bluuebunny/crossref_metadata_2025_split huggingface dataset:
Richard Strauss (1864–1949)
Authors: Phillips Lois 
Published: November 2023

Abstract
Yes, you know, dear heart, that far from you I am tormented. Love makes the heart sick–for this I give thanks!
Once, reveller of freedom, I raised high a goblet of amethyst, and you blessed the draught–for this I give thanks!
And you drove the evil away, till I was purified as never before, and sank on your breast–for this I give thanks!
Criticism
Authors: Pratt George 
Published: November 2023

Abstract
Most of the exercises in the three previous chapters have been concerned with identifying the presence of particular musical features but not necessarily deciding whether their presence is desirable. The process has been one of observation rather than exercising critical judgement. In the timbral analysis of six bars of Britten’s ‘Narcissus’ (Ex. 6.2a) there proved to be a remarkable number of differences between the four performances. Yet we have studiously avoided declaring that one performance was ‘better’ than the others, or even that the use of a single accent, any one moment of vibrato, a specific gradient of dynamic change, was preferable to the other performers’ interpretations.
The American and the European Models of Society: Not so Different After All
Authors: Martinelli Alberto 
Published: November 2023

Abstract
The aim of this concluding chapter is to discuss the basic questions of this work in light of the findings of the various chapters. More specifically: (a) What kind of society do the United States and the European Union constitute?How similar and how diﬀerent are they?Are they two variants of Western modernity or two wholly distinct models of society (American exceptionalism and European uniqueness)?Are the two societal models converging or diverging?(b) Which are the distinctive features of the American model of society?Is it departing from its core culture and institutions?(c ) Is there a European society in the making?How diverse are the member countries of the EU?What shape is taking the European project of building unity through diver sity?and (d) Which model of society seems more reactive to the challenges of globalization?In the first part of this concluding chapter, I discuss salient similarities and diﬀerences and interpret trends of convergence and divergence in selected aspects of European and American societies, building on the analyses of previous chapters.
Variational formulation of elliptic problems
Authors: Allaire Gregoire 
Published: November 2023

Abstract
In this chapter we are interested in the mathematical analysis of elliptic partial differential equations (PDEs) (see definition 1.5.5). In general, these elliptic equations correspond to stationary physical models, that is, models which are independent of time. We shall see that boundary value problems are well-posed for these elliptic PDEs, that is, they have a solution which is unique and depends continuously on the data. The approach that we shall follow is called the variational approach First we should say that the interest of this approach goes far beyond the framework of elliptic PDEs and even the framework of the ‘pure’ mathematical analysis to which we restrict ourselves.
Eigenvalue problems
Authors: Allaire Gregoire 
Published: November 2023

Abstract
This chapter is dedicated to the spectral theory of partial differential equations, that is, to the study of eigenvalues and eigenfunctions of these equations. The motivation of this study is twofold. On the one hand, this will allow us to study particular solutions, which are oscillations in time (or vibrations), of the evolution problems associated with these equations. On the other hand, we shall deduce a general method for solving these evolution problems which we shall implement in Chapter 8.
Introduction to optimization
Authors: Allaire Gregoire 
Published: November 2023

Abstract
Optimization is a very old subject, which has shown a resurgence since the appearance of computers and whose methods are applied in numerous domains: economics, management, planning, logistics, robotics, optimal design, engineering, signal processing, etc. Optimization is also a vast subject which touches on calculus of variations, operations research (optimization of management or decision processes), and optimal control. We will only mention these subjects since we would need complete notes for each of them if we want to treat them thoroughly.
Optimality conditions and algorithms
Authors: Allaire Gregoire 
Published: November 2023

Abstract
In Chapter 9 we were interested in questions of existence of a minimum in optimization problems. In this chapter, we shall obtain necessary and sometimes sufficient conditions for minimality. The objective is in a certain way much more practical, since these optimality conditions will be more often used to try to calculate a minimum (sometimes even without having shown its existence!). The general idea of optimality conditions is the same as writing that the derivative must be zero, when we calculate the extremum of a function over ℝ.
Methods of operational research
Authors: Allaire Gregoire 
Published: November 2023

