bluuebunny/crossref_metadata_2025_split huggingface dataset:
The Ant In The Labyrinth
Authors: Hughes Barry D 
Published: November 2023

Abstract
It is generally believed that the qualitative properties of myopic (Polya) ants and blind ants are similar, but one important difference when the ant is introduced on a finite cluster has been noted by Mitescu and Roussenq (1983): the ‘equilibrium’ probability distributions of the ant, approached asymptotically as the number of steps grows without bound, differ for the two models. The existence of equilibrium probability distributions on finite clusters can be discussed from the point of view of Markov chains (Feller 1970), where such distributions are called ‘invariant measures’, but here we shall confirm their existence by elementary arguments.
Numerical Invariants
Authors: Goldman William m. 
Published: November 2023

Abstract
This chapter summarizes several invariants in complex hyperbolic geometry. First, the “invariante angulaire” discussed by Cartan [21] is presented. This invariant is associated to triples of points on the absolute and has been used by Toledo in his investigation [41, 163, 162] of surface group actions on complex hyperbolic space. Following that is the “complex cross-ratio” introduced by Koranyi and Reimann in [105]. Finally, inspired by these invariants and thedistance formulas, we introduce an invariant associated to a real geodesic and a complex hyperplane, which is used in the following chapter to investigate intersections of bisectors.
Introduction
Authors: Hannabuss Keith 
Published: November 2023

Abstract
In the first quarter of this century physicists were slowly and somewhat reluctantly forced to realize that the view of the physical world, so painstakingly built up over the preceding four centuries, was in serious need of revision. In particular, the laws that governed the motion of particles on the atomic scale were not those of classical mechanics. Physics found itself catapulted into the strange new world of quantum theory in which the very notion of position or velocity of a particle became blurred and statistical laws dominated everything.
Scattering and tunnelling
Authors: Hannabuss Keith 
Published: November 2023

Abstract
Ever since Rutherford’s pioneering work, passing alpha rays through a metal foil target, beams of particles have provided a means of probing the fine details of subatomic structure. Modern accelerators hurl particles through a target at velocities only slightly less than that of light. The wavelength of each particle shrinks as its momentum increases and it becomes possible to distinguish features far beyond the resolving power of any microscope. In the simplest cases (such as Rutherford’s sedate Edwardian experiments) the particles emerge from their encounter unscathed, and it is by analysing the changes to their momentum that one must build up a picture of the target. To develop some feeling for what happens we shall look at the simplest case in which the particle suffers no deflection. We therefore consider particles moving along a line on which there is some kind of potential barrier.
The mathematical structure of quantum theory
Authors: Hannabuss Keith 
Published: November 2023

Abstract
We have already mentioned that Schriöidinger’s formulation of quantum mechanics was slightly preceded by a totally different algebraic formulation proposed by Heisenberg. Although Schriöidinger’s methods were so much simpler that they were generally preferred, both approaches seemed to give the same answers, so it was natural to ask how they were related. This was particularly important because some features of quantum theory were easier to understand in Heisenberg’s formalism. In fact, as we have already noted, Schriöidinger was able to show that the two methods were essentially equivalent. Soon mathematicians like Hermann Weyland John von Neumann were able to find a general mathematical scheme that encompassed both approaches, and it is this that we shall now describe.
Variational methods
Authors: Hannabuss Keith 
Published: November 2023

Abstract
Variational methods exploit an alternative characterization of eigenvectors and eigenvalues which lends itself better to approximation schemes. This is motivated by the geometrical fact that the points on a quadric, x.A.x = 1, that are closest to or furthest from the centre lie on the principal axes, and these point along eigenvectors of the matrix, A, defining the quadric.
Relativistic wave equations
Authors: Hannabuss Keith 
Published: November 2023

