Formulas

This book shows that the semantic analysis of modal notions of possibility and necessity can be used to enhance our understanding of the interpretation of reports of belief or emotional state. It introduces intuitive notation and terminology to express ideas in modern theories of modal interpretation that are normally represented in complex logical formulas, effectively updates the 1960s-era link between possible worlds and the semantics of propositional attitude ascriptions, and reconciles two disparate views of the role of events in semantic interpretation, that of Donald Davidson and that of David Lewis. It reduces a host of variable behaviors of propositional attitude ascription to an intuitive and precise distinction between ascriptions that merely express a commitment to propositional content versus ones that attribute a mental state to the holder of the propositional attitude. This leads to an explanation of the nature and effects of the language disorder of fluent aphasia.

functions and Hecke L-functions of an imaginary quadratic field，and various problems on elliptic modular forms. As to the values of Dirichlet L-functions， all previous papers and books reiterate a single old result with a single old method. After a review ofelementary Fourier analysis， the author presents completely new results with new methods. though old results will also be proved. No advanced knowledge of number theory is required up to this point. As applications， new formulas for the second factor ofthe class number of a cyclotomic field will be given. The second half of the book assumes familiarity with basic knowledge ofmodular forms. However，all definitions and facts are clearly stated， and precise references are given. The notion ofnearly holomorphic modular forms is introduced and applied to the determination of the critical values of Hecke L-functions of an imaginary quadratic field. Other notable features of the book are： (1) some new results on classical E

This combination of text and reference book describes the physical, plasma and chemical processes controlling the behaviour of ionospheres, upper atmospheres and exospheres. It summarises the structure, chemistry, dynamics and energetics of the terrestrial ionosphere and other solar system bodies, and discusses the processes, mechanisms and transport equations for solving fundamental research problems. This second edition incorporates new results, model developments and interpretations from the last ten years. It includes the latest material on neutral atmospheres; the terrestrial ionosphere at low, middle and high latitudes; and planetary atmospheres and ionospheres, where results from recent space missions have yielded fresh data. Appendices outline physical constants, mathematical formulas, transport coefficients, and other important parameters for ionospheric calculations. This is an essential resource for researchers studying ionospheres, upper atmospheres, aeronomy and plasma phy

Learn to calculate drug dosages safely and accurately! Math Calculations for Pharmacy Technicians, 3rd Edition helps you master the competencies required by the American Society of Health-System Pharmacists (ASHP). Designed specifically for Pharmacy Technicians, this practical worktext simplifies key calculation concepts and lets you work through hundreds of practice problems. Coverage includes a review of basic math skills, conversions between measurement systems, interpreting drug labels and physicians' orders, and calculating medication dosages based on a patient's age or body weight. The worktext format distills complex content into easy-to-understand concepts and calculations. Math Calculations for Pharmacy Technicians helps you develop the competencies you'll need for a successful career as a Pharmacy Technician.Hundreds of practice problems throughout covering calculations, conversions, and measurements.Step-by-step examples to break down complex equations and formulas into simp

A comprehensive account of both basic and advanced material in phylogeny estimation, focusing on computational and statistical issues. No background in biology or computer science is assumed, and there is minimal use of mathematical formulas, meaning that students from many disciplines, including biology, computer science, statistics, and applied mathematics, will find the text accessible. The mathematical and statistical foundations of phylogeny estimation are presented rigorously, following which more advanced material is covered. This includes substantial chapters on multi-locus phylogeny estimation, supertree methods, multiple sequence alignment techniques, and designing methods for large-scale phylogeny estimation. The author provides key analytical techniques to prove theoretical properties about methods, as well as addressing performance in practice for methods for estimating trees. Research problems requiring novel computational methods are also presented, so that graduate stud

