bluuebunny/crossref_metadata_2025_split huggingface dataset:
Lifetime distributions
Authors: Ansell J I , Phillips M J 
Published: November 2023

Abstract
This chapter introduces the basic ideas of parametric lifetime distributions, by firstly defining expectation, the median, and the mode, and then giving details of the most important examples encountered in reliability. These are the gamma, Weibull, extreme value, and normal distributions. In all cases the probability density functions are illustrated and for the gamma and Weibull cases the hazard functions are illustrated. After a treatment of the various kinds of censoring mechanisms that can produce examples of censored data, the problem of estimation is considered from the non-parametric standpoint. The well-known Kaplan-Meier and Nelson-Altschuler estimators for right censored data are described. When using parametric lifetime distributions values of the parameters have to be chosen. The ‘best’ values have to be chosen (estimated) on the basis of the information from the data available. The various methods of estimating parameters in parametric models from the classical, likelihood, and Bayesian viewpoints are explained. The chapter is concluded with an account of hypothesis testing which is applied to the question of the goodness-of-fit of a hypothesized lifetime distribution for censored and truncated samples.
System reliability
Authors: Ansell J I , Phillips M J 
Published: November 2023

Abstract
This chapter introduces the basic ideas for analysing system reliability. In Chapters 2 and 3 methods of analysing single components or systems were presented and no account was taken of the construction of the systems from components (or subsystems). Often there is information on the per formance of these components (or subsystems) and it is sensible to use this information in deciding on the reliability of the system. If data are available on the performance of components it is possible to calculate (estimate) the reliability of these components. Then it is necessary to have methods for calculating (estimating) the reliability of the system constructed from these components. The basic ideas and methods are presented in this chapter. Firstly, the composition (structure) of the system must be defined in terms of its components. This is done using the structure function with the associated ideas of paths and cuts. These are illustrated using simple examples of series and parallel systems, as well as the important k-out-of-n system. The structure function can be used for probability calculations to obtain the reliability of the system. (The reliability function has been introduced as a function of time, t. In this chapter it will be assumed that a particular value of t is of interest, and this will not be changed during the calculations. Hence, for this reason, the time notation will not be used in this chapter.) For simplicity the probabilistic results are restricted to systems with coherent structure functions, which is all that is needed for most practical applications. If the components operate independently and have identical probabilistic mechanisms then the calculation of the reliability of the system is simplified and a number of results follow. One of the most important is that the reliability function of the system of n components is a linear combination of the reliability function of k-out-of-n systems. As these calculations are by no means as easy for non-identical components there is a real need for good methods which can be used to give bounds on the system reliability. The important topic of three-state reliability, which covers the problem of two kinds of failure, is expounded.
Models for repairable systems
Authors: Ansell J I , Phillips M J 
Published: November 2023

Abstract
Previous chapters have dealt with the distribution of lifetimes of single components and the structure of systems. In this chapter the modelling and assessment of systems whose components may be repaired is explored. These are probably the most common type of system studied in reliability engineering. The introduction of repair brings with it a whole realm of new problems. The simplest case is if repair is instantaneous. The system would then be continuously working though it would experience events (failures). The frequency of the failures would be of interest. However, in many cases the repairs will take time and may consist of a sequence of events such as identifying the failure, sending for a repair team, the repair of a component, and the recommissioning of it. Whilst it would be possible to devote the whole chapter to characterizing repair and the types of strategies used, only a brief outline will be given at the beginning of the chapter. At the end of the chapter optimal replacement strategies will be considered. The subject can be studied in more depth by consulting Aven and Bergman (1986), Barlow and Hunter (1960b), and G.L. Glasser (1967). The main focus, though, of this chapter will be on the description of systems behaviour through stochastic processes. Simple stochastic process models which describe the system’s performance will be presented first before more complex models, which are closer to the real world, are considered. These include the modified renewal process, the alternating renewal process, the non-homogeneous Poisson process and the superimposed renewal process. Markovian models are also widely used to model many reliability systems and the analysis of these models is illustrated by methods which use differential equations. The practical application of these models is far from straightforward. There is the need to select the appropriate model and then follow the practicalities of fitting such a model.
Dependency analysis
Authors: Ansell J I , Phillips M J 
Published: November 2023