Abstract
One serious objection to the whole of quantum theory as we have developed it so far, is that it is inconsistent with the theory of relativity. In order to see how we may overcome this defect, at least as far as the special theory of relativity is concerned, we shall first recall some of its basic features. Shortly after Einstein’s original 1905 papers on the subject, Minkowski realized that the physical ideas could also be understood geometrically, by combining space and time into a single four-dimensional real vector space, M, whose elements we shall call four-vectors.
Skew-Symmetric Scalar Products
Authors: Lancaster Peter , Rodman Leiba 
Published: November 2023

Abstract
Chapter 2 was concerned with complex spaces having an indefinite scalar product. The detailed study of Riccati equations with real coefficients requires that we also consider scalar products on ℝn generated by real, invertible, skew-symmetric matrices; a further step away from the familiar euclidean situation. Nevertheless, the connections with the indefinite scalar products introduced in Chapter 2 are strong. For example, if K and A are real n x n matrices with K nonsingular and skew-symmetric, A will be said to be skew-symmetric with respect to K if KA is symmetric (see Section 3.2 below). On the other hand, iK is hermitian and because (iK)(iA) is also real and symmetric, it follows that iA is iK-self-adjoint in the sense of Section 2.2. Thus, the theory of Chapter 2 applies as well, but the investigations of this chapter in terms of real matrices yield more detailed information in situations relevant to our subsequent study of real Riccati equations.
Gemetric Theory: The Complex Case
Authors: Lancaster Peter , Rodman Leiba 
Published: November 2023

Abstract
Using some of the material developed in Part I we can now begin with the first central chapter on solution of Riccati equations. The “geometric theory” of the title refers to the geometry of subspaces in a finite dimensional complex linear space. It is shown that solutions of Riccati equations, and hermitian solutions in particular, are strongly connected with invariant subspaces of a certain operator defined by the coefficients of the equation. By examining these invariant subspaces in the context of a suitable indefinite scalar product (see Chapter 2) considerable information on the structure of the solution set of the Riccati equation is obtained. Of course, the “solution set” here admits both real and complex matrices.
Hermitian Solutions and Factorizations of Rational Matrix Functions
Authors: Lancaster Peter , Rodman Leiba 
Published: November 2023

Abstract
Chapters 7 and 8 focus on a geometric theory connecting hermitian solutions of the symmetric algebraic Riccati equation (7.2.1) with invariant subspaces of the associated Hamiltonian matrix . In Chapter 9 a quite different approach is developed using an iterative process. In the present chapter a third, apparently quite different, line of attack is developed. It begins with the easy observation that, if (7.2.1) (or (10.1.1) below) has a hermitian solution X then the rational matrix function
Perturbation Theory
Authors: Lancaster Peter , Rodman Leiba 
Published: November 2023

Abstract
In this chapter we present the basic results concerning behaviour of hermitian solutions of algebraic Riccati equations under perturbations, or changes, of the coefficient matrices of the CARE (10.1.1). In the first section we consider the problem of existence of hermitian solutions, while in the later sections the focus is on the behaviour of extremal solutions or, more generally, on unmixed solutions.
Propositional calculus
Authors: Ince D C 
Published: November 2023

Abstract
To describe the nature of propositions and propositional expressions. To describe what mathematical proof involves. To describe how rules of inference can be used in the proof process. To show how propositional calculus can be used during requirements analysis and system specification. The process of system specification and requirements analysis involves examining the behaviour of a proposed software system and asking questions which enable a correct system specification to be developed. For example, the text of a statement of requirements may contain sentences such as If the reactor is on-line and the operator has typed in a query command, then the query log will be updated.
Operations and objects in Z
Authors: Ince D C 
Published: November 2023

Abstract
To describe a large part of the Z toolkit. To describe the use of schemas in the definition of generics. To provide further practice in the use of schemas. The primary aim of this chapter is to look at the facilities offered within the Z language. These facilities which include basic data types such as the natural numbers also include operations on set, function and sequence data types. The facilities are frequently referred to as the Z toolkit.
Zand design
Authors: Ince D C 
Published: November 2023

