bluuebunny/crossref_metadata_2025_split huggingface dataset:
Abstract logics
Authors: John P. Cleave 
Published: November 2023

Abstract
There are many formal logics- classical logic (already encountered in Chapter 2), intuitionistic logic, various modal and temporal logics, and numerous logics arising in various ways from applications such as the logic of automata and the logic of quantum mechanics. Moreover, there are many structures-such as context-free languages, combinatorial systems, etc.-which are sufficiently logic-like to deserve the name logic. Many logics are primarily the embodiment of some notion of truth. They are thereby mainly concerned with the generating theories-a corpus of theorems or ‘universal truths’--thus tending to obscure the view of formal logic as the science of valid inference. In Chapter 1, §1.3.2, there arose the problem of treating neutrality as if it were a truth-value. What has to be done to it to make a logic out of truth, falsehood and neutrality’? Truth-values alone do not constitute a logic. Our strategy must clearly be guided by the various extant logics. In the brief treatment of classical logic in Chapter 2 the notion of logical consequence played some part, though it was subordinate to the idea of theoremhood. But in the discussion of scientific theories in Chapter 1 special significance was given to the deductive postulate. On grounds of generality, it can be claimed that logical consequence is more fundamental than theoremhood, as all that needs to be said about theoremhood can also be stated in terms of logical consequence.
Modal logics
Authors: Cleave John P 
Published: November 2023

Abstract
Questions about modal logic were posed by Aristotle and were thoroughly investigated by the Scholastics, but the subject seems to have been completely neglected until it acquired a new lease of life in mathematical logic, particularly through the work of McColl and Lewis. A recent nodal point in the development of the modal industry was the introduction of ‘possible world’ semantics (Kripke) which has lead to an unprecedented boom.
Finite Geometries via Algebraic Affine Buildings
Authors: Kantor’ William M 
Published: November 2023

Abstract
Thepurpose of this note is (1) to give a vague description of algebraic affine buildings, (2) to give a brief description of arithmetic groups, and then (3) to combine these subjects in order to discuss finite quotients of algebraic affine buildings modulo suitable arithmetic groups. is intended to be thought of in terms of matrix groups, in which entries are taken from the indicated rings.) Using G(Q) and B,an affine building .6. is obtained as follows (cf. [10]):The maximal simplexes (chambers) are j11St the conjugates of B.There are ntypes of vertices, which are the conjugates of the subgroups of matrices blocked as follows:* Supported in part by NSF grant DMS 87-01794 and NSA Grant MDA 904-88-H-2040. special amounts to the fact that the associated diagram is the extended Dynkin diagram corresponding to the Dynkin diagram of the finite group G(k); the group G(K)always contains such subgroups [10]. In the example given above, all the vertex stabilizers are special.
Local recognition of graphs, buildings, and related geometries
Authors: Cohen Arjeh M 
Published: November 2023

Abstract
Brief overview of results and problems concerning the local recognition f graphs is given, and special attention is drawn toward graphs related to uildings. here Xstands for the class of all grids.Although it was probably apparent to quite a few finite group theorists 1at some of the local characterization problems in the classification of finite local recognition problems for graphs. These are the two main reasons by I want to survey what is known on the local recognition problem.Much of the material in this paper can be found scattered in [BCN 989]. For notions of shadow space, point-line geometry and the like, the ader is referred to [Cob 1986].
Special Graphs
Authors: Read Ronald C , Wilson Robin J 
Published: November 2023

Abstract
In this chapter we depict a number of sped.al graphs:
Platonic graphs: these are the graphs formed by the vertices and edges of the Platonic solids—the polyhedra in which all the faces are identical regular polygons and where the arrangement of polygons at each vertex is the same. There are five Platonic graphs, corresponding to the tetrahedron, octahedron, cube, icosahedron and dodecahedron.
Archimedean graphs: these are the graphs formed by the vertices and edges of the Archimedean solids—the polyhedra in which each face is a regular polygon (but not all faces are of the same type) and where the arrangement of polygons at each vertex is the same; these arrangements of polygons are indicated under the diagrams. There are thirteen such graphs, and two infinite families—the prisms and the antiprisms.
Polynomials
Authors: Read Ronald C , Wilson Robin J 
Published: November 2023

