bluuebunny/crossref_metadata_2025_split huggingface dataset:
The State of the Art in Numerical Analysis
Authors: Duff I S , Watson G A 
Published: November 2023

Abstract
The 1996 conference on the State of the Art in Numerical Analysis was organized to provide the numerical analysis community, and users of numerical methods, with a forum where an account of the important recent developments in the subject could be presented in a coherent and concentrated way in a manner accessible to the non-specialist in the sub-area. This volume extends to a much wider audience the opportunity given to those who attended the meeting. It contains full versions of all the papers presented, with one exception on Neural Nets. In addition to recent developments in mainstream topics, linear algebra, ordinary differential equations, approximation and optimization, it contains papers devoted to two important application areas, numerical tomography and image processing. Compare with the corresponding 1986 volume, some topics show a continuous and natural development, while others show significant departure from conventional trends. A recurring theme is the solution of large problems and exploitation of structure. Underlying many of the developments is the fact that increasingly complicated and sophisticated problems are now amenable to an increasingly powerful range of numerical techniques. This is greatly helped by the advent of excellent computer languages, like MATLAB, and state of the art Fortran software such as LAPACK, so that the fundamental building blocks for much of the armoury of a numerical analysis are now readily accessible.
Interior Point Methods for Linear and Nonlinear Programming
Authors: Shanno David F , Simantiraki Evangelia M 
Published: November 2023

Abstract
The paper first discusses recent advances in interior point methods for linear programming, including infeasibility detecting codes, target following, and better handling of dense columns. Computational results on the Netlib test suite using CPLEX 4.0 will be given. The paper then discusses two alternative methods for solving nonlinear programming problems using interior point methods, both designed to overcome the well-known difficulties with the classical barrier method. The first is a penalty-barrier method based on Polyak’s modified barrier method, the second a method closely allied with sequential quadratic programming which handles nonlinear constraints via the classical barrier method applied to slack variables. Comparative numerical results will be given.
Helix structure and molecular recognition by B-DNA
Authors: Dickerson Richard E 
Published: November 2023

Abstract
One day in 1980, Francis Crick arrived in Pasadena from the Salk Institute to visit James Olds of the Biology Division at Caltech. While on campus, he came by my laboratory to see graduate student Horace Drew’s new DNA dodecamer structure, CGC-GAATTCGCG, the first single-crystal X-ray structure analysis of B-DNA. By chance the only people in the laboratory that afternoon were Horace, my long-time scientific colleague Mary Kopka, and myself. The four of us huddled around contoured plexiglas sheets stacked atop a light box in a darkened room, in that pre-computer graphics age.
RNA structure in solution
Authors: Nowakowski Jacek , Tinoco Ignacio 
Published: November 2023

Abstract
Knowledge of the structures of the molecules involved in a biological reaction is necessary for deducing a mechanism for the reaction. Structures and mechanisms can lead to rational design of drugs, and effective methods for controlling biological reactions. This chapter summarizes what has been learned about the structures of RNA molecules by solution methods, mainly nuclear magnetic resonance spectroscopy. Specific structures will be described with emphasis on the generalizations that can be deduced from the structures. Coordinates for most of the structures described are available in the Protein Data Bank and the Nucleic Acid Data Base (see Chapter 3). For a thorough discussion of nucleic acid structure with an exhaustive bibliography of structural information on nucleic acids see Principles of Nucleic Acid Structure (1984) by Wolfram Saenger.
Hypercomplex Manifolds and the Space of Framings
Authors: Hitchin Nigel 
Published: November 2023

Abstract
In general relativity, one commonly formulates Einstein’s equations as evolution equations for a metric and second fundamental form on a hypersurface. A rather different approach was adopted in the paper of Ashtekar, Jacobson and Smolin (1988), which in particular reduced the equations for a ‘positive definite self-dual spacetime (a 4-dimensional hyperkahler manifold in other language) to Nahm’s equations for a triple of volume-preserving vector fields on a 3-manifold M. The initial aim of this paper is to relax the volume-preserving condition and to place this result in a general framework. Here we regard the triple of vector fields as a trivialization of the tangent bundle of M—a framing.
Penrose Tilings and Quasicrystals Revisited
Authors: Steinhardt Paul J 
Published: November 2023

