The present collection of formulas has been composed for students of economics or management science at universities, colleges and trade schools. It contains basic knowledge in mathematics, financial mathematics and statistics in a compact and clearly arranged form. This volume is meant to be a reference work to be used by students of undergraduate courses together with a textbook, and by researchers in need of exact statements of mathematical results. People dealing with practical or applied problems will also find this collection to be an efficient and easy-to-use work of reference.
This proceedings volume is from the international conference on Banach Algebras and Their Applications held at the University of Alberta (Edmonton). It contains a collection of refereed research papers and high-level expository articles that offer a panorama of Banach algebra theory and its manifold applications. Topics in the book range from - theory to abstract harmonic analysis to operator theory. It is suitable for graduate students and researchers interested in Banach algebras.
The origins of the mathematics in this book date back more than two thou sand years, as can be seen from the fact that one of the most important algorithms presented here bears the name of the Greek mathematician Eu clid. The word "algorithm" as well as the key word "algebra" in the title of this book come from the name and the work of the ninth-century scientist Mohammed ibn Musa al-Khowarizmi, who was born in what is now Uzbek istan and worked in Baghdad at the court of Harun al-Rashid's son. The word "algorithm" is actually a westernization of al-Khowarizmi's name, while "algebra" derives from "al-jabr," a term that appears in the title of his book Kitab al-jabr wa'l muqabala, where he discusses symbolic methods for the solution of equations. This close connection between algebra and al gorithms lasted roughly up to the beginning of this century; until then, the primary goal of algebra was the design of constructive methods for solving equations by means of symbolic transformations. During the second half of the nineteenth century, a new line of thought began to enter algebra from the realm of geometry, where it had been successful since Euclid's time, namely, the axiomatic method.
The theory of traces employs techniques and tackles problems from quite diverse areas which include formal language theory, combinatorics, graph theory, algebra, logic, and the theory of concurrent systems. In all these areas the theory of traces has led to interesting problems and significant results. It has made an especially big impact in formal language theory and the theory of concurrent systems. In both these disciplines it is a well-recognized and dynamic research area. Within formal language theory it yields the theory of partially commutative monoids, and provides an important connection between languages and graphs. Within the theory of concurrent systems it provides an important formal framework for the analysis and synthesis of concurrent systems.This monograph covers all important research lines of the theory of traces; each chapter is devoted to one research line and is written by leading experts. The book is organized in such a way that each chapter can be read independently ? and hence it is very suitable for advanced courses or seminars on formal language theory, the theory of concurrent systems, the theory of semigroups, and combinatorics. An extensive bibliography is included. At present, there is no other book of this type on trace theory.
Ernst Specker has made decisive contributions towards shaping direc tions in topology, algebra, mathematical logic, combinatorics and algorith mic over the last 40 years. We have derived great pleasure from marking his seventieth birthday by editing the majority of his scientific publications, and thus making his work available in a unified form to the mathematical community. In order to convey an idea of the richness of his personality, we have also included one of his sermons. Of course, the publication of these Selecta can pay tribute only to the writings of Ernst Specker. It cannot adequately express his originality and wisdom as a person nor the fascination he exercises over his students, colleagues and friends. We can do no better than to quote from Hao Wang in the 'Festschrift' Logic and Algorithmic I: Specker was ill for an extended period before completing his formal education. He had the leisure to think over many things. This experi ence may have helped cultivating his superiority as a person. In terms of traditional Chinese categories, I would say there is a taoist trait in him in the sense of being more detached, less competitive, and more under standing. I believe he has a better sense of what is important in life and arranges his life better than most logicians. We are grateful to Birkhauser Verlag for the production of this Selecta volume. Our special thanks go to Jonas Meon for sharing with us his intimate knowledge of his friend Ernst Specker.
The idea behind this book is to provide the mathematical foundations for assessing modern developments in the Information Age. It deepens and complements the basic concepts, but it also considers instructive and more advanced topics. The treatise starts with a general chapter on algebraic structures; this part provides all the necessary knowledge for the rest of the book. The next chapter gives a concise overview of cryptography. Chapter 3 on number theoretic algorithms is important for developping cryptosystems, Chapter 4 presents the deterministic primality test of Agrawal, Kayal, and Saxena. The account to elliptic curves again focuses on cryptographic applications and algorithms. With combinatorics on words and automata theory, the reader is introduced to two areas of theoretical computer science where semigroups play a fundamental role.The last chapter is devoted to combinatorial group theory and its connections to automata. Contents: Algebraic structures Cryptography Number theoretic algorithms Polynomial time primality test Elliptic curves Combinatorics on words Automata Discrete infinite groups
Storage Management in Data Centers helps administrators tackle the complexity of data center mass storage. It shows how to exploit the potential of Veritas Storage Foundation by conveying information about the design concepts of the software as well as its architectural background. Rather than merely showing how to use Storage Foundation, it explains why to use it in a particular way, along with what goes on inside. Chapters are split into three sections: An introductory part for the novice user, a full-featured part for the experienced, and a technical deep dive for the seasoned expert. An extensive troubleshooting section shows how to fix problems with volumes, plexes, disks and disk groups. A snapshot chapter gives detailed instructions on how to use the most advanced point-in-time copies. A tuning chapter will help you speed up and benchmark your volumes. And a special chapter on split data centers discusses latency issues as well as remote mirroring mechanisms and cross-site volume maintenance. All topics are covered with the technical know how gathered from an aggregate thirty years of experience in consulting and training in data centers all over the world.
