bluuebunny/crossref_metadata_2025_split huggingface dataset:
Matrices And Atlases
Authors: Dunn J Michael , Hardegree Gary M 
Published: November 2023

Abstract
We have introduced the notion of matrices in Chapter 5. Before introducing abstract notions, as matrix product and matrix homomorphisms, we devote this section to an overview of several logically important matrices. This also gives us a chance to familiarize the reader with the abstract notions, which will be formally defined later, on concrete examples. After outlining some basics, we present the Lukasiewicz (and Kleene) matrices, the G Ö del matrices and the Sugihara matrices. We furnish examples of submatrices, matrix isomorphism and-homomorphism, product and preservation of tautologies. We conclude this section with a quick look at infinite generalizations and different philosophical interpretations.
Fundamental facts and concepts
Authors: Diestel Reinhard 
Published: November 2023

Abstract
This chapter gives an introduction to those facts and concepts that are fundamental to the theory of simplicial decompositions. We begin with a short section on terminology and notation, whose main purpose is to introduce simplicial decompositions in a formal way. There will also be a few other definitions, which may not actually be used until somewhere later in the book. They are included for completeness only and will be recalled when they are needed.
Separating simplices and the existence of prime decompositions
Authors: Diestel Reinhard 
Published: November 2023

Abstract
Does every graph admit a simplicial decomposition into primes? And if not, which graphs do? It is not difficult to guess from the second of these questions that the answer to the first must be ‘no’—which, on the face of it, may not even seem very surprising. After all, it is a big step from observing that a particular graph contains a separating simplex, i.e. is not itself prime, to finding a set of prime induced subgraphs, complete with well-ordering, that satisfies such specific conditions as (S1)–(S3).
Simplicial minors and the existence of prime decompositions
Authors: Diestel Reinhard 
Published: November 2023

Abstract
In this chapter we shall pursue further, and to some extent round off, the problem of the existence of simplicial tree-decompositions of countable graphs into primes. Our first existence theorem, Theorem 3.1 of Chapter 2, has already given us some insight into the structure of a countable graph not admitting a prime decomposition; recall that such a graph G contains a separating simplex S with an inaccessible side C, where in addition S is essentially attached to another component C′ of G\S. The phrase ‘essentially attached’ here means that the sub simplex S [ C′] of S need not cover S entirely, but is still large enough not to possess a prime extension into C.
Applications of simplicial decompositions
Authors: Diestel Reinhard 
Published: November 2023

Abstract
This chapter is different in aim and character from the previous chapters. Rather than exploring further the theory of simplicial decompositions, we give a brief overview of their applications, in a self-contained yet fairly concise. form. We shall omit all proofs (except where a proof follows directly from results described earlier in this book); instead, detailed references will be given.
Order and lattices
Authors: John P. Cleave 
Published: November 2023

Abstract
As in algebraic systems, the subsystems (closed sets) of logic are ordered by the relation of inclusion and in Chapter 3, §3.10, this relation was represented by ‘lattice diagrams’. This itself is sufficient reason for developing a theory about this ordering. But, more importantly, the logical consequence of a logic itself defines an order relation, implication (Definition 3.8), which has familiar properties (Example 3.4(ii)). The notion of logical equivalence is defined in terms of this relation.
Quasi-Boolean algebras and empirical continuity
Authors: John P. Cleave 
Published: November 2023

Abstract
A class of lattices called quasi-Boolean algebras (QBA’s) is examined in this chapter. These lattices include Boolean algebras, but the relation between the two classes is stronger than mere inclusion, as is shown in §7.5. The main reason for studying QBA’s is that they are structures underlying Korner’s theory of inexactness and empirical continuity (§§7.7, 7.8) and his three-valued logic of inexactness discussed in Chapter 8.
A Census of Finite Generalized Quadrangles
Authors: Payne Stanley E 
Published: November 2023

