The pioneering work of Pierre de Fermat has attracted the attention of mathematicians for over 350 years. This book provides an overview of the many properties of Fermat numbers and demonstrates their applications in areas such as number theory, probability theory, geometry, and signal processing. It is an ideal introduction to the basic mathematical ideas and algebraic methods connected with the Fermat numbers.
The authors assemble a fascinating collection of topics from analytic number theory that provides an introduction to the subject with a very clear and unique focus on the anatomy of integers, that is, on the study of the multiplicative structure of the integers. Some of the most important topics presented are the global and local behavior of arithmetic functions, an extensive study of smooth numbers, the Hardy-Ramanujan and Landau theorems, characters and the Dirichlet theorem, the $abc$ conjecture along with some of its applications, and sieve methods. The book concludes with a whole chapter on the index of composition of an integer. One of this book's best features is the collection of problems at the end of each chapter that have been chosen carefully to reinforce the material. The authors include solutions to the even-numbered problems, making this volume very appropriate for readers who want to test their understanding of the theory presented in the book.
This volume contains selected refereed papers based on lectures presented at the "Integers Conference 2011", an international conference in combinatorial number theory that was held in Carrollton, Georgia, United States in October 2011. This was the fifth Integers Conference, held bi-annually since 2003. It featured plenary lectures presented by Ken Ono, Carla Savage, Laszlo Szekely, Frank Thorne, and Julia Wolf, along with sixty other research talks. This volume consists of ten refereed articles, which are expanded and revised versions of talks presented at the conference. They represent a broad range of topics in the areas of number theory and combinatorics including multiplicative number theory, additive number theory, game theory, Ramsey theory, enumerative combinatorics, elementary number theory, the theory of partitions, and integer sequences.
The book is mostly devoted to the study of the prime factors of integers, their size and their quantity, to good bounds on the number of integers with different properties (for example, those with only large prime factors) and to the distribution of divisors of integers in a given interval. In particular, various estimates concerning smooth numbers are developed. A large emphasis is put on the study of additive and multiplicative functions as well as various arithmetic functions such as the partition function. More specific topics include the Erdos-Kac Theorem, cyclotomic polynomials, combinatorial methods, quadratic forms, zeta functions, Dirichlet series and $L$-functions. All these create an intimate understanding of the properties of integers and lead to fascinating and unexpected consequences. The volume includes contributions from leading participants in this active area of research, such as Kevin Ford, Carl Pomerance, Kannan Soundararajan and Gerald Tenenbaum.
Aging population and the thereby ever-rising cost of health services call for novel and innovative solutions for providing medical care and services. So far, medical care is primarily provided in the form of time-consuming in-person appointments with trained personnel and expensive, stationary instrumentation equipment. As for many current and past challenges, the advances in microelectronics are a crucial enabler and offer a plethora of opportunities. With key building blocks such as sensing, processing, and communication systems and circuits getting smaller, cheaper, and more energy-efficient, personal and wearable or even implantable point-of-care devices with medicalgrade instrumentation capabilities become feasible. Device size and battery lifetime are paramount for the realization of such devices. Besides integrating the required functionality into as few individual microelectronic components as possible, the energy efficiency of such is crucial to reduce battery size, usually being the dominant contributor to overall device size. In this thesis, we present two major contributions to achieve the discussed goals in the context of miniaturized medical instrumentation: First, we present a synchronization solution for embedded, parallel near-threshold computing (NTC), a promising concept for enabling the required processing capabilities with an energy efficiency that is suitable for highly mobile devices with very limited battery capacity. Our proposed solution aims at increasing energy efficiency and performance for parallel NTC clusters by maximizing the effective utilization of the available cores under parallel workloads. We describe a hardware unit that enables fine-grain parallelization by greatly optimizing and accelerating core-to-core synchronization and communication and analyze the impact of those mechanisms on the overall performance and energy efficiency of an eight-core cluster. With a range of digital signal processing (DSP) applications typical for the targeted systems, the proposed hardware unit improves performance by up to 92% and 23% on average and energy efficiency by up to 98% and 39% on average. In the second part, we present a MCU processing and control subsystem (MPCS) for the integration into VivoSoC, a highly versatile single-chip solution for mobile medical instrumentation. In addition to the MPCS, it includes a multitude of analog front-ends (AFEs) and a multi-channel power management IC (PMIC) for voltage conversion. ...