Stochastic Processes for Insurance and Finance offers a thorough yet accessible reference for researchers and practitioners of insurance mathematics. Building on recent and rapid developments in applied probability, the authors describe in general terms models based on Markov processes, martingales and various types of point processes. Discussing frequently asked insurance questions, the authors present a coherent overview of the subject and specifically address: The principal concepts from insurance and finance Practical examples with real life data Numerical and algorithmic procedures essential for modern insurance practices Assuming competence in probability calculus, this book will provide a fairly rigorous treatment of insurance risk theory recommended for researchers and students interested in applied probability as well as practitioners of actuarial sciences. Wiley Series in Probability and Statistics
A comprehensive summary of the fundamental mathematical principles behind key topics in geophysics and geodesy. Each section begins with a problem in gravimetry, geomagnetics or seismology and analyses its mathematical features. With each chapter ending with a series of review questions, this is a valuable reference for students and researchers.
The theory of random dynamical systems originated from stochastic differential equations. It is intended to provide a framework and techniques to describe and analyze the evolution of dynamical systems when the input and output data are known only approximately, according to some probability distribution. The development of this field, in both the theory and applications, has gone in many directions. In this manuscript we introduce measurable expanding random dynamical systems, develop the thermodynamical formalism and establish, in particular, the exponential decay of correlations and analyticity of the expected pressure although the spectral gap property does not hold. This theory is then used to investigate fractal properties of conformal random systems. We prove a Bowen’s formula and develop the multifractal formalism of the Gibbs states. Depending on the behavior of the Birkhoff sums of the pressure function we arrive at a natural classification of the systems into two classes: quasi-deterministic systems, which share many properties of deterministic ones; and essentially random systems, which are rather generic and never bi-Lipschitz equivalent to deterministic systems. We show that in the essentially random case the Hausdorff measure vanishes, which refutes a conjecture by Bogenschutz and Ochs. Lastly, we present applications of our results to various specific conformal random systems and positively answer a question posed by Bruck and Buger concerning the Hausdorff dimension of quadratic random Julia sets.
Computer Simulation and Computer Algebra. Starting from simple examples in classical mechanics, these introductory lectures proceed to simulations in statistical physics (using FORTRAN) and then explain in detail the use of computer algebra (by means of Reduce). This third edition takes into account the most recent version of Reduce (3.4.1) and updates the description of large-scale simulations to subjects such as the 170000 X 170000 Ising model. Furthermore, an introduction to both vector and parallel computing is given.
Examines 58 letters written by Katerina Lemmel, a wealthy Nuremberg widow, who in 1516 entered the abbey of Maria Mai in south Germany, and rebuilt the monastery using her own resources and the donations she solicited from relatives"--Provided by publisher.
Joseph Beuys’s work continues to influence and inspire practitioners and thinkers all over the world, in areas from organizational learning, direct democracy and new money forms to new art pedagogies and ecological art practices. Here, in dialogue with Volker Harlan - a close colleague, whose own work also revolves around understandings of substance and sacrament that are central to Beuys - the deeper motivations and insights underlying ‘social sculpture’, Beuys’s expanded conception of art, are illuminated. His profound reflections, complemented with insightful essays by Volker Harlan, give a sense of the interconnectedness between all life forms, and the foundations of a path towards an ecologically sustainable future. This volume features over 40 b/w illustrations.
This self-contained textbook takes a matrix-oriented approach to linear algebra and presents a complete theory, including all details and proofs, culminating in the Jordan canonical form and its proof. Throughout the development, the applicability of the results is highlighted. Additionally, the book presents special topics from applied linear algebra including matrix functions, the singular value decomposition, the Kronecker product and linear matrix equations. The matrix-oriented approach to linear algebra leads to a better intuition and a deeper understanding of the abstract concepts, and therefore simplifies their use in real world applications. Some of these applications are presented in detailed examples. In several ‘MATLAB-Minutes’ students can comprehend the concepts and results using computational experiments. Necessary basics for the use of MATLAB are presented in a short introduction. Students can also actively work with the material and practice their mathematical skills in more than 300 exercises.