WEBASSIGN: FINITE MATHEMATICS FOR THE MANAGERIAL, LIFE, AND SOCIAL SCIENCES, Twelfth Edition, is fully supported by WebAssign, the powerful online homework and course management system that engages students in learning the math. WebAssign includes new end-of-chapter exercises and pre-built assignments vetted by trusted subject matter experts along with robust course, section, assignment, and question settings and online testing to help instructors foster a deeper understanding of course concepts.CAREFULLY-CRAFTED EXERCISE SETS: SECTION EXERCISE SETS include Self-Check Exercises that let students solve problems and check their work against worked-out solutions, Concept Exercises that let students gauge their understanding, and Exercise Sets with a mix of rote and applied problems. CHAPTER REVIEW EXERCISE SETS include Summary of Principal Formulas and Terms for easy reference, fill-in-the-blank Concept Review questions that reinforce chapter terms and concepts, Review Exercises, and Befo

Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. This volume, the third publication in the Perspectives in Logic series, is a much-needed monograph on the metamathematics of first-order arithmetic. The authors pay particular attention to subsystems (fragments) of Peano arithmetic and give the reader a deeper understanding of the role of the axiom schema of induction and of the phenomenon of incompleteness. The reader is only assumed to know the basics of mathematical logic, which are reviewed in the preliminaries. Part I develops parts of mathematics and logic in various fragments. Part II is devoted to incompleteness. Finally, Part III studies systems that have the induction schema restricted to bounded formulas (bounded arithmetic).

Statistics is one of the most practical and essential courses that you will take, and a primary goal of this popular text is to make the task of learning statistics as simple as possible. Straightforward instruction, built-in learning aids, and real-world examples have made STATISTICS FOR THE BEHAVIORAL SCIENCES, 10th Edition the text selected most often by instructors for their students in the behavioral and social sciences. The authors provide a conceptual context that makes it easier to learn formulas and procedures, explaining why procedures were developed and when they should be used. This text will also instill the basic principles of objectivity and logic that are essential for science and valuable in everyday life, making it a useful reference long after you complete the course.

This thorough work presents the fundamental results of modular function theory as developed during the nineteenth and early-twentieth centuries. It features beautiful formulas and derives them using skillful and ingenious manipulations, especially classical methods often overlooked today. Starting with the work of Gauss, Abel, and Jacobi, the book then discusses the attempt by Dedekind to construct a theory of modular functions independent of elliptic functions. The latter part of the book explains how Hurwitz completed this task and includes one of Hurwitz's landmark papers, translated by the author, and delves into the work of Ramanujan, Mordell, and Hecke. For graduate students and experts in modular forms, this book demonstrates the relevance of these original sources and thereby provides the reader with new insights into contemporary work in this area.

This comprehensive, full-color guide provides detailed, easy-to-follow instructions for making and using approximately 250 herbal medicines at home, including practical tips and numerous effective formulas developed and tested by the authors, both expert herbalists with years of experience. Readers who appreciate the health-giving properties of herbal medicines but are discouraged by the high price of commercial products can now make their own preparations for a fraction of the cost. The authors tell you everything you need to know about harvesting, preparing, and administering herbs in many different forms, including fresh, bulk dried herbs, capsules, extracts in water, alcohol, glycerin, vinegar and oil, and even preparations like essential oils and flower essences. The book also covers topical applications of herbs as salves, lotions, poultices, tooth powders, ear drops, and more, and includes an extensive chapter on herbal hydrotherapy.The Modern Herbal Dispensary explains why diff

Networks are everywhere, from the internet, to social networks, and the genetic networks that determine our biological existence. Illustrated throughout in full colour, this pioneering textbook, spanning a wide range of topics from physics to computer science, engineering, economics and the social sciences, introduces network science to an interdisciplinary audience. From the origins of the six degrees of separation to explaining why networks are robust to random failures, the author explores how viruses like Ebola and H1N1 spread, and why it is that our friends have more friends than we do. Using numerous real-world examples, this innovatively designed text includes clear delineation between undergraduate and graduate level material. The mathematical formulas and derivations are included within Advanced Topics sections, enabling use at a range of levels. Extensive online resources, including films and software for network analysis, make this a multifaceted companion for anyone with an

This book shows that the semantic analysis of modal notions of possibility and necessity can be used to enhance our understanding of the interpretation of reports of belief or emotional state. It introduces intuitive notation and terminology to express ideas in modern theories of modal interpretation that are normally represented in complex logical formulas, effectively updates the 1960s-era link between possible worlds and the semantics of propositional attitude ascriptions, and reconciles two disparate views of the role of events in semantic interpretation, that of Donald Davidson and that of David Lewis. It reduces a host of variable behaviors of propositional attitude ascription to an intuitive and precise distinction between ascriptions that merely express a commitment to propositional content versus ones that attribute a mental state to the holder of the propositional attitude. This leads to an explanation of the nature and effects of the language disorder of fluent aphasia.

