The Curves The Point of View of Max Noether Probably the oldest references to the problem of resolution of singularities are found in Max Noether's works on plane curves [cf. [148], [149]]. And probably the origin of the problem was to have a formula to compute the genus of a plane curve. The genus is the most useful birational invariant of a curve in classical projective geometry. It was long known that, for a plane curve of degree n having l m ordinary singular points with respective multiplicities ri, i E {1, . . . , m}, the genus p of the curve is given by the formula = (n - l)(n - 2) _ ~ "r. (r. _ 1) P 2 2 L. . ,. •• . Of course, the problem now arises: how to compute the genus of a plane curve having some non-ordinary singularities. This leads to the natural question: can we birationally transform any (singular) plane curve into another one having only ordinary singularities? The answer is positive. Let us give a flavor (without proofs) 2 on how Noether did it • To solve the problem, it is enough to consider a special kind of Cremona trans formations, namely quadratic transformations of the projective plane. Let ~ be a linear system of conics with three non-collinear base points r = {Ao, AI, A }, 2 and take a projective frame of the type {Ao, AI, A ; U}.
The Curves The Point of View of Max Noether Probably the oldest references to the problem of resolution of singularities are found in Max Noether's works on plane curves [cf. [148], [149]]. And probably the origin of the problem was to have a formula to compute the genus of a plane curve. The genus is the most useful birational invariant of a curve in classical projective geometry. It was long known that, for a plane curve of degree n having l m ordinary singular points with respective multiplicities ri, i E {1, . . . , m}, the genus p of the curve is given by the formula = (n - l)(n - 2) _ ~ "r. (r. _ 1) P 2 2 L. . ,. •• . Of course, the problem now arises: how to compute the genus of a plane curve having some non-ordinary singularities. This leads to the natural question: can we birationally transform any (singular) plane curve into another one having only ordinary singularities? The answer is positive. Let us give a flavor (without proofs) 2 on how Noether did it • To solve the problem, it is enough to consider a special kind of Cremona trans formations, namely quadratic transformations of the projective plane. Let ~ be a linear system of conics with three non-collinear base points r = {Ao, AI, A }, 2 and take a projective frame of the type {Ao, AI, A ; U}.
These stories, along with others, are randomly scattered among the pages of Troubled Water & other irregularities, The Devil in French & other musings, When it was the War & other conflicts, Second Coming & other upheavals, and The View from Below & other peerings.
Using forty-five interviews with former members and sympathisers, this book traces the development of the Women's section of the Franco government from its roots in the Spanish fascist party to its role in the dictatorship up to 1959. The study reveals that despite its anti-feminist agenda, the section was, in some areas, a catalyst for women's emancipation in post-Franco Spain.
These stories, along with others, are randomly scattered among the pages of 'Troubled Water ... & other irregularities', 'The Devil in French ... & other musings', 'When it was the War ... & other conflicts', 'Second Coming ... & other upheavals', and 'The View from Below ... & other peerings'.
Want to teach English in Mexico? Don't know where to start? Does Costa Rica sound good? Are there jobs there? Want to drive to Honduras? Is it safe? This 'Handbook' will answer these questions and many more. It is a fact-filled guide for finding teaching jobs in Mexico and Central America. It describes the job market and gives concrete information about where and how to look. There's also a mini-course on teaching English to help you in those all-important job interviews. And once you've found that job, the 'Handbook' provides practical teaching suggestions to help you survive. But it doesn't stop there. There are four personal commentaries by people who have done just what you want to do. And throughout the 'Handbook,' the author draws on her experiences from more than ten years of teaching (and driving) south of the border to give you that edge.
The already broad range of applications of ring theory has been enhanced in the eighties by the increasing interest in algebraic structures of considerable complexity, the so-called class of quantum groups. One of the fundamental properties of quantum groups is that they are modelled by associative coordinate rings possessing a canonical basis, which allows for the use of algorithmic structures based on Groebner bases to study them. This book develops these methods in a self-contained way, concentrating on an in-depth study of the notion of a vast class of non-commutative rings (encompassing most quantum groups), the so-called Poincaré-Birkhoff-Witt rings. We include algorithms which treat essential aspects like ideals and (bi)modules, the calculation of homological dimension and of the Gelfand-Kirillov dimension, the Hilbert-Samuel polynomial, primality tests for prime ideals, etc.