Abstract
A construction is given for each known isomorphism class of finite generalized quadrangles. Generalized quadrangles, as a special case of generalized polygons, were introduced by J. Tits in 1959 [26]. There he gave what are considered to be the classical exmples. As special cases of other types of geometries, these classical examples appeared elsewhere, most notably among the partial geometries of R. C. Bose [3]. The first nonclassical examples were also found by J. Tits in the mid-1960s and first appeared in P. Dembowski [5]. All these examples had parameters (s,t)of the form (q,q),, ,(q,q), or (q,q), where qis an arbitrary prime power. independently by M. Hall, Jr. [9]. Shortly afterwards, S. E. Payne [17] gave an abstractly more general construction which was shown in [18] to produce a new family for qany power of 2. More recently, starting with a construction of W. M. Kantor [10], several new families with parameters have been discovered, often with restrictions on the prime power q.Although the point-line dual of a GQ with parameters (s,t)is a GQ with parameters (t,s), implying that one could assume thats isnever larger than t,we often find it interesting to mention both a GQ and its point-line dual. In any case, each finite GQ known to us is isomorphic to at least one of the constructions given below or to its point-line dual.
Representation Theory of Chambersysterns of Affine Type
Authors: Ott Udo 
Published: November 2023

Abstract
For more than ten years geometry has been in an important period dominated by ideas developed in the course of laying the foundation for Lie geometries. Recent work on certain classification problems for geometries of spherical type point to the significance of representation theory for the ana1ysis of these geometries. The general method of using Hecke algebras provides the appropriate tool for studying certain aspects of the subject.The question arises whether the Hecke algebra will continue to be useful in problems involving chambersystems of affine type. The purpose of this summary is to give a report on the program to find a workable description of the finite dimensional irreducible representations of the affine Hecke algebras.Remarkably enough, at this early stage representation theory enables us to introduce the notion of dimension for affine chambersystems.
The geometry of trilinear forms
Authors: Aschbacher”‘ Michael 
Published: November 2023

Abstract
All of us at this conference are familar with projective geometry on a vector space Vover a field F,and the refinements of projective geometry induced by a bilinear form on V.This note discusses the analogous geometries induced by trilinear forms on V.There does not seem to be much in the literature on this subject. In [4], Cohen and Helminck determine all alternating trilinear forms of dimension at most 7 over fields of cohomological dimension at most 1. In (1], [2], [3] there is some discussion of alternating and symmetric trilinear forms. There is of course an extensive literature on Lie algebras and Jordan algebras which is of some relevance. In the case of bilinear forms, the study of alternating forms is easier than the study of symmetric forms. The same seems to be true of trilinear forms. Nevertheless I will restrict my discussion to symmetric trilinear forms, as I have done more work with symmetric forms than alternating forms. However much of the discussion carries over to alternating forms.
Planar Graphs
Authors: Read Ronald C , Wilson Robin J 
Published: November 2023

Abstract
A graph G is planar if it can be drawn in the plane or on the surface of a sphere so that no two edges meet, except at a vertex at which both are incident. Such a drawing partitions the set of points of the plane or sphere not lying on G into faces; for example, the following drawing has 6 faces.
A graph G is outerplanar if G can be drawn in the plane so that all the vertices lie on the boundary of the exterior face. Euler’s formula states that, if a connected planar graph G has n vertices and e edges, then any drawing of G in the plane or on the sphere has/ faces, where n −e +f = 2.
Problems for investigation
Authors: Gofman Judita 
Published: November 2023

Abstract
Even at a very early age, investigating a pattern of numbers or shapes can lead to intriguing discoveries (no matter how small) and may raise a number of challenging questions. Therefore investigative work seems to provide a suitable introduction to the art of problem solving. What should one investigate? And how? This chapter contains a selection of problems, based on some popular types of investigation, such as: iterating a certain procedure and analysing the results; search for patterns; looking for exceptions, or special cases in a pattern; generalizing given problems; studying converse problems.
The Calculus of Variations
Authors: Collins Peter J 
Published: November 2023