Abstract
In this chapter, we present several tools from OR (operational research). In OR, the word ‘operational’ was initially used in its proper sense: OR was born, mainly, from planning problems which arose during the Second World War and shortly after. Thus G. Dantzig, the inventor of the simplex algorithm, was an adviser for the American airforce, and the planning of the Berlin airlift in 1943 is a famous application of linear programming (see [31] for more detail). Since then the domain has been considerably developed and civilized.
Examples in algebra and analysis
Authors: Scarani Valerio , Thew Rachael 
Published: November 2023

Abstract
Algebra is what most people associate with mathematics. In a sense, this is justiﬁed. Mathematics is the study of abstract objects, numerical, logical, or geometrical, that follow a set of several carefully chosen axioms. And basic algebra is about the simplest meaningful thing that can satisfy the above deﬁnition of mathematics. There are only a dozen or so postulates, but that is enough to make the system beautifully symmetric.
Euclidean geometry
Authors: Scarani Valerio , Thew Rachael 
Published: November 2023

Abstract
Euclidean geometry was the ﬁrst branch of mathematics to be treated in anything like the modern fashion (with postulates, deﬁnitions, theorems, and so forth); and even now geometry is conducted in a very logical, tightly knit fashion. There are several basic results which can be used to systematically attack and resolve questions about geometrical objects and ideas. This idea can be taken to extremes with coordinate geometry, which transforms points, lines, triangles, and circles into a quadratic mess of coordinates, crudely converting geometry into algebra.
Lie groups and homogeneous spaces
Authors: Félix Yves , Oprea John , Tanré Daniel 
Published: November 2023

Abstract
Lie groups and homogeneous spaces form an important family of examples of manifolds. We will use them systematically in many different parts of this book, to give an illustration for a specific method or, as well, to show that new viewpoints can be obtained by using algebraic models. Therefore, it is important for us to understand basic ideas and results about Lie groups in order to appreciate the development and application of algebraic models to geometry in general. What we also want to articulate in the next several chapters is that some of the basic ideas of Sullivan’s rational homotopy theory were already present in this particular case.
Manifolds
Authors: Félix Yves , Oprea John , Tanré Daniel 
Published: November 2023

Abstract
A smooth compact manifold has many properties that make it distinct from an ordinary topological space. From the topological viewpoint, the existence of Poincaré duality in (co)homology is crucial to almost any result about the manifold. From the geometric viewpoint, the existence of a Riemannian metric allows the manifold to be studied using analytic techniques. In subsequent chapters, we shall see how these two points of view mix together to yield interesting results in both directions: topology applied to geometry and geometry applied to topology.
Blow-ups and Intersection Products
Authors: Félix Yves , Oprea John , Tanré Daniel 
Published: November 2023

Abstract
As we mentioned in the Preface, models play an important role in understanding various properties of complex and symplectic blow-ups. They also can be used to study features of the Chas–Sullivan loop product, a rather mysterious new topological tool. In this chapter we will consider two types of questions.
Students Of Gene H. Golub
Authors: Chan Raymond H , Greif Chen , O’Leary Dianne P 
Published: November 2023

Abstract
Roger Hockney 1966
Richard Bartels 1968
Michael Jenkins 1969
Lyle Smith 1969
George Ramos 1970
Richard Brent 1971
Michael Saunders 1972
John Palmer 1974
Richard Underwood 1975
Dianne Prost O’Leary 1976
John Lewis 1976
Margaret Wright 1976
Michael Heath 1978
Franklin Luk 1978
Michael Overton 1979
Petter Bjørstad 1980
Daniel Boley 1981
Eric Grosse 1981
Stephen Nash 1982
Mark Kent 1989
Ray Tuminaro 1990
Hongyuan Zha 1993
Oliver Ernst 1994
Xiaowei Zhan 1997
Tong Zhang 1998
Nhat Nguyen 2000
Urmi Holz 2002
Yong Sun 2003
James Lambers 2003
Commentary, By Anne Greenbaum
Authors: Chan Raymond H , Greif Chen , O’Leary Dianne P 
Published: November 2023

