The theory of elliptic curves is distinguished by its long history and by the diversity of the methods that have been used in its study. This book treats the arithmetic approach in its modern formulation, through the use of basic algebraic number theory and algebraic geometry. Following a brief discussion of the necessary algebro-geometric results, the book proceeds with an exposition of the geometry and the formal group of elliptic curves, elliptic curves over finite fields, the complex numbers, local fields, and global fields. Final chapters deal with integral and rational points, including Siegels theorem and explicit computations for the curve Y = X + DX, while three appendices conclude the whole: Elliptic Curves in Characteristics 2 and 3, Group Cohomology, and an overview of more advanced topics.
John Scott and Philip Lannes walked together down a great boulevard of Paris. The young American's heart was filled with grief and anger. The Frenchman felt the same grief, but mingled with it was a fierce, burning passion, so deep and bitter that it took a much stronger word than anger to describe it. Both had heard that morning the mutter of cannon on the horizon, and they knew the German conquerors were advancing. They were always advancing. Nothing had stopped them. The metal and masonry of the defenses at Liège had crumbled before their huge guns like china breaking under stone. The giant shells had scooped out the forts at Maubeuge, Maubeuge the untakable, as if they had been mere eggshells, and the mighty Teutonic host came on, almost without a check. John had read of the German march on Paris, nearly a half-century before, how everything had been made complete by the genius of Bismarck and von Moltke, how the ready had sprung upon and crushed the unready, but the present swoop of the imperial eagle seemed far more vast and terrible than the earlier rush could have been. A month and the legions were already before the City of Light. Men with glasses could see from the top of the Eiffel Tower the gray ranks that were to hem in devoted Paris once more, and the government had fled already to Bordeaux. It seemed that everything was lost before the war was fairly begun. The coming of the English army, far too small in numbers, had availed nothing. It had been swept up with the others, escaping from capture or destruction only by a hair, and was now driven back with the French on the capital. John had witnessed two battles, and in neither had the Germans stopped long. Disregarding their own losses they drove forward, immense, overwhelming, triumphant. He felt yet their very physical weight, pressing upon him, crushing him, giving him no time to breathe. The German war machine was magnificent, invincible, and for the fourth time in a century the Germans, the exulting Kaiser at their head, might enter Paris. The Emperor himself might be nothing, mere sound and glitter, but back of him was the greatest army that ever trod the planet, taught for half a century to believe in the divine right of kings, and assured now that might and right were the same. Every instinct in him revolted at the thought that Paris should be trodden under foot once more by the conqueror. The great capital had truly deserved its claim to be the city of light and leading, and if Paris and France were lost the whole world would lose. He could never forget the unpaid debt that his own America owed to France, and he felt how closely interwoven the two republics were in their beliefs and aspirations.
Résumé : This book integrates a stakeholder perspective with an issues-oriented approach so students look at how a business's actions affect not just share price and profit but the well-being of employees, customers, suppliers, the local community, the larger society, other nations, and the environment. Fourteen of the twenty-three cases are brand new to this edition, touching on issues such as cyberbullying, fracking, neuromarketing, and for-profit education and involve institutions like Goldman Sachs, Google, Kaiser Permanente, Walmart, Ford, and Facebook. The text has been updated with the latest research, including new national ethics survey data, perspectives on generational differences, and global and international issues. Each chapter includes recent business press stories touching on ethical issues. Several chapters now feature a Point/Counterpoint exercise that challenges students to argue both sides of a contemporary issue, such as too-big-to-fail institutions, the Boston bomber Rolling Stone cover, student loan debt, online file sharing, and questions raised by social media. --
The first part written by Joseph Lipman, accessible to mid-level graduate students, is a full exposition of the abstract foundations of Grothendieck duality theory for schemes (twisted inverse image, tor-independent base change,...), in part without noetherian hypotheses, and with some refinements for maps of finite tor-dimension. The ground is prepared by a lengthy treatment of the rich formalism of relations among the derived functors, for unbounded complexes over ringed spaces, of the sheaf functors tensor, hom, direct and inverse image. Included are enhancements, for quasi-compact quasi-separated schemes, of classical results such as the projection and Künneth isomorphisms. In the second part, written independently by Mitsuyasu Hashimoto, the theory is extended to the context of diagrams of schemes. This includes, as a special case, an equivariant theory for schemes with group actions. In particular, after various basic operations on sheaves such as (derived) direct images and inverse images are set up, Grothendieck duality and flat base change for diagrams of schemes are proved. Also, dualizing complexes are studied in this context. As an application to group actions, we generalize Watanabe's theorem on the Gorenstein property of invariant subrings.
