This book is concerned with two areas of mathematics, at first sight disjoint, and with some of the analogies and interactions between them. These areas are the theory of linear differential equations in one complex variable with polynomial coefficients, and the theory of one parameter families of exponential sums over finite fields. After reviewing some results from representation theory, the book discusses results about differential equations and their differential galois groups (G) and one-parameter families of exponential sums and their geometric monodromy groups (G). The final part of the book is devoted to comparison theorems relating G and G of suitably "corresponding" situations, which provide a systematic explanation of the remarkable "coincidences" found "by hand" in the hypergeometric case.

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.

L-functions for the classical groups.- L-functions for G×GL(n).

This series of papers is the result of the Academy's scientist-in reseidence program honoring Professor Harary on May 2-6, 1977.

Excerpt from The Geographical and Geological, Distribution of Animals In the preparation of the following pages the author has had two objects in view: that of presenting to his readers such of the more significant facts connected with the past and present distribution of animal life as might lead to a proper conception of the relations of existing faunas; and, secondly, that of furnishing to the student a work of general reference, wherein the more salient features of the geography and geology of animal forms could be sought after and readily found. The need of such a work has been frequently felt and expressed. As far as he is aware, no work of that kind has as yet appeared, and therefore, to a certain extent, this publication stands alone in the field it is intended to cover. Necessarily, much that it embraces can be found elsewhere, and treated even at considerably greater length; but the matter is not contained under a single cover, and where a special subject is expounded in extenso the treatment is usually too exhaustive to permit of immediate use by the general reader. This applies particularly to zoogeography. With reference to geological distribution there is little connectedly written - indeed, beyond what is found in text-books largely devoted to cognate subjects, practically nothing. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

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 was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. 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. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

This is a reproduction of a book published before 1923. This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book.

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. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

A. Gro8en- und Einheitensysteme Westphal, Physik, 25./26. Auf!., §§ 2, 3; ferner: Die Grundlagen des physikalismen Begriffssystems. 1. GroBen, Zahlenwerte und Einheiten Das Ergebnis jeder physikalisehen Messung ist die Angabe einer physika- /ischen Grof3e Gals Produkt aus einem Zahlenwert {G} und einer Ein- heit [G], also G = {G} [G]. Einheiten sind vereinbarte Vertreter der be- treffenden GroBenart, deren es oft mehrere gibt. Eine physikalisehe GroBe ist aber eine von der Einheitenwahl unabhangige (invariante) Gegebenheit. Geht man von einer Einheit [G] zu einer anderen Einheit [G]' iiber, so andert sich zwar der Zahlenwert von {G} in {G}', aber nieht die GroBe. Es ist G = {G} [G] = {G}' [G]'. Eine Lange bleibt die gleiehe GroBe, ganz gleieh, ob man sie als 1 = 1,500 m oder als 1 = 1500 mm besehreibt. Dem- naeh ist {G}'/{G} = [G]/[G]'. Je groBer die Einheit, um so kleiner der Zahlenwert. Unter einer Grof3enart (GroBenklasse) versteht man eine unendliche Mannig- faltigkeit gleichartiger GroBen, z. B. alIer Langen, Zeiten, Temperaturen usw. Mit Hilfe einiger weniger Basisgrof3en (Grundgrof3en) konnen aIle weiteren physikalischen GroBen ihrer Art nach als Potenzprodukte von Basisgrof3en definiert werden (abgeleitete Grof3en). Die Anzahl der fiir ein Teilsystem der Physik unerllilSlich notigen BasisgroBen lliBt sich ermitteln; ihre Auswahl steht innerhalb gewisser Grenzen frei. BasisgroBen konnen nieht definiert, sondern nur durch eine Aussage als solche eingefilhrt werden.

This book commemorates the eclectic intellectual life of scientist and artist Walter Gilbert. It presents all of his most influential works throughout his scientific career. His scientific explorations covered a broad spectrum of fields: theoretical physics; molecular biology, from finding messenger RNA to elucidating the regulation of the lac operon to understanding DNA replication; gene evolution and origin of life; genomics; bioinformatics; and beyond. He created widely used concepts such as 'Exon', 'Intron' and 'RNA World'. Eleven reflective essays by Gilbert are included for the first time, discussing both his scientific studies and anecdotes from his own life. These firsthand accounts record the historical and intellectual contexts for his most monumental scientific discoveries, including his Nobel Prize-winning sequencing method. Memorial chapters, contributed by Gilbert Laboratory alumni, describe the passion, ambition, and efforts of Gilbert and several generations of young scientists under his leadership. Finally, the book collects a few fine pieces of artwork created by Gilbert in recent years. It documents a life of genius and creativity that could inspire others for years to come.

This is a reproduction of a book published before 1923. This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book.

Minimal Shelf Wear.