Nowadays, Web applications are almost omnipresent. The Web has become a platform not only for information delivery, but also for eCommerce systems, social networks, mobile services, and distributed learning environments. Engineering Web applications involves many intrinsic challenges due to their distributed nature, content orientation, and the requirement to make them available to a wide spectrum of users who are unknown in advance. The authors discuss these challenges in the context of well-established engineering processes, covering the whole product lifecycle from requirements engineering through design and implementation to deployment and maintenance. They stress the importance of models in Web application development, and they compare well-known Web-specific development processes like WebML, WSDM and OOHDM to traditional software development approaches like the waterfall model and the spiral model. .
This classic study notes the origin of a mathematical symbol, the competition it encountered, its spread among writers in different countries, its rise to popularity, and its eventual decline or ultimate survival. 1929 edition.
Corporate consulting, a one-time seemingly marvelous mixture of bare-knuckle rationalization, esoterica, and visionary futurism, is invariably deployed when business structures threaten to lose their equilibrium. What it actually means to be consulted, the part played by media in consulting, and how the branch of corporate consulting became a system of knowledge with such a socially important role is the object of this book. For the first time, it explores the ways in which the latest media technology, avant-garde aesthetics, economic pressures, and holistic philosophy together constituted the form of consulting dominant today, and which consequences arise from this. Thus it follows the work of early corporate consultants like Frank and Lillian Gilbreth and H. L. Gantt, while analyzing and describing their visual consulting models. The book develops a new, innovative, interdisciplinary approach, situated between media and business history, media archeology, and social theory, and thereby charts the genesis of modern consulting knowledge. It reveals that corporate consulting must be conceptualized in close relation to the visual culture that prevailed during this time, one which drew from nineteenth-century visualization methods and, more particularly, the new medium of film. Consulting is a cultural technique that is markedly characterized by media processes, in which the boundaries of economic logic and legitimacy emerge, and which, at the same time, considerably shapes and stabilizes this modus operandi up to the present day"--
Originally issued in 1893, this popular Fifth Edition (1991) covers the period from antiquity to the close of World War I, with major emphasis on advanced mathematics and, in particular, the advanced mathematics of the nineteenth and early twentieth centuries. In one concise volume this unique book presents an interesting and reliable account of mathematics history for those who cannot devote themselves to an intensive study. The book is a must for personal and departmental libraries alike. Cajori has mastered the art of incorporating an enormous amount of specific detail into a smooth-flowing narrative. The Index—for example—contains not just the 300 to 400 names one would expect to find, but over 1,600. And, for example, one will not only find John Pell, but will learn who he was and some specifics of what he did (and that the Pell equation was named erroneously after him). In addition, one will come across Anna J. Pell and learn of her work on biorthogonal systems; one will find not only H. Lebesgue but the not unimportant (even if not major) V.A. Lebesgue. Of the Bernoullis one will find not three or four but all eight. One will find R. Sturm as well as C. Sturm; M. Ricci as well as G. Ricci; V. Riccati as well as J.F. Riccati; Wolfgang Bolyai as well as J. Bolyai; the mathematician Martin Ohm as well as the physicist G.S. Ohm; M. Riesz as well as F. Riesz; H.G. Grassmann as well as H. Grassmann; H.P. Babbage who continued the work of his father C. Babbage; R. Fuchs as well as the more famous L. Fuchs; A. Quetelet as well as L.A.J. Quetelet; P.M. Hahn and Hans Hahn; E. Blaschke and W. Blaschke; J. Picard as well as the more famous C.E. Picard; B. Pascal (of course) and also Ernesto Pascal and Etienne Pascal; and the historically important V.J. Bouniakovski and W.A. Steklov, seldom mentioned at the time outside the Soviet literature.
In 1893, colonial officials from thirteen countries abandoned imperial rivalry and established the International Colonial Institute to take control of the world's colonial policy. Florian Wagner argues that colonial internationalists reshaped colonialism as a transimperial governmental policy to perpetuate empires well into the twentieth century.
