bluuebunny/crossref_metadata_2025_split huggingface dataset:
Number of Symbols in Frege Proofs with and without the Deduction Rule
Authors: Bonet* Maria Luisa 
Published: November 2023

Abstract
Abstract
Frege systems with the deduction rule produce at most quadratic speedup over .F’rege systems using as a measure of length the number of symbols in the proof. We study whether that speedup is in reality smaller. We show that the speedup is linear when the Frege proofs are tree-like. Also, two groups of formulas, permutation formulas and transitive closure formulas, that seemed most likely to produce an almost quadratic speedup when using the deduction rule, are shown to produce only log n and log2 n factors respectively.
Poisson Processes
Authors: Kingman J F C 
Published: November 2023

Abstract
In the theory of random processes there are two that are fundamental, and occur over and over again, often in surprising ways. There is a real sense in which the deepest results are concerned with their interplay. One, the Bachelier Wiener model of Brownian motion, has been the subject of many books. The other, the Poisson process, seems at first sight humbler and less worthy of study in its own right. Nearly every book mentions it, but most hurry past to more general point processes or Markov chains. This comparative neglect is ill judged, and stems from a lack of perception of the real importance of the Poisson process. This distortion partly comes about from a restriction to one dimension, while the theory becomes more natural in more general context. This book attempts to redress the balance. It records Kingman's fascination with the beauty and wide applicability of Poisson processes in one or more dimensions. The mathematical theory is powerful, and a few key results often produce surprising consequences.
Recent developments of the Lagrange-Galerkin method
Authors: Priestley Andrew 
Published: November 2023

Abstract
The Lagrange-Galerkin method, which combines the ideas of the method of characteristics with the finite element method, has been popular for solving fluid flow problems for some years now, and has proved very successful in a number of problem areas, such as oil recovery, Navier-Stokes and the shallow water equations, see, for example, Benqué et al. (1982), Bercovier & Pironneau (1982), Douglas & Russell (1982), Lesaint (1977), Morton et al. (1988) & Siili (1988a). The method is very accurate and, because it deals with the advection terms in a Lagrangian fashion, has no CFL limit. This leads, in principle, to unconditionally stability. It can work equally well on unstructured triangular grids or tetrahedral meshes in 3-D.
Iterative solution techniques for the Lagrange-Galerkin method
Authors: Ramage Alison , Wathen Andrew J 
Published: November 2023

Abstract
One area of practical importance in the field of computational fluid dynamics is the solution of convection-dominated diffusion problems for in-compressible viscous flow. The Lagrange-Galerkin method is a numerical technique designed particularly with such problems in mind (see e.g. Morton 1990). The various (weak and direct) forms of the scheme involve using the method of characteristics with a Galerkin finite element approach, combining the power of the latter method with a relatively straightforward finite difference approximation of the Lagrangian material derivative along particle trajectories. If the inner products involved are assumed to be evaluated exactly, the method is unconditionally stable and convergent for a wide range of problems.
Multi-stage Jacobi relaxation as smoother in a multigrid method for steady Euler equations
Authors: Dick Erik , Riemslagh Kris 
Published: November 2023

Abstract
By the use of upwind methods of flux-difference type on steady Euler equations, the first order accurate discretization leads to a set of equations of so-called positive type. This set can be solved by any classical relaxation method in multigrid form. The set of equations generated by the second order accurate discretization does not have this property and as a consequence cannot be solved in the same way. The common approach is then to use defect correction [1, 2, 3]. In this procedure the multigrid method is based on the first order accurate formulation, used as an inner iteration for a second order correction only performed on the finest grid. This procedure proves to work well in many applications. The speed of convergence is however largely determined by the outer iteration and sometimes is found to be rather disappointing, especially when the second order solution is significantly different from the first order solution. It can be expected that if the second order approximation also could be used in the multigrid itself a much better performance could be obtained. A second difficulty is that often convergence cannot be obtained unless a suitable initial flow field is specified, i.e. there is a serious risk of choosing an initial approximation which is out of the attraction region of the iterative method.
Basic Category Theory
Authors: Poigné Axel 
Published: November 2023