With this comprehensive guide you will learn how to apply Bayesian machine learning techniques systematically to solve various problems in speech and language processing. A range of statistical models is detailed, from hidden Markov models to Gaussian mixture models, n-gram models and latent topic models, along with applications including automatic speech recognition, speaker verification, and information retrieval. Approximate Bayesian inferences based on MAP, Evidence, Asymptotic, VB, and MCMC approximations are provided as well as full derivations of calculations, useful notations, formulas, and rules. The authors address the difficulties of straightforward applications and provide detailed examples and case studies to demonstrate how you can successfully use practical Bayesian inference methods to improve the performance of information systems. This is an invaluable resource for students, researchers, and industry practitioners working in machine learning, signal processing, and sp

The recent financial crisis has heightened the need for appropriate methodologies for managing and monitoring complex risks in financial markets. The measurement, management, and regulation of risks in portfolios composed of credits, credit derivatives, or life insurance contracts is difficult because of the nonlinearities of risk models, dependencies between individual risks, and the several thousands of contracts in large portfolios. The granularity principle was introduced in the Basel regulations for credit risk to solve these difficulties in computing capital reserves. In this book, authors Patrick Gagliardini and Christian Gouriéroux provide the first comprehensive overview of the granularity theory and illustrate its usefulness for a variety of problems related to risk analysis, statistical estimation, and derivative pricing in finance and insurance. They show how the granularity principle leads to analytical formulas for risk analysis that are simple to implement and accurate e

The recent financial crisis has heightened the need for appropriate methodologies for managing and monitoring complex risks in financial markets. The measurement, management, and regulation of risks in portfolios composed of credits, credit derivatives, or life insurance contracts is difficult because of the nonlinearities of risk models, dependencies between individual risks, and the several thousands of contracts in large portfolios. The granularity principle was introduced in the Basel regulations for credit risk to solve these difficulties in computing capital reserves. In this book, authors Patrick Gagliardini and Christian Gouriéroux provide the first comprehensive overview of the granularity theory and illustrate its usefulness for a variety of problems related to risk analysis, statistical estimation, and derivative pricing in finance and insurance. They show how the granularity principle leads to analytical formulas for risk analysis that are simple to implement and accurate e

This book is a comprehensive study of the Radon transform, which operates on a function by integrating it over hyperplanes. The book begins with an elementary and graphical introduction to the Radon transform, tomography and CT scanners, followed by a rigorous development of the basic properties of the Radon transform. Next the author introduces Grassmann manifolds in the study of the k-plane transform (a version of the Radon transform) which integrates over k-dimensional planes rather than hyperplanes. The remaining chapters are concerned with more advanced topics, such as the attenuated Radon transform and generalized Radon transforms defined by duality of homogeneous spaces and double fibrations. Questions of invertibility and the range of the Radon transform are dealt with and inversion formulas are developed with particular attention to functions on L2 spaces and some discussion of the case of Lp spaces.

The Dirichlet space is one of the three fundamental Hilbert spaces of holomorphic functions on the unit disk. It boasts a rich and beautiful theory, yet at the same time remains a source of challenging open problems and a subject of active mathematical research. This book is the first systematic account of the Dirichlet space, assembling results previously only found in scattered research articles, and improving upon many of the proofs. Topics treated include: the Douglas and Carleson formulas for the Dirichlet integral, reproducing kernels, boundary behaviour and capacity, zero sets and uniqueness sets, multipliers, interpolation, Carleson measures, composition operators, local Dirichlet spaces, shift-invariant subspaces, and cyclicity. Special features include a self-contained treatment of capacity, including the strong-type inequality. The book will be valuable to researchers in function theory, and with over 100 exercises it is also suitable for self-study by graduate students.