Abstract
Aims To describe the difference between functional specification and design. To show one use of mathematical proof within formal software development. The previous chapters have described the process whereby a system is specified in terms of mathematics, using a language for specifying stored data, data invariants, pre-conditions, and post-conditions. A point which was made at the beginning of the book was that discrete mathematics is an excellent medium for specifying a system, because it just describes the bare bones of that system. A feature of the specifications that have been presented in the last two chapters is that they do not contain any design directives: the behaviour of the system is specified in terms of operations on mathematical structures, many of which are not implemented in programming languages.
Chronicle completion in 𝒦-IA
Authors: Sandewall Erik 
Published: November 2023

Abstract
As defined in Chapter 2, subsection 2.3.1, a chronicle in 𝒦-IA is a tuple of the form
〈 𝒦, 0, 〉IA, LAW〈SCD, OBS〉
The DFL logic from Chapter 6 provides a formal language for expressing the action laws, the schedule, and the observations. The preSCDt chapter uses the trajectory semantics to define the relationship between a 𝒦-IA chronicle consisting of DFL formulae on one hand, and a set of IDS developments on the other. It applies equally for linear and for branching time.
Probability Density Estimation
Authors: Bishop Christopher M 
Published: November 2023

Abstract
Density estimation can also be applied to unlabelled data (that is data without any class labels) where it has a number of applications. In the context of neural networks it can be applied to the distribution of data in the input space as part of the training process for radial basis function networks (Section 5.9), and to provide a method for validating the outputs of a trained neural network (Bishop, 1994b). In Chapter 6, techniques for density estimation are combined with neural network models to provide a general framework for modelling conditional density functions.
Complete and categorical theories
Authors: Manzano María 
Published: November 2023

Abstract
This chapter is devoted essentially to the study of completeness of theories and the introduction of various methods for verifying this property, which were defined in Chapter 4. As we indicated in Chapter 5, a complete theory syntactically characterized is in itself a decision procedure; every sentence is either deducible or refutable using the theory itself as an oracle. As we will see, this means that the class of models of a complete theory is strongly connected by means of the relation of elementary equivalence.
CoBase: a cooperative database system*
Authors: Chu Wesley W , Chen Q , Merzbacher M 
Published: November 2023

Abstract
This chapter proposes the use of the type abstraction hierarchy (TAH) as a framework for deriving cooperative query answers (CQA). The TAH integrates abstraction with the subsumption (is-a) and composition (part-of) semantics found in the type hierarchy. This framework provides a multi-level object representation that is an important aspect of cooperative query answering. Patterns, which specify one or more conditions on an object, are introduced as a small granularity structure with specific semantic information. Cooperative query answering uses the TAH and patterns to provide query relaxation, generalization, and specialization. Relaxation can be explicitly controlled by the user, implicitly performed by the system, or both. An explanation system is also included to present the relaxation path, as well as a nearness measure between the approximate answer and the exact answer.
On using logic to represent belief
Authors: Nossum Rolf T 
Published: November 2023

Abstract
The overall goal of this chapter is to convey knowledge of some techniques for representing and reasoning about intentional concepts in non-classical logics. Such logics are of central importance in representing and reasoning about belief and knowledge, intention and obligation, planning and acting, and other concepts. Philosophers aptly call them logics of Practical Reasoning. These logics are gaining wide acceptance as representational vehicles for advanced applications in databases, artificial intelligence, intelligent tutoring, and other fields. These logics are gaining wide acceptance as representational vehicles for advanced applications in databases, artificial intelligence, intelligent tutoring, and other fields.
Deriving answer for safty queries
Authors: Demolombe Robert , Jones Andrew 
Published: November 2023

