bluuebunny/crossref_metadata_2025_split huggingface dataset:
Long-term potentiation in the Eocene
Authors: Lynch G 
Published: November 2023

Abstract
The first ten years of long-term potentiation (LTP) research are reviewed. Surprisingly, given the intensity of current interest, the discovery paper did not trigger a wave of follow-on experiments. Despite this, the initial work laid out what ultimately became standard questions and paradigms. The application of the then still novel hippocampal slice technique oriented LTP towards basic neuroscience, perhaps somewhat at the cost of lesser attention to its functional significance. The use of slices led to the discovery of the events that trigger the formation of LTP and provided some first clues about its extraordinary persistence.
Classical logic
Authors: John P. Cleave 
Published: November 2023

Abstract
For the established naive realist view permeating mathematics and science the classical two-valued logic is the logic, which is naturally and unquestionably supreme. Other conceptions of logic or mathematics are quaintly ideological; other people’s ideas are distinctly metaphysical. Nevertheless, the usually unspoken classical view is a definite philosophical stance whose metaphysical presuppositions are the legacy of history. Mathematical and logical truths are a reflection of an objective external structure--they are seen as analogous to a universe of clear-cut objects and relations between them essentially set apart from the knowing subject, the community, and institutions of mathematics and science. Truths, like supermarket commodities, are discovered, not invented. It is assumed that each well-formed formula of logic has one of the truth-values truth or falsehood independently of proof and the way in which it is determined (hence the Aristotelian principle of the excluded middle), i.e. it is truth-definite. This realist view was explicitly stated by the mathematician G. H. Hardy:
Logical operations
Authors: John P. Cleave 
Published: November 2023

Abstract
In the preceding chapter the notion of a logic was defined. A language Qf2, suitable for expressing conditions satisfied by logics, was defined. Various examples were given in Chapters 1 and 2. The present chapter is a taxonomic exercise—we define some important classes of logics axiomatically using logical operations as the principle of classification (for an algebraic treatment see Rasiowa (1974)). These axiomo/ are all expressible as simple definite program clauses and are therefore subject to the transfer theorems of Chapter 3, §3.4.
Three-valued logic
Authors: John P. Cleave 
Published: November 2023

Abstract
The main aim of this chapter is to study the logic of inexactness arising from Korner’s theory of inexact classes and predicates (Chapter 1, §1.3.2 and Chapter 7, §7.7). We first study logics whose truth-values are the QBA’s B2, N3, and Q4 (Chapter 7, Fig. 7.1). Though the centre of attention is N3, a completeness proof is given which is applicable in all three cases (§8.8).
Relevance
Authors: Cleave John P 
Published: November 2023

Abstract
In many of the standard formulations of the classical propositional calculus there are to found the theorems A ⊃ [B ⊃ A] and -7A ⊃ [,A ⊃ B]. The sense of the first is frequently expressed by saying that if a proposition is true then any proposition whatever implies it. The sense of the second is expressed by asserting that if a proposition is false then it implies any proposition. These theorems are often called the ‘paradoxes of (material) implication’. Certain related kinds of implication such as AA‘B and B ⟶ A v A’ are sometimes regarded as fallacious or paradoxical, even though classically correct, on the grounds that AA‘ (or A v A’) is irrelevant to the arbitrary proposition B. Much of the criticism of such implications has focused on the nature of disjunction.
The Theory of Transformation Groups
Authors: Kawakubo Katsuo 
Published: November 2023