Abstract
Spectral polynomials: we list the spectral (characteristic) polynomials of graphs, trees, cubic graphs and quartic graphs. For graphs and trees, each polynomial is presented in power form, together with its frequency and its spectrum (usually with zeroand integer eigenvalues listed first, and the remainder listed in decreasing order); for cubic and quartic graphs, only the polynomial is given.
The spectral polynomials of graphs with up to 7 vertices are listed on pages 402–419. The spectral polynomials of trees with up to 12 vertices are listed on pages 420–432. When the number of vertices is even, each spectrum number denotes two roots, one positive and one negative; when the number of vertices is odd, then there is one extra zero root. The spectral polynomials of cubic graphs with up to 14 vertices are listed on pages 433–441, and those for quartic graphs with up to 11 vertices are listed on pages 442–446.
Some Preliminaries
Authors: Collins Peter J 
Published: November 2023

Abstract
A number of elementary results in real analysis will be used continually in the sequel. For ease of reference, we gather together here some that are more important or commonly found. Though we shall be careful, and encourage the reader to be careful, to give appropriate, sufficient conditions by means of justification, we shall not always be concerned with stating the sharpest possible results. In particular, we shall generally assume that a function is continuous when sometimes integrability over a bounded interval would suffice. Further, we shall not be concerned that differentiability is on occasion enough but normally, in these circumstances, assume that a function is continuously differentiable in the sense of the following definition. We now list some propositions, giving each a label in square brackets which we shall use subsequently for the purpose of reference. The notation (a, b) and [a, b] will be used, respectively, for open and closed intervals in ℝ.
Phase-Plane Analysis
Authors: Collins Peter J 
Published: November 2023

Abstract
The systems with which this chapter is concerned are those of the form satisfied by the functions x = x(t), y = y(t), where X and Y are continuous real-valued functions and dot denotes differentiation with respect to the real variable t. They are often referred to as ‘plane autonomous systems of ordinary differential equations’. Here, ‘plane’ indicates that just two functions x, y, dependent on the variable t, are involved and ‘autonomous’ that neither of the functions X, Y contains this variable explicitly. It is not in general possible to find an analytic solution to an arbitrary differential equation and, even when it is, the solution is often expressed in a form (such as a series or integral, or implicitly) which does not allow easy discussion of its more important properties. This chapter provides an introduction to a qualitative study in which one can locate properties of a differential equation without having to find a solution. Every student of differential equations should be aware of phase-plane methods. When the real plane ℝ2, with axes x and y, is used to plot solutions x = x(t), y = y(t) of (A), it will be referred to as the phase-plane. The curve traced out by (x(t), y(t)) as t varies (usually over some finite or infinite interval) is called a phase-path or trajectory. A diagram depicting the phase-paths is called a phase-diagram.
Project 9
Authors: Grandine Thomas A 
Published: November 2023

Abstract
A certain division of the company, namely the ACME Team Research Organization Committee for Investigating Oceans and Underwater Stuff, has sent one of its research ships, S.S. Gaussian Rule, on a voyage to gather data off the coast of Venezuela. Under orders from ATROCIOUS, Gaussian Rule has spent the last few days in the triangular region of ocean whose vertices are at 12° North latitude 65° West longitude, 12° North 64° West, and 13° N. 65° W., just north of Blanquilla Island. The ship is equipped with (among other things) two different recording devices for measuring oceanographic data. The French Remote Offshore Gauge records subtle differences in pressure at sea level, while the Temperate Offshore Analytic Device records weak shifts in the earth’s electromagnetic field.
Project 17
Authors: Grandine Thomas A 
Published: November 2023