Abstract
From the very early days, Gene Golub has been a driving force in the development and analysis of iterative methods for solving large sparse linear systems – problems for which Gaussian elimination is often prohibitive in terms of both storage and computation time. We review five of his seminal papers in this field. Chebyshev semi-iterative methods, successive over-relaxation iterative methods, and second-order Richardson iterative methods, Parts I and II, by Golub and Varga [10] This paper is probably less well-known today than it should be. In it the authors show the remarkable similarity between the Chebyshev semi-iterative method, the successive overrelaxation (SOR) method applied to an expanded matrix equation, and the second-order Richardson iterative method. They conclude that the Chebyshev semi-iterative method is to be preferred over the other two, since its iteration matrix has the smallest spectral norm, while the work per iteration is the same as that for the other methods. They present numerical results with the different methods used to solve elliptic difference equations.
Hermitian And Skew-Hermitian Splitting Methods For Non-Hermitian Positive Definite Linear Systems (With Zhong-Zhi Bai And Michael K. Ng)
Authors: Chan Raymond H , Greif Chen , O’Leary Dianne P 
Published: November 2023

Abstract
It was in 1997 when I first met Gene at Hong Kong on the Workshop on Scientific Computing dedicated to his 65th birthday. Then Gene introduced me to my first two foreign teachers, Iain S. Duff and Andrew J. Wathen, whom I visited for one year from August 1997 to August 1998. The communication and discussion with Gene, Iain, and Andy on solving nonsymmetric linear systems arising from discretization of the convection–diffusion equations by making use of efficient preconditioning techniques changed my research interest and also my academic life, as I then began to study more application-oriented problems and computation-based methods.
Commentary, By ake Bjo Rck
Authors: Chan Raymond H , Greif Chen , O’Leary Dianne P 
Published: November 2023

Abstract
The method of least squares has been the standard procedure for the analysis of data from the beginning of the 1800s. A famous example of its use is when Gauss successfully predicted the orbit of the asteroid Ceres in 1801. In the simplest case The five papers collected here are all related to various least squares problems.
Numerical Methods For Solving Linear Least Squares Problems
Authors: Chan Raymond H , Greif Chen , O’Leary Dianne P 
Published: November 2023

Abstract
A common problem in a Computer Laboratory is that of finding linear least squares solutions. These problems arise in a variety of areas and in a variety of contexts. Linear least squares problems are particularly difficult to solve because they frequently involve large quantities of data, and they are ill-conditioned by their very nature. In this paper, we shall consider stable numerical methods for handling these problems. Our basic tool is a matrix decomposition based on orthogonal House-holder transformations.
Calculating The Singular Values And Pseudo-Inverse Of A Matrix (With W. Kahan)
Authors: Chan Raymond H , Greif Chen , O’Leary Dianne P 
Published: November 2023

Abstract
But in floating-point calculations it may not be so easy to decide whether some number is effectively zero or not. Rather, one will try to determine the rank r by observing whether all rows after the rth are negligible in comparison to the first r, with the expectation that the same will be true of the singular values. Even this criterion is hard to apply, as the following ex-ample.
J. H. Welsch)
Authors: Chan Raymond H , Greif Chen , O’Leary Dianne P 
Published: November 2023

Abstract
Several algorithms are given and compared for computing Gauss quadrature rules. It is shown that given the three term recurrence relation for the orthogonal polynomials generated by the weight function, the quadrature rule may be generated by computing the eigenvalues and first component of the orthornormalized eigenvectors of a symmetric tridiagonal matrix. An algorithm is also presented for computing the three term recurrence relation from the moments of the weight function.
Commentary, By G. W. Stewart
Authors: Chan Raymond H , Greif Chen , O’Leary Dianne P 
Published: November 2023