Counterinsurgency has staked its claim in the new century as the new American way of war. Yet, the wars in Afghanistan and Iraq have revived a historical debate about the costs - monetary, political and moral - of operations designed to eliminate insurgents and build nations. Today's counterinsurgency proponents point to 'small wars' past to support their view that the enemy is 'biddable' if the correct tactical formulas are applied. Douglas Porch's sweeping history of counterinsurgency campaigns carried out by the three 'providential nations' of France, Britain and the United States, ranging from nineteenth-century colonial conquests to General Petraeus' 'Surge' in Iraq, challenges the contemporary mythologising of counterinsurgency as a humane way of war. The reality, he reveals, is that 'hearts and minds' has never been a recipe for lasting stability and that past counterinsurgency campaigns have succeeded not through state-building but by shattering and dividing societies while uns

Counterinsurgency has staked its claim in the new century as the new American way of war. Yet, the wars in Afghanistan and Iraq have revived a historical debate about the costs - monetary, political and moral - of operations designed to eliminate insurgents and build nations. Today's counterinsurgency proponents point to 'small wars' past to support their view that the enemy is 'biddable' if the correct tactical formulas are applied. Douglas Porch's sweeping history of counterinsurgency campaigns carried out by the three 'providential nations' of France, Britain and the United States, ranging from nineteenth-century colonial conquests to General Petraeus' 'Surge' in Iraq, challenges the contemporary mythologising of counterinsurgency as a humane way of war. The reality, he reveals, is that 'hearts and minds' has never been a recipe for lasting stability and that past counterinsurgency campaigns have succeeded not through state-building but by shattering and dividing societies while uns

A concise introduction to Feynman diagram techniques, this book shows how they can be applied to the analysis of complex many-particle systems, and offers a review of the essential elements of quantum mechanics, solid state physics and statistical mechanics. Alongside a detailed account of the method of second quantization, the book covers topics such as Green's and correlation functions, diagrammatic techniques and superconductivity, and contains several case studies. Some background knowledge in quantum mechanics, solid state physics and mathematical methods of physics is assumed. Detailed derivations of formulas and in-depth examples and chapter exercises from various areas of condensed matter physics make this a valuable resource for both researchers and advanced undergraduate students in condensed matter theory, many-body physics and electrical engineering. Solutions to exercises are available online.

The third edition of this classic textbook is a quantitative introduction for advanced undergraduates and graduate students. It gently guides students from Newton's gravitational theory to special relativity, and then to the relativistic theory of gravitation. General relativity is approached from several perspectives: as a theory constructed by analogy with Maxwell's electrodynamics, as a relativistic generalization of Newton's theory, and as a theory of curved spacetime. The authors provide a concise overview of the important concepts and formulas, coupled with the experimental results underpinning the latest research in the field. Numerous exercises in Newtonian gravitational theory and Maxwell's equations help students master essential concepts for advanced work in general relativity, while detailed spacetime diagrams encourage them to think in terms of four-dimensional geometry. Featuring comprehensive reviews of recent experimental and observational data, the text concludes with

This textbook, based on the authors' fifteen years of teaching, is a complete teaching tool for turning students into logic designers in one semester. Each chapter describes new concepts, giving extensive applications and examples. Assuming no prior knowledge of discrete mathematics, the authors introduce all background in propositional logic, asymptotics, graphs, hardware and electronics. Important features of the presentation are: • All material is presented in full detail. Every designed circuit is formally specified and implemented, the correctness of the implementation is proved, and the cost and delay are analyzed • Algorithmic solutions are offered for logical simulation, computation of propagation delay and minimum clock period • Connections are drawn from the physical analog world to the digital abstraction • The language of graphs is used to describe formulas and circuits • Hundreds of figures, examples and exercises enhance understanding. The extensive website (http://www.en