Abstract
If asked for a single reason for the attention that category theory, at least as a language, enjoys in some areas of computer science, I wou its attraction stems from being a foundational theory of fun ld guess that ctions which provides a sound basis for (functional) programming and programming logic. If asked for more reasons I would recollect the familiar arguments, namely that category theory
Equational Reasoning and Term Rewriting Systems
Authors: Plaisted David A 
Published: November 2023

Abstract
Anequational system is a set of equations. Often we are interested in knowing if an equation follows logically from the given set. For example, given the equationsx + y = y + x, (x + y) + z = x 4-(y 4-z), and — ( —(x +y) + - (x + -y)) = x, we might want to know if the equation — ( —(x +y) + - (x + -y)) = x is a logical consequence. As another example, we might want to know if x *y = y * x in a group in whichx =e for allx. Such systems are of interest for computer scientists as well as mathematicians. Common data structures like lists and stacks can often be described by such sets of equations. Furthermore, systems for mechanizing such proofs on a computer are becoming more and more powerful. In addition, a functional program is essentially a set of equations, typically with higher order functions, and the execution of a program is then a kind of equational reasoning. We will discuss methods of inference that are particularly adapted to equational systems without explicit higher order functions. We will also discuss systems in which the equations may have conditions attached. Next we will consider the use of equational reasoning in general theorem proving programs.
Some Direct Theories of Nonmonotonic Inheritance
Authors: Horty John F 
Published: November 2023

Abstract
Inheritance systems were originally developed within artificial intelligence in response to the practical need for an efficient way of representing and accessing taxonomic information. These systems, along with network representations more generally, were first presented without any semantic analysis at all, or else only with a procedural semantics, according to which the meaning of the representations was supposed to be specified implicitly by the programs operating on them.
Autoepistemic Logic
Authors: Konolige Kurt 
Published: November 2023

Abstract
The subject matter of autoepistemic (AE) logic is the belief set of an agent who has introspective capabilities. It is a modal logic similar in many respects to standard epistemic logics, so that there are modal expressions Lϕ in the language referring to the agent’s beliefs. Where AE logic differs from standard modal systems is in its semantics, that is, the formal account of what an agent’s ‘belief set’ is. To explain the semantics, even informally, requires making the distinction between internal and external logics of belief.
Lambda Calculi with Types
Authors: Barendregt H P 
Published: November 2023

Abstract
The lambda calculus was originally conceived by Church [Church, 193233] as part of a general theory of functions and logic, intended as a foundation for mathematics. Although the full system turned out to be inconsistent, as shown in [Kleene and Rosser, 1935], the subsystem dealing with functions only became a successful model for the computable functions. This system is called now the lambda calculus. Books on this subject e.g. are [Church, 1941], [Curry and Feys, 1958], [Curry et al., 1972], [Barendregt, 1984], [Hindley and Seldin, 1986) and [Krivine, 1990].
Temporal Logic
Authors: Gabbay Dov M , Reynolds Mark A , Finger Marcelo 
Published: November 2023

Abstract
This is the second volume of this respected work in temporal logic. Whereas volume 1 dealt primarily with basic concepts and methods, volume 2 discusses the more applicable aspects of temporal logics. The first four chapters continue the more theoretical presentations in volume 1, covering automata, branching time and labelled deduction. The rest of the book discusses temporal databases, temporal execution and programming, actions and planning.
Modal Logic
Authors: Chagrov Alexander , Zakharyaschev Michael 
Published: November 2023