Abstract
It is to Queen Dido of Carthage, in the ninth century b.c., that the oldest problem in the Calculus of Variations has been attributed. The ancient Greeks certainly formulated variational problems. Most of the more celebrated analysts of the last three centuries have made substantial contributions to the mathematical theory and, in particular, the names of Bernoulli, Newton, Leibnitz, de l’Hôpital, Euler, Lagrange, Legendre, Dirichlet, Riemann, Jacobi, Weierstrass and Hilbert are attached to important phenomena or results. Nowadays, the Calculus of Variations not only has numerous applications in rigorous pure analysis and in physical applied mathematics (notably in classical and quantum mechanics and potential theory), but it is also a basic tool in operations research and control theory. We shall in this chapter use the notation f ∈ C m(A) to indicate that f is a real-valued function, defined and m-times continuously differentiable on A, where A ⊆ ℝn and m, n are positive integers.
Introduction
Authors: Grandine Thomas A 
Published: November 2023

Abstract
The projects in this book are intended to accomplish several things. The first is to present numerical computations in a context in which they might actually occur. Thus, the students, under the guise of completing various tasks for a fictitious company, gain insight into the role that numerical methods play in science and industry. The projects are all constructed so that the solutions have physical meaning for the particular problem which must be solved. In addition, the problems occasionally require two or more numerical methods in order to obtain the solution. This means that the projects are occasionally unpredictable: a student never knows exactly when a numerical method discussed earlier in the course is going to be required to solve a current problem. This global view of the subject makes it possible for the student to realize that real-world problems are never as straightforward as many textbooks would have you believe. Thus, an appreciation for the relevancy of the material is enhanced.
The setup
Authors: Grandine Thomas A 
Published: November 2023

Abstract
As a recent graduate of the Binary Institute of Technology, one of the leading institutions of science and engineering in the world, you have just entered the job market. After locating the college placement office on the campus BIT map, you have wandered in to begin your search for an exciting and challenging career. The people there have scheduled several interviews for you, and you have begun your job search by talking to representatives of several big companies. After careful consideration of the dozen or more job offers which are currently in front of you, you have decided to accept the job with the Applied Computational Mathematics and Engineering Company. ACME is a huge international corporation with many very diverse interests. Some of these are computers, energy, construction, pharmaceuticals, chemicals, mineral exploration, and oceanography.
Project 3
Authors: Grandine Thomas A 
Published: November 2023

Abstract
One division of ACME, the Heuristic Algorithm and Copious Kilobyte Exchange Regulatory agency, is currently designing a package of subroutines for one of ACME’s new computer systems. The system, Super-powered Laserized Industrial Development Engine for Rapid, Useful, Logarithmic Encryption, is intended primarily as a supercomputer for numerical computation. The SLIDE RULE should be a revolutionary new tool with which difficult numerical problems might be solved. The HACKER agency is short-handed at the moment, and they are going to need help to complete the programming of the subroutine package. Since SOLVE is not terribly busy at present, many of its consultants are being assigned to HACKER to finish the job. Since you are relatively new to ACME, you have drawn this particular task as your current project. Your individual task is a relatively straightforward one. Your job is to write a subroutine which solves quadratic equations.
Project 10
Authors: Grandine Thomas A 
Published: November 2023

Abstract
The Superconductor Hotshot Operational Research Team, a division of ACME, has been producing an electronic device, called the Fortified Utility Switching Engine, for the Bureaucratic, Large, Overblown, Washington Network, a branch of the federal government. The SHORT FUSE has been manufactured under strict specifications, which SHORT has supposedly upheld. Recently, however, some of the BLOWN FUSEs have begun to fail, and BLOWN is preparing to cancel its contract with ACME, claiming that the SHORT FUSEs have not been manufactured to specifications. Naturally, SOLVE has been called in to investigate this matter. Since you have much expertise in this area, you have been selected by Biro Kratt as the individual responsible for discovering just what is going on and who is to blame. The successful completion of this project may well allow SHORT to retain its multimillion-dollar contract with BLOWN. A personal salary increase may also be in the offing if you are successful.
Project 15
Authors: Grandine Thomas A 
Published: November 2023

