principle (S.R. Buss) and the equipartition principle (A. Goerdt).
Marked Poisson processes
Authors: Kingman J F C 
Published: November 2023

Abstract
It was noted in Section 1.2 that the Poisson distribution has a characteristic property in relation to the binomial distribution. If the random variable N has distribution p(µ) and if a second random variable M has a conditional distribution, given N, of the form B(N, p), then M and N - M are independent Poisson variables, with respective means pµ and (1- p )µ.
Phase Regions, Control Volumes, and Inflows
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 Ω 2 (t) for the corresponding phase regions, the subregions of the body occupied by phase 1 and phase 2.
Review of Single-Phase Thermodynamics
Authors: Gurtin Morton E 
Published: November 2023

Abstract
We assume that the body occupies a fixed region Ω in ℝ, and that the material is immobile, incapable of deformation, with heat conduction the sole transport mechanism. We base the theory on dynamical versions of the first two laws applied to arbitrary control volumes (subregions R of Ω). The first law, balance of energy, asserts that the internal energy of R change at a rate balanced by the heat flow into R and the power expended on R. The second law, growth of entropy, requires that the entropy of R change at a rate not less than the entropy flow into R. (14.1) For this single-phase theory there is no expense of power, since the bulk material is immobile, and since there is no phase interface.
Super-viscosity and spectral approximations of nonlinear conservation laws
Authors: Tadmor Eitan 
Published: November 2023

Abstract
Let PN stand for one of the standard spectral projections, such as Fourier, Chebyshev or Legendre. It is well known that such spectral projections, PNu , provide highly accurate approximations for sufficiently smooth u . This superior accuracy is destroyed if u contains discontinuities. Indeed, PNu produces 0(1) Gibbs oscillations in the local neighbourhoods of the discontinuities, and moreover, their global accuracy is deteriorated to first-order.
Computing steady incompressible flows past blunt bodies—A historical overview
Authors: Fornberg Bengt 
Published: November 2023

Abstract
There is a special fascination associated with problems which
Although there may be many more surprises left, and several technical details in the present models are extremely complex, the problem of determining the structure of steady incompressible flows past ‘simple’ blunt bodies (like a cylinder, a sphere, a flat plate perpendicular to free stream, arrays of such bodies etc.) can be said to fall in this category.
Simplified multi-dimensional flux limiter methods
Authors: LeVeque Randall J 
Published: November 2023

Abstract
The aim of this paper is to present a simplified framework for developing high resolution finite volume methods for multi-dimensional systems of conservation laws, such as the Euler equations of compressible flow. For simplicity, we consider the system
Ut + f(u)x + g(u)y = 0 (1.1)
On the eigensystems associated with numerical boundary schemes for hyperbolic equations
Authors: Zingg David W , Lomax Harvard 
Published: November 2023

Abstract
The linear convection equation is often used as a model equation in the study of numerical methods for hyperbolic partial differential equations. With periodic boundary conditions, the accuracy and stability of semidiscrete (spatial differences only) and fully-discrete approximations can be studied using Fourier analysis. The resulting matrix operator is circulant, the eigenvectors are the Fourier modes, and Fourier analysis is a simple means of obtaining the eigenvalues. For computations on a finite domain, entry changes can be required among the first few rows and the last few rows of the spatial operator matrix, depending on the interior difference operator. The difference approximations which provide the entries in these rows are called numerical boundary schemes (NBS’s).
Error estimates for adaptive cell vertex finite volume algorithms
Authors: Mackenzie J A , Mayers D F , Mayfield A J 
Published: November 2023

Abstract
Fundamental to the success of adaptive mesh generation – and adaptive methods in general – is the use of reliable and efficient error estimators. A reliable error estimator is one which can bound above and below the norm of the error. An efficient error estimator is one which does not dramatically over or underestimate the error.
SFDN-α-GMRES and SQN-α-GMRES methods for fast high resolution N-S simulations
Authors: Qin N , Xu X , Richards B E 
Published: November 2023

Abstract
The existence of strong shock waves, thin shear layers and their interaction in hypersonic flows requires the use of a high resolution scheme for an accurate numerical simulation. Through an extensive study (6] of different flux formulae on their capabilities of capturing both shock waves and shear layers, the Osher flux difference splitting scheme has been found to be satisfactory. However, high resolution schemes usually involve more complicated formulation and thus longer computation time per iteration as compared to the simpler central differencing scheme. Therefore, the acceleration of the convergence for high resolution schemes becomes an increasingly important issue.
First Order Logic
Authors: Davis Martin 
Published: November 2023

Abstract
The task of providing a mathematical basis for logical reasoning was already clearly posed by Leibniz in the 17th century. However, it was not until the work of Boole two hundred years later that any substantial progress was made. Boole’s work set the stage for the rapid development of modern logic, but in itself the logic of Boole suffered from a crippling defect from which presentations of formal logic had been suffering from the time of Aristotle.
General Patterns in Nonmonotonic Reasoning
Authors: Makinson David 
Published: November 2023