Abstract
So far it has been assumed that the lifetimes of components (or subsystems) are independent. This chapter explores approaches which do not make this assumption. A recent review of the area has been carried out by Ansell and Walls (1990, 1992). Modelling and the analysis of data from systems where components (subsystems) are dependent are becoming increasingly important as it is realized that dependency may significantly affect the reliability of the system. This has been particularly noted for safety systems when redundancy did not produce the expected level of performance owing to dependency amongst the components. The assumption of dependency leads to a number of problems including its definition. In statistical terms two events are independent if their joint probability is the product of their marginal probabilities so that for two events A and B
The Tate Conjecture for Almost Ordinary Abelian Varieties over Finite Fields
Authors: Lenstra Hendrik W , Zarhin Yuri G 
Published: November 2023

Abstract
This conjecture has been proved in certain cases, e.g., Fermat hypersurfaces satisfying certain numerical conditions [Sh, Y], elliptic K3 surfaces [AS], 1{3 surfaces of finite height [N, NO] and powers of ordinary K3 surfaces [Z3].
Arithmetic of Subvarieties of Abelian and Semiabelian Varieties
Authors: Vojta Paul 
Published: November 2023

Abstract
We will discuss work of Faltings concerning rational points on subvarieties of abelian varieties. In the talk given at the conference, the present author announced a generalization of this theorem to the case of integral points on semiabelian varieties. The proof has some serious flaws, however, so the generalization still remains a conjecture.
Shimura Reciprocity for Modular Functions with Rational Fourier Coefficients
Authors: Laing Alan J 
Published: November 2023

Abstract
We give an exposition of the computational aspects of Shimura’s explicit reciprocity law. First we discuss the classical formulation as in Shimura [4), Thm 6.31, and Lang [2], 11 §1 Thm 1. Then we consider Robert’s formulation in the case that we have rational Fourier coefficients. Finally, we interpret Robert’s formulation in terms of matrices and give an example.
On Serre’s conjecture (3.2.4?) and vertical Weil curves
Authors: Lario Joan-C 
Published: November 2023

Abstract
The first purpose of this contribution is to obtain a general criterion in order to verify this conjecture. In a joint work with P.Bayer [2], we verify (3.2.4?) for the Galois representations defined by the ρ-torsion points of ρ-vertical Weil curves (i.e., modular elliptic curves having bad but potentially good ordinary reduction at ρ, for ρ &gt; 7. Here, we obtain another proof for this case as an application of our general criterion.
Une Relation Ent re les Points Entiers sur une Courbe Algébrique et les Points Rationnels de la Jacobienne
Authors: Hirata-Kohno Noriko 
Published: November 2023

Abstract
Nous donnons ici des minorations de la distance entre des points rationnels distincts d’une variété abélienne. Ces minorations impliquent une majoration de la hauteur des points rationnels de dénominateurs homes sur une courbe algebrique de genre 1 (cf. le théoréme 3.1). Nos résultats donnent alors une version quantitative du theoreme de Siegel sur la finitude des points entiers de telle courbe.
Symplectic Geometry
Authors: Woodhouse N M J 
Published: November 2023

Abstract
Finite-dimensional symplectic manifolds arise as the phase spaces of classical systems with a finite number of degrees of freedom, where the sym plectic form w is the geometric structure that underlies the definitions of Hamiltonian vector fields and Poisson brackets. Infinite-dimensional sym plectic manifolds arise in field theory. They are less straightforward objects and their study is complicated by some subtle analytical questions. There are, for example, a number of different forms of the no degeneracy condition on w, and for infinite-dimensional manifolds they are not equivalent. For the moment we shall concentrate on the finite-dimensional case.
Logarithms and exponentials
Authors: Reutenauer Christophe 
Published: November 2023