Abstract
The Dependable Industrial Reprehensible Toxic Yuck company, a national chemical company, is having trouble at one of its many plants. It seems that many of the employees are developing a strange disease. DIRTY claims that the disease is caused by a virus which just happens to be going around, but the Environmental Protection Agency isn’t quite so sure, and it has hired the Corporate Liaison for Engineering Air Niceness, a division of ACME, to investigate the matter. The plant in question produces a chemical called convexitygen, a chemical with many industrial uses (it is used in the manufacture of cramerrulic, for example). The reaction which produces convexitygen takes place in a fairly simple reactor. Two compounds, arithmetic acid and boundary valuum are placed in the reactor. They react to form convexitygen. However, the convexitygen reacts with the boundary valuum to produce a waste chemical, determinantanol, which is quite toxic.
Lattices
Authors: Potter Michael D 
Published: November 2023

Abstract
What we now call the theory of lattices originated in the late nineteenth century from two sources: Dedekind came upon the notion of a Dualgruppe — what is now called a ‘modular lattice’ — in his investigation of the theory of divisibility; the other motivating example is the algebra of classes — theory of logical equivalence of propositions — which was studied by Boole, Schröder, and others. The work we shall be describing in this chapter is almost all the product of research in the 1930s by Birkhoff and Øre. Since then lattices have found natural application in functional analysis, projective geometry, set theory, logic, quantum mechanics, computer science, group theory, and number theory: ‘Mathematical objects have lattices as dogs, fleas’ (Isbell 1984, p. 94).
From the internal language to the topos
Authors: McLarty Colin 
Published: November 2023

Abstract
The reader is warned that this sequent does not say that for every generalized element yϵ B there is some xϵT A with y = fx. It says internally that every y in B is the image of some x in A, but externally this only means thatf:is epic and not necessarily split epic (see Exercise 18.5).
Factorization of polynomials
Authors: Chatters A W , Hajarnavis C R 
Published: November 2023

Abstract
In order to motivate the material of this chapter, consider the fo11owing simple-looking problem: Set f(X) = 8X9 + 56X4 + 49X + 28; can f(X) be written as the product of two polynomials of lower degree with rational number coefficients? The most direct approach would seem to be to suppose that f(X) does factorize, equate it to the product of two factors with unknown coefficients, multiply the factors together and equate coefficients to get a set of equations for the unknown coefficients, solve these equations or show that they have no solution; but f(X) might be the product of polynomials of degrees 1 and 8, or 2 and 7, or 3 and 6, or 4 and 5; it is starting to look very complicated and messy.
Finite cyclic groups and finite fields
Authors: Chatters A W , Hajarnavis C R 
Published: November 2023

Abstract
The main result of this chapter is that if F is a field and G is a finite subgroup of the multiplicative group of non-zero elements of F then G is cyclic. The proof is an elegant combination of elementary group theory and the theory of polynomial equations over a field. An immediate consequence of the main theorem is that if p is a prime number then the group of non-zero elements of ‘11../p”ll. under multiplication is cyclic. We shall also prove some general results about finite cyclic groups. For instance, if G is a cyclic group with n elements then G has precisely one subgroup of order d for each positive divisor d of n.
BTOP/S AS A 2-Category
Authors: Johnstone Peter T 
Published: November 2023

Abstract
In this chapter we shall study the remarkable 2-categorical structure of the 2-category BTop/S of bounded S-toposes, where S is a fixed topos. We shall restrict ourselves entirely to bounded geometric morphisms throughout the chapter: although some of our results can be extended to unbounded morphisms, the structure of Top/S is much more delicate, and the gain in generality does not seem worth the extra trouble that would be involved in formulating all our results so as to apply to unbounded morphisms. In this first section, our aim is to construct finite weighted limits (in the sense of 1.1.5) in BTop/S.
A First Course in Mechanics
Authors: Lunn Mary 
Published: November 2023