Providing a fundamental introduction to all aspects of modern plasma chemistry, this book describes mechanisms and kinetics of chemical processes in plasma, plasma statistics, thermodynamics, fluid mechanics and electrodynamics, as well as all major electric discharges applied in plasma chemistry. Fridman considers most of the major applications of plasma chemistry, from electronics to thermal coatings, from treatment of polymers to fuel conversion and hydrogen production and from plasma metallurgy to plasma medicine. It is helpful to engineers, scientists and students interested in plasma physics, plasma chemistry, plasma engineering and combustion, as well as chemical physics, lasers, energy systems and environmental control. The book contains an extensive database on plasma kinetics and thermodynamics and numerical formulas for practical calculations related to specific plasma-chemical processes and applications. Problems and concept questions are provided, helpful in courses relate

This textbook presents the chemistry of the environment using the full strength of physical, inorganic and organic chemistry, in addition to the necessary mathematics and physics. It provides a broad yet thorough description of the environment and the environmental impact of human activity using scientific principles. It gives an accessible account while paying attention to the fundamental basis of the science, showing derivations of formulas and giving primary references and historical insight. The authors make consistent use of professionally accepted nomenclature (IUPAC and SI), allowing transparent access to the material by students and scientists from other fields. This textbook has been developed through many years of feedback from students and colleagues. It includes more than 400 online student exercises that have been class tested and refined. The book will be invaluable in environmental chemistry courses for advanced undergraduate and graduate students and professionals in ch

This textbook presents the chemistry of the environment using the full strength of physical, inorganic and organic chemistry, in addition to the necessary mathematics and physics. It provides a broad yet thorough description of the environment and the environmental impact of human activity using scientific principles. It gives an accessible account while paying attention to the fundamental basis of the science, showing derivations of formulas and giving primary references and historical insight. The authors make consistent use of professionally accepted nomenclature (IUPAC and SI), allowing transparent access to the material by students and scientists from other fields. This textbook has been developed through many years of feedback from students and colleagues. It includes more than 400 online student exercises that have been class tested and refined. The book will be invaluable in environmental chemistry courses for advanced undergraduate and graduate students and professionals in ch

Formal systems that describe computations over syntactic structures occur frequently in computer science. Logic programming provides a natural framework for encoding and animating such systems. However, these systems often embody variable binding, a notion that must be treated carefully at a computational level. This book aims to show that a programming language based on a simply typed version of higher-order logic provides an elegant, declarative means for providing such a treatment. Three broad topics are covered in pursuit of this goal. First, a proof-theoretic framework that supports a general view of logic programming is identified. Second, an actual language called λProlog is developed by applying this view to higher-order logic. Finally, a methodology for programming with specifications is exposed by showing how several computations over formal objects such as logical formulas, functional programs, and λ-terms and π-calculus expressions can be encoded in λProlog.

Scientists need statistics. Increasingly this is accomplished using computational approaches. Freeing readers from the constraints, mysterious formulas and sophisticated mathematics of classical statistics, this book is ideal for researchers who want to take control of their own statistical arguments. It demonstrates how to use spreadsheet macros to calculate the probability distribution predicted for any statistic by any hypothesis. This enables readers to use anything that can be calculated (or observed) from their data as a test statistic and hypothesize any probabilistic mechanism that can generate data sets similar in structure to the one observed. A wide range of natural examples drawn from ecology, evolution, anthropology, palaeontology and related fields give valuable insights into the application of the described techniques, while complete example macros and useful procedures demonstrate the methods in action and provide starting points for readers to use or modify in their ow

Building upon the ideas introduced in their previous book, Derivatives in Financial Markets with Stochastic Volatility, the authors study the pricing and hedging of financial derivatives under stochastic volatility in equity, interest-rate, and credit markets. They present and analyze multiscale stochastic volatility models and asymptotic approximations. These can be used in equity markets, for instance, to link the prices of path-dependent exotic instruments to market implied volatilities. The methods are also used for interest rate and credit derivatives. Other applications considered include variance-reduction techniques, portfolio optimization, forward-looking estimation of CAPM 'beta', and the Heston model and generalizations of it. 'Off-the-shelf' formulas and calibration tools are provided to ease the transition for practitioners who adopt this new method. The attention to detail and explicit presentation make this also an excellent text for a graduate course in financial and ap

The subject of special functions is often presented as a collection of disparate results, which are rarely organised in a coherent way. This book answers the need for a different approach to the subject. The authors' main goals are to emphasise general unifying principles coherently and to provide clear motivation, efficient proofs, and original references for all of the principal results. The book covers standard material, but also much more, including chapters on discrete orthogonal polynomials and elliptic functions. The authors show how a very large part of the subject traces back to two equations - the hypergeometric equation and the confluent hypergeometric equation - and describe the various ways in which these equations are canonical and special. Providing ready access to theory and formulas, this book serves as an ideal graduate-level textbook as well as a convenient reference.