Abstract
The various characterizations of Lie polynomials obtained in Chapter 1 are extended to Lie series, in a straightforward way. These results become really interesting when one considers exponentials of Lie series. This leads naturally to the Campbell–Baker–Hausdorff formula. Section 3.2 is devoted to the canonical projections of the free associative algebra, especially the first one, whose image is the free Lie algebra and which is obtained by a logarithm. Section 3.3 is devoted to the computation of the coefficients of the Hausdorff series. A generalization of this series leads again to the canonical projection. The computation is done using descent numbers of permutations and shuffle algebra. Several properties of the coefficients are established: symmetries, generating functions, and recursions. The last section presents the original methods of Campbell, Baker, and Hausdorff, which explains the introduction of Bernoulli numbers. A closed formula is also given for the Hausdorff series.
Shuffle Algebra and Subwords
Authors: Reutenauer Christophe 
Published: November 2023

Abstract
The shuffle algebra is a free commutative algebra over the set of Lyndon words; this result is presented in Section 6.1, together with a precise identity on the shuffie product of Lyndon words, which implies that actually there is a canonical structure of algebra of divided powers. In Section 6.2 a remarkable presentation of the shuffle algebra is given; the generators are the nonempty words, and the relations the nontrivial shuffle products. In Section 6.3 we introduce subword functions on the free group, the Magnus transformation of the free group, the algebra structure on the module of subword functions, and the fact that this algebra is generated by the particular subword functions corresponding to Lyndon words. The main tools arc the concept of representative, or recognizable functions on the free group, and the infiltration product of Chen, Fox and Lyndon. Section 6.4 presents the commutator calculus of P. Hall, and its generalizations. There are many results involving the lower central series of the free group, the Magnus transformation, and the algebra of subword functions.
Introduction
Authors: Freeden W , Gervens T , Schreiner M 
Published: November 2023

Abstract
During recent decades technological progress has completely changed the observational methods in all fields of geosciences and geoengineering: the trend is to achieve immediate results, thus reducing time and costs. Modern high speed computers and satellite based techniques are entering more and more disciplines such as cartography, climate investigation, geodesy, geology, geophysics, meteorology, navigation, oceanography, and many others.
Approximate Integration
Authors: Freeden W , Gervens T , Schreiner M 
Published: November 2023

Abstract
The method of expanding a function into a Fourier series in terms of trial functions (for example, spherical harmonics, certain types of radial basis functions) amounts to the problem of evaluating the expansion coefficients by integration. In practical applications (e.g. in many problems of geodesy or geophysics), however, the integrand is often not known continuously over all of n. Instead we are confronted with the situation that experimental data or measured values yielding the function only at prescribed points must be integrated. This gives rise to approximate integration. The aim of this chapter is to present in more detail some procedures of numerical integration on the sphere. The first one is a low discrepancy method (Section 7.1). It is based on the idea of equidistribution. The conceptual background is a spherical version of the Koksma-Hlawka formula corresponding to invariant pseudodifferential operators. Because of their simple structure and flexibility low discrepancy methods can be recommended for problems involving a large number of densely spaced data points, and under this assumption the method is satisfactory.
Vector Spherical Harmonics
Authors: Freeden W , Gervens T , Schreiner M 
Published: November 2023

Abstract
Vector spherical harmonics (as well as tensor spherical harmonics) occur in many areas of theoretical physics and engineering. In particular, they are used in quantum mechanics, or whenever one has to deal with vector fields of any geophysical nature. Important examples are gravitational fields, magnetic fields, electromagnetic fields, or elastic fields (for deformation analysis of the earth’s surface using vector spherical harmonics see for example A. BEN-MENAHEM, S.J. SINGH (1981), E.W. GRAFAREND (1982, 1986), J. BRUD0WSKY et al.(1992), w. FREEDEN et al.(1996), and M. TUCKS (1996)). Moreover, in all geosciences there is also a growing need for dealing with vector and tensor fields in spherical geometry, as more and more measurements of vectorial and tensorial type become available by modern space techniques such as satellite-to-satellite tracking or satellite gradiometry.
Abbreviating proofs using metamathematical rules
Authors: Hájek Petr , Montagna Franco , Pudlá Pavel 
Published: November 2023