Abstract
This textbook provides a simple introduction to mechanics for students coming to the subject for the first time. The text is based on courses given to first and second year undergraduates and has been written with this audience in mind. Prerequisites are only a basic familiarity with vectors, matrices, and elementary calculus. The author's aim is to provide an understanding of Newtonian mechanics using the tools of modern algebra. The first chapters of the book introduce the fundamentals of the motion of rigid bodies: Newton's laws, forces, linear and angular momentum, and the conservation of energy. In the later chapters the theory of Lagrangian mechanics is developed and extended to cover applications to impulsive forces. Throughout, the theory is illustrated with many worked examples, and numerous exercises (some with solutions) are provided.
1-based theories and groups
Authors: Pillay Anand 
Published: November 2023

Abstract
The notion ‘1-based’ turned up naturally in Chapter 2, as, for example, a way of describing the global behaviour of forking in a superstable theory of finite U-rank all of whose minimal types are locally modular. In this chapter we study arbitrary (stable) theories which are 1-based, and also (∞)-definable sets which are 1-based, without any assumption of finite U-rank, or even superstability. In section 1 we give various equivalences of the 1-based property. In sections 2 and 3 we show that under various additional assumptions (triviality, NDOP, few types) 1-basedness of a theory implies that the theory is ‘superstable-like’ in the sense that types have finite weight, and enough regular types exist. In section 4, we begin to study definable groups in 1-based theories, or even ∞-definable groups which are 1-based. These turn out to be essentially ‘abelian structures’, that is abelian groups equipped with predicates for subgroups. It will also be seen (in Chapter 5) that any ‘non-triviality’ of forking in a stable 1-based theory immediately gives rise to definable groups, so this analysis is quite pertinent. In section 5, we characterize the geometries attached to (locally) modular minimal groups.
Curve and Surface Fitting with Splines
Authors: Dierckx Paul 
Published: November 2023

Abstract
The fitting of a curve or surface through a set of observational data is a very frequent problem in different disciplines (mathematics, engineering, medicine, ...) with many interesting applications. This book describes the algorithms and mathematical fundamentals of a widely used software package for data fitting with (tensor product) splines. As such it gives a survey of possibilities and benefits but also of the problems to cope with when approximating with this popular type of function. In particular it is demonstrated in detail how the properties of B-splines can be fully exploited for improving the computational efficiency and for incorporating different boundary or shape preserving constraints. Special attention is also paid to strategies for an automatic and adaptive knot selection with intent to obtain serious data reductions. The practical use of the smoothing software is illustrated with many examples, academic as well as taken from real life.
More Smoo Hing Spline Curves
Authors: Dierckx Paul 
Published: November 2023

Abstract
In this chapter, we will see how the smoothing criterion of Chapter 5 can be extended in various ways.
It is often noticed that the quality of a spline approximation is somewhat inferior towards the end points of the approximation interval (see e.g. Example 5.3). This is not really surprising, considering the fact that on one side only enough information (data points) is available. Sometimes we can cope with such an unfavourable situation by imposing appropriate boundary constraints. How these can be implemented efficiently will be illustrated by a number of examples.
We will also show how the algorithms can be adapted for fitting data which describe an arbitrary curve, closed or otherwise. Finally we will make a link to computer aided geometric design (CAGD), another research area in which spline functions are extremely useful.
Fit Ing With Convexity Cons Raints
Authors: Dierckx Paul 
Published: November 2023

Abstract
In Chapter 6 we saw how to determine smoothing splines with B-spline coefficients that satisfy some simple equality constraints. On the other hand, certain shape preserving approximation problems result in linear inequality constraints for these coefficients. How they can be incorporated efficiently will be the topic of this chapter. : ‘.\rotably, we will describe in detail an algorithm for fitting cubic splines with local convexity constraints.
In problems of data fitting it is often required that the approximating function should mimic certain properties of the function underlying the data. If it is known. for instance, that this function is strictly positive or monotonically increasing or perhaps convex, it is desirable that the approximation has the same properties. Another reason why it can be very useful to impose monotonicity or convexity constraints is that they may prevent undesirable inflections or oscillations of the fit.
From the positiYity property (1.21) of B-splines, it immediately follows that a spline approximation s(x) in the form (1.30) is positive on the interval [a. b] if all its B-spline coefficients are non-negative, i.e. if
Sur A.Ce Itting: An Introduction
Authors: Dierckx Paul 
Published: November 2023