Abstract
In addition to asking questions concerning the actual content of the database, a user may also wish to query the reliability of the messages it contains. We argue that, in reasoning about the reliability of the information in his database ( or its ‘Safety’, as we choose to call it), the database administrator will need to consider the source, or sources, which sent in the signals containing this information. In attempting to answer ‘Safety queries’, therefore, the administrator will need to be able to consider not only what is believed or known to be the case, but also the signalling acts which various agents have performed when supplying input. Here we show how some tools from applied modal logic–specifically, the logic of action, and logics of belief and knowledge–may be used to represent reasoning about Safety. We supply both a general formal analysis of the concepts involved, and a simplified formalization suitable for implementation. This is a preliminary report on work in progress, and so we conclude with a list of problems that might be investigated within this framework.
A modal analysis of subjunctive queries
Authors: Boutilier Craig 
Published: November 2023

Abstract
An important and well-studied problem in philosophical logic, artificial intelligence, and database systems is that of modelling theory change or belief revision. That is, given a knowledge base KB, we want to characterize semantically the knowledge base that results after learning a new fact α. However, the question of how to revise KB is important not just in the case of changing information, but also when we want to investigate questions of the form ‘What if A were true?’ A subjunctive conditional A &gt; B is one of the form‘If A were the case then B would be true.’ Subjunctives have been widely studied in philosophy and it is generally accepted that (some variant of) the Ramsey test is adequate for evaluating the truth of such conditionals
A Theory and its Metatheory in FS
0
Authors: Matthews Seán 
Published: November 2023

Abstract
Feferman, in the previous chapter, has proposed FS, a theory of finitary inductive systems, as a framework theory that allows a user to reason both in and about an encoded theory. I look here at how practical FS really is. To this end I formalise a sequent calculus presentation of classical propositional logic, and show this can be used for work in both the theory and the metatheory. The latter is illustrated with a discussion of a proof of Gentzen’s Hauptsatz.
A Unified View of Consequence Relation, Belief Revision, and Conditional Logic *
Authors: Katsuno Hirofumi , Satoh Ken 
Published: November 2023

Abstract
The notion of minimality is proving to be a key unifying idea in three different areas of Artificial Intelligence: non-monotonic reasoning, belief revision, and conditional reasoning. However, it is difficult for the readers of the literature in these areas to perceive the similarities clearly. The models used in each area differ, sometimes superficially and sometimes in depth, and the notation is different. This makes it hard to apply results on, say, conditional logic to, say, belief revision. Even within the same area there is confusion, as, for example, different authors use different formalisms for conditional logic, sometimes without relating their proposals to the literature. We therefore present a uniform view of how minimality is used in these three areas, shedding light on deep connections among the areas. We clarify differences and similarities between different approaches by classifying them according to the notion of minimality on which they are based.
Later Analysis and the Infinite
Authors: Russ Steve 
Published: November 2023

Abstract
The final group of works translated here, RZ, F, F+, and PU date from the last two decades of Bolzano’s life and the earliest of them (RZ and F) were written about fifteen years after the publication of his early analysis works BL, RB, and DP. Those years had been a momentous middle period of Bolzano’s life. He had been deposed from his university post in 1819 and forced to retreat from public life. He turned this to advantage by composing his fourvolume Wissenschaftslehre where he develops the conceptual and philosophical framework that is necessary for his views and contributions in the fields of logic and the theory of knowledge.
Vegard’s law in random two-dimensional alloys
Authors: Thorpe M F , Jin, W , Mahanti S D 
Published: November 2023

Abstract
In all the work on the vibrational spectra of disordered alloys, much less attention has been given to changes in bond lengths, than has been given to changes in masses and force constants. However, length changes are often important in determining both local and global properties. In this paper, we focus on length changes in the simplest non-trivial systems. We have found it convenient to set up an effective medium theory, of the kind that Roger Elliott has exploited so effectively in many problems. In the end we find simple qualitative explanations for our results that have direct and obvious experimental consequences.
Raman scattering from multilayers
Authors: Barrio Rafael A 
Published: November 2023