Abstract
There are examples of sentences which are provable in theory T but which have only very long proofs. All the known examples have the property that at the same time there is a simple meta mathematical argument which shows that they are provable; thus, they have short proofs in some stronger theory whose soundness is as acceptable as the soundness of the original one. Such a phenomenon, which one calls speed up by provability, was first studied by Parikh. He proved in [Par71] that, if T is a recursively enumerable extension of Peano Arithmetic PA, then there is a sentence φ such that the formalization of “ φ is provable in T” has a much shorter proof than φ. This result is generalized in [DM89] and in (Mon90].
Sums over Poisson processes
Authors: Kingman J F C 
Published: November 2023

Abstract
where f is a real-valued function on the state space of a Poisson process IT. There are a number of simple, but very important, results which give conditions for the (absolute) convergence of such sums, and expressions for the expectation, variance, and characteristic function of the random variable L. In this section we shall derive the form of these results without rigorous proof, the latter being deferred to the next section.
Poisson Processes on the line
Authors: Kingman J F C 
Published: November 2023

Abstract
We have been studiously avoiding the most important example of the state space S, the whole real line IR or a subinterval of it. This has been done to stress that most of the general results have nothing to do with the special structure of IR and are equally applicable to Poisson processes in the plane, in 3-space, or in more general spaces S like those we shall meet in Chapter 7. The time has now come to link this general theory with the peculiar properties of IR, notably its order structure.
Curves
Authors: Gurtin Morton E 
Published: November 2023

Abstract
A curve is a set 𝒾 in ℝ together with a smooth map p↦ r(p) from an interval of ℝ into ℝ such that:
𝒾 is the range of r;
5 rPnever vanishes;
the domain of r is either all of ℝ or a bounded interval [P, Q];
if the domain is ℝ, either r is periodic,6 or | r(p) | → ∞ as IPI → ∞.
The function r is a parametrization of 𝒾; the variable p is the parameter; the interval [P, Q] (or ℝ) is the parameter interval; r(P) and r(Q) are the initial and terminal points (or collectively, the endpoints) of 𝒾, and we say that 𝒾 is from r(P) to r(Q).
Digression: Statical Theory of Interfacial Stability; Convexity, The Frank Diagram, and Corners; Wulff Regions
Authors: Gurtin Morton E 
Published: November 2023

Abstract
It is a basic physical premise that stable configurations of a mechanical system minimize energy. In this section we will discuss the ramifications of this premise for the phase interface. Aside from being important in its own right, the discussion will furnish a derivation of the (statical) balance relations for capillary forces as Euler – Lagrange equations corresponding to stationary values of the energy, and will provide a physical basis for certain assumptions we will make concerning the interfacial energy.
Free-Boundary Problems
Authors: Gurtin Morton E 
Published: November 2023

Abstract
The equations derived thus far combine to form an important free-boundary problem for the temperature. The differential equation to be satisfied in bulk is balance of energy supplemented by the constitutive equations (cf. (14.27)): [eq]The evolving interface forms a free boundary, and the corresponding free-boundary conditions follow from the force and energy balances for the interface.
Grid generation as a discrete optimisation problem
Authors: Farmer C L 
Published: November 2023

Abstract
Numerical grid generation involves the problems of:
Boundary fitted coordinates—deforming a regular Cartesian grid to fit complicated boundaries, some of which may be internal.
Scattered data interpolation—deforming a grid so that a fixed set of points lie at grid cell centres or coincide with grid points.
Function approximation with adjustable nodes—deforming a grid so that a given function is equi-distributed.
Methods based on the solution of partial differential equations, variational principles and the direct minimisation of discrete mesh functions have been tried. These techniques generally require a good starting guess and are prone to grid tangling.
Practical flow simulation employing high order accuracy, implicit, finite element based algorithms
Authors: Hickmott S , Hutton A G , Rabbitt M , Smith R M 
Published: November 2023