Abstract
In little more than a decade, a number of different approaches to nonmonotonic reasoning have been devised. Each of them proposes a framework for ‘jumping to conclusions’, that is, for tentatively inferring from given information rather more than is deductively implied. They are nonmonotonic in the sense that increasing the amount of information available as premises may sometimes lead to loss of some of the conclusions that can be drawn.
Brancing time
Authors: Gabbay Dov M , Reynolds Mark A , Finger Marcelo 
Published: November 2023

Abstract
In this chapter we shall consider logics and languages that are appropriate for describing events in branching time. Much of the motivation for considering time to be branching comes from the idea of using different branches to represent different possible histories of some part of the world. Thus, we are really looking at logics which combine temporal aspects with features of a modal logic of possibility and necessity.
Metatem In Intensive Care
Authors: Gabbay Dov M , Reynolds Mark A , Finger Marcelo 
Published: November 2023

Abstract
In these days with complex systems designed to cope with anything from exchanging stocks and shares to dispatching ambulances, it becomes increasingly more important to make sure that the design is adequate. Of course, it is not possible to be perfectly sure about the adequacy of a design. However, there are ways of attempting to be more certain and two of the most satisfactory are reasoned justification and testing. This chapter is about both.
Incompleteness
Authors: Chagrov Alexander , Zakharyaschev Michael 
Published: November 2023

Abstract
In the preceding chapter we saw that many standard superintuitionistic and normal modal logics are Kripke complete, even finitely approximable and so decidable. Many of them turned out to be canonical and hence strongly Kripke complete, with their canonical frames satisfying good first order properties. Now we are facing the natural question: isn’t it possible to extend these completeness results to all logics in Extlnt and NExtK? To present examples of incomplete (in one sense or another) logics in these classes and elucidate to some extent the origin of the incompleteness is the main aim of this chapter.
Relational Semantics
Authors: Chagrov Alexander , Zakharyaschev Michael 
Published: November 2023

Abstract
Having solved the completeness problem, the algebraic semantics, introduced in the previous chapter, deprives us, however, of that transparent interpretation of logical connectives which made it possible to construct models for formulas by analyzing step by step their subformulas and adding new points, if necessary. In other words, we have lost that thread which connected the structure of formulas with the “geometry” of their models. Fortunately, this is not that case when “gaining in force we lose in distance”. In this chapter we define a more general concept of frame, combining in itself the merits of both algebras and Kripke frames.
A Plain TEX Primer
Authors: Clark Malcolm 
Published: November 2023

Abstract
This primer is an introduction to TeX and provides the reader with sufficient information to get started with the majority of tasks which he or she may wish to tackle. It explains why TeX approaches its subject in the way it does, and provides the "context' into which it fits. Plain TeX is the common starting point for TeX users and can be extended or modified to suit individual needs. With the aid of this book, scientists and researchers preparing their own books and papers, or technical typists, used to the conventions and jargon of their field, will find little difficulty in adopting TeX's approach.
Percolation Thresholds
Authors: Hughes Barry D 
Published: November 2023

Abstract
For several two-dimensional lattices, the percolation thresholds are known exactly. Exact values of bond thresholds are discussed in §3.1, and site thresholds in §3.2. No exact rigorous values are currently available for percolation thresholds of three-dimensional lattices. We discuss bounds, conjectures and empirical formulae in §3.3, and the numerical estimation of thresholds in §3.4. For most lattices of real interest, very accurate estimates of bond and site thresholds are available. For the most part, the discussion is restricted to Bernoulli percolation models, though a few remarks on directed problems are included in §3.3 and §3.4.
Stationary perturbation theory
Authors: Hannabuss Keith 
Published: November 2023

Abstract
For most physically interesting systems it is not possible to find simple closed formulae for the energy levels and wave functions. Generally the best that one can do is to find numerical approximations and iterative schemes. Since Schrodinger’s equation is a differential equation there are many standard numerical methods that can supply approximate solutions, but there are also various special techniques tailored to this particular situation, which we shall describe over the next chapters.
A Comparison of Notions of Negation as Failure
Authors: Schlipf John S 
Published: November 2023

Abstract
When logic programming was generalized to allow negative subgoals, difficulties immediately arose concerning the meaning of negation as failure in the context of these subgoals. Various semantics have been proposed, each attempting to capture natural intuitions about negation as failure and to preserve other intuitive properties. We discuss several such semantics for normal logic programs here: the minimal model semantics, the perfect model semantics for stratified programs, the two- and three-valued program completion semantics, and the stable and well-founded semantics. We contrast them in various ways: we present some examples and intuitions that might be used to justify them, discuss which violate or preserve certain properties of more classical logics and which allow modular programming, and present some results about expressive powers and computational complexity.
Commonsense Entailment: A Conditional Logic for Some Generics
Authors: * Nicholas Asher 
Published: November 2023