The seventh edition of this pragmatic guide to determining right and wrong in the workplace is updated with new case studies, exercises, and ancillary materials. Joseph Weiss's Business Ethics is a pragmatic, hands-on guide for determining right and wrong in the business world. To be socially responsible and ethical, Weiss maintains, businesses must acknowledge the impact their decisions can have on the world beyond their walls. An advantage of the book is the integration of a stakeholder perspective with an issues and crisis management approach so students can look at how a business's actions affect not just share price and profit but the well-being of employees, customers, suppliers, the local community, the larger society, other nations, and the environment. Weiss includes twenty-three cases that immerse students directly in contemporary ethical dilemmas. Eight new cases in this edition include Facebook's (mis)use of customer data, the impact of COVID-19 on higher education, the opioid epidemic, the rise of Uber, the rapid growth of AI, safety concerns over the Boeing 737, the Wells Fargo false saving accounts scandal, and plastics being dumped into the ocean. Several chapters feature a unique point/counterpoint exercise that challenges students to argue both sides of a heated ethical issue. This edition has eleven new point/counterpoint exercises, addressing questions like, Should tech giants be broken apart? What is the line between free speech and dangerous disinformation? Has the Me Too movement gone too far? As with previous editions, the seventh edition features a complete set of ancillary materials for instructors: teaching guides, test banks, and PowerPoint presentations.
This text focuses on a variety of topics in mathematics in common usage in graduate engineering programs including vector calculus, linear and nonlinear ordinary differential equations, approximation methods, vector spaces, linear algebra, integral equations and dynamical systems. The book is designed for engineering graduate students who wonder how much of their basic mathematics will be of use in practice. Following development of the underlying analysis, the book takes students through a large number of examples that have been worked in detail. Students can choose to go through each step or to skip ahead if they so desire. After seeing all the intermediate steps, they will be in a better position to know what is expected of them when solving assignments, examination problems, and when on the job. Chapters conclude with exercises for the student that reinforce the chapter content and help connect the subject matter to a variety of engineering problems. Students have grown up with computer-based tools including numerical calculations and computer graphics; the worked-out examples as well as the end-of-chapter exercises often use computers for numerical and symbolic computations and for graphical display of the results.
Regularization becomes an integral part of the reconstruction process in accelerated parallel magnetic resonance imaging (pMRI) due to the need for utilizing the most discriminative information in the form of parsimonious models to generate high quality images with reduced noise and artifacts. Apart from providing a detailed overview and implementation details of various pMRI reconstruction methods, Regularized image reconstruction in parallel MRI with MATLAB examples interprets regularized image reconstruction in pMRI as a means to effectively control the balance between two specific types of error signals to either improve the accuracy in estimation of missing samples, or speed up the estimation process. The first type corresponds to the modeling error between acquired and their estimated values. The second type arises due to the perturbation of k-space values in autocalibration methods or sparse approximation in the compressed sensing based reconstruction model. Features: Provides details for optimizing regularization parameters in each type of reconstruction. Presents comparison of regularization approaches for each type of pMRI reconstruction. Includes discussion of case studies using clinically acquired data. MATLAB codes are provided for each reconstruction type. Contains method-wise description of adapting regularization to optimize speed and accuracy. This book serves as a reference material for researchers and students involved in development of pMRI reconstruction methods. Industry practitioners concerned with how to apply regularization in pMRI reconstruction will find this book most useful.
Joseph J. Randazzo, Writer – Publisher - Executive Producer Presents The Historical Classic Collectors Issue Vol April / May 1994. 80 Pages. Full-Color. The International UFO Library Magazine. Featuring Articles from Around the World. Page 8. Star Trek – Does Capt. Picard have a Crush on Dr. Crusher? by Will Edwards. Page 14. USA – Children of Abductions by Preston Dermitt. Page 16. Iceland – Confirmation at Sea by Anthony Dodd. Page 18. Abduction Update – A Spiritual Experience by Virgil Armstrong. Page 20. Contactee Update – Adamski and UFO’s: The Final Answer by W.D. Clendenon. Page 22. Russia – Part 2 What’s Happening in Russia by Brian Grish. Page 24. Europe – Crop Circles by J.J. Hurtak Ph.D Page 26. Mars – The Search for Life on Mars by J.J.Hurtak Ph.D Page 30. Israel – An Embassy for Extraterrestrials by Felix Clairvoyant. Page 45. Cosmic – Astrology From Angels by Loma Gopi Saravati Page 50. Universal – Who Has The Right Stuff by Joseph J. Randazzo. Page 51. Celebrity Corner – Take Some Steps Up by Roberta Leighton. Page 58. Pleiadians – Bean Ship From The Pleiades by J. Randolph Winters. Page 60. Argentina – Galicia – Land of Mystery by Scott Corrales. The collectors' information and articles in the International UFO Library Magazine published decades ago where the effort and prodigy of traveling to over twenty countries around the world with Emmy award winning film crews for over five years by Writer, Executive Producer, Joseph J Randazzo and Company. Hundreds of one-on-one interviews were conducted to seek out and amass a library of information questioning the UFO / ET subject matter with a goal to question and then compare cases, notes and references from Researchers, Abductees and Contactees. The information collected was far ahead of its time and still shows a straightforward presentation to learn form. Let us learn from this information and grow into the absolute best we can become as a humanity.