Abstract
The four papers treated here reflect Gene Golub’s interest in eigenvalue problems. However, they do not exhibit a general theme. Rather the papers are organized around specific problems or topics and have little connection with one another. For this reason we will treat the papers separately and make no attempt to describe interconnections. This paper is a potpouri of problems that can be resolved by considering the eigensystems of certain matrices.
Some Modified Matrix Eigenvalue Problems
Authors: Chan Raymond H , Greif Chen , O’Leary Dianne P 
Published: November 2023

Abstract
We consider the numerical calculation of several matrix eigenvalue problems which require some manipulation before the standard algorithms may be used. This includes finding the stationary values of a quadratic form subject to linear constraints and determining the eigenvalues of a matrix which is modified by a matrix of rank one. We also consider several inverse eigenvalue problems. This includes the problem of determining the coefficients for the Gauss-Radau and Gauss-Lobatto quadrature rules. In addition, we study several eigenvalue problems which arise in least squares.
The Block Lanczos Method For Computing Eigenvalues (With R. Underwood)
Authors: Chan Raymond H , Greif Chen , O’Leary Dianne P 
Published: November 2023

Abstract
In this paper, we describe a Block Lanczo method for computing a few of the least or greatest eigenvalues of a sparse symmetric matrix. A basic result of tactile and Paige describing the reset of convergence of Lanczos’ method will be effctended to the Block Lanczos method. The results of experiments conducted with this methods will be presented and discussed.
Geometrical Aspects Of Plane Autonomous Systems
Authors: Jordan D W , Smith P 
Published: November 2023

Abstract
In this chapter, we discuss several topics which are useful for establishing the structure of the phase diagram of autonomous systems. The ‘index ‘ of an equilibrium point provides supporting information on its nature and complexity, particularly in strongly nonlinear cases, where the linear approximation is zero. Secondly, the phase diagram does not give a complete picture of the solutions; it is not sufficiently specific about the behaviour of paths at infinity beyond the boundaries of any diagram, and we show various projections which include ‘points at infinity ‘ and give the required overall view.
Singular Perturbation Methods
Authors: Jordan D W , Smith P 
Published: November 2023

Abstract
This chapter is concerned with approximating to the solutions of differential equations containing a small parameter ε in what might be called difficult cases where, for one reason or another, a straightforward expansion of the solution in powers of ε is unobtainable or unusable. Often in such cases it is possible to modify the method so that the essential features of such expansions are redeemed. Ideally, we wish to be able to take a few terms of an expansion, and to be able to say that for some small fixed numerical value of ε supplied in a practical problem the truncated series is close to the required solution for the whole range of the independent variable in the differential
Plane autonomous systems and linearization
Authors: Jordan D W , Smith P 
Published: November 2023

Abstract
2.1. A classification table for equilibrium points of the general linear system is given in Section 2.5 (see also Figure 2.10 in NODE). The key parameters are p a d, q ad bc, p 4q. All the systems below have an isolated equilibrium point at the origin. The scales on the axes are the same for each phase diagram but actual scales are unnecessary since the equations are homogeneous in x and y. Directions are determined by continuity from directions of x and y at convenient points in the plane. Alternatively, classification can be decided by finding the eigenvalues of the matrix of The eigenvalues take the imaginary values ±2i, which is to be expected for a centre.
Probability
Authors: Krzanowski Wojtek J 
Published: November 2023

Abstract
Much, if not most, statistical reasoning is built upon a foundation of probability; so if a good understanding of statistical principles is to be gained, then the basic ideas of probability must ﬁrst be understood. This is the reason why many introductory books on statistics begin with a survey of probability theory. However, an equally compelling reason might be the increasing importance that probability in its own right is playing in the world about us, and the fact that some facility with probability calculations or assessments can be invaluable in our day-to-day lives. Most people are perfectly comfortable with simple probability statements, such as that there is an even chance of obtaining a head as opposed to a tail on the spin of a coin, but once familiar physical frameworks are abandoned then the ground quickly becomes shakier.
Population Models
Authors: Krzanowski Wojtek J 
Published: November 2023