Using a historical analogy as a research strategy: histories of the sea and cyberspace, comparison, and locating the analogy in time -- History of the loosely governed sea between the 16th-19th century: from the age of privateering to its abolition -- Brief history of cyberspace: origins and development of (in-)security in cyberspace -- The sea and cyberspace: comparison and analytical lines of inquiry applying the analogy to cybersecurity -- Cyber pirates and privateers: state proxies, criminals, and independent patriotic hackers -- Cyber mercantile companies conflict and cooperation.
Traditionally, fiscal data for policy analysis are derived from official reports that, depending on the country, are published either monthly, quarterly or annually, often with significant time lags. However, innovations in digitalization of government payments and accounting systems mean that real-time daily fiscal data exist in many countries. In this paper, we argue that these data contain valuable, but underutilized and underexploited information. Possible uses include (i) realtime fiscal surveillance which allows for much more timely responses to emerging signs of fiscal stress, and (ii) nowcasting economic activity, which is especially useful in countries where higher frequency GDP statistics are unavailable.
This book constitutes the refereed proceedings of the 7th International Algorithmic Number Theory Symposium, ANTS 2006, held in Berlin, Germany in July 2006. The 37 revised full papers presented together with 4 invited papers were carefully reviewed and selected for inclusion in the book. The papers are organized in topical sections on algebraic number theory, analytic and elementary number theory, lattices, curves and varieties over fields of characteristic zero, curves over finite fields and applications, and discrete logarithms.
As the attacks in Norway, Munich and most recently Christchurch have shown: a new threat is now shaking liberal Western societies. Radicalized right-wing extremists – so-called lone wolves – are engaging in individually planned terror attacks. Written by an expert on terrorism and populism, this book highlights the dynamics of this new breed of terrorism. By providing in-depth insights into the biographies of individual perpetrators, it illustrates the changing profile of the typical lone terrorist. This new kind of terrorist engages in violence without being a member of a party or organization, yet is radicalized by a global right-wing subculture that communicates in virtual networks. This startling and well-written book reveals the ideological roots of lone wolf terrorism and urges governments and civil society to take the threat seriously and implement suitable countermeasures.
A laboratory study that investigates how algorithms come into existence. Algorithms--often associated with the terms big data, machine learning, or artificial intelligence--underlie the technologies we use every day, and disputes over the consequences, actual or potential, of new algorithms arise regularly. In this book, Florian Jaton offers a new way to study computerized methods, providing an account of where algorithms come from and how they are constituted, investigating the practical activities by which algorithms are progressively assembled rather than what they may suggest or require once they are assembled.
Principles of International Criminal Law is one of the leading textbooks in the field of international criminal justice. This fourth edition retains the detailed and systematic approach of previous editions, whist adding substantial new material on new theories, laws, and prosecutions.
In this new book, Florian Klinger gives readers a basic action-theoretical account of the aesthetic. While normal action fulfills a determinate concept, Klinger argues, aesthetic action performs an indeterminacy by suspending the action's conceptual resolution. Taking as examples work by Tino Sehgal, Kara Walker, Mazen Kerbaj, Marina Abramović, Cy Twombly, and Franz Kafka, the book examines indeterminacy in such instances as a walk that is at once leisurely and purposeful, a sound piece that is at once joyous and mournful and mechanical, or a sculpture that at once draws one in and shuts one out. Because it has irresolution as its point, aesthetic action presents itself as an unsettling of ourselves, our ways, our very sense of who we are. As performers of such action, we don't recognize one another as bearers of a shared human form as we normally would, but find ourselves tasked anew with figuring out what sharing a form would mean. In conversation with philosophers such as Kant, Hegel, Wittgenstein, and Anscombe; political thinkers such as Marx and Lorde; and contemporary interlocutors such as Michael Thompson, Sebastian Rödl, and Thomas Khurana, Klinger's book makes a case for a conception of the human form that systematically includes the aesthetic: an actualization of the form that is indeterminate and nevertheless rational. The book gives the project of Western philosophical aesthetics a long-overdue formulation for our present that aims to do justice to contemporary aesthetic production as it actually exists. It will appeal to those working in philosophy, art, and political thought.
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