This book examines how national law is treated in WTO law, both in the WTO treaty and dispute settlement cases. The WTO treaty contains a set of far-reaching obligations establishing a systemic and constitutional framework of interaction between WTO law and national law. WTO dispute settlement operates as an international layer of judicial review of national laws and administrative, judicial or quasi-judicial measures. Consequently, much of the WTO dispute settlement decisions and rulings relate in different ways to Members' national laws. Yet, up until the publication of this book, there was no systematic analysis of this vastly important subject. This book provides a thorough map of an increasingly complex field. In doing so, it extends the enquiry beyond well-known formulas and combines practical analysis with principled discussion of how the treatment of national law in international law can and should ensure effectiveness of international rules and promote good governance within n

This 1908 work supplements Hall's Studies in English Official Historical Documents. It gives examples of a wide range of English diplomatic documents from the seventh to the nineteenth centuries. These are arranged according to type and purpose, the majority in Latin, but others in French or English. The intention is to assist the user of such archival materials, by familiarising them with the format and language used in each kind of document, and explaining why and how they were written. The 211 transcriptions were made by palaeography students at the London School of Economics, and classified and edited with extensive notes by Mr Hall. They are not literal transcriptions, as contractions have been expanded, and the punctuation and capitalisation modernised. To save space, standard formulas have not been repeated each time. Despite the lack of any illustrations of originals, the book filled a need long felt by students of history.

This 1909 work forms a second supplement to Hall's Studies in English Official Historical Documents. It gives examples of a wide range of English ministerial and judicial documents from the ninth to the seventeenth centuries. These are arranged according to type and purpose, the majority in Latin. The intention is to assist the user of such archival materials, by familiarising them with the format and language used in each kind of document, and explaining why and how they were written. The 80 transcriptions were made by palaeography students at the London School of Economics, and classified and edited with extensive notes by Mr Hall. They are not literal transcriptions, as contractions have been expanded, and the punctuation and capitalisation modernised. To save space standard formulas have not been repeated each time. Despite the lack of any illustrations of originals, the book filled a need long felt by students of history.

This is a self-contained 2010 account of the state of the art in classical complex multiplication that includes recent results on rings of integers and applications to cryptography using elliptic curves. The author is exhaustive in his treatment, giving a thorough development of the theory of elliptic functions, modular functions and quadratic number fields and providing a concise summary of the results from class field theory. The main results are accompanied by numerical examples, equipping any reader with all the tools and formulas they need. Topics covered include: the construction of class fields over quadratic imaginary number fields by singular values of the modular invariant j and Weber's tau-function; explicit construction of rings of integers in ray class fields and Galois module structure; the construction of cryptographically relevant elliptic curves over finite fields; proof of Berwick's congruences using division values of the Weierstrass p-function; relations between ell

A reader-friendly introduction to geostatistics for students and researchers struggling with statistics. Using simple, clear explanations for introductory and advanced material, it demystifies complex concepts and makes formulas and statistical tests easy to apply. Beginning with a critical evaluation of experimental and sampling design, the book moves on to explain essential concepts of probability, statistical significance and type 1 and type 2 error. An accessible graphical explanation of analysis of variance (ANOVA) leads onto advanced ANOVA designs, correlation and regression, and non-parametric tests including chi-square. Finally, it introduces the essentials of multivariate techniques, multi-dimensional scaling and cluster analysis, analysis of sequences and concepts of spatial analysis. Illustrated with wide-ranging examples from topics across the Earth and environmental sciences, Geostatistics Explained can be used for undergraduate courses or for self-study and reference. Wor