Abstract
The Raman effect is a complicated interaction of light with matter in which photons, electrons, and phonons play an equally important role. The experiment itself is very simple. One illuminates a sample with a beam of monochromatic light of fixed frequency and detects the intensity of light emanating from the sample at a certain angle and with different frequencies. The difference between the frequency of the incident and of the scattered light (Raman shift) is due to the creation or annihilation of phonons in the sample; therefore, a Raman spectrum gives information about the normal modes of vibration of the atoms in the material. The rigorous description of the Raman effect is not a simple task, since a good knowledge of the electronic bands and of the electron-phonon interaction is needed. Nevertheless, Raman scattering has become a familiar and useful technique to characterize molecules and perfect crystals because symmetry imposes severe selection rules due to momentum conservation.
Exactly solvable problem for the polar optical phonon Green’s function and the phonon distribution function in the vibrational spectrum diffusion region of uniaxial crystal solid solutions
Authors: Jpatova P , Shchukin V A 
Published: November 2023

Abstract
The electron energy spectrum of three-dimensional disordered systems such as mixed crystals is known to contain a diffusion region situated between the continuous spectrum formed by extended electron states and the density-of-states tail created by localized electron states. The electron mean free path l in the diffusion region is of the order of magnitude of the electron wavelength A, and the electron motion is controlled by collisions. There is no small parameter in the diffusion region of three-dimensional disordered systems; therefore both: (1) the electron multiple scattering by isolated fluctuations of composition; and (2) the interference of scattering processes from different fluctuations are of the same order of magnitude.
Spin fluctuations in antiferromagnets and superconductors
Authors: Fleury Paul A 
Published: November 2023

Abstract
Until the early 1960s, inelastic light scattering was confined to the study of vibrational degrees of freedom in condensed matter through the familiar Raman effect. With the invention of the laser and the development of improved photon detectors and spectrometers, the utility of inelastic light scattering for the study of essentially all types of elementary excitations in condensed matter rapidly advanced. A key element in advance was a short paper in 1963 by Roger Elliott and Rodney Loudon which first raised the possibility of what they called ‘the electronic Raman effect’. This paper also carried a prediction that inelastic light scattering could be used to study one-magnon excitations in antiferromagnets.
A new approach to the calculation of spectra for strongly correlated systems
Authors: Costi T A , Hewson A C 
Published: November 2023

Abstract
Direct diagonalization of a small cluster embedded within a larger system gives some information about the larger system but only over the largest energy scale. Such cluster calculations may help to identify peaks in XPS and other spectra in this energy range, but are of little direct use in giving information about the lower energy excitations and thermodynamic properties. For these lower energy excitations larger range correlations have to be taken into account. Whatever the computing resources, there is a rather sharp cut-off on the size of the cluster that can be diagonalized numerically. There are various possibilities for extending these to obtain results on smaller energy scales and larger clusters.
One-dimensional magnets and conformal invariance
Authors: Ziman Timothy 
Published: November 2023

Abstract
One-dimensional magnetism began as a testing ground for theoretical models but has become a subject of experimental investigation as well. Nowadays we know a number of insulating materials that provide good realizations of one-dimensional antiferromagnets of various quantum spin S: CuC122NC5H5, which has spin S = ½; CsNiCl3 and Ni(C2H8N2)iNO2(ClO4), both with S = 1; CsVCl3 (S = i); and (CH3 )4NC5H5MnCl3, which has S = i (Steiner et al. 1976; Renard et al. 1988). To a first approximation the magnetic ions of each material form well separated chains each of which can be described by the very simple Hamiltonian.
The t-1
4 universality class: theory and simulation of slow domain growth after quenches to low and finite temperatures
Authors: Lindgard Per-Anker , Castan Teresa 
Published: November 2023

Abstract
The kinetics of domain growth is of relevance for the formation of polycrystalline microstructures. This is of considerable importance in surface science (Wang and Lu 1983), metallurgy (Hashimoto et al. 1976), and earth science (Salje 1988). It is, in practice, the complexity of the microstructures, which is decisive for the physical properties.