Abstract
Lions eat zebras, Quakers are pacifists, or birds fly are examples of generic statements. I believe that such statements should be represented logically as quantified conditionals and thus that the study of generic statements can reveal something of interest about the logical properties of conditionals that we find expressed in natural languages. One indication that this view may be right is that generic statements behave like quantified conditionals. They license certain patterns of inference that look much like those supported by some conditionals. Like almost all forms of conditionals, generics support an inference of weakening of the consequent: lions eat zebras implies lions eat zebras or kangaroos.
Conditional Action
Authors: Segerberg Krister 
Published: November 2023

Abstract
Normally one would expect the As to be pairwise inconsistent and jointly exhaustive, but there is no need to require that this be the case. In a situation where several As obtain, the claim of (§) amounts to the claim that all the corresponding Bs hold. If none of the As obtains, then the claim is vacuous and hence considered to be trivially true.
In a similar way there is a concept of action by cases in dynamic logic. The corresponding concept is a 2n-ary operator (operating on n programs and n propositions to form a new program):
Conditional Implications and Non-monotonic Consequence
Authors: Gabbay Dov M 
Published: November 2023

Abstract
The study of non-monotonic reasoning through properties of its consequence relation was first proposed by Gabbay [5]. Let L be a language and let |˜ a relation between sets of well-formed formulas (wffs) Δ and single wffs A, of the form Δ|˜A. Gabbay proposed three minimal conditions on a relation ˜ to be considered as a non-monotonic logic. These are as follows.
Millet and Rice
Authors: Kangshen Shen , Crossley John N , Lun Anthony W -C 
Published: November 2023

Abstract
The reader may find it convenient to refer to Section 0.2 on Metrological Systems, in the Introduction, p. 6, in particular the units of length, p. 6, capacity, p. 9, and weight, p. 9. The subsections there provide the conversions between the various units used throughout Chapter 2.
Short Width
Authors: Kangshen Shen , Crossley John N , Lun Anthony W -C 
Published: November 2023

Abstract
This Chapter exhibits calculations working backwards to find a side or diameter, etc., from a known area or volume. For example, to find a side of a rectangle whose area and other side are known, to find the side of a square whose area is known, to find the side of a cube of known volume, to find the circumference of a circle whose area is known or to find the diameter of a sphere whose volume is known. These five kinds of problems were collected into one Chapter. The original inspiration for the development of the numerical solution of equations of high degree is closely related to these backwards computations.
From CPA to nonlinearity and mesostructures in condensed matter
Authors: Krumhansl James A 
Published: November 2023

Abstract
During the years 1966-72, Roger Elliott, Paul Leath, and I collaborated on the theory of randomly disordered systems (cf. Elliott et al. 1974). This collaboration laid the groundwork for much of my own research over the past 17 years, the subject of which is summarized in the chapter title. The workhorse of many theoretical studies in condensed matter, of both electronic properties and atom dynamics (phonons), for the past three decades has been the method of thermodynamic Green’s functions. Elliott and several of his students developed much of its earliest application to the lattice dynamics of crystals with defects in a series of papers in the early-1960s. The especially persuasive features of the Green’s function method were: (1) the procedure was systematic; (2) experimental quantities could be extracted directly from the Green’s function. Much experimental work on localized and resonant defect modes was stimulated thereby.
Study of tin in amorphous germanium
Authors: Taguena-Martinez J , Barrio, R A , Chambouleyron I 
Published: November 2023

Abstract
For multiple-band solar cells and other optoelectronic devices, the absorption edge of the semiconducting layers must be adjusted to some optimum value. This can be done by alloying both elemental semiconductors (amorphous silicon and amorphous germanium) with other elements. The energy gap can be widened by adding carbon or nitrogen (Tawada et al. 1982) and narrowed by introducing tin (Mahan et al. 1984). However, preserving good optoelectronic properties in these alloys is not an easy problem. In particular, tin in amorphous germanium induces new electronic states in the pseudogap (Chambouleyron et al. 1988; Chambouleyron and Marques 1989).
Frothy disputes-the evolution of the structure of two-dimensional froth
Authors: Weaire D 
Published: November 2023

Abstract
A former Trinity College Dublin scientist described the state of physics in his period (the late seventeenth century) as ‘an heap of froathy disputes’. The phrase is very apt for our subject. Ordinary froth or foam commends itself as an apparently very simple disordered system, yet its properties have proved difficult to pin down conclusively. In particular, it coarsens with time, and the asymptotic form of this evolution has been a subject of debate, if not dispute, for the last 10 years. At the present point, we are approaching a somewhat anticlimactic conclusion, which returns to the original point of view of Cyril Stanley Smith, who first analysed the problem around 1950.