A reader-friendly introduction to geostatistics for students and researchers struggling with statistics. Using simple, clear explanations for introductory and advanced material, it demystifies complex concepts and makes formulas and statistical tests easy to apply. Beginning with a critical evaluation of experimental and sampling design, the book moves on to explain essential concepts of probability, statistical significance and type 1 and type 2 error. An accessible graphical explanation of analysis of variance (ANOVA) leads onto advanced ANOVA designs, correlation and regression, and non-parametric tests including chi-square. Finally, it introduces the essentials of multivariate techniques, multi-dimensional scaling and cluster analysis, analysis of sequences and concepts of spatial analysis. Illustrated with wide-ranging examples from topics across the Earth and environmental sciences, Geostatistics Explained can be used for undergraduate courses or for self-study and reference. Wor

Written by a former news reporter and editor, News Talk gives us an insider's view of the media, showing how journalists select and construct their news stories. Colleen Cotter goes behind the scenes, revealing how language is chosen and shaped by news staff into the stories we read and hear. Tracing news stories from start to finish, she shows how the actions of journalists and editors - and the limitations of news writing formulas - may distort a story that was prepared with the most determined effort to be fair and accurate. Using insights from both linguistics and journalism, News Talk is a remarkable picture of a hidden world and its working practices on both sides of the Atlantic. It will interest those involved in language study, media and communication studies and those who want to understand how media shape our language and our view of the world.

Written by a former news reporter and editor, News Talk gives us an insider's view of the media, showing how journalists select and construct their news stories. Colleen Cotter goes behind the scenes, revealing how language is chosen and shaped by news staff into the stories we read and hear. Tracing news stories from start to finish, she shows how the actions of journalists and editors - and the limitations of news writing formulas - may distort a story that was prepared with the most determined effort to be fair and accurate. Using insights from both linguistics and journalism, News Talk is a remarkable picture of a hidden world and its working practices on both sides of the Atlantic. It will interest those involved in language study, media and communication studies and those who want to understand how media shape our language and our view of the world.

This combination of text and reference book describes the physical, plasma and chemical processes controlling the behaviour of ionospheres, upper atmospheres and exospheres. It summarises the structure, chemistry, dynamics and energetics of the terrestrial ionosphere and other solar system bodies, and discusses the processes, mechanisms and transport equations for solving fundamental research problems. This second edition incorporates new results, model developments and interpretations from the last ten years. It includes the latest material on neutral atmospheres; the terrestrial ionosphere at low, middle and high latitudes; and planetary atmospheres and ionospheres, where results from recent space missions have yielded fresh data. Appendices outline physical constants, mathematical formulas, transport coefficients, and other important parameters for ionospheric calculations. This is an essential resource for researchers studying ionospheres, upper atmospheres, aeronomy and plasma phy

Sure to be influential, this book lays the foundations for the use of algebraic geometry in statistical learning theory. Many widely used statistical models and learning machines applied to information science have a parameter space that is singular: mixture models, neural networks, HMMs, Bayesian networks, and stochastic context-free grammars are major examples. Algebraic geometry and singularity theory provide the necessary tools for studying such non-smooth models. Four main formulas are established: 1. the log likelihood function can be given a common standard form using resolution of singularities, even applied to more complex models; 2. the asymptotic behaviour of the marginal likelihood or 'the evidence' is derived based on zeta function theory; 3. new methods are derived to estimate the generalization errors in Bayes and Gibbs estimations from training errors; 4. the generalization errors of maximum likelihood and a posteriori methods are clarified by empirical process theory o

In 1821, the French mathematician Augustin-Louis Cauchy published Cours d'Analyse de L'École Royale Polytechnique, a textbook designed to teach his students the basic theorems of calculus in as rigorous a way as possible. Cauchy was a pioneer of mathematical analysis, a branch of mathematics concerned with the idea of a limit, whether of a sequence or of a function. This book consists of 12 chapters that discuss real functions, infinitely small and large quantities, substitution groups, symmetrical functions, unknown variables, imaginary functions, and rational fractions in a recurrent series. It also provides formulas for solving various problems, such as converting the sine and cosine of a multiple polynomial arc and the Lagrange interpolation. Cauchy built on the work of Leibniz and Newton and is generally regarded as one of the greatest mathematicians in history. This is a reissue of one of his most important contributions.