Abstract
The aim of this book is to present an introduction to the theory of transformation groups which will be suitable for all those coming to the subject for the first time. The emphasis is on the study of topological groups and, in particular, the study of compact Lie groups acting on manifolds. Throughout, much care is taken to illustrate concepts and results with examples and applications. Numerous exercises are also included to further extend a reader's understanding and knowledge. Prerequisites are a familiarity with algebra and topology as might have been acquired from an undergraduate degree in Mathematics. The author begins by introducing the basic concepts of the subject such as fixed point sets, orbits, and induced transformation groups. Attention then turns to the study of differentiable manifolds and Lie groups with particular emphasis on fibre bundles and characteristic classes. The latter half of the book is devoted to surveying the main themes of the subject: structure and decomposition theorems, the existence and uniqueness theorems of principal orbits, transfer theorems, and the Lefschetz fixed point theorem.
Spheres of Radius 2 in Triangle Buildings. I
Authors: Tits Jacques 
Published: November 2023

Abstract
As on the picture, we shall always number 0, 1, 2 the three types of vertices of .6.. We denote by Verta (resp. Vert;.6.) the set of all vertices (resp. all vertices of type i) of a, and always suppose a to be thick, in which case all 1-simplices are contained in the same number of2-simplices (or chambers);We distinguish thoee two classes by means of an invariant taking its values in Z/2Z. Computing that invariant in the case of the four buildings obtained, after M. Ronan, by amalgamation of three Frobenius groups of order 21 (cf. [3], {5], {6]) enables us to show that those four buildings are pairwise nonisomorphic and that two of them are not classical, that is, are not isomorphic to affine buildings of groups of type A2over a locally compact local field (whereas the two others are known to be classical: cf. [1] and [21). The 44 buildings of order 8 obtained by amalgamation of three Frobenius groups of order 9 73 (cf. [6], 3.2) can be approached by similar (but considerably more involved) methods, as I hope to show in a forthcoming paper.
Approaches to problem solving
Authors: Gofman Judita 
Published: November 2023

Abstract
‘Devising a plan, conceiving the idea of an appropriate action, is the main achievement in the solution of a problem’, claims Polya in his famous book on problem solving, How to Solve It. According to Polya, a good idea is a piece of good fortune and we have to deserve it by perseverance: An oak is not felled at one stroke. If at first you don’t succeed, try, try again. It is not enough to try repeatedly. We must try different means, vary our trials.
Differential and Integral Equations
Authors: Collins Peter J 
Published: November 2023

Abstract
Differential and integral equations involve important mathematical techniques, and as such will be encountered by mathematicians, and physical and social scientists, in their undergraduate courses. This text provides a clear, comprehensive guide to first- and second-order ordinary and partial differential equations, whilst introducing important and useful basic material on integral equations. Readers will encounter detailed discussion of the wave, heat and Laplace equations, of Green's functions and their application to the Sturm-Liouville equation, and how to use series solutions, transform methods and phase-plane analysis. The calculus of variations will take them further into the world of applied analysis. Providing a wealth of techniques, but yet satisfying the needs of the pure mathematician, and with numerous carefully worked examples and exercises, the text is ideal for any undergraduate with basic calculus to gain a thorough grounding in 'analysis for applications'.
Project 1
Authors: Grandine Thomas A 
Published: November 2023

Abstract
The BUG is a fully functioning device, at least in terms of what it was designed to do. Nevertheless, your predecessor was unable to explain the behavior of this routine (hence the reason for his dismissal). Your boss would really like to know just why this routine for the BUG works the way it does on 32 bit machines. Check it out on your computer and explain the results.
Natural transformations
Authors: McLarty Colin 
Published: November 2023

Abstract
Given a parallel pair of functors F, G: A→B, a natural transformation from F to G is a family of arrows vA: FA→ GA, one for each object A of A, such that for every arrow f: A→ A' of A the following square commutes: Suppose that A is Cartesian closed and take any object A of A.
Basics
Authors: McLarty Colin 
Published: November 2023

Abstract
A topos is a Cartesian closed category with a sub-object classifier. A subobject classifier is an object Q and a global element t: 1 → Q such that for any monic s:S →A there is a unique arrow xS:A → that makes the following a pullback: Throughout the rest of this chapter we assume that we are working with a topos E.
The fundamental theorem
Authors: McLarty Colin 
Published: November 2023