Abstract
The Board of Engineers for Aqueous Voluminous Edifices and Restraints, the civil engineering division of ACME, is currently working on the design for a dam to be constructed in the Oscillating Gorge on the Interpolant River, not far from the town of Runge’s Mill. Recently, however, an environmentalist group, the Demagogues Against Mutilating Nature, have begun to protest against the construction of the Oscillating Gorge Dam. The DAMN outcry ‘Stop the damn dam’ has been so successful, in fact, that ACME has been served with a court injunction preventing the start of the actual construction. In order for BEAVER to continue work on its dam, ACME is going to have to get DAMN satisfied. The environmental impact of the dam is a complex issue, especially because the flow rate of the Interpolant River is so variable. One of the problems in answering the DAMN concerns is that no one is really quite sure what the hydrostatic pressure behind the dam is going to be as a function of the height of the water. Because the flow rate is so variable, the dam is going to have to be built in order to withstand greatly varying pressures. In order for the engineers to submit an acceptable design, it is going to be necessary to know just what those pressures are. This is where you come in. You are going to have to determine the hydrostatic pressure. Biro Kratt has assigned you to this project because of your reputation for integrity, knowing that DAMN will abide by your findings.
Project 18
Authors: Grandine Thomas A 
Published: November 2023

Abstract
ACME is conducting an important experiment aboard the space shuttle Discovery on its historic mission to the Asteroid Belt between Mars and Jupiter. Because of the importance of these experiments, you have been ordered to go along to assist. While you have been assigned several other important computations to perform during the six month flight, you have also been assigned the task of assisting the navigator during the mission. In particular, it will be your job to help the navigator avoid the asteroids. There will be one part of the journey that will be especially tricky for the pilot to steer. Three rather large asteroids will be in the vicinity of Discovery within a particular ten-hour period of time. You are going to have to compute and plot the trajectories of these three asteroids during that ten-hour period.
Project 19
Authors: Grandine Thomas A 
Published: November 2023

Abstract
The city of Cyborg has a problem. It has just been invaded by malfunctionis equipmentatis, a species of insect which likes to nest inside high-tech electrical equipment. Unfortunately, this peculiar nesting habit is wreaking havoc throughout Cyborg, since the bugs are causing equipment failures everywhere. In order to combat this infestation, the Cyborg city council has asked Quellers United Against Surviving Hexapods, a local exterminating company, to submit a bid for spraying to eliminate the pests. Simultaneously, it has hired the National Unit for Insecticide Spraying to Aid a Nice, Clean Environment, a division of ACME, to study the situation. Assuming that QUASH gets the contract to spray to eliminate the pests, it will be the job of NUISANCE to determine the effects of the spraying. For some reason, you have been assigned to this project. Your briefing papers are deliberately vague, and it is not at all clear just how your presence is going to be helpful. However, ACME has flown you to Cyborg to join the team from NUISANCE, so you have taken your camera along to take pictures of butterflies and birds as it is very unlikely that there will be much else for you to do there. After stopping at a bookstore to buy a butterfly book, you decide to spend the day at the park.
Project 20
Authors: Grandine Thomas A 
Published: November 2023

Abstract
The Telephone Operators Union for Calling Home is unhappy about the quality of the telephone lines in one of their main districts. As it turns out, a subsidiary of ACME, the Reprehensible Enterprise for Auditory Communication and Hearing, a local telephone company, is responsible for maintaining the phone lines in that district. In response to the complaints from TOUCH, REACH has ordered new fiber optic cables to install to replace the worn out copper wires still in service. Another division of ACME, the Organization for Using Telephones, manufactures optic fibers, and they will be supplying the new materials for REACH. Optic fiber manufacture is a tricky business, though, and because REACH is determined to improve the quality of its phone lines, they are insisting on using high quality optic fibers. In order for OUT to be able to produce fibers of this quality, there is one engineering difficulty that is going to have to be ironed out. This involves a computation to determine just how fast the silicon rods should be fed into the furnace to produce the desired optic fibers. It will be your job to help the people at REACH, OUT, and TOUCH. Someone there has specifically asked for you, since by now you have an ACME-wide reputation for doing an excellent job.
Project 21
Authors: Grandine Thomas A 
Published: November 2023

