bluuebunny/crossref_metadata_2025_split huggingface dataset:
Continuous Wavelet Transform
Authors: Freeden W , Gervens T , Schreiner M 
Published: November 2023

Abstract
The objective of this chapter is to generalize the important subject of the continuous wavelet transform to the spherical case. The spherical continuous wavelet transform arises naturally as a result of an integral reproducing formula that is closely related to the theory of singular integral operators. In the spherical continuous wavelet transform the rotation and dilation parameters vary continuously, i.e. such a reconstruction requires global information at allscales ρand positions η.
Vectorial Approximation Methods
Authors: Freeden W , Gervens T , Schreiner M 
Published: November 2023

Abstract
This chapter combines scalar constructive approximation theory with the vectorial concept of spherical harmonics. It turns out that the presented notation and basic settings lead in canonical way to vectorial generalizations of Sobolev spaces, pseudodifferential operators, radial basis functions, splines, singular integrals, wavelets, etc. It should be noted, however, that we have made no attempt to be comprehensive in the coverage of constructive vectorial approximation. Only the cornerstones are mentioned, to enable readers to extract more specialized information from the scalar part of this book for themselves.
Postscript: A Broader, not Only Professional View
Authors: Kreisel Georg 
Published: November 2023

Abstract
The material below may be of use to some of those readers who have gone through the paper above, and have its mathematical ideas at their fingertips; in whatever sense this phrase is appropriate, to temperament and education of a particular reader. Beyond this, as a corollary to a simple, but important home truth repeated since Pindar, the readers should not — even feel to be — so wise that the facts are enough for them. The material is concerned with an interpretation, in particular, by means of relations to broad proof-theoretic experience. Since it is not only possible, but common, to assume that scholarly traditions are suitable for such an enterprise, a general disclaimer is necessary here; to be bolstered by specifics when occasions arise.
The Poisson-Dirichlet distribution
Authors: Kingman J F C 
Published: November 2023

Abstract
The parameters α j may take any strictly positive values, and the character of the distribution changes markedly as these vary. If α j = 1 for all j we have the uniform distribution on Δ n If the α j = are large, (9.3) concentrates probability well away from the boundaries of Δ n, corresponding to distributions p which are fairly evenly spread. On the other hand, small values of the α j = concentrate near the boundary of Δ n, corresponding to highly disparate p with a few large p j and the others small.
Stationary Interfaces and Steadily Evolving Interfaces
Authors: Gurtin Morton E 
Published: November 2023

Abstract
We assume throughout this chapter that the interfacial energy is strictly stable, so that
This chapter is restricted to evolving interfaces that are admissible; to avoid repetition, we will omit the term ‘admissible’ in most of the ensuing discussion.
Evolving interfaces are, by definition, smooth, a limitation that involves no loss in generality, since the interfacial energy is strictly stable (cf. (7.30)).
Unstable Interfacial Energies and Interfaces with Corners
Authors: Gurtin Morton E 
Published: November 2023

Abstract
Suppose now that
the interfacial energy is regular, hut not stable
(cf. the last paragraph of Section 7.3). Then an admissible evolving interface must, by virtue of its smoothness, involve normal angles at which the evolution equations are backward parabolic. Two ways of overcoming this difficulty are to:
regularize the evolution equations;
allow corners that correspond to jumps in 0 across the unstable portions of .f(θ).
Non-Smooth Interfacial Energies; Crystalline Energies
Authors: Gurtin Morton E 
Published: November 2023

Abstract
Material scientists often consider interfacial energies that are continuous but have derivatives that suffer jump discontinuities. We now discuss a particular class of energies with this property. These energies, termed crystalline, have convexified Frank diagrams that are polygonal. As we shall see, crystalline energies are compatible with fully faceted interfaces.
We assume that the energy f(θ) is crystalline; precisely, we assume that f(θ) is continuous, piecewise-smooth, strictly positive, and consistent with the following two conditions.
Material scientists often consider interfacial energies that are continuous but have derivatives that suffer jump discontinuities. We now discuss a particular class of energies with this property. These energies, termed crystalline, have convexified Frank diagrams that are polygonal. As we shall see, crystalline energies are compatible with fully faceted interfaces.
We assume that the energy f(θ) is crystalline; precisely, we assume that f(θ) is continuous, piecewise-smooth, strictly positive, and consistent with the following two conditions.
Solution adaptivity with structured grids
Authors: Catherall D 
Published: November 2023

Abstract
This paper considers the problem of solution-adaptive meshes from the point of view of mesh movement, rather than the currently more popular methods involving the embedding of regions of finer mesh. These latter methods are, to some extent, easier to apply, since they affect a mesh only locally, whereas as will be seen, with mesh movement methods the whole mesh is adapted, introducing global problems of mesh quality. In the concluding remarks at the end of the paper a short discussion is included on the relative merits of the two approaches.
Convergence acceleration for first order systems
Authors: Gustafsson Bertil , Per LÖtstedt 
Published: November 2023