Abstract
The fundamental theorem of toposes says that every slice of a topos is also a topos and, for every arrow f: A→ B of E, the functorf:*:E/B→ E/A has a right adjoint 77f and a left adjoint Xf. This makes indexed families of objects and arrows in a topos easy to handle, and it proves a great deal about the structure of a topos. The last two sections of this chapter discuss aspects of Boolean logic in toposes, and show that in toposes the axiom of choice implies the law of excluded middle. Unless otherwise noted, objects and arrows are understood to be those of a fixed topos E.
Relations in regular categories
Authors: McLarty Colin 
Published: November 2023

Abstract
Regular categories, defined below, support a nice theory of relations. We follow Freyd and Scedrov (1990) in extending any regular category C to a regular category Map(C) with quotients for all equivalence relations. Then we give a necessary and sufficient condition for Map(C) to be a topos. We begin by assuming that Chas allfinite limits, and that it is regular, once we have defined that.
Lagrangian mechanics
Authors: Lunn Mary 
Published: November 2023

Abstract
In previous chapters we have seen how the vector equations of motion are formulated both for particles and for rigid bodies. There are a limited number of examples in which a full analytic solution is possible. At some stage in the development of each solution it is necessary to think about a set of scalar coordinates which are appropriate to the geometry of the system under consideration. Sometimes this choice of coordinate system is clear cut. There is no need to use anything other than Cartesian corrdinates in the case of a projectile. On the other hand an angular coordinate is obviously a more suitable choice for a particle moving on a circular path. Consideration of the motion of a planet about a star is neatly tackled using plane polar coordinates given that such motion occurs in a plane. We should ask whether it is possible to cut out the initial stage of setting up the equations of motion using vectors and to move straight to the equations involving a chosen coordinate system. Lagrangian mechanics provides the means to do precisely that.
The Theory and Numerics of Differential-Algebraic Equations
Authors: Rheinholdt Werner C 
Published: November 2023

Abstract
These notes introduce some typical applications and basic properties of differential-algebraic systems of equations (DAEs) and then present an overview of recent, new existence theories for such systems based on differential geometric considerations and on a numerical approach derived from these theories. In the presentation the stress is on general concepts, results and applications rather than on detailed proofs.
Bivariate Splines
Authors: Dierckx Paul 
Published: November 2023

Abstract
The theory of univariate splines has been extended in different ways to functions of more than one variable. Among all these generalizations, the so-called tensor product splines (for an introduction see e.g. de Boor (1978) or Cox (1975)) are certainly the ea.5iest to handle. We will describe how the algorithms of Chapter 1 can be used in a very straightforward way for efficiently calculating with these functions. The resulting evaluation and differentiation algorithms are the basis of all tensor product spline packages. Further we will also consider a less trivial application (for use in Chapter 11), i.e. the computation of the spherical harmonic coefficients of a tensor product spline. Finally, we will briefly comment on the graphical representation of bivariate splines and illustrate how knot insertion might be useful in that respect.
Tensor product splines also have disadvantages as will be apparent in further chapters of this book. Additionally we will therefore briefly discuss and compare two other types of spline generalizations which have been used for surface fitting purposes. They share the property that they can both be defined on arbitrary triangulations. For this reason they are definitely more flexible than tensor product splines which are tied to rectangular domains. As we will see, however, they are also far more complex and therefore computationally less attractive.
Visual Complex Analysis
Authors: Needham Tristan 
Published: November 2023

Abstract
This radical first course on complex analysis brings a beautiful and powerful subject to life by consistently using geometry (not calculation) as the means of explanation. Aimed at undergraduate students in mathematics, physics, and engineering, the book's intuitive explanations, lack of advanced prerequisites, and consciously user-friendly prose style will help students to master the subject more readily than was previously possible. The key to this is the book's use of new geometric arguments in place of the standard calculational ones. These geometric arguments are communicated with the aid of hundreds of diagrams of a standard seldom encountered in mathematical works. A new approach to a classical topic, this work will be of interest to students in mathematics, physics, and engineering, as well as to professionals in these fields.
The structure of totally categorical structures
Authors: Hodges Wilfrid 
Published: November 2023