Abstract
Most of the curve fitting algorithms described have been generalized for fitting a smooth surface to a discrete set of data (xr, yr, zr). As in Chapter 3 we will first give a review of published spline fitting methods with references to available code. The software resources are basically the same (NAG. IMSL. DASL. fitpack, FITPACK, netlib/dierckx, netlib/fitpack, netlib/gcv): the yield, however, is less abundant and diverse this time. Finally, we will also briefly comment on the variational surface fitting approach as opposed to the adopted constructive approach
MORE MESH DATA SMOOTHING
Authors: Dierckx Paul 
Published: November 2023

Abstract
In Chapter 10 we demonstrated how least-squares and smoothing splines can be calculated very efficiently if the data are given at the nodes of a rectangular grid. In this chapter we will show how the calculations can be adapted if we want to approximate a function over a disk or a sphere, provided that the data are now given on a radius-.angle or latitude..longitude grid respectively. Furthermore we will also consider the problem of reconstructing a surface from a set of cross-sectional contours and make a link to computer aided geometric design.
Automata and Languages
Authors: Howie John M 
Published: November 2023

Abstract
Theoretical models of simple computing machines, known as automata, play a central role in theoretical computer science. This textbook presents an introduction to the theory of automata and to their connections with the study of languages. At the heart of the book is the notion that by considering a language as a set of words it is possible to construct automata which `recognize' words in the language. Consequently one can generate a correspondence between a hierarchy of machines and a corresponding hierarchy of grammars and languages. Professor Howie leads the reader from finite state automata through pushdown automata to Turing machines. He demonstrates clearly and elegantly the fundamental connections between automata and abstract algebra via the notions of syntactic monoid and minimal automaton. The author presupposes a basic familiarity with modern algebra, but beyond this the book is self-contained. As a result, the book will make ideal reading for students of mathematics and computer science approaching this subject for the first time.
Nilpotent Groups
Authors: Borovik Alexandre , Nesin Ali 
Published: November 2023

Abstract
With the general theory of the previous chapter in hand, we can begin the structural analysis of groups of finite Morley rank. The general theory occupies Chapters 6 through 9. The present chapter deals with the structure theory for nilpotent groups. For the study of simple groups on the whole, the structure of solvable groups in general is of more significance than the special case of nilpotent groups, but in any case we will see in Section 6.2 that there is a general structure theory for nilpotent groups which is remarkably close to the structure theory available in the abelian case (Exercise 9, page 72).
Permutation Groups
Authors: Borovik Alexandre , Nesin Ali 
Published: November 2023

Abstract
This is a long chapter on permutation groups of finite Morley rank. The reader will find numerous challenging open problems. We start with a generalization of Clifford’s Theorem to the context of groups of finite Morley rank. Our proof follows the standard proof and we do not claim any originality. We continue with an investigation of Frobenius groups where the reader can already find some number of open problems. A group B with a proper subgroup T is said to be a Frobenius group if for b ∈ B, Tb n T ≠I- 1 implies b ∈ T. As we will see, the Frobenius groups arise naturally in the theory of permutation groups.
Complex Functions as Transformations
Authors: Needham Tristan 
Published: November 2023

Abstract
A complex function fis a rule that assigns to a complex number zan image complex number w= f(z). In order to investigate such functions it is essential that we be able to visualize them. Several methods exist for doing this, but (until Chapter 10) we shall focus almost exclusively on the method introduced in the previous chapter. That is, we shall view zand its image was points in the complex plane, so that fbecomes a transformation of the plane.