Abstract
We have seen that the population is generally the focus of any statistical investigation. It is the collection of all possible individuals that we think are relevant to our study, and the purpose of most statistical investigations is to obtain information about some specific measurement of interest in this population. Usually, the population is too large for us to be able to observe every individual in it, so we will hardly ever be in a position to know all we can about this measurement of interest.
Statistical Inference—the Frequentist Approach
Authors: Krzanowski Wojtek J 
Published: November 2023

Abstract
So far we have looked mainly at the ideas of probability, with their extension to the concept of a population of individuals having a probability distribution of some measurements of interest. However, we have also gone on to consider probability models for populations, the collection and summarisation of sample data from these populations, and the use of the sample data to guide us when formulating probability models. All these topics form the necessary base for one of the central topics in statistics, namely the use of sample data in making statements about populations.
The historiography and history of mathematics in the Third Reich
Authors: Siegmund-Schultze Reinhard 
Published: November 2023

Abstract
After Hitler became chancellor of the German Reich on 30 January 1933 and the Nazi regime consolidated its power in March 1933, serious effects for science and mathematics became visible. Mathematics was, by and large, less important to the regime than biology, chemistry, the technical sciences, or history. It could not be used for propaganda like biology and historiography and it did not have immediate importance for armament and war production (with the possible exceptions of aerodynamics and ballistics).
Assessing the Effect of Genetic Mutation: A Bayesian Framework for Determining Population History from DNA Sequence Data
Authors: Brooks S P , Manolopoulou I , Emerson B C 
Published: November 2023

Abstract
In cases where genetic sequence data are collected together with associated physical traits it is natural to want to link patterns observed in the trait values to the underlying genealogy of the individuals. If the traits correspond to specific phenotypes, we may wish to associate specific mutations with changes observed in phenotype distributions, whereas if the traits concern spatial information, we may use the genealogy to look at population movement over time.In this paper we discuss the standard approach to analyses of this sort and propose a new framework which overcomes a number of shortcomings in the standard approach. In particular, we allow for uncertainty associated with the underlying genealogy to fully propagate through the model to directly interact with the inferences of primary interest, namely the effects of genetic mutations on phenotype and/or the dispersal patterns of populations over time.
A Gamma Model for DNA Mixture Analyses*
Authors: Cowell Robert G , Lauritzen Steffen L , Mortera Julia 
Published: November 2023

Abstract
We present a new methodology for analysing forensic identification problems involving DNA mixture traces where several individuals may have contributed to the trace. The model used for identification and separation of DNA mixtures is based on a gamma distribution for peak area values. In this paper we illustrate the gamma model and apply it on a real example from forensic casework.
Identification of Thyroid Gland Activity in Radiotherapy*
Authors: Jirsa Ladislav , Quinn Anthony , Varga Ferdinand 
Published: November 2023

Abstract
The Bayesian identification of a linear regression model for time dependence of thyroid gland activity in 131I radiotherapy is presented. Prior knowledge is elicited via hard parameter constraints and via the merging of information from an archive of patient records. This prior regularization is shown to be crucial in the reported context, where data typically comprise only 2-3 highnoise measurements. The posterior distribution is simulated via a Langevin diffusion algorithm, whose optimization for the thyroid activity application is explained. Improved patient-specific predictions of thyroid activity are reported. The posterior inference of the total patient radiation dose is presented, allowing the uncertainty of the dose to be quantified in a consistent manner.
Logistic Regression Modelling of Proteomic Mass Spectra in a Case-Control Study on Diagnosis for Colon Cancer*
Authors: Mertens Bart J A 
Published: November 2023

Abstract
We adapt logistic regression modelling for the evaluation of mass spectroscopic data in proteomic case-control studies. Instead of a direct attempt to model the observed case-control data as regression on peaks, we parameterize the predictor as a linear combination of Gaussian basis functions along the mass/charge axis. The location of these basis functions is treated as a random variable and must be estimated from the data. A fully Bayesian implementation is pursued, which allows the number of functional components within the regression parameter vector to be specified as a random variable. Calculations are implemented through birth–death process modelling.