Abstract
Among the many programmes that go to make up research in model theory today, one of the most elegant is the programme to catalogue all the countable models of totally categorical theories. Morley (1965, 1967) and Baldwin and Lachlan (1971) laid the foundations. Between about 1976 and 1984, Zil’ber made enormous progress, but a large part of his work was unavailable in English until the recent translation of his doctoral thesis (Zil’ber, 1993). In the meantime, hints were published (Zil’ber, 1979, 1984b, and elsewhere), enough for workers in the West to carry the work forward. Hrushovski, Ahlbrandt and Ziegler all published papers that cast fresh light. More is on its way into print, and indeed I know that there are people who know many things not yet known to me. So this account makes no claim to completeness. I aim only to tell a good story.
Permutations and the axiom of choice
Authors: Truss J K 
Published: November 2023

Abstract
The purpose of this paper is to explore the connections between permutation groups, definability, and the axiom of choice (AC). The fact that these three topics are closely related is perhaps rather well known, but it is possible to bring out into the open some of the precise connections, which may be spelt out in quite a systematic way. To start from a particular point of view, in the original models for the negation of the axiom of choice there was an explicit use of permutation groups. I refer to the Fraenkel-Mostowski method. Moreover, this was developed to a high degree of elegance, particularly in the work of Mostowski where he was able, by careful choice of the group and the ‘support structure’, to illustrate non-implications between various weak versions of AC. For instance, he found a model in which every set can be linearly ordered (the ordering principle) but AC fails (Mostowski, 1939), and (1945) he investigated the connections between versions of AC for families of finite sets. More sophisticated constructions were used by other authors, for instance Lauchli (1964), who gave a model in which any family of non-empty finite sets has a choice function, but the ordering principle fails.
Theory of surface waves
Authors: Rahman Matiur 
Published: November 2023

Abstract
As we know in practice, real water waves propagate in viscous oceans over an irregular rough bottom of varying permeability. However, a striking feature of the water waves in oceans is that in most cases the main body of the fluid motion is nearly irrotational such that the viscosity which causes the rotation may be negligible. Another remarkable fact is that water can be reasonably regarded as incompressible and, consequently, a velocity potential and a stream function should exist for wave propagation in oceans. We have already remarked in Chapter 2 about these two mathematical entities and their importance in the solution process of water wave mechanics.
Inverse scattering transforms and the theory of solitons
Authors: Rahman Matiur 
Published: November 2023

Abstract
The theory of solitons and the method of inverse scattering transforms have received extreme interest from applied mathematicians and physicists in recent years, due to the most recent and fascinating achievements in the domain of applied mathematics. The KdV equation which leads to the theory of solitons has been the object of intensive scientific research in different branches of physics. We have already seen in Chapter 9, that under certain periodic boundary conditions, the KdV equation admits solitary wave solutions. These solitary waves which travel at different speeds may pass through one another without any change in the original structures; the only effect of the interaction is a change of phase.
Wavelets
Authors: Holschneider M 
Published: November 2023

Abstract
Wavelets analysis--a new and rapidly growing field of research--has been applied to a wide range of endeavors, from signal data analysis (geoprospection, speech recognition, and singularity detection) to data compression (image and voice-signals) to pure mathematics. Written in an accessible, user-friendly style, Wavelets: An Analysis Tool offers a self-contained, example-packed introduction to the subject. Taking into account the continuous transform as well as its discretized version (the ortho-normal basis) the book begins by introducing the continuous wavelets transform in one dimension. It goes on to provide detailed discussions of wavelet analysis of regular functions, tempered distributions, square integrable functions, and the continuous wavelet transform. Throughout, the language of group theory is used to unify various approaches. Profusely illustrated and containing information not available elsewhere, this book is ideal for advanced students and researchers in mathematics, physics, and signal processing engineering.
Analytic Theory of Polynomials
Authors: Rahman Q I , Schmeisser G 
Published: November 2023