Abstract
The Big Remote Army Supply Station, a military installation of great importance to the defense of much of the western world, has just been penetrated by an agent working for the Spaceage Proliferation of Industrial Espionage Society. The security people working at BRASS have discovered that the agent, working from the inside, managed to secure blueprints for an important new jet. Fortunately, the SPIES agent has not yet had an opportunity to deliver the plans, so there is still a chance of capturing him before he reports his findings. By working with BRASS, American Intelligence has learned that the agent is currently hiding in a small boat moored some distance offshore. Blackford Oakes, the man that American Intelligence has sent to recapture the agent, is quite capable and daring, and he intends to seize the boat by parachuting onto it under cover of darkness.
Documentation
Authors: Grandine Thomas A 
Published: November 2023

Abstract
The following pages contain excerpts from the NAG FORTRAN Workstation Library documentation. More complete documentation may be found in the NAG FORTRAN Workstation Library Manuals. Before using any of these routines, please refer to the appropriate Appendix of the NAG FORTRAN Workstation Library Manuals to determine the interpretation of bold italicized terms and other implementation dependent details. In particular, the routine name may be precision dependent. Thus, in certain implementations, the last letter of the routine name may be different, and real may be interpreted as DOUBLE PRECISION. The pages that follow have been reprinted by permission of NAG, Ltd. The copyright of the following pages remains the property of NAG, Ltd.
Collections
Authors: Potter Michael D 
Published: November 2023

Abstract
In every part of mathematics we study objects. Whether these objects be numbers, points in space, or elements of a locally convex topological vector space, they can be formed into collections. In this chapter (and indeed throughout the book) we shall study the properties which collections have simply by virtue of being collections, no matter what they are collections of In other words, we shall be concerned only with properties arising from the relationship which holds between an object and any collection to which it belongs: this relationship is called membership.
Basic set theory
Authors: Potter Michael D 
Published: November 2023

Abstract
None of the axioms we have stated so far prevents the possibility that all collections are finite. So if we want to be able to construct infinite collections in our theory-which we do-we must make the further assumption that such collections exist. There are two ways of doing this: we can assert either that there are infinitely many individuals (that, in the terminology suggested by Fig. 1, the universe is infinitely wide) or that there are infinitely many days (that the universe is infinitely long). We shall take the latter path here: we can achieve what we want by asserting the existence of at least one limit day. (The definition of ‘infinite’ will not be given until Chapter 4; in the meantime we rely on naive notions for our discussion.) With this addition we obtain a system called ZA which is adequate for the presentation of much of modern mathematics.
Highest common factor
Authors: Chatters A W , Hajarnavis C R 
Published: November 2023

Abstract
In this chapter we shall consider divisibility, common factors, and the existence of highest common factors in arbitrary integral domains. From this work we shall deduce properties of integers which, as well as being of interest in their own right, will be needed in later chapters. Although our main interest in the short term is the ring of integers, we shall prove some of the results in a more general form which will be useful for later applications. Roughly speaking, the sort of results which we are interested in for integers can usually be extended to arbitrary Euclidean domains with only minor modifications to the proofs.
Fields and polynomials
Authors: Chatters A W , Hajarnavis C R 
Published: November 2023

Abstract
The two most important results which we shall prove in this chapter are the division algorithm for polynomials in one indeterminate over a field, and that the integers modulo p form a field for every prime number p (thus providing our first examples of finite fields). We gave the definition of a field earlier in Chapter 2. Fields and polynomials over them play an important role in algebra. In this chapter we collect together some of the elementary but important properties which we shall need later.