This is the second updated and extended edition of the successful book on Feynman-Kac theory. It offers a state-of-the-art mathematical account of functional integration methods in the context of self-adjoint operators and semigroups using the concepts and tools of modern stochastic analysis. The first volume concentrates on Feynman-Kac-type formulae and Gibbs measures.
The construction of a software system is a task that has to be structured toensure that the software product fulfills all expectations and the process of producing it remains manageable and reliable. Mathematical methods, including logic, algebra and functional calculus, are needed to support structuring and provide notations and basic formal concepts for the foundations of software engineering. Mathematical methods of programming reflect the need for modularization and abstraction and suggest appropriate goal-directed procedures for the construction of software programs. This volume contains the proceedings of an International Summer School held at Marktoberdorf in 1990, the 11th in a series on mathematical methods in programming. Outstanding scientists contributed papers centered around logical and functional calculi for the specification, refinement and verification of programs and program systems, and remarkable examples for the formal development of proofs and algorithms are given.
This book explores finite element methods for incompressible flow problems: Stokes equations, stationary Navier-Stokes equations and time-dependent Navier-Stokes equations. It focuses on numerical analysis, but also discusses the practical use of these methods and includes numerical illustrations. It also provides a comprehensive overview of analytical results for turbulence models. The proofs are presented step by step, allowing readers to more easily understand the analytical techniques.
The renowned WWII historian’s definitive biography of the notorious German SS officer convicted of war crimes for his role in the Holocaust. Described as one of the greatest mass-murderers in history, Rudolf Höss was the longest-serving commandant of the Auschwitz concentration and extermination camps in Nazi-occupied Poland. He was one of the chief architects behind Hitler’s Final Solution. In The Commandant of Auschwitz, Volker Koop details Höss’s military career, his conversion to Nazi ideology, and his ruthless commitment to the Nazi cause. At the age of fourteen, Höss joined the 21st Regiment of Dragoons and rose through the ranks to become the youngest non-commissioned officer in the German Army. After joining the Nazi party in 1922, he was convicted of participating in at least one political assassination, for which he spent six years in prison. In 1934, Höss became a Block Leader at Dachau concentration camp. By 1940, he would be given command of his own camp near the town of Auschwitz. Charged with carrying out the Final Solution of the Jewish question, Höss set about his task with relish. By his own estimation, he was responsible for the deaths of at least 3,000,000 individuals. Justice caught up with Höss after the German surrender. He was arrested on March 11th, 1946, after a year of posing as a gardener under a false name. He was found guilty of war crimes and hanged on April 16th, 1947.
This book constitutes the refereed proceedings of the 22nd Annual Symposium on Theoretical Aspects of Computer Science, STACS 2005, held in Stuttgart, Germany in February 2005. The 54 revised full papers presented together with 3 invited papers were carefully reviewed and selected from 217 submissions. A broad variety of topics from theoretical computer science are addressed, in particular complexity theory, algorithmics, computational discrete mathematics, automata theory, combinatorial optimization and approximation, networking and graph theory, computational geometry, grammar systems and formal languages, etc.
This volume provides readers with a detailed introduction to the amenability of Banach algebras and locally compact groups. By encompassing important foundational material, contemporary research, and recent advancements, this monograph offers a state-of-the-art reference. It will appeal to anyone interested in questions of amenability, including those familiar with the author’s previous volume Lectures on Amenability. Cornerstone topics are covered first: namely, the theory of amenability, its historical context, and key properties of amenable groups. This introduction leads to the amenability of Banach algebras, which is the main focus of the book. Dual Banach algebras are given an in-depth exploration, as are Banach spaces, Banach homological algebra, and more. By covering amenability’s many applications, the author offers a simultaneously expansive and detailed treatment. Additionally, there are numerous exercises and notes at the end of every chapter that further elaborate on the chapter’s contents. Because it covers both the basics and cutting edge research, Amenable Banach Algebras will be indispensable to both graduate students and researchers working in functional analysis, harmonic analysis, topological groups, and Banach algebras. Instructors seeking to design an advanced course around this subject will appreciate the student-friendly elements; a prerequisite of functional analysis, abstract harmonic analysis, and Banach algebra theory is assumed.
This book provides analytical and numerical methods for the estimation of dimension characteristics (Hausdorff, Fractal, Carathéodory dimensions) for attractors and invariant sets of dynamical systems and cocycles generated by smooth differential equations or maps in finite-dimensional Euclidean spaces or on manifolds. It also discusses stability investigations using estimates based on Lyapunov functions and adapted metrics. Moreover, it introduces various types of Lyapunov dimensions of dynamical systems with respect to an invariant set, based on local, global and uniform Lyapunov exponents, and derives analytical formulas for the Lyapunov dimension of the attractors of the Hénon and Lorenz systems. Lastly, the book presents estimates of the topological entropy for general dynamical systems in metric spaces and estimates of the topological dimension for orbit closures of almost periodic solutions to differential equations.