Abstract
For a novice this book is a mathematically-oriented introduction to modal logic, the discipline within mathematical logic studying mathematical models of reasoning which involve various kinds of modal operators - `like it is necessary' in philosophy, `it is believed' in cognitive science, `it is provable' in mathematics and `it is true after executing a program' in computer science. It is an advanced text which starts with very fundamental concepts and gradually proceeds to the front line of current research, introducing in full details the modern semantical and algebraic apparatus and covering practically all classical results in the field. It contains both numerous exercises and open problems, and presupposes only minimal knowledge in mathematics. A specialist can use the book as a source of references. For the first time results and methods of many directions in propositional modal logic - from completeness and duality to algorithmic problems - are collected and systematically presented in one volume. Unlike other books, modal logic is treated here as a uniform theory rather than a collection of a few particular systems. It is the only book presenting the theory of superintuitionistic logics.
Bounding pp(μ) when μ &lt; cf( μ) &gt; N0 using ranks normal filters [Sh 386]
Authors: Shelah Saharon 
Published: November 2023

Abstract
Using quite complete (mainly normal) filters to get bounds (even equalities) in Cardinal Arithmetic has a long history. Scott [Sc] proved that for « measurable if GCH holds below k it holds for k by taking ultrapower of the universe, which is still well founded and include P(k). Solovay [Sol] proved that above a compact cardinal.
Cardinal Arithmetic [Sh 400]
Authors: Shelah Saharon 
Published: November 2023

Abstract
We arrived to it for a question for which it gives a satisfying answer. Since the work of Easton we know that if we add (something equivalent to) λcfλ = λ,+ + 2cfλ to the rules of cardinal arithmetic known at this time, then there are essentially no further restrictions. Since the works Devlin and Jensen [DeJ] and Dodd and Jensen [DJ2], we know that this rule holds when there is no 0# and even no inner model with measurables; so if it holds we will say cardinal arithmetic is trivial. It is generally agreed that at least for major problems it is important to find their exact consistency strength. Lately Gitik [Gil] continuing works of Magidor [Mg] and Woodin, show ZFC + 0(k:) = k:++ is an upper bound for consistency strength of “cardinal arithmetic non-trivial”.
The associated Lie ring of a group
Authors: Vaughan-Lee Michael 
Published: November 2023

Abstract
In this chapter we introduce the associated Lie ring of a group. Most of the detailed information we obtain in later chapters about finite groups of prime-power exponent will come from studying their associated Lie rings, and studying the identities which these Lie rings satisfy. First, we establish some of the basic facts we need about the lower central series and the lower exponent-p-central series of a group. We then define the associated Lie ring of a group, describe some of its properties, and go on to determine an explicit basis for the multilinear identities which hold in the associated Lie rings of groups of prime-power exponent.
Kostrikin’s Theorem
Authors: Vaughan-Lee Michael 
Published: November 2023

Abstract
In this chapter we prove:
Kostrikin’s Theorem Let L be a finitely generated Lie algebra over a field of characteristic p, and suppose that L satisfies the (p−1)-Engel identity xyp−1 = 0. Then L is nilpotent.
This theorem, together with Corollary 2.4.8, shows that the associated Lie rings of groups of exponent pare locally nilpotent, and so solves the restricted Burnside problem for exponent p. We give proofs of Kostrikin’s Theorem for p = 2, 3, 5, and 7 in §3.1, and we give a general proof for p ≥5 in §3.2 and §3.3.
Razmyslov’s Theorem
Authors: Vaughan-Lee Michael 
Published: November 2023

Abstract
In this chapter we prove Razmyslov’s Theorem that if q is a prime power and q≥4 then there exists a non-solvable locally finite group of exponent q. (The theorem for p = 5 was originally proved by Bachmuth et al. [3].) Note that Razmyslov’s Theorem does not hold for prime powers q &lt; 4 since groups of exponent 2 are abelian, and groups of exponent 3 are nilpotent of class at most 3 and hence metabelian.
Groups of exponent four
Authors: Vaughan-Lee Michael 
Published: November 2023

Abstract
In this chapter we prove that groups of exponent 4 are locally finite. This means that the nilpotent quotient algorithm can be used to compute power-commutator presentations for B(r, 4) for small values of r. Such presentations have been obtained for r = 2, 3, 4, 5 and we make extensive use of them to establish commutator identities which hold in groups of exponent 4.
Random Walk In A Random Environment
Authors: Hughes Barry D 
Published: November 2023