Abstract
Roger Penrose’s ingenious invention of five-fold symmetric, non-periodic tilings has inspired the proposal of a new form of solid, known as a quasicrystal. Quasicrystals are solids with quasiperiodic atomic structures and symmetries forbidden to ordinary, periodic crystals, e.g., three-dimensional icosahedral symmetry. Here we discuss some new properties of Penrose tilings uncovered in recent months which suggest a new, simple picture of the structure of quasicrystals and shed new light on why they form.
The Twistor Diagram Programme
Authors: Hodges Andrew P 
Published: November 2023

Abstract
Recent advances in twistor diagram theory vindicate the ideas embodied in Roger Penrose’s original proposals. The novel treatment of gauge fields is given particular attention. Twistor diagrams were first written down by Roger Penrose, as an early part of the twistor programme for reformulating fundamental physics. Twistor diagrams define integrals which yield scattering amplitudes for elementary particles in flat space, and thus are roughly analogous to Feynman diagrams in standard quantum field theory (QFT). It was an essential ingredient in Penrose’s programme that the divergence problems which plague QFT should be resolved in the new setting offered by twistor geometry, that twistor diagrams should be manifestly finite; and that they should supersede, rather than merely reformulate, the predictive calculus supplied by Feynman diagrams.
Spin Networks and Topology
Authors: Kauffman Louis H 
Published: November 2023

Abstract
This paper discusses Penrose spin networks in relation to physics and low dimensional topology. This paper is an introduction to the relationship between Penrose spin networks and structures in physics and low dimensional topology. The paper is organised as follows. Section 2 discusses the theme of networks and discretization. Section 3 introduces the bracket model for the Jones polynomial invariant of knots and links. In Section 4 we show how the bracket state model is a natural generalization of the original Penrose spin networks, and how this model is related to the quantum group corresponding to SL(2,C).
An Unorthodox View of GR via Characteristic Surfaces
Authors: Frittelli Simonetta , Newman, E T , Kozameh Carlos 
Published: November 2023

Abstract
We would like to describe a novel and unorthodox approach to GR that is based on the existence of special families of 3-surfaces in a four manifold. (The details, with proofs, have been given elsewhere (Frittelli et al. 1995a, 1995b, 1995c, 1995d).) However, before saying what this novel approach is, we discuss the background and some issues of motivation. We (with many others) feel that finding the relationship between GR and quantum theory, QT, is (one of) the most fundamental problems of theoretical physics and perhaps one of the most difficult.
Abstract /Virtual/Reality/Complexity
Authors: Sparling George 
Published: November 2023

Abstract
This work is dedicated to Roger Penrose, mentor and friend. I thank the Conference Committee for inviting me; I especially thank Hermann Bondi, who introduced me (then a schoolboy) to relativity and Christopher Isham who gave twistor theory crucial early support. The twistor diagram of the title pays tribute to the many workers who have advanced the theory. The diagram has only single lines emerging from it indicating that it is an interaction diagram, part of a larger whole, as yet undiscovered. The dashed lines represent essential poles using infinity twistors: this reflects the idea that twistor theory should be tied to an understanding of gravity.
Penrose Transform for Flag Domains
Authors: Gindikin Simon 
Published: November 2023

Abstract
It is a great pleasure for me to talk at this conference in Roger’s honor on the Penrose transform with which I have been friends for the last 18 years of my mathematical life. I chose to talk about a generalized Penrose transform. There are two sides of the Penrose transform which are at the focus of possible generalizations: cohomological representations of solutions of a class of differential equations and representations of higher 8-cohomology in a holomorphic language. We need to understand on which equations and complex manifolds it is possible to generalize Penrose’s constructions. It is not necessary to connect them with group actions, but it is reasonable to start experimental work with homogeneous manifolds, and flag domains (homogeneous domains on flag manifolds) are an appropriate class for such a consideration. Some results of W. Schmid on realizations of the discrete series of representations are already fragments of the theory. We will not review here known results on the Penrose transform on some flag domains. I prefer to describe what the final theory is supposed to look like and to formulate a chain of conjectures without technical details. In this theory the central role must be played by explicit formulas for some intertwining operators and that is why I will start off the introduction with a short review of formulas for the usual Penrose transform.
Preliminaries
Authors: Priestley H A 
Published: November 2023

