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Herbert Scarf's Contributions to Economics, Game Theory and Operations Research: Volume 3: Production in Indivisibilities: A Contribution to the Theories of Large Firms
Herbert Scarf is a distinguished economist and has made a number of extraordinarily significant contributions to economics, game theory and operations research. This work has generated a major research field in economics termed Applied General Equilibrium Analysis. This book comprises all his research articles and consists of four volumes.
Hydrodynamic Behavior and Interacting Particle Systems (The IMA Volumes in Mathematics and its Applications #9)
This IMA Volume in Mathematics and its Applications HYDRODYNAMIC BEHAVIOR AND INTERACTING PARTICLE SYSTEMS is in part the proceedings of a workshop which was an integral part of the 1985-86 IMA program on STOCHASTIC DIFFERENTIAL EQUATIONS AND THEIR APPLICATIONS. We are grateful to the Scientific Committee: Daniel Stroock (Chairman) Wendell Fleming Theodore Harris Pierre-Louis Lions Steven Orey George Papanicolaou for planning and implementing an exciting and stimulating year-long program. We especially thank the Program Organizer, George Papanicolaou for orga nizing a workshop which brought together scientists and mathematicians in a variety of areas for a fruitful exchange of ideas. George R. Sell Hans Weinberger PREFACE A workshop on the hydrodynamic behavior of interacting particle systems was held at the Institute for Mathematics and its Applications at the University of Minnesota during the week of March 17, 1986. Fifteen papers presented at the workshop are collected in this volume. They contain research in several different directions that are currently being pursued. The paper of Chaikin, Dozier and Lindsay is concerned with experimental results on suspensions in regimes where modern mathematical methods could be useful. The paper of Fritz gives an introduction to these methods as does the paper of Spohn. Analytical methods currently used by in the physics and chemistry literature are presented in the paper of Freed, Wang and Douglas. The paper of Caflisch deals with time dependent effects in sedimentation.
Iamblichus: On the General Science of Mathematics (Ancient Commentators on Aristotle)
On the General Science of Mathematics is the third of four surviving works out of ten by Iamblichus (c. 245 CE–early 320s) on the Pythagoreans. He thought the Pythagoreans had treated mathematics as essential for drawing the human soul upwards to higher realms described by Plato, and downwards to understand the physical cosmos, the products of arts and crafts and the order required for an ethical life. His Pythagorean treatises use edited quotation to re-tell the history of philosophy, presenting Plato and Aristotle as passing on the ideas invented by Pythagoras and his early followers. Although his quotations tend to come instead from Plato and later Pythagoreanising Platonists, this re-interpretation had a huge impact on the Neoplatonist commentators in Athens. Iamblichus' cleverness, if not to the same extent his re-interpretation, was appreciated by the commentators in Alexandria.
Imagine Math 7: Between Culture and Mathematics
Imagine mathematics, imagine with the help of mathematics, imagine new worlds, new geometries, new forms. Imagine building mathematical models that make it possible to manage our world better, imagine solving great problems, imagine new problems never before thought of, imagine combining music, art, poetry, literature, architecture, theatre and cinema with mathematics. Imagine the unpredictable and sometimes counterintuitive applications of mathematics in all areas of human endeavour. This seventh volume starts with a homage to the Italian artist Mimmo Paladino who created exclusively for the Venice Conference 2019 ten original and unique works of art paper dedicated to the themes of the meeting. A large section is dedicated to the most recent Fields Medals including a Homage to Maryam Mirzakhani including a presentation of the exhibition on soap bubbles in art and science that took place in 2019. A section is dedicated to cinema and theatre including the performances by Claire Bardainne & Adrien Mondot. A part of the conference focused on the community of mathematicians, their role in literature and even in politics with the extraordinary example of Antanas Mockus Major of Bogotá. Mathematics in the constructions of bridges, in particular in Italy in the Sixties was presented by Tullia Iori. A very particular contribution on Origami by a mathematician, Marco Abate and an artist, Alessandro Beber. And many other topics. As usual the topics are treated in a way that is rigorous but captivating, detailed and full of evocations. This is an all-embracing look at the world of mathematics and culture. The world, life, culture, everything has changed in a few weeks with the Coronavirus. Culture, science are the main ways to safeguard people's physical and social life. Trust in humanity's creativity and ability. The motto today in Italy is Everything will be fine.This work is addressed to all those who have an interest in Mathematics.