Abstract
Any finite difference, volume or element approximation of a steady state flow problem gives rise to a large system of nonlinear algebraic equations. A direct solver for the linear systems arising from Newton’s (or similar methods) requires too much CPU-time and too much memory even on the fastest supercomputer for real problems in three space dimensions. It has been tried for 2-D problems in [1], but even for such problems it can hardly be considered as a general purpose method.
Iterative defect correction and multigrid accelerated explicit time stepping for the steady Euler equations
Authors: Koren Barry 
Published: November 2023

Abstract
The computational grid is obtained by a hybrid finite element - finite volume partition. A (possibly unstructured) finite-element triangularization is used as the basic partition. A cell-centered finite-volume partition is derived from the finite-element partition by connecting the centers of the triangle sides in the manner illustrated in Figure 1. The finite-volume grid gives us the easy possibility of grouping together the nodes associated with contiguous finite volumes.
Adaptive concepts for the resolution of compressible flow by upwind finite volume methods
Authors: Sonar Th. , Hannemann V , Friedrich O 
Published: November 2023

Abstract
The details of the scheme will be described in a forthcoming paper elsewhere. The construction outlined leads to a robust and accurate scheme capable of computing strong shocks as well as contact discontinuities. Figure 1 shows the density distribution in the Mach 3 forward-facing step example of Woodward and Colella [5]. The grid used consists of 14297 points and the result shown was obtained at time t=4 (using the same non-dimensionalisation as Woddward and Colella). In [5] a cartesian grid with more than 19000 points was used to compare several high-resolution finite-difference schemes. As can be seen by comparison with [5] the result of our scheme compares quite well with the result of high-resolution finite-difference methods.
Local uniform mesh refinement and brine transport in porous media
Authors: Trompert Ron 
Published: November 2023

Abstract
An adaptive-grid finite-difference method is applied to a model for unsteady, isothermal, coupled flow and transport of brine in porous media. In the vicinity of rock salt formations, the salt concentration may become large giving rise to disparate scales in the salt concentration profiles. A typical situation one encounters is that of a sharp fresh-salt water interface that moves in time. For such problems, a single uniform space grid held fixed throughout the entire time evolution can be computationally very inefficient, since, to afford an accurate approximation, such a grid would easily have to contain an excessive number of nodes, particularly so for two and three space dimensions.
Orthogonal block structured surface grids
Authors: Arina R , Tarditi S 
Published: November 2023

Abstract
One of the main issues in grid generation is the improvement of the grid quality, both for structured and unstructured meshes. In the present work we focus our attention on the generation of structured grids. It is important to develop structured grid generation systems able to give “good” grids in topologically complex regions, because in this way it is possible to reduce the effort of block decomposition, with considerable improvement of the flow solver efficiency. By “good” meshes, we mean grids sufficiently smooth, and orthogonal along part of the boundary (for example along solid walls). Moreover, along the interior boundaries connecting different blocks, it is advisable to have the possibility of controlling both the grid point positions and the slope of the coordinate lines. The aim of this work is to present a mesh generation method for structured grids, able to solve the main issues pointed out above, specifically: a) smoothness, b) orthogonality control, c) specification of the grid point position and coordinate line slope along each boundary at the same time.
Grid quality: an interplay of grid and solver
Authors: Veldman A E P , Botta E F F 
Published: November 2023

Abstract
Currently, much attention is being paid to the development of adaptive grid generation methods, which generate grids that are highly nonuniform. Firstly, this is motivated by the expectation that a high density of grid points is only necessary in regions of large solution activity (steep gradients, large curvature, etc.), whereas in the smoother regions of the solution larger grid cells can be used. Secondly, and more important, it is believed that a reduction in the number of grid points will also lead to a reduction of computational effort.
A high resolution discontinuous Galerkin method for hyperbolic problems on unstructured grids
Authors: F. Bassi , S. Rebay , M. Savini 
Published: November 2023

Abstract
In recent years successful results have been obtained in the numerical solution of Euler equations by means of total variation stable finite difference (volume) schemes. These methods, which in the earliest versions were restricted to first order accuracy and to one dimensional problems, have been successively extended to higher-order accuracy and, despite the lack of a rigorous mathamatical theory, to multidimensional problems. These extensions have been obtained by using wider stencils to increase the order of the numerical approximation and by means of one dimensional algorithms applied in prescribed directions to handle multidimensional problems. In practice, due to the presence of points aligned with logical directions, this approach is straightforward only when using structured grids. However, it is well known that structured grids suffer from heavy limitations when used for problems characterized by complicated geometry or when the grid has to be adapted to local features of the solution. For this reason in recent times a lot of research efforts have been devoted to the development of computational techniques suited to unstructured grids. Unfortunately, in the unstructured case the extension of higher-order one dimensional numerical schemes is by no means an easy task. Some attempts in this direction can be found for example in the work of Barth
On the steady-state accuracy of an implicit Navier-Stokes solver of Lax-Wendroff type
Authors: Lacombe G , Lerat A 
Published: November 2023