In the introduction to the first volume of The Arithmetic of Elliptic Curves (Springer-Verlag, 1986), I observed that "the theory of elliptic curves is rich, varied, and amazingly vast," and as a consequence, "many important topics had to be omitted." I included a brief introduction to ten additional topics as an appendix to the first volume, with the tacit understanding that eventually there might be a second volume containing the details. You are now holding that second volume. it turned out that even those ten topics would not fit Unfortunately, into a single book, so I was forced to make some choices. The following material is covered in this book: I. Elliptic and modular functions for the full modular group. II. Elliptic curves with complex multiplication. III. Elliptic surfaces and specialization theorems. IV. Neron models, Kodaira-Neron classification of special fibers, Tate's algorithm, and Ogg's conductor-discriminant formula. V. Tate's theory of q-curves over p-adic fields. VI. Neron's theory of canonical local height functions.
This history of post-Emancipation German Jewry and of the Holocaust aftermath has received considerable scholarly attention. The study of Jewish life in Germany in the 1930s and the migration impelled by the Nazi period has, on the other hand, been comparatively neglected. The work of Werner J. Cahnman (1902-1980) goes a long way toward filling this gap.Cahnman's examination of "the Jewish people that dwells among the nations" is focused on Germany because it was the country "where in modern times the symbiosis . . . has been most intimate and it also has been the country where the conflict degenerated into the monstrosity of the Holocaust." This representative anthology of his essays shares a common theme, although the examples differ in thought, method and style. Whether he explores the stratification of pre-Emancipation German Jewry, the rise of the Jewish national movement in Austria, or such an esoteric topic as the influence of the kabbalistic tradition on German idealist philosophy; whether he muses on the writing of Jewish history or reports on his firsthand experience in Dachau, Cahnman's work reflects central concerns of his personal and scholarly existence as a German Jew. Because he usually combined extensive empirical data with his own background and personal experience, he is able to craft a penetrating analysis of the recent history of Jewish life in Central Europe. Werner Cahnman believed that the "writing of history is vital for the continued cultural identity of the human kind.
In The Edges of the Field Harvard law professor Joseph William Singer offers a brilliant and cogent look at America's complex relation to property and ownership. Incorporating examples as far-reaching as the experience of Malden Mills owner and Polartec manufacturer Aaron Feuerstein, the Torah, and the musical Rent, Singer reminds us that ownership is a curious blend of security and vulnerability between owner and nonowner. He proposes that the manner in which property shapes social relations of power is as important as ownership rights.
This book examines interactions of polyhedral discrete geometry and algebra. What makes this book unique is the presentation of several central results in all three areas of the exposition - from discrete geometry, to commutative algebra, and K-theory.
Two central aspects of Cartan's approach to differential geometry are the theory of exterior differential systems (EDS) and the method of moving frames. This book presents thorough and modern treatments of both subjects, including their applications to both classic and contemporary problems in geometry. It begins with the classical differential geometry of surfaces and basic Riemannian geometry in the language of moving frames, along with an elementary introduction to exterior differential systems. Key concepts are developed incrementally, with motivating examples leading to definitions, theorems, and proofs. Once the basics of the methods are established, the authors develop applications and advanced topics. One notable application is to complex algebraic geometry, where they expand and update important results from projective differential geometry. As well, the book features an introduction to G-structures and a treatment of the theory of connections. The techniques of EDS are also applied to obtain explicit solutions of PDEs via Darboux's method, the method of characteristics, and Cartan's method of equivalence. This text is suitable for a one-year graduate course in differential geometry, and parts of it can be used for a one-semester course. It has numerous exercises and examples throughout. It will also be useful to experts in areas such as geometry of PDE systems and complex algebraic geometry who want to learn how moving frames and exterior differential systems apply to their fields. The second edition features three new chapters: on Riemannian geometry, emphasizing the use of representation theory; on the latest developments in the study of Darboux-integrable systems; and on conformal geometry, written in a manner to introduce readers to the related parabolic geometry perspective.
This will help us customize your experience to showcase the most relevant content to your age group
Please select from below
Login
Not registered?
Sign up
Already registered?
Success – Your message will goes here
We'd love to hear from you!
Thank you for visiting our website. Would you like to provide feedback on how we could improve your experience?
This site does not use any third party cookies with one exception — it uses cookies from Google to deliver its services and to analyze traffic.Learn More.