Abstract
This text presents easy to understand proofs of some of the most difficult results about polynomials. It encompasses a self-contained account of the properties of polynomials as anlytic functions of a special kind. The zeros of compositions of polynomials are also investigated along with their growth and some of these considerations lead to the study of analogous questions for trigonometric polynomials and certain transcendental entire functions. The strength of methods are fully explained and demonstrated by means of applications.
Derivative Sampling-A Paradigm Example of Multichannel Methods
Authors: Higgins J R 
Published: November 2023

Abstract
This chapter is a short account of derivative sampling, the name usually given to the process of reconstructing a suitable function from a knowledge of its values and values of some of its derivatives at a discrete subset of its domain. Here, particularly in §3.4, we shall also take it to mean the dual problem of constructing a function which is to have given values and given derivative values on a given set (more remarks about this kind of duality can be found in Higgins 1996, p. 2, et seq.).
Approximation by Translates of a Radial Function
Authors: Dyn M 
Published: November 2023

Abstract
The study of approximation schemes based on translates of a radial function to a set of points (centres) in ℝ d is a central subject in multivariate approximation theory. Here we study the L ∞-approximation orders of such schemes, first for centres constituting a regular grid, and then for quasi-uniformly scattered centres.
Recovering Geometries from Diagrams
Authors: Pasini Antonio 
Published: November 2023

Abstract
We now start the job we promised to do at the end of Chapter 3: given a diagram, we try to describe the geometries belonging to that diagram, either classifying them, or at least characterizing them by other axioms of ‘global’ nature which are presumably more familiar to the reader. The tools we can use at this stage are very few and seemingly weak: we only have some results on disconnected diagrams (in particular, the direct sum theorem), the concept of geometric poset for string diagrams, the construction of Grassmann geometries and a number of results on intersection properties. However, we can already obtain many characterizations, in spite of the poverty of our equipment.
The General Theory of Integration
Authors: Henstock Ralph 
Published: November 2023

Abstract
Written by one of the subject's foremost experts, this is the first book on division space integration theory. It is intended to present a unified account of many classes of integrals including the Lebesgue-Bochner, Denjoy-Perron gauge, Denjoy-Hincin, Cesaro-Perron, and Marcinkiewicz-Zygmund integrals. Professor Henstock develops here the general axiomatic theory of Riemann-type integration from first principles in such a way that familiar classes of integrals (such as Lebesgue and Wiener integrals) are subsumed into the general theory in a systematic fashion. In particular, the theory seeks to place Feynman integration on a secure analytical footing. By adopting an axiomatic approach, proofs are, in general, simpler and more transparent than have previously appeared. The author also shows how one proof can prove corresponding results for a wide variety of integrals. As a result, this book will be the central reference work in this subject for many years to come.
Generalized hypergeometric functions
Authors: Dwork Bernard 
Published: November 2023

Abstract
Hypergeometric functions have occupied a significant position in mathematics for over two centuries. This monograph, by one of the foremost experts, is concerned with the Boyarsky principle which expresses the analytical properties of a certain proto-gamma function. Professor Dwork develops here a theory which is broad enough to encompass several of the most important hypergeometric functions in the literature and their cohomology. A central theme is the development of the Laplace transform in this context and its application to spaces of functions associated with hypergeometric functions. Consequently, this book represents a significant further development of the theory and demonstrates how the Boyarsky principle may be given a cohomological interpretation. The author includes an exposition of the relationship between this theory and Gauss sums and generalized Jacobi sums, and explores the theory of duality which throws new light on the theory of exponential sums and confluent hypergeometric functions.