Abstract
We present below the fundamental notions which we use in a number of contexts, establish notation, and draw attention to features of particular importance for us. The contents of this chapter may be treated as a list of prerequisites for the remainder of the book. The early chapters draw only on those parts of this list which might be expected to be known by a reader familiar with elementary differential calculus but who has only limited experience of ε-δ analysis.
Approximations
Authors: Priestley H A 
Published: November 2023

Abstract
Suppose you are given a particular continuous function f on a compact interval [a, b] and want to work out ∫b af but can’t find an antiderivative for f. Your calculator will, in many cases, present you with an answer, to an impressive number of decimal places. Methods for estimating integrals are obviously programmed into calculators—how is this done and how accurate are the results? Numerical integration is a specialized topic, and we do no more here than indicate some rudimentary techniques and show how our theory gives error estimates.
Fourier transforms
Authors: Priestley H A 
Published: November 2023

Abstract
This chapter introduces the theory of the Fourier transform, parallel to the treatment of Fourier series in Chapters 29 and 30. We deal very briefly with the ‘pointwise’ theory and its applications. This rests heavily on methods from complex analysis, and is discussed, along with the Laplace transform, in Chapter 9 of [13]. It is possible to regard the Fourier transform as a limiting case of a Fourier series, by scaling to smaller and smaller intervals. A discussion of this process can be found in [4] and [11]. We do not take this route but draw heavily on the parallels between Fourier series and transforms for motivation.
Fast Parallel Algorithms for Graph Matching Problems
Authors: Karpinski Marek , Rytter Wojciech 
Published: November 2023

Abstract
The matching problem is one of the central problems in graph theory as well as in the theory of algorithms and their applications. This book will provide the reader with a comprehensive and straightforward introduction to the basic methods of designing efficient parallel algorithms for graph matching problems. The text is written for students at the beginning graduate level. The exposition is mostly self-contained and example-driven. Prerequisites have been kept to a minimum by including relevant background material. The book contains full details of several new techniques and should also be of interest to research workers in computer science, operations research, discrete mathematics, and electrical engineering. The main theoretical tools are combined into three independent chapters, devoted to combinatorial tools, probabilistic tools, and algebraic tools. One of the main goals of the book is to bring together these three approaches and highlight how their combination works in the development of efficient parallel algorithms. The reader will be provided with a simple and transparent presentation of a variety of interesting algorithms, including many examples and illustrations. The combination of different approaches makes the matching problem and its applications an attractive and fascinating subject. It is hoped that the book represents a meeting point of interesting algorithmic techniques and opens up new algebraic and geometric areas. Marek Karpinski is Chair Professor of Computer Science at the University of Bonn. Wojciech Rytter is Professor of Computer Science at the University of Warsaw and at the University of Liverpool.
Application of matrix methods
Authors: Boos Johann , Cass Peter 
Published: November 2023

Abstract
In Section 1.1 and also in the Introduction of the book we remarked that, in attempting to formulate a notion of convergence which is application oriented, summability methods have been (and will further be) developed. On the other hand, by the investigation of these summability methods and the concomitant development of summability, the application of summability methods has been made possible in various fields of mathematics.
X-ray analysis of precipitation-related crystals with dislocation substructure
Authors: Barabash R I 
Published: November 2023

Abstract
In this chapter, peculiarities of X-ray analysis of precipitation-related crystals having certain dislocation substructure will be considered. The described procedure is applied to the investigation of Ni-based superalloys hardened by particles of a Ni3Al-type phase. Their growth conditions and subsequent treatment result in the formation of dislocation ensembles in them.
Accounting for size and microstrain in whole-powder pattern fitting
Authors: Bail A Le 
Published: November 2023