Abstract
When solving the Euler and Navier-Stokes equations, a key point is to avoid numerical instability and spurious oscillations without adding too much numerical dissipation. To overcome this difficulty for steady aerodynamic problems, an implicit unsteady method of Lax-Wendroff type has been developed at ENSAM and ONERA (Lerat 1983; Lerat and Sides 1988; Hollanders et al. 1983; Khalfallah et al. 1991; Lacombe and Lerat 1992). The original feature of this method is to produce efficient 2D and 3D flow calculations without artificial viscosity, upwinding or any correction (except in the hypersonic regime where some corrections may be required).
A solution method for the shallow water Quasi-equilibrium equations on the sphere
Authors: Mawson Mark H 
Published: November 2023

Abstract
A fundamental relationship in the atmosphere is the balance between the zeroth order approximation to the wind field and the pressure gradient force. In qualitative terms the wind field blows at right-angles to the pressure gradient. Current models of the atmosphere can be derived from the Navier-Stokes equations by making certain simplifying assumptions appropriate to the scales of motion current computer power allows us to resolve, typically 100km in the horizontal and 1km in the vertical, but do not include this fundamental relationship explicitly. Here we seek to develop a numerical method to solve a set of equations in which this property is enforced, namely the Quasi-equilibrium equations. The equations are obtained by adding this extra constraint into the usual set used in atmospheric modelling. A discussion of the possible benefits of using these equations can be found in (Cullen sl et al. 1987). A procedure for solving the three¬dimensional form of these equations on the sphere was given in (Mawson sl et al. 1990) but the method proved unstable in polar regions. Here we develop a solution procedure for the shallow-water form of the equations which remains stable.
Contamination of laminar boundary layers by artificial dissipation in Navier-Stokes solutions
Authors: Allmaras Steven R 
Published: November 2023

Abstract
Recent grid refinement studies conducted at Boeing for 2-D transonic airfoils revealed poor grid convergence characteristics for laminar boundary layers predicted by Navier-Stokes solvers using central differencing with scalar artificial dissipation (Jou et al. 1992). The studies showed that as the grid is refined, the skin friction in turbulent regions of the airfoil boundary layer becomes grid-converged before it does in laminar regions. These results were disturbing for two reasons. First, the laminar boundary layer regions had adequate resolution based on grid requirements for accurate solutions in boundary layer equation solvers. Second, the same Navier- Stokes solvers are known to perform well in low Reynolds number flows (Re ∼ 0(1000)).
Multigrid convergence acceleration of an upwind Euler algorithm on multiply-embedded meshes
Authors: Onslow S H , Albone C M 
Published: November 2023

Abstract
A multigrid convergence-acceleration scheme is derived and implemented within an upwind Euler method on three-dimensional, multiply-embedded Cartesian meshes. The multigrid scheme is a generalisation to embedded meshes of an earlier two-dimensional scheme due to Albone (1985) and is enhanced through the use of upwind-biased interpolation. The Euler algorithm is based upon the split-coefficient matrix method of Chakravarthy et al (1980) in its first-order accurate form. It is made spatially second-order accurate through the use of a defect-correction scheme which is a generalisation of an earlier scheme due to Albone (1988). The multiply-embedded Cartesian meshes are generated within the Feature Associated Mesh Embedding (FAME) method of Albone and Joyce (1990).
A new approach to finite element error control for time-dependent problems
Authors: Jimack P K 
Published: November 2023

Abstract
The vast majority of time-dependent partial differential equations (p.d.e.’s) cannot be accurately solved using numerical methods which do not permit some form of adaptivity in either in space or time. For most problems in CFD it is clear that both spatial and temporal adaptivity will be essential if we are to be able perform useful numerical simulations for a reasonable computational effort.
Recursion Theory
Authors: Phillips I C C 
Published: November 2023

Abstract
Computability theory might be a better name for recursion theory, since it is the mathematical study of what is computable. However the name is traditional. It arose because recursion theory started as the study of the recursive functions, a mathematical characterization of the functions which are computable (by some program). ‘Recursive’ because, just as in most programming languages, recursion is an important and very powerful mechanism for constructing these functions.
The Role(s) of Logic in Artificial Intelligence
Authors: Israel David J 
Published: November 2023