Abstract
We now turn from steady-state conduction problems to problems in which a time-evolving random process takes place in a random environment. Our discussion here is restricted to processes on lattices, and in the main to one spatial dimension. Some higher-dimensional problems are addressed briefly in §6.5.3, but the most interesting problems in higher dimensions, those in which percolation phenomena arise, are deferred to Chapter 7. In §6.1-§6.3 we discuss in detail a discrete-time model of random walk in a random environment. A continuous-time model based on a master equation with randomized rate coefficients is discussed briefly in §6.4. Some interesting generalizations of these models are surveyed in §6.5.
Reasoning about knowledge: a survey
Authors: Gardenfors Peter , Rott Hans 
Published: November 2023

Abstract
The bird caught in the trap is white. C Now suppose that, as a matter of fact, the bird caught in the trap turns out to be black. This means that you want to add the fact -&gt;C, i.e., the negation of C, to the database. But then the database becomes inconsistent. If you want to keep the database consistent—which is normally a sound methodology—you need to revise it. This means that some of the beliefs in the original database must be retracted. You don’t want to give up all of the beliefs since this would be an unnecessary loss of valuable information. So you have to choose between retracting A, B1, B1 -&gt; B, or A A B C. When giving up a belief you have to decide which of the reasons for this belief to retain and which to retract (this is the backward direction).
Preliminaries From the Theory of Matrices
Authors: Lancaster Peter , Rodman Leiba 
Published: November 2023

Abstract
We consider n x n matrices A with complex entries (i.e. entries in the field of complex numbers ℂ). In a natural way A represents a linear transformation from (ℂn into (ℂn, where ℂn stands for the vector space of n-component columns with complex components. This linear transformation will be denoted by the same letter A. We have therefore the linear transformation A : (ℂn → ℂn defined by A(x) = Ax, x ∈ ℂn, where Ax is the matrix vector product of the matrix A and the column x.
Constructive Existence and Comparison Theorems
Authors: Lancaster Peter , Rodman Leiba 
Published: November 2023

Abstract
Consider the symmetric algebraic Riccati equation XDX−XA-A*X−C= 0. The main theme of this chapter concerns comparison results of the following nature: suppose the coefficients of the equation are changed, resulting in the equation XD′X−XA ′−A ′*X−C ′ = 0. If the first equation has hermitian solutions, when can we say that the second also has solutions? Is there some relationship between maximal solutions of the two equations? The methods of this chapter are based on a constructive iterative procedure, in contrast with Chapter 7 where the methods use geometrical properties of invariant subspaces.
Constructive Existence and Comparison Theorems
Authors: Lancaster Peter , Rodman Leiba 
Published: November 2023

Abstract
This chapter is an analogue of Chapter 9, in which existence and comparison theorems for the DARE (12.1.1) are developed, rather than for the CARE of (9.1.1). Throughout this chapter it is assumed that, in (12.1.1), Q = Q* and R =R* Additional hypotheses on A and B (such as d-stabilizability, as defined in Section 4.4) are assumed as required. The most important results of this kind for the DARE with complex coefficient matrices are stated and proved. The corresponding results for real solutions of the DARE with real coefficients (i.e. equation (12.7.1)) can be obtained as simple special cases of the results for the case of complex coefficient matrices, and are not considered explicitly.
Statistical Pattern Recognition
Authors: Bishop Christopher M 
Published: November 2023

Abstract
The term pattern recognition encompasses a wide range of information processing problems of great practical significance, from speech recognition and the classification of handwritten characters, to fault detection in machinery and medical diagnosis. Often these are problems which many humans solve in a seemingly effortless fashion. However, their solution using computers has, in many cases, proved to be immensely difficult. In order to have the best opportunity of developing effective solutions, it is important to adopt a principled approach based on sound theoretical concepts.
Single-Layer Networks
Authors: Bishop Christopher M 
Published: November 2023