Information Technology in Medical Diagnostics III: Metrological Aspects of Biomedical Research
The science of biomedical measurements is experiencing a period of rapid development. Biomedical measuring systems are becoming increasingly accurate on the one hand and complex on the other. In order to make progress in this field, metrological problems must be solved using a systemic and formal approach. To this end, it is necessary to define the components of the system and the rules for their interaction, which allows the creation of a mathematical model. In this way, any technology or object can be presented in the form of a structure on which the necessary estimates can be formulated and synthesis, including metrological one, can be made. The authors have observed that despite the significance of the problem, few scientific centres deal with this issue in a generalised manner. Hence the idea of bringing together the achievements of the centres from Russia, Poland and Kazakhstan in one joint publication. The first and second volumes of Information Technology in Medical Diagnostics found readers not only in Poland, Ukraine, and Kazakhstan but also Spain, Russia and the Czech Republic. Following the readers’ suggestions, in the third volume of ITMD we returned to the formula of closed chapters known from volume one. Due to its limited volume, the book deals with the aforementioned issues in only selected areas of biomedical engineering. The book will be of interest not only for academics and engineers but also for professionals involved in biomedical engineering, seeking solutions for the problems that cannot be solved using "traditional" technologies or trying to improve existing measurement systems.
Information Theory: Poincaré Seminar 2018 (Progress in Mathematical Physics #78)
This eighteenth volume in the Poincaré Seminar Series provides a thorough description of Information Theory and some of its most active areas, in particular, its relation to thermodynamics at the nanoscale and the Maxwell Demon, and the emergence of quantum computation and of its counterpart, quantum verification. It also includes two introductory tutorials, one on the fundamental relation between thermodynamics and information theory, and a primer on Shannon's entropy and information theory. The book offers a unique and manifold perspective on recent mathematical and physical developments in this field.
Integration in Finite Terms: Fundamental Sources (Texts & Monographs in Symbolic Computation)
This volume gives an up-to-date review of the subject Integration in Finite Terms. The book collects four significant texts together with an extensive bibliography and commentaries discussing these works and their impact. These texts, either out of print or never published before, are fundamental to the subject of the book. Applications in combinatorics and physics have aroused a renewed interest in this well-developed area devoted to finding solutions of differential equations and, in particular, antiderivatives, expressible in terms of classes of elementary and special functions.
Intelligent Systems and Interfaces (International Series in Intelligent Technologies #15)
This volume offers comprehensive coverage of intelligent systems, including fundamental aspects, software-, sensors-, and hardware-related issues. Moreover, the contributors to this volume provide, beyond a systematic overview of intelligent interfaces and systems, deep, practical knowledge in building and using intelligent systems in various applications. Special emphasis is placed on specific aspects and requirements in applications.
IUTAM Symposium on 150 Years of Vortex Dynamics: Proceedings of the IUTAM Symposium “150 Years of Vortex Dynamics” held at the Technical University of Denmark, October 12-16, 2008 (IUTAM Bookseries #20)
In 1858 Hermann von Helmholtz published a paper that today is recognized as the foundation of vortex dynamics. To celebrate the sesquicentennial of Helmholtz’s paper, IUTAM sponsored a symposium that was held at the technical university of Denmark in October 2008. The papers presented at the symposium gave a good overview of where the field of vortex dynamics stands today. This volume contains almost all of the papers presented as lectures at the symposium, and also a few of the poster papers. In this volume the reader will find up-to-date, state-of-theart papers on Point vortices, vortex sheets, vortex filaments, vortex rings, vortex patches, vortex streets, the vortex dynamics of swimming and flying, vortex knots, vortices in turbulent flows, vortices in computational fluid dynamics, the topology of vortex wakes, stability of vortex configurations, vortices on a sphere, geophysical vortices, cosmic vortices and much more.
Jacobi's Lectures on Dynamics: Delivered at the University of Konigsberg in the Winter Semester 1842-1843 and According to the Notes Prepared by C. W. Brockardt (Texts and Readings in Mathematics)
The name of C. G. J. Jacobi is familiar to every student of mathematics, thanks to the Jacobion determinant, the Hamilton-Jacobi equations in dynamics, and the Jacobi identity for vector fields. Best known for his contributions to the theory of elliptic and abelian functions, Jacobi is also known for his innovative teaching methods and for running the first research seminar in pure mathematics. A record of his lectures on Dynamics given in 1842-43 at Konigsberg, edited by A. Clebsch, has been available in the original German. This is an English translation. It is not just a historical document; the modern reader can learn much about the subject directly from one of its great masters.