Abstract
From the very beginnings of research in artificial intelligence (AI), logic has played a central role. Rather, it has played a number of important roles. More recently, AI has begun to present exciting new challenges and open new lines of inquiry for logic. In this essay, we shall briefly sketch some of the roles logic plays in Al; we shall end with some mention of these recent challenges and lines of inquiry. This essay is not meant as a survey. The Handbook as a whole serves that purpose admirably; as, for each area covered, does each of its parts. Nor is it an editorial introduction to this volume or to the Handbook as a whole; there will, of course, be pointers into the Handbook where relevant. There are many aspects of the relation between work in logic and research in Al that we shall not discuss here. Most of these are dealt with extensively in the Handbook, many more than once.
Modal and Temporal Logics
Authors: Stirling Colin 
Published: November 2023

Abstract
In achieving their goals, programs manipulate data and thereby may change th state of the computer. Regarded as a dynamic system, the computer responds to program instructions and in so doing may change state. Activity and change are formalized by the operational semantics of programs and systems. Modal and temporal logics can directly express activity with their paradigm operators such as [a) (box a) when a is an action, and F. Where Φ is a proposition, [a)Φ expresses after every a action Φ holds while FΦ expresses eventually Φ holds. The modal operator [a] highlights the action that may provoke change of state whereas the temporal operator F focuses on the resulting changes. In both cases these operators may express properties of events that happen during a run of a system, events that may be crucial to understanding its overall behaviour. It is no accident that these logics can be used to express such notions. For their models comprehend structures that are encountered in operational semantics of programs and systems. These structures, (labelled) transition systems, are pivotal to this chapter.
Labelled deduction presentation of temporal logics
Authors: Gabbay Dov M , Reynolds Mark A , Finger Marcelo 
Published: November 2023

Abstract
This chapter develops proof theory for temporal logic within the framework of labelled deductive systems [Gabbay, 1996).
To motivate our approach consider a temporal formula a = FA A. PB A. C.
This formula says that we want A to hold in the future (of now), B to hold in the past and C to hold now. It represents the following temporal configuration:
However, by far the simplest approach is to allow names of points in the language and write s : A to mean that we want s F A to hold. Then we can write a theory 6. as
the above ordering relations hold and the respective formulae are satisfied in the appropriate points.
The above language has turned temporal logic into a labelled deductive system (LDS). It has brought some of the semantics into the syntax.
Temporal logic programming
Authors: Gabbay Dov M , Reynolds Mark A , Finger Marcelo 
Published: November 2023

Abstract
We can distinguish two views of logic, the declarative and the imperative. The declarative view is the traditional one, and it manifests itself both syntactically and semantically. Syntactically a logical system is taken as being characterized by its set of theorems. It is not important how these theorems are generated. Two different algorithmic systems generating the same set of theorems are considered as producing the same logic. Semantically a logic is considered as a set of formulae valid in all models.
Combining temporal logic system
Authors: Gabbay Dov M , Reynolds Mark A , Finger Marcelo 
Published: November 2023

Abstract
This chapter is a continuation of the work started in Volume 1, Chapter 14 (which also appeared as [Finger and Gabbay, 1992]) on combining temporal logics. Here, four combination methods are described and studied with respect to the transfer of logical properties from the component one-dimensional temporal logics to the resulting combined two-dimensional temporal logic. Three basic logical properties are analysed, namely soundness, completeness and decidability. Meanwhile Gabbay’s [Gabbay, 1998) book Fibring Logics has appeared.
Extensional semantics
Authors: Gabbay Dov M , Reynolds Mark A , Finger Marcelo 
Published: November 2023

Abstract
In Volume 1, and in some of the preceding chapters, we have seen how temporal logic can be used to reason about program behaviour. In describing a new programming language (or a new way of constructing reactive systems) we can often use temporal logic to specify the desired behaviour of any given program. Thus we are giving temporal semantics to the language. There are two main ways of approaching this task: intensionally or extensionally. Real programs will exhibit extensional actions, i.e. observable changes in values of program variables. However, specifiers may want to describe the behaviour in terms of states and transitions between them. These intensional states are abstract objects in their own right and are not necessarily determined by the values they associate with program variables. An example of this approach is the fair transitions system of [Manna and Pnueli, 1981] and [Pnueli, 1986] which generalizes such approaches as CSP and Petri nets. If such intensional states determine values for the observable variables, which they generally do, then it is straightforward to associate an extensional action--a change in variable values-with each transition between intensional states. However, the converse relationship is more problematic and there is not necessarily exactly one or indeed any one intensional transition associated with each extensional action.
Temporal Active Databases: A Background For Creating And Detecting Time Paradoxes
Authors: Gabbay Dov M , Reynolds Mark A , Finger Marcelo 
Published: November 2023

Abstract
In this chapter we show how to create logical links between information associated to possibly distinct times in history. We can then discuss the effects that changes in history may have upon those temporal links.
For the purpose of establishing these links, we extend a valid-time database with temporal rules, and we provide those rules with an execution semantics; the resulting combined system is called an active valid-time database.