The "European Yearbook" promotes the scientific study of European organisations and the Organisation for Economic Co-operation and Development. Each volume contains a detailed survey of the history, structure and yearly activities of each organisation and an up-to-date chart providing a clear overview of the member states of each organisation. In addition, a number of articles on topics of general interest are included in each volume. A general index by subject and name, and a cumulative index of all the articles which have appeared in the "Yearbook," are included in every volume and provide direct access to the "Yearbook's" subject matter. Each volume contains a comprehensive bibliography covering the year's relevant publications. This is an indispensable work of reference for anyone dealing with the European institutions.
This book aims to provide scientists with information about a series of techniques that can be used with a view to facilitating the transformation of the sample to an appropriate state for subsequent detection or quantitation of its components of interest. The techniques dealt with range from the very simple ones (e.g. freeze-drying) to other more complex ones (e.g. glow discharge and laser-induced breakdown sampling). This is the first compilation ever on the subjects of acceleration of solid sample pretreatment; automation of solid sample pretreatment; and integration of solid sample pretreatment and detection. Readers will find here the information required to compare and select the best choice for each sample treatment need and ways to facilitate or automate the most complex and time-consuming step of the analytical process when solid samples are involved.
What is text mining, and how can it be used? What relevance do these methods have to everyday work in information science and the digital humanities? How does one develop competences in text mining? Working with Text provides a series of cross-disciplinary perspectives on text mining and its applications. As text mining raises legal and ethical issues, the legal background of text mining and the responsibilities of the engineer are discussed in this book. Chapters provide an introduction to the use of the popular GATE text mining package with data drawn from social media, the use of text mining to support semantic search, the development of an authority system to support content tagging, and recent techniques in automatic language evaluation. Focused studies describe text mining on historical texts, automated indexing using constrained vocabularies, and the use of natural language processing to explore the climate science literature. Interviews are included that offer a glimpse into the real-life experience of working within commercial and academic text mining. Introduces text analysis and text mining tools Provides a comprehensive overview of costs and benefits Introduces the topic, making it accessible to a general audience in a variety of fields, including examples from biology, chemistry, sociology, and criminology
The porphyrins are a class of naturally-occurring macrocycles and are ubiquitous in our world. As such, they have been called the Pigments of Life. This auspicious designation reflects their importance in numerous biological functions. Indeed, life as we understand it relies on the full range of biological processes that are either performed by or catalyzed by porphyrin-containing proteins. Chlorophyll-containing photosynthetic reaction centers in plants, for instance, convert light energy into chemical energy while producing oxygen along the way. It is this oxygen, evolved from photosynthesis, that is transported, stored, and reduced by heme-containing proteins in many organisms, including mammals. Not surprisingly, therefore, these molecules remain of fundamental interest to chemists and biochemists. Indeed, they continue to be intensely investigated by researchers world-wide. Inspired by the importance of the porphyrins, a new research direction has emerged in recent years that is devoted to the preparation and study of non-porphyrin polypyrrole macrocycles. Here, the principal objectives have been to generate completely synthetic systems that bear some structural resemblance to naturally-occurring porphyrin derivatives while being quite different in their specific chemical makeup. Within this context, three different research directions have evolved, namely those involving the syntheses of contracted, isomeric, and expanded porphyrins, respectively. It is the chemistry of these systems that is the subject of this book. Because of the newness of the field, the emphasis of this book will be on synthesis and characterization (all work on porphyrin isomers and much of that associated with expanded porphyrins has only appeared in the last 10 years). One chapter on applications has, however, been included. Also, in the context of the preparative portions of the text, some efforts have been made to explain why various porphyrin analogue targets are of interest.
But more important, he introduced the practice of writing down coordinates of latitude and longitude for every feature drawn on a world map, so that someone else possessing only the text of the Geography could reproduce Ptolemy's map at any time, in whole or in part, at any scale." "Historians of science, classicists, and anyone who enjoys beautiful maps or map making will find this work an indispensable addition to their library."--BOOK JACKET.
Biografia homenaje a Pedro casaldàliga, testigo del evangelio de Jesús, a quien conocí siendo joven y cuya esleta me ha acompañado y acompaña a lo largo de mi vida
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