Abstract
The complexity of most fluid dynamic phenomena is such that, traditionally, practical CFD solvers have adopted fairly simple representations in space and time, embedded in explicit numerical algorithms, in order to render practical problems tractable on available computers. These technologies have been refined to considerable power and sophistication. In the main, they are identified with monotonic finite difference operators written on structured grids (i.e. simple connectivity) facilitating the use of iterative solvers requiring only moderate computer resources.
Physical and numerical aspects of non-equilibrium flows
Authors: Pandolfi Maurizio 
Published: November 2023

Abstract
We look at non-equilibrium phenomena that occur throughout unsteady flows of a compressible, inviscid and non-conductive fluid. The fluid dynamics is then governed by the Euler equations. For the sake of simplicity, and without loss of generality, the flow is assumed to be one-dimensional in the following analysis.
Boundary fitted grid generation using tensor product B-splines
Authors: Saunders Bonita V 
Published: November 2023

Abstract
In recent years grid generation, the numerical development of curvilinear coordinate systems, has been instrumental in the development of finite difference and finite element methods for solving partial differential equations (pdes) on arbitrarily shaped domains. In addition to computational aero-dynamics, grid generation is applicable to many diverse areas including hydrodynamics, metallurgy, electromagnetism and other areas involving the solution of pdes over a physical domain.
Riemann solvers: linearizations and adaption
Authors: Toro E F 
Published: November 2023

Abstract
Riemann-problem based methods are one of the most significant contributions to the algorithm-development side of CFD in the last decade. Compared to traditional methods, they are however more complex as well as more demanding on processing power. The solution of the local Riemann problem lies at the centre of both of these disadvantages. Linearized Riemann solvers (eg. Roe, 1981; Botta & Pandolfi, 1989) meant a significant step forward in simplifying algorithms and reducing cost. Practical applications however have shown that the gains may have been at the price of loosing robustness and accuracy.
Algebraic Semantics
Authors: Wagner Eric G 
Published: November 2023

Abstract
The term ‘algebraic semantics’ as used in this chapter, refers to certain approaches to the study of iteration and recursion using either universal algebra or the categorical approach to universal algebra based on Lawvere’s ‘algebraic theories’. The aim of this work is to provide a unified theory of iteration and recursion which covers the common properties of all examples of iteration and recursion. Thus, as we will show, algebraic semantics provides a uniform treatment of the theory of such seemingly diverse subjects as context-free grammars, flowcharts, recursion schemata, and recursively defined domains.
Non-Monotonic Coding Of The Declarative Past
Authors: Gabbay Dov M , Reynolds Mark A , Finger Marcelo 
Published: November 2023

Abstract
Mrs Smith is running a babysitter service. She has a list of reliable teenagers who can take on a babysitting job. A customer interested in a babysitter would call Mrs Smith and give the date on which the babysitter is needed. Mrs Smith then calls a teenager employee of hers and arranges the job. She may need to call several of her teenagers until she finds one who accepts. The customer pays Mrs Smith and the service pays the teenager. The rate is 10 per night unless the job requires overtime (after midnight) in which case it jumps to 15.
A Logical View Of Temporal Database Dynamics
Authors: Gabbay Dov M , Reynolds Mark A , Finger Marcelo 
Published: November 2023

Abstract
In traditional databases, the update of a piece of data means the replacement of the current value of the data by a new one. In temporal databases we are presented with the extra possibility of changing the past, the present and the future. In a nutshell, a temporal update is a ‘change in history’. Note the double reference to time in such an expression: change relates to temporal evolution, while history refers to temporal record. These two notions of time are independent and coexistent. In analysing updates in temporal databases we have to be able to cope simultaneously with those two notions of time. For that, we present next a two-dimensional temporal logic, a formalism that will allow for the simultaneous handling of two references of time.