Abstract
22.1 Introduction
The main two objectives for doing a whole-powder pattern fitting (WPPF) are: (i) obtaining an estimation of all the structure factor amplitudes for an ab initio structure determination and (ii) refining the mean tridimensional structure by the Rietveld method (1967, 1969). In the state of the art, any individual peak showing good statistics can be fitted perfectly (RP &lt; 2%). As a consequence, the whole pattern could be fitted perfectly too, if no constraint is applied. However, such an unconstrained fit would be meaningless in the case of a large degree of overlap. Individually fitting hundreds or thousands of (more or less) overlapping reflections is excluded; therefore, WPPF is accomplished ‘automatically by algorithms using constraints supposed to apply to all reflections. For purpose (i), these constraints may force some parameters to respect a cell, a space group, a selected profile shape, a predefined width angular variation law, the h=f*g (experimental, sample and instrumental profiles, respectively) convolution with g fixed (...) or all simultaneously. For purpose (ii), the structure constraint is added, making the reflection intensities no longer free parameters; however, the structure need not be complete, but a partial model sufficient to start least-squares refinements is required (for an overview on powder pattern fitting methods, see Grzeta and Toraya, 1994; Toraya, 1994). Although WPPF without constraint is possible for simple cases, this chapter considers only WPPF with at least the cell constraint.
Basic Geometric Measure Theory
Authors: Ambrosio Luigi , Fusco Nicola , Pallara Diego 
Published: November 2023

Abstract
In the first chapter we developed a rather abstract theory based only on the structures of measure space and metric space: in fact no gain would be obtained by restricting to particular cases like euclidean spaces. In the present chapter, instead, we leave the general setting and deal with measures in euclidean spaces, heavily exploiting the interplay between the above-mentioned structures and the vector space structure of RN.
Introduction
Authors: Braides Andrea , Defranceschi Anneliese 
Published: November 2023

Abstract
The object of homogenization theory is the description of the macroscopic properties of media with fine microstructure, covering a wide range of applications that run from the study of the properties of composites to optimal design. The structures under consideration may model composites, fiber materials, stratified or porous media, finely damaged materials, compliance problems, materials with many holes or cracks. In mathematical terms, this study can be translated into the asymptotic analysis of f oscillating ordinary or partial differential equations and systems, or integral functionals, depending on a small-scale parameter e, as this parameter tends to 0.
The structure of quasiconvex functions
Authors: Braides Andrea , Defranceschi Anneliese 
Published: November 2023

Abstract
From Remark 5.17 we deduce that quasiconvexity is a sufficient condition for the lower semicontinuity of integral functionals with respect to the weak* convergence in W hence quasiconvex functions are rank-1-convex by Corollary 4.12.
Direct methods. An integral representation result
Authors: Braides Andrea , Defranceschi Anneliese 
Published: November 2023

Abstract
The direct methods of ┌-convergence for integral functionals consist in proving general abstract compactness results that assure the existence of ┌-converging sequences, and then in recovering enough information on the structure of the ┌-limits as to obtain a representation in a suitable form. For this purpose, it is useful to consider at the same time the dependence of the ┌-limits as set functions and as integrals.
Almost-periodic homogenization
Authors: Braides Andrea , Defranceschi Anneliese 
Published: November 2023

Abstract
In this chapter we generalize the Homogenization Theorem to uniformly almost¬ periodic functions, and to integrands of the form f(x,u,A). Note that in this case, even if f is I-periodic in the first two variables, the function x f(x, Ax,A) is in general non-periodic; this remark suggests that almost-periodic methods are particularly suited also for some apparently periodic situations.
Cathepsin K (EC 3.4.22.38)
Authors: Kirschke Heidrun , Barrett Alan J , Rawlings Neil D 
Published: November 2023