This book provides a comprehensive introduction to complex analysis in several variables. One major focus of the book is extension phenomena alien to the one-dimensional theory (Hartog's Kugelsatz, theorem of Cartan-Thullen, Bochner's theorem). The book primarily aims at students starting to work in the field of complex analysis in several variables and teachers who want to prepare a university lecture. Therefore, the book contains more than 50 examples and more than 100 supporting exercises.
The notion of amenability has its origins in the beginnings of modern measure theory: Does a finitely additive set function exist which is invariant under a certain group action? Since the 1940s, amenability has become an important concept in abstract harmonic analysis (or rather, more generally, in the theory of semitopological semigroups). In 1972, B.E. Johnson showed that the amenability of a locally compact group G can be characterized in terms of the Hochschild cohomology of its group algebra L^1(G): this initiated the theory of amenable Banach algebras. Since then, amenability has penetrated other branches of mathematics, such as von Neumann algebras, operator spaces, and even differential geometry. Lectures on Amenability introduces second year graduate students to this fascinating area of modern mathematics and leads them to a level from where they can go on to read original papers on the subject. Numerous exercises are interspersed in the text.
This should be a revelation for mathematics undergraduates. Having evolved from Runde’s notes for an introductory topology course at the University of Alberta, this essential text provides a concise introduction to set-theoretic topology, as well as some algebraic topology. It is accessible to undergraduates from the second year on, and even beginning graduate students can benefit from some sections. The well-chosen selection of examples is accessible to students who have a background in calculus and elementary algebra, but not necessarily in real or complex analysis. In places, Runde’s text treats its material differently to other books on the subject, providing a fresh perspective.
In der 1968 gegründeten Reihe erscheinen Monographien aus den Gebieten der Griechischen und Lateinischen Philologie sowie der Alten Geschichte. Die Bände weisen eine große Vielzahl von Themen auf: neben sprachlichen, textkritischen oder gattungsgeschichtlichen philologischen Untersuchungen stehen sozial-, politik-, finanz- und kulturgeschichtliche Arbeiten aus der Klassischen Antike und der Spätantike. Entscheidend für die Aufnahme ist die Qualität einer Arbeit; besonderen Wert legen die Herausgeber auf eine umfassende Heranziehung der einschlägigen Texte und Quellen und deren sorgfältige kritische Auswertung.
Master's Thesis from the year 2005 in the subject Law - Comparative Legal Systems, Comparative Law, grade: 53(60), Université Paul Cézanne Aix - Marseille III, course: European Master in Law and Economics, language: English, abstract: Copyright protection in the media and especially in the music industry is a widely discussed topic since several years. In fact new technologies based on Internet changed the situation for the classic business model of the music labels dramatically. CDs become more and more superfluous with the advent of digital media and thus the traditional business model producing and selling them. The music industry of course makes these new technologies responsible for their decline in sales while others argue that the new technologies moreover offer great opportunities for the industry to expand their markets. However I will not join the discussion whether online file sharing is responsible for the decline in record sales2. I rather will show that the new technologies being introduced offer great chances for new ways of producing and distribution of music, no matter the impact it has on the old and outdated business models by selling CDs. In my thesis I try to give some insights into the current dilemma, discuss the most appealing proposals advanced by legal and economic scholars and, finally, provide my own suggestions without neglecting the current political circumstances. Therefore I will give some background information of what is actually going on right now in the markets for music in the second chapter. Then I will shed some light on the basic foundations of copyright, its economic impacts and of course its inefficiencies according the music business. After having analyzed the economic consequences of current copyright laws I will introduce and comment on some recent suggestions to ameliorate the inefficiencies. This will be proposals from single changes of particular parts of copyright to radical abandonment of copyright law at all. In ord
Seminar paper from the year 2007 in the subject English - Pedagogy, Didactics, Literature Studies, grade: 1,0, http: //www.uni-jena.de/ (Institut f r Anglistik/Amerikanistik), course: Teaching the New English Cultures, 22 entries in the bibliography, language: English, abstract: Several current curricula for the German secondary EFL classroom (Rahmenrichtlinien) now include some of the so-called new English cultures, like Australia, New Zealand, and Canada. Especially Canada, considering its geographical and cultural proximity to the nowadays almost omnipresent USA, presents itself as a natural addition to the "traditional" Anglophone cultures. I argue in favour of a didactic approach not only via history, geography, or any other specific 'Cultural' aspect alone, but via a mixture of both 'big c' Culture and 'small c' culture using a selection of different authentic media and texts.
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