Joachim Lambek: The Interplay of Mathematics, Logic, and Linguistics (Outstanding Contributions to Logic #20)
This book is dedicated to the life and work of the mathematician Joachim Lambek (1922–2014). The editors gather together noted experts to discuss the state of the art of various of Lambek’s works in logic, category theory, and linguistics and to celebrate his contributions to those areas over the course of his multifaceted career. After early work in combinatorics and elementary number theory, Lambek became a distinguished algebraist (notably in ring theory). In the 1960s, he began to work in category theory, categorical algebra, logic, proof theory, and foundations of computability. In a parallel development, beginning in the late 1950s and for the rest of his career, Lambek also worked extensively in mathematical linguistics and computational approaches to natural languages. He and his collaborators perfected production and type grammars for numerous natural languages. Lambek grammars form an early noncommutative precursor to Girard’s linear logic. In a surprising development (2000), he introduced a novel and deeper algebraic framework (which he called pregroup grammars) for analyzing natural language, along with algebraic, higher category, and proof-theoretic semantics. This book is of interest to mathematicians, logicians, linguists, and computer scientists.
Kooperation und Innovation für eine nachhaltige Stadtentwicklung: Forschung mit innovativen Kommunen
Die Autoren stellen die Ergebnisse des Projekts IER-SEK zusammenfassend vor. IER-SEK ist das Instrument zur Entscheidungsunterstützung für Großvermieter zur Realisierung von Stadtentwicklungskonzepten und wurde im Rahmen der BMBF-Initiative Kommunen innovativ gefördert. Das Buch gibt aber auch einen Ausblick auf weitere Themen, welche die nachhaltige Stadtentwicklung beeinflussen, dazu gehören Stadtentwicklung und Mensch sowie Technologie und Energie.Die Herausgeber:M.Sc. Tim Neumann ist wissenschaftlicher Mitarbeiter an der Westsächsischen Hochschule Zwickau. Dipl.-Ing. Uwe Ziesler arbeitet in der Stabsstelle Stadtentwicklung der Stadt Zwickau. Prof. Dr. rer. pol. habil. Dr.-Ing. Tobias Teich ist Professor für Vernetzte Systeme in der Betriebswirtschaft an der Westsächsischen Hochschule Zwickau.
Kurt Gödel: The Princeton Lectures on Intuitionism (Sources and Studies in the History of Mathematics and Physical Sciences)
Paris of the year 1900 left two landmarks: the Tour Eiffel, and David Hilbert's celebrated list of twenty-four mathematical problems presented at a conference opening the new century. Kurt Gödel, a logical icon of that time, showed Hilbert's ideal of complete axiomatization of mathematics to be unattainable. The result, of 1931, is called Gödel's incompleteness theorem. Gödel then went on to attack Hilbert's first and second Paris problems, namely Cantor's continuum problem about the type of infinity of the real numbers, and the freedom from contradiction of the theory of real numbers. By 1963, it became clear that Hilbert's first question could not be answered by any known means, half of the credit of this seeming faux pas going to Gödel. The second is a problem still wide open. Gödel worked on it for years, with no definitive results; The best he could offer was a start with the arithmetic of the entire numbers. This book, Gödel's lectures at the famous Princeton Institute for Advanced Study in 1941, shows how far he had come with Hilbert's second problem, namely to a theory of computable functionals of finite type and a proof of the consistency of ordinary arithmetic. It offers indispensable reading for logicians, mathematicians, and computer scientists interested in foundational questions. It will form a basis for further investigations into Gödel's vast Nachlass of unpublished notes on how to extend the results of his lectures to the theory of real numbers. The book also gives insights into the conceptual and formal work that is needed for the solution of profound scientific questions, by one of the central figures of 20th century science and philosophy.
Kurt Gödel: Results on Foundations (Sources and Studies in the History of Mathematics and Physical Sciences)
Kurt Gödel (1906-1978) gained world-wide fame by his incompleteness theorem of 1931. Later, he set as his aim to solve what are known as Hilbert's first and second problems, namely Cantor's continuum hypothesis about the cardinality of real numbers, and secondly the consistency of the theory of real numbers and functions. By 1940, he was halfway through the first problem, in what was his last published result in logic and foundations. His intense attempts thereafter at solving these two problems have remained behind the veil of a forgotten German shorthand he used in all of his writing. Results on Foundations is a set of four shorthand notebooks written in 1940-42 that collect results Gödel considered finished. Its main topic is set theory in which Gödel anticipated several decades of development. Secondly, Gödel completed his 1933 program of establishing the connections between intuitionistic and modal logic, by methods and results that today are at the same time new and 80 years old.The present edition of Gödel's four notebooks encompasses the 368 numbered pages and 126 numbered theorems of the Results on Foundations, together with a list of 74 problems on set theory Gödel prepared in 1946, and a list of an unknown date titled "The grand program of my research in ca. hundred questions.''
Learning and Doing Mathematics
Based on a unit of the Open University foundation course in mathematics, this book is not intended to teach any new mathematics, but to improve the ability to assimilate new ideas and to approach problems in a systematic and constructive way and to gain enjoyment from the learning process itself.
The Legacy of Kurt Schütte
This book on proof theory centers around the legacy of Kurt Schütte and its current impact on the subject. Schütte was the last doctoral student of David Hilbert who was the first to see that proofs can be viewed as structured mathematical objects amenable to investigation by mathematical methods (metamathematics). Schütte inaugurated the important paradigm shift from finite proofs to infinite proofs and developed the mathematical tools for their analysis. Infinitary proof theory flourished in his hands in the 1960s, culminating in the famous bound Γ0 for the limit of predicative mathematics (a fame shared with Feferman). Later his interests shifted to developing infinite proof calculi for impredicative theories. Schütte had a keen interest in advancing ordinal analysis to ever stronger theories and was still working on some of the strongest systems in his eighties. The articles in this volume from leading experts close to his research, show the enduring influence of his work in modern proof theory. They range from eye witness accounts of his scientific life to developments at the current research frontier, including papers by Schütte himself that have never been published before.
Lesson Study with Mathematics and Science Preservice Teachers: Finding the Form (WALS-Routledge Lesson Study Series)
This insightful volume offers an overview of the fundamentals of lesson student practice in US teacher education as well as examples from math and science teacher educators using lesson study in their local contexts. The number of teacher educators using lesson study with preservice teachers is small but growing. This book is aimed at teacher educators who may want to try lesson study in university contexts without the challenge of translating the practice from the K-12 context on their own. In this volume, lesson study is broadly overviewed, attention is given to its constituent steps, and examples of lesson study in preservice contexts are shared. Given the broad array of teacher education program designs, numerous contingencies guide teacher educators in their implementation of lesson study, given their contextual affordances and limitations. The lesson study descriptions and cases in this book will support teacher educators and scholars across subject specialities and geographic lines, as they seek instructional frameworks to advance their pedagogical goals.
The Lineaments of Population Policy in India: Women and Family Planning
India is the first country in the world to have an official programme for family planning that commenced in 1952. It has also seen a strong women’s movement to assert reproductive and contraceptive rights. This book brings to the fore several contestations and negotiations between public policy and the women’s movement in India. The comprehensive volume puts together key documents from archival records and authoritative sources, and traces the contours that have marked and defined the population policy in India as well as rights issues for women. A major intervention in the field, this book will be indispensable for scholars and researchers in public policy, public health, demography, gender studies, social policy, development studies, sociology, social justice, human rights, politics and those interested in the study of modern India.
Linear Representations of Groups (Birkhäuser Advanced Texts Basler Lehrbücher)
This book gives an exposition of the fundamentals of the theory of linear representations of finite and compact groups, as well as elements of the the ory of linear representations of Lie groups. As an application we derive the Laplace spherical functions. The book is based on lectures that I delivered in the framework of the experimental program at the Mathematics-Mechanics Faculty of Moscow State University and at the Faculty of Professional Skill Improvement. My aim has been to give as simple and detailed an account as possible of the problems considered. The book therefore makes no claim to completeness. Also, it can in no way give a representative picture of the modern state of the field under study as does, for example, the monograph of A. A. Kirillov [3]. For a more complete acquaintance with the theory of representations of finite groups we recommend the book of C. W. Curtis and I. Reiner [2], and for the theory of representations of Lie groups, that of M. A. Naimark [6]. Introduction The theory of linear representations of groups is one of the most widely ap plied branches of algebra. Practically every time that groups are encountered, their linear representations play an important role. In the theory of groups itself, linear representations are an irreplaceable source of examples and a tool for investigating groups. In the introduction we discuss some examples and en route we introduce a number of notions of representation theory. O.
Linear Systems, Signal Processing and Hypercomplex Analysis: Chapman University, November 2017 (Operator Theory: Advances and Applications #275)
This volume includes contributions originating from a conference held at Chapman University during November 14-19, 2017. It presents original research by experts in signal processing, linear systems, operator theory, complex and hypercomplex analysis and related topics.
The Logic of Poverty: The Case of the Brazilian Northeast (Routledge Revivals)
First published in 1981, The Logic of Poverty consists of eight essays that share at least one assumption: that Northeast Brazil provides a startling example of inhumane economic development. The contributors have all worked in the area, and know it at first hand. They look at rural structure and the role of the unemployed ‘reserve army’, the state of the sugar industry, the ineffectiveness of the irrigation schemes, the stagnation in the fishing sector, the lack of credit available to peasants and the role of SUDENE, the first development agency in the region. Together they paint a picture of poverty and of the factors that allow it to continue, and they place that poverty in the context of the wider economy of Brazil, relating it to the extraordinary transformation that has been called ‘the Brazilian miracle’. This book will be of interest to students of geography, anthropology, economics and sociology.
The Logical Writings of Karl Popper (Trends in Logic #58)
This open access book is the first ever collection of Karl Popper's writings on deductive logic.Karl R. Popper (1902-1994) was one of the most influential philosophers of the 20th century. His philosophy of science ("falsificationism") and his social and political philosophy ("open society") have been widely discussed way beyond academic philosophy. What is not so well known is that Popper also produced a considerable work on the foundations of deductive logic, most of it published at the end of the 1940s as articles at scattered places. This little-known work deserves to be known better, as it is highly significant for modern proof-theoretic semantics.This collection assembles Popper's published writings on deductive logic in a single volume, together with all reviews of these papers. It also contains a large amount of unpublished material from the Popper Archives, including Popper's correspondence related to deductive logic and manuscripts that were (almost) finished, but did not reach the publication stage. All of these items are critically edited with additional comments by the editors. A general introduction puts Popper's work into the context of current discussions on the foundations of logic. This book should be of interest to logicians, philosophers, and anybody concerned with Popper's work.
Louis Couturat: The History of Modern Symbolic Logic and Other French Manuscripts (Publications des Archives Henri Poincaré Publications of the Henri Poincaré Archives)
This volume features a critical edition of the recently rediscovered manuscripts written by the French philosopher Louis Couturat (1868-1914). It includes the transcriptions of three of his believed to be lost manuscripts: first the “Cours de Caen: 1898-99” on various systems of symbolic logic, second his lecture at the Collège de France “Histoire de la logique formelle moderne", and third his textbook on mathematical logic. The manuscripts document the early reception of mathematical logic in France and provide insights into the first introduction of the French reader to the work of Gottlob Frege and Bertrand Russell. It is the aim of the editors of this volume to contribute to the history of symbolic logic, particularly the history of its dissemination and its teaching in France. At the same time, the volume contributes to an alternative history and conception of philosophy in which semiotics and concrete mathematical practice stand in focus. The book is interesting for students and researchers in the history of philosophy, mathematics, and logic.
Martin Kneser Collected Works (Contemporary Mathematicians)
This volume presents the collection of mathematical articles by Martin Kneser, reprinted in the original language – mostly German –, including one yet unpublished. Moreover, also included is an article by Raman Parimala, discussing Kneser’s work concerning algebraic groups and the Hasse principle, which has been written especially for this volume, as well as an article by Rudolf Scharlau about Kneser’s work on quadratic forms, published elsewhere before. Another commentary article, written by Günter M. Ziegler especially for this volume, describes the astounding influence on the field of combinatorics of what was published as “Aufgabe 360” and its subsequent solution in 1955 resp. 1957 in the “Jahresbericht der Deutschen Mathematiker-Vereinigung”. However, as the titles of the articles show, Kneser’s mathematical interests were much broader, which is beautifully discussed in an obituary by Ulrich Stuhler, included as well in this volume.