Abstract
peptidase named OC-2. In the same year, human equivalents of the rabbit gene were mentioned independently in two abstracts by Drake et al. [1787] and Li et al. [1797] and the sequence was published in 1995 (in order of date of submission) by Li et al. [ 1798], lnaoka et al. [1792], Shi et al. [1811] and Br6mme and Okamoto [1780]. The cDNA of cathepsin K from mouse [1642, 1806] and chicken [1520] have also been cloned. Names such as cathepsin X [1798], cathepsin K [1792], cathepsin O [1811, 1760, 1643] and cathepsin 02 [1780] were given to the novel human osteoclast cysteine peptidase - but the name eventually recommended by the nomenclature committee of the I UBJ\IB was cathepsin K.
Unlike cathepsins B, Land H, cathepsin K shows a restricted tissue distribution, being found pre dominantly in osteoclasts [1201, 1288, 1645, 1780, 1792, 1798].
Structures and evolution
Authors: Kirschke Heidrun , Barrett Alan J , Rawlings Neil D 
Published: November 2023

Abstract
The lysosomal cysteine peptidases considered here belong to the papain family of peptidases, termed family Cl by Rawlings and Barrett [1187]. (At the time of writing, it is just emerging that legumain, an endopeptidase specific for the hydrolysis of asparaginyl bonds, is probably an additional lysosomal cysteine proteinase, of a separate family, C13 [1783]. It is too early to say much more about this, at this time.) Among the amino acid sequences known for the papain family, numbering more than 250, are those of enzymes from bacteria, fungi, protozoa and plants, as well as animals. Most of the proteins in the family are endopeptidases, but there are also some exopeptidases and proteins without known catalytic activity. The available amino acid sequences of vertebrate lysosomal cysteine peptidases (Table 19) provide a basis for dividing them into three groups, as is illustrated by a dendrogram for the human enzymes in Fig. 14 (below). One group contains enzymes that are closest in structure to papain: cathepsins H, K, L and S, whereas cathepsin B and dipeptidyl peptidase I represent separate groups, remote from the cathepsin L set and from each other.
Representation theory of symmetric algebras
Authors: Geck Meinolf , Pfeiffer Golz 
Published: November 2023

Abstract
In the previous chapters, we have studied the irreducible characters of finite Coxeter groups. For this purpose, we have only required some basic knowledge about the character theory of finite groups, as can be found, for example, in [Isaacs 1976]. In later chapters, we will want to study in a similar way the irreducible representations and characters of Iwahori-Hecke algebras. For example, we would like to have analogous versions of the usual orthogonality relations for the irreducible characters of a finite group. The purpose of this chapter is to lay the foundations for such a more general theory.
Computing character values and generic degrees
Authors: Geck Meinolf , Pfeiffer Golz 
Published: November 2023

Abstract
In this chapter, we describe methods for computing Schur elements and character tables of generic Iwahori-Hecke algebras of any type. These methods are partly presented in the form of algorithms which have been implemented in CHEVIE. As an application, we obtain the Schur elements and character tables for the exceptional types H3, H4, F4, E6, E7 and E8. Together with the results in Section 8.3 (type l2(m)) and Chapter 10 (classical types), this completes the determination of Schur elements and character tables for all types.
MMP sequences
Authors: Woessner J Frederick , Nagase Hideaki 
Published: November 2023

Abstract
There are 96 amino acid alignments presented at the end of the book. These arc linked to a more complete description of each sequence presented in Table 3. For each item in Table 3 there is a corresponding number giving the line number in the alignment table. The two tables are in the same order (with a few additional inserts in Table 3) so that matching the items is simplified. In this first section, the major features of the alignments domains, invariant amino acids, etc. will be pointed out. The roles of these various regions and domains will then be discussed in detail below in the section on domains and inserts.
The Finite Element Method
Authors: Babuška Ivo , Strouboulis Theofanis 
Published: November 2023

Abstract
In this chapter, we present the finite element method for our model problem. We first describe the Galerkin method which constructs approximate solutions uS(n) , by satisfying the variational problem on finite-dimensional spaces S(n) ⊆ 𝓊 namely: