Despite its seemingly deterministic nature, the study of whole numbers, especially prime numbers, has many interactions with probability theory, the theory of random processes and events. This surprising connection was first discovered around 1920, but in recent years the links have become much deeper and better understood. Aimed at beginning graduate students, this textbook is the first to explain some of the most modern parts of the story. Such topics include the Chebychev bias, universality of the Riemann zeta function, exponential sums and the bewitching shapes known as Kloosterman paths. Emphasis is given throughout to probabilistic ideas in the arguments, not just the final statements, and the focus is on key examples over technicalities. The book develops probabilistic number theory from scratch, with short appendices summarizing the most important background results from number theory, analysis and probability, making it a readable and incisive introduction to this beautiful area of mathematics.
Analytic Number Theory distinguishes itself by the variety of tools it uses to establish results. One of the primary attractions of this theory is its vast diversity of concepts and methods. The main goals of this book are to show the scope of the theory, both in classical and modern directions, and to exhibit its wealth and prospects, beautiful theorems, and powerful techniques. The book is written with graduate students in mind, and the authors nicely balance clarity, completeness, and generality. The exercises in each section serve dual purposes, some intended to improve readers' understanding of the subject and others providing additional information. Formal prerequisites for the major part of the book do not go beyond calculus, complex analysis, integration, and Fourier series and integrals. In later chapters automorphic forms become important, with much of the necessary information about them included in two survey chapters.
Representation theory is an important part of modern mathematics, not only as a subject in its own right but also as a tool for many applications. It provides a means for exploiting symmetry, making it particularly useful in number theory, algebraic geometry, and differential geometry, as well as classical and modern physics. The goal of this book is to present, in a motivated manner, the basic formalism of representation theory as well as some important applications. The style is intended to allow the reader to gain access to the insights and ideas of representation theory--not only to verify that a certain result is true, but also to explain why it is important and why the proof is natural. The presentation emphasizes the fact that the ideas of representation theory appear, sometimes in slightly different ways, in many contexts. Thus the book discusses in some detail the fundamental notions of representation theory for arbitrary groups. It then considers the special case of complex representations of finite groups and discusses the representations of compact groups, in both cases with some important applications. There is a short introduction to algebraic groups as well as an introduction to unitary representations of some noncompact groups. The text includes many exercises and examples.
Among the modern methods used to study prime numbers, the 'sieve' has been one of the most efficient. Originally conceived by Linnik in 1941, the 'large sieve' has developed extensively since the 1960s, with a recent realization that the underlying principles were capable of applications going well beyond prime number theory. This book develops a general form of sieve inequality, and describes its varied applications, including the study of families of zeta functions of algebraic curves over finite fields; arithmetic properties of characteristic polynomials of random unimodular matrices; homological properties of random 3-manifolds; and the average number of primes dividing the denominators of rational points on elliptic curves. Also covered in detail are the tools of harmonic analysis used to implement the forms of the large sieve inequality, including the Riemann Hypothesis over finite fields, and Property (T) or Property (tau) for discrete groups.
Among the modern methods used to study prime numbers, the 'sieve' has been one of the most efficient. Originally conceived by Linnik in 1941, the 'large sieve' has developed extensively since the 1960s, with a recent realization that the underlying principles were capable of applications going well beyond prime number theory. This book develops a general form of sieve inequality, and describes its varied applications, including the study of families of zeta functions of algebraic curves over finite fields; arithmetic properties of characteristic polynomials of random unimodular matrices; homological properties of random 3-manifolds; and the average number of primes dividing the denominators of rational points on elliptic curves. Also covered in detail are the tools of harmonic analysis used to implement the forms of the large sieve inequality, including the Riemann Hypothesis over finite fields, and Property (T) or Property (tau) for discrete groups.
Analytic Number Theory distinguishes itself by the variety of tools it uses to establish results. One of the primary attractions of this theory is its vast diversity of concepts and methods. The main goals of this book are to show the scope of the theory, both in classical and modern directions, and to exhibit its wealth and prospects, beautiful theorems, and powerful techniques. The book is written with graduate students in mind, and the authors nicely balance clarity, completeness, and generality. The exercises in each section serve dual purposes, some intended to improve readers' understanding of the subject and others providing additional information. Formal prerequisites for the major part of the book do not go beyond calculus, complex analysis, integration, and Fourier series and integrals. In later chapters automorphic forms become important, with much of the necessary information about them included in two survey chapters.
Representation theory is an important part of modern mathematics, not only as a subject in its own right but also as a tool for many applications. It provides a means for exploiting symmetry, making it particularly useful in number theory, algebraic geometry, and differential geometry, as well as classical and modern physics. The goal of this book is to present, in a motivated manner, the basic formalism of representation theory as well as some important applications. The style is intended to allow the reader to gain access to the insights and ideas of representation theory--not only to verify that a certain result is true, but also to explain why it is important and why the proof is natural. The presentation emphasizes the fact that the ideas of representation theory appear, sometimes in slightly different ways, in many contexts. Thus the book discusses in some detail the fundamental notions of representation theory for arbitrary groups. It then considers the special case of complex representations of finite groups and discusses the representations of compact groups, in both cases with some important applications. There is a short introduction to algebraic groups as well as an introduction to unitary representations of some noncompact groups. The text includes many exercises and examples.
An information system may be regarded as an organized set of resources, both technological and human. Security should take this specificity into consideration in order to ensure an overall security of information systems. The security of information systems is usually tackled in a technological perspective. This book proposes to focus not only on information systems' security in a technological perspective, but also in a human, managerial and organizational perspective.
1917. Nivelle – ‘the butcher’ – commands the French Army, and the attacks he keeps ordering are pointless slaughters. The soldiers can’t take it any more. Discontent is turning into rebellion, and a petition is being circulated in secret. When it makes its way to the men of Sergeant Sabiane, something snaps in them, and what begins as a simple cry of defiance becomes a full-blown mutiny when a handful of them decide to take the petition to Paris ...
Drastic improvements in both access to satellite images and data processing tools today allow near real-time observation of Earth surface deformations. Remote sensing imagery is thus a powerful, reliable and spatially dense source of information that can be used to understand the Earth and its surface manifestations as well as mitigate natural hazards. This book offers for the first time a complete overview of the methodological approaches developed to measure surface displacement using synthetic aperture radar (SAR) and optical imagery, as well as their applications in the monitoring of major geophysical phenomena. More specifically, the first part of the book presents the theory behind SAR interferometry (InSAR) and image correlation and its latest developments. In the second part, most of the geophysical phenomena that trigger Earth surface deformations are reviewed. Surface Displacement Measurement from Remote Sensing Images unveils the potential and sensitivity of the measurement of Earth surface displacements from remote sensing imagery.
Industrialization drives the sustained growth in jobs and productivity that marks the developmental take-off of most developed economies. Yet, academics and policy makers have questioned the role of manufacturing in development for late industrializers, especially ith more job creation. Industrialization drives the sustained growth in jobs and productivity that marks the developmental take-off of most developed economies. Yet, academics and policy makers have questioned the role of manufacturing in development for late industrializers, especially in view of rapid advancements in technologies and restructuring of international trade.Concurrently, industrialization and structural transformation are integral to the African Union’s Agenda 2063 and the development strategies of several countries in Sub-Saharan Africa (SSA). Given this renewed interest in industrialization across the region, a central question is not whether SSA countries should pursue industrialization as a potential path to sustainable growth but how to promote the prospects of industrialization. Industrialization in Sub-Saharan Africa: Seizing Opportunities in Global Value Chains addresses this question by reassessing the prospects for industrialization in SSA countries through integration into global value chains. It also examines the role of policy in enhancing these prospects. The main findings indicate that • SSA has not experienced premature deindustrialization; the region has witnessed substantial growth in manufacturing jobs despite a lack of improvement in the contribution of manufacturing value-added to GDP. • The region’s integration into manufacturing global value chains is reasonably high but it is dominated by exports of primary products and engagement in low-skill tasks. • Global value chain integration has led to job growth, and backward integration is associated with more job creation. The report emphasizes the role of policy in maintaining a competitive market environment, promoting productivity growth, and investing in skills development and enabling sectors such as infrastructure and finance. Policy makers can strengthen the global value chain linkages by (1) increasing the value-added content of current exports, (2) upgrading into high-skill tasks, and (3) creating comparative advantages in knowledge-intensive industries.
Lieutenant Kazinsky has finally proven his loyalty once and for all to his small band of rebels. The ambush he set for their pursuers with Sergeant Sabiane destroyed their vehicles and even injured their leader, Morvan. But ‘the Puzzle’ never gives up on a prey. Soon, the mutineers must face the hardest choice of all. Continuing means killing other Frenchmen. Stopping means abandoning their friends, maybe even betraying them. In the end, do they even stand a chance of succeeding?
In most developed countries there is a palpable sense of confusion about the contemporary state of the world. Much that was taken for granted a decade or two ago is being questioned, and there is a widespread urge to try and understand how we reached our present situation, and where we are heading. In this major new book, the leading sociologist, historical anthropologist and demographer Emmanuel Todd sheds fresh light on our current predicament by reconstructing the historical dynamics of human societies from the Stone Age to the present. Eschewing the tendency to attribute special causal significance to the economy, Todd develops an anthropological account of history, focusing on the long-term dynamics of family systems and their links to religion and ideology – what he sees as the slow-moving, unconscious level of society, in contrast to the conscious level of the economy and politics. He also analyses the dramatic changes brought about by the spread of education. This enables him to explain the different historical trajectories of the advanced nations and the growing divergence between them, a divergence that can be observed in such phenomena as the rise of the Anglosphere in the modern period, the paradox of a Homo americanus who is both innovative and archaic, the startling electoral success of Donald Trump, the lack of realism in the will to power shown by Germany and China, the emergence of stable authoritarian democracy in Russia, the new introversion of Japan and the recent turbulent developments in Europe, including Brexit. This magisterial account of human history brings into sharp focus the massive transformations taking place in the world today and shows that these transformations have less to do with the supposedly homogenizing effects of globalization and the various reactions to it than with an ethnic diversity that is deeply rooted in the long history of human evolution.
Génératrice d’emplois et de productivité, l’industrialisation est un vecteur de croissance qui coïncide souvent avec l’accélération du développement dans les économies les plus avancées. Cela étant, du fait de la rapidité des avancées technologiques et des restructurations qu’a connues le commerce international, certains chercheurs et décideurs remettent aujourd’hui en cause les contributions de l’industrie manufacturière au développement dans les Etats où son apparition est tardive. Dans le même temps, l’industrialisation et les transformations structurelles font partie intégrante de l’Agenda 2063 de l’Union africaine et des stratégies de développement de nombreux pays d’Afrique sub-saharienne. A la lumière de ce regain d’intérêt pour l’industrialisation dans l’ensemble de la région, il importe moins de savoir si les pays d’Afrique sub-saharienne doivent considérer l’industrialisation comme l’une des voies vers la croissance durable que de promouvoir effi cacement les perspectives ouvertes par cette dernière. L’industrialisation en Afrique subsaharienne : Saisir les opportunités offertes par les chaînes de valeur mondiales se penche sur cette question en proposant de réévaluer les perspectives d’industrialisation des pays d’Afrique sub-saharienne au travers de leur intégration dans les chaînes de valeur mondiales et en examinant le rôle de la politiques dans le renforcement de ces perspectives.Les principaux enseignements de cette étude indiquent que • L’Afrique sub-saharienne n’a pas connu de désindustrialisation précoce; au contraire, la région a bénéfi cié d’une croissance substantielle de l’emploi manufacturier en dépit d’une contribution toujours limitée de la valeur ajoutée industrielle au PIB. • L’intégration de la région aux chaînes de valeur industrielles mondiales reste relativement élevée, bien qu’elle soit marquée par la présence dominante des produits primaires et par le recours à l’emploi peu qualifi é. • L’intégration aux chaînes de valeur mondiales conduit à des créations d’emplois et l’intégration verticale en amont permet d’en créer encore davantage. Le présent ouvrage souligne l’importance des politiques dans le maintien d’un marché compétitif, dans la promotion d’une hausse de la productivité, dans l’encouragement du développement des compétences et dans l’accompagnement de secteurs tels que les infrastructures et la fi nance. Les décideurs politiques peuvent renforcer les connections des chaînes de valeur mondiales 1) en augmentant la valeur ajoutée des produits d’export existants, 2) en encourageant la reconversion vers l’emploi hautement qualifi é et 3) en créant des avantages comparatifs pour les industries centrées sur les savoirs.
This book starts off from a philosophical premise: nobody can be in the world unless they are born into the world. It examines this premise in the light of the theological belief that birth serves, or ought to serve, as a model for understanding what resurrection could signify for us today. After all, the modern Christian needs to find some way of understanding resurrection, and the dogma of the resurrection of the body is vacuous unless we can relate it philosophically to our own world of experience. Nicodemus first posed the question "How can anyone be born after having grown old? Can one enter a second time into the mother's womb and be born?" This book reads that problem in the context of contemporary philosophy (particularly the thought of Husserl, Heidegger, Sartre, Merleau-Ponty, and Deleuze). A phenomenology of the body born "from below" is seen as a paradigm for a theology of spiritual rebirth, and for rebirth of the body from "on high." The Resurrection changes everything in Christianity—but it is also our own bodies that must be transformed in resurrection, as Christ is transfigured. And the way in which I hope to be resurrected bodily in God, in the future, depends upon the way in which I live bodily today.
TOPICS IN THE BOOK Tender Evaluation Process and Operational Performance of Service State Corporations in Kenya Emerging Trends in Healthcare Supply Chain: An Approach to Agile Services Logistics Innovation and Its Influence on Performance of Building and Construction Manufacturing Firms in Kenya Green Distribution Systems and Performance of Building and Construction Manufacturing Firms in Kenya Transactional Supply Chain Governance and Performance of Agro Processing Firms in Kenya The Influence of Information Security Management on Operational Performance of Humanitarian Value Chains in Arid and Semi-Arid Lands of Kenya
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