Abstract
In Chapter 1 we showed that the optimal decision rule for minimizing the probability of misclassification requires a new pattern to be assigned to the class having the largest posterior probability. We also showed how the posterior probabilities can be related to class-conditional densities through Bayes’ theorem, and in Chapter 2 we described several techniques for estimating these densities. An alternative approach, which circumvents the determination of probability densities, is based on the idea of a discriminant function, also introduced in Chapter 1. In a practical application of discriminant functions, specific parametrized functional forms are chosen, and the values of the parameters are then determined from a set of training data by means of a suitable learning algorithm.
From Concurrent Logic Programming to Concurrent Constraint Programming
Authors: de Boer Frank S , Palamidessi Catuscia 
Published: November 2023

Abstract
The endeavor to extend logic programming to a language suitable for concurrent systems has stimulated in the last decade an intensive research, resulting in a large variety of proposals. A common feature of the various approaches is the attempt to define mechanisms for concurrency within the logical paradigm, the driving ideal being the balance between expressiveness and declarative reading. In this survey we present the motivations, the principal lines along which the field has developed, the various paradigms which have been proposed, and the main approaches to the semantic foundations.
Interior point algorithms for integer programming
Authors: Mitchell John E 
Published: November 2023

Abstract
An algorithm for solving linear programming problems can be used as a subroutine in methods for more complicated problems. Such methods usually involve solving a seque:1ce of related linear programming problems, where the solution to one linear program is close to the solution to the next, that is, it provides a warm start for the next linear program. The branch and cut method for solving integer programming problems is of this form: linear programming relaxations are solved unti eventually the integer programming problem has been solved. Within the last ten years, interior point methods have become accepted as powerful tools for solving linear programming problems. It appears that interior point methods may well solve large linear programs substantially faster than the simplex method. A natural question, therefore, is whether interior point methods can be successfully used to solve integer programming problems. This requires the ability to exploit a warm start.
The Nine Chapters on the Mathematical Art
Authors: Kangshen Shen , Crossley John N , Lun Anthony W -C 
Published: November 2023

Abstract
The Nine Chapters on the Mathematical Art is a classic text: the most important mathematical source in China during the past 2000 years, and comparable in significance to Euclid's Elements in the West. This volume contains the first complete English translation of the Nine Chapters, together with two commentaries written in the 3rd and 7th centuries AD, and a further commentary by the translators. The Nine Chapters contains 246 problems and their solutions, which fall into nine categories that are firmly based on practical needs. There are methods for solving problems in areas such as land measurement, construction, agriculture, commerce, and taxation. The Chinese commentators provided the algorithms needed to solve the problems, and explanations of how the algorithms work. The translators' commentary provides clear and accessible background material for the Western reader, explanations of technicalities, and notes on the treatment of similar or identical mathematical problems in other countries. The Nine Chapters quickly acquired a distinguished reputation, and was the standard mathematics textbook in China and the surrounding regions until Western science was introduced in about 1600. This English translation gives the reader an idea of the distinctive style and important contributions of traditional Chinese mathematics.
Leonardo Da Vinci
Authors: Coolidge Julian Lowell , Gray Jeremy 
Published: November 2023

Abstract
Of all the sons of men of whom we have any record, none had a greater intellectual appetite, or shall we say, a more omnivorous curiosity, than the great Florentine whose name appears at the head of the chapter. He is the closest approach we have to that unattainable ideal, the universal man. The Italian Renaissance produced a number of men who stood out both in science and art, but Leonardo was supreme.
Conceptual revolutions and the history of mathematics: two studies in the growth of knowledge (1984)*
Authors: Dauben Joseph 
Published: November 2023

Abstract
It has often been argued that revolutions do not occur in the history of mathematics and that, unlike the other sciences, mathematics accumulates positive knowledge without revolutionizing or rejecting its past.1 But there are certain critical moments, even in mathematics, that suggest that revolutions do occur—that new orders are brought about and eventually serve to supplant an older mathematics. Although there are many important examples of such innovation in the history of mathematics, two are particularly instructive: the discovery by the ancient Greeks of incommensurable magnitudes, and the creation of transfinite set theory by Georg Cantor in the nineteenth century. Both examples are as different in character as they are separated in time, and yet each provides a clear instance of a major transformation in mathematical thought.