Resolution of Curve and Surface Singularities in Characteristic Zero

Resolution of Curve and Surface Singularities in Characteristic Zero
Author: K. Kiyek
Publisher: Springer Science & Business Media
Total Pages: 506
Release: 2012-09-11
Genre: Mathematics
ISBN: 1402020295

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}.

Kumba Africa

Kumba Africa
Author: Sampson Ejike Odum
Publisher: iUniverse
Total Pages: 123
Release: 2020-11-03
Genre: Fiction
ISBN: 1663205043

‘KUMBA AFRICA’, is a compilation of African Short Stories written as fiction by Sampson Ejike Odum, nostalgically taking our memory back several thousands of years ago in Africa, reminding us about our past heritage. It digs deep into the traditional life style of the Africans of old, their beliefs, their leadership, their courage, their culture, their wars, their defeat and their victories long before the emergence of the white man on the soil of Africa. As a talented writer of rich resource and superior creativity, armed with in-depth knowledge of different cultures and traditions in Africa, the Author throws light on the rich cultural heritage of the people of Africa when civilization was yet unknown to the people. The book reminds the readers that the Africans of old kept their pride and still enjoyed their own lives. They celebrated victories when wars were won, enjoyed their New yam festivals and villages engaged themselves in seasonal wrestling contest etc; Early morning during harmattan season, they gathered firewood and made fire inside their small huts to hit up their bodies from the chilling cold of the harmattan. That was the Africa of old we will always remember. In Africa today, the story have changed. The people now enjoy civilized cultures made possible by the influence of the white man through his scientific and technological process. Yet there are some uncivilized places in Africa whose people haven’t tested or felt the impact of civilization. These people still maintain their ancient traditions and culture. In everything, we believe that days when people paraded barefooted in Africa to the swarmp to tap palm wine and fetch firewood from there farms are almost fading away. The huts are now gradually been replaced with houses built of blocks and beautiful roofs. Thanks to modern civilization. Donkeys and camels are no longer used for carrying heavy loads for merchants. They are now been replaced by heavy trucks and lorries. African traditional methods of healing are now been substituted by hospitals. In all these, I will always love and remember Africa, the home of my birth and must respect her cultures and traditions as an AFRICAN AUTHOR.

Yvain

Yvain
Author: Chretien de Troyes
Publisher: Yale University Press
Total Pages: 242
Release: 1987-09-10
Genre: Poetry
ISBN: 0300187580

The twelfth-century French poet Chrétien de Troyes is a major figure in European literature. His courtly romances fathered the Arthurian tradition and influenced countless other poets in England as well as on the continent. Yet because of the difficulty of capturing his swift-moving style in translation, English-speaking audiences are largely unfamiliar with the pleasures of reading his poems. Now, for the first time, an experienced translator of medieval verse who is himself a poet provides a translation of Chrétien’s major poem, Yvain, in verse that fully and satisfyingly captures the movement, the sense, and the spirit of the Old French original. Yvain is a courtly romance with a moral tenor; it is ironic and sometimes bawdy; the poetry is crisp and vivid. In addition, the psychological and the socio-historical perceptions of the poem are of profound literary and historical importance, for it evokes the emotions and the values of a flourishing, vibrant medieval past.

Matrix Algebra for Applied Economics

Matrix Algebra for Applied Economics
Author: Shayle R. Searle
Publisher: Wiley-Interscience
Total Pages: 0
Release: 2001-09-13
Genre: Mathematics
ISBN: 9780471322078

Coverage of matrix algebra for economists and students ofeconomics Matrix Algebra for Applied Economics explains the important tool ofmatrix algebra for students of economics and practicing economists.It includes examples that demonstrate the foundation operations ofmatrix algebra and illustrations of using the algebra for a varietyof economic problems. The authors present the scope and basic definitions of matrices,their arithmetic and simple operations, and describe specialmatrices and their properties, including the analog of division.They provide in-depth coverage of necessary theory and deal withconcepts and operations for using matrices in real-life situations.They discuss linear dependence and independence, as well as rank,canonical forms, generalized inverses, eigenroots, and vectors.Topics of prime interest to economists are shown to be simplifiedusing matrix algebra in linear equations, regression, linearmodels, linear programming, and Markov chains. Highlights include: * Numerous examples of real-world applications * Challenging exercises throughout the book * Mathematics understandable to readers of all backgrounds * Extensive up-to-date reference material Matrix Algebra for Applied Economics provides excellent guidancefor advanced undergraduate students and also graduate students.Practicing economists who want to sharpen their skills will findthis book both practical and easy-to-read, no matter what theirapplied interests.

Charles Pettigrew, First Bishop-elect of the North Carolina Episcopal Church

Charles Pettigrew, First Bishop-elect of the North Carolina Episcopal Church
Author: Bennett H Wall
Publisher: Hassell Street Press
Total Pages: 32
Release: 2021-09-10
Genre:
ISBN: 9781015031500

This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

Truth Is a Woman

Truth Is a Woman
Author: Loren Jakobov
Publisher: Createspace Independent Publishing Platform
Total Pages: 72
Release: 2017-09-12
Genre:
ISBN: 9781548454883

Truth Is A Woman is a poetry collection by Loren Jakobov written in response to her friends tragic death in 2015 as a victim of rape and murder. The poems discuss the World from the eyes of a woman, the pain and the beauty that lies therein.