This book is intended as an introduction to Probability Theory and Mathematical Statistics for students in mathematics, the physical sciences, engineering, and related fields. It is based on the author’s 25 years of experience teaching probability and is squarely aimed at helping students overcome common difficulties in learning the subject. The focus of the book is an explanation of the theory, mainly by the use of many examples. Whenever possible, proofs of stated results are provided. All sections conclude with a short list of problems. The book also includes several optional sections on more advanced topics. This textbook would be ideal for use in a first course in Probability Theory. Contents: Probabilities Conditional Probabilities and Independence Random Variables and Their Distribution Operations on Random Variables Expected Value, Variance, and Covariance Normally Distributed Random Vectors Limit Theorems Introduction to Stochastic Processes Mathematical Statistics Appendix Bibliography Index
Most introduction to proofs textbooks focus on the structure of rigorous mathematical language and only use mathematical topics incidentally as illustrations and exercises. In contrast, this book gives students practice in proof writing while simultaneously providing a rigorous introduction to number systems and their properties. Understanding the properties of these systems is necessary throughout higher mathematics. The book is an ideal introduction to mathematical reasoning and proof techniques, building on familiar content to ensure comprehension of more advanced topics in abstract algebra and real analysis with over 700 exercises as well as many examples throughout. Readers will learn and practice writing proofs related to new abstract concepts while learning new mathematical content. The first task is analogous to practicing soccer while the second is akin to playing soccer in a real match. The authors believe that all students should practice and play mathematics. The book is written for students who already have some familiarity with formal proof writing but would like to have some extra preparation before taking higher mathematics courses like abstract algebra and real analysis.
This text considers a specific Volterra integral operator and investigates its degree of compactness in terms of properties of certain kernel functions. In particular, under certain optimal integrability conditions the entropy numbers $e_n(T_{\rho, \psi})$ satisfy $c_1\norm{\rho\psi}_r0$.
We consider the Volterra integral operator $T_{\rho,\psi}:L_p(0,\infty)\to L_q(0,\infty)$ for $1\leq p,q\leq \infty$, defined by $(T_{\rho,\psi}f)(s) =\rho(s)\int_0^s \psi(t) f(t) dt$ and investigate its degree of compactness in terms of properties of the kernel functions $\rho$ and $\psi$. In particular, under certain optimal integrability conditions the entropy numbers $e_n(T_{\rho,\psi})$ satisfy $c_1\Vert{\rho\,\psi}\Vert_r\leq \liminf_{n\to\infty} n\, e_n(T_{\rho,\psi}) \leq \limsup_{n\to\infty} n\, e_n(T_{\rho,\psi})\leq c_2\Vert{\rho\,\psi}\Vert_r$ where $1/r = 1- 1/p +1/q >0$. We also obtain similar sharp estimates for the approximation numbers of $T_{\rho,\psi}$, thus extending former results due to Edmunds et al. and Evans et al.. The entropy estimates are applied to investigate the small ball behaviour of weighted Wiener processes $\rho\, W$ in the $L_q(0,\infty)$-norm, $1\leq q\leq \infty$. For example, if $\rho$ satisfies some weak monotonicity conditions at zero and infinity, then $\lim_{\varepsilon\to 0}\,\varepsilon^2\,\log\mathbb{P}(\Vert{\rho\, W}\Vert_q\leq \varepsilon) = -k_q\cdot\Vert{\rho}\Vert_{{2q}/{2+q}}^2$.
This book is devoted to the study of stable measures on Banach spaces. The first part presents the classical approach via infinitely divisible measures (the Levy-Khinchin representation) and establishes some general properties of stable measures, such as Levy's spectral representation and the tail behaviour of stable measures. The second part is devoted to a comparatively new functional analytic approach, and an investigation is made of operators T from E' to Lp which generate p-stable symmetric measures on the Banach space E.
This book is intended as an introduction to Probability Theory and Mathematical Statistics for students in mathematics, the physical sciences, engineering, and related fields. It is based on the author’s 25 years of experience teaching probability and is squarely aimed at helping students overcome common difficulties in learning the subject. The focus of the book is an explanation of the theory, mainly by the use of many examples. Whenever possible, proofs of stated results are provided. All sections conclude with a short list of problems. The book also includes several optional sections on more advanced topics. This textbook would be ideal for use in a first course in Probability Theory. Contents: Probabilities Conditional Probabilities and Independence Random Variables and Their Distribution Operations on Random Variables Expected Value, Variance, and Covariance Normally Distributed Random Vectors Limit Theorems Introduction to Stochastic Processes Mathematical Statistics Appendix Bibliography Index
This thoroughly updated version of the German authoritative work on self-organization has been completely rewritten by internationally renowned experts and experienced book authors to also include a review of more recent literature. It retains the original enthusiasm and fascination surrounding thermodynamic systems far from equilibrium, synergetics, and the origin of life, representing an easily readable book and tutorial on this exciting field. The book is unique in covering in detail the experimental and theoretical fundamentals of self-organizing systems as well as such selected features as random processes, structural networks and multistable systems, while focusing on the physical and theoretical modeling of natural selection and evolution processes. The authors take examples from physics, chemistry, biology and social systems, and include results hitherto unpublished in English. The result is a one-stop resource relevant for students and scientists in physics or related interdisciplinary fields, including mathematical physics, biophysics, information science and nanotechnology.
This book provides an up-to-date survey of modern industrial inorganic chemistry in a clear and concise manner. Production processes are described in close detail, aspects such as the disposition of raw materials and energy consumption, the economic significance of the product and technical applications, as well as ecological problems, being discussed. From reviews of the previous edition: '... Overall this is an extremely useful, authoritative reference book dealing with a topic in which it is often difficult to obtain up-to-date information. ...' Chemistry and Industry 'One of few texts available that concisely describes the current state of industrial inorganic chemistry. ...' The New York Public Library '... and as for modern uses of inorganic chemistry, I'd recommend this book as a welcome addition to any professional library...' Chemtech 'This book fills an important niche in its sector. Industrial scientists and engineers, academics, and students can be recommended to turn to it with reasonable confidence that the most important areas are described. ...' Endeavour '... it fills a currently existing gap in the market.' Journal of Chemical Technology and Biotechnology
For the first time Ruegemer presents a typology of the new financial players who became dominant since the deregulation and the last financial crisis. Large capital organizers, private equity funds, hedgefonds, venture capital investors and private investment banks became much more influential as the traditional banks. These new financial players organize worldwide selling, buying and restructuring banks, companies and public enterprises. They exercise no responsibility against the national economic situation. Influencing governments and international financial institutions they lower the labour incomes and increase the part of private gains, also by using financial havens. They act in collaboration with law firms, rating and PR agencies, management consultants, chartered accountants and central banks. Ruegemer outlines the relations between the European Union and the USA concerning transatlantic capital, military and secret service interlocking and the open also as the latent conflicts. The book shows also the other way of capitalism under state directory in the People's Republic of China: How the imported capitalism from the USA, Japan, Taiwan and western Europe is in the process of transformation. So the incomes of all classes and also especially the labour incomes are continually rising. China is shown with his alternative way of globalisation which is not accompanied by military expansion. Finally the book asks about the way of the human society if it follows the international law of the UNO and the human rights including social and labour rights.
This book presents both the fundamentals and the major research topics in statistical physics of systems out of equilibrium. It summarizes different approaches to describe such systems on the thermodynamic and stochastic levels, and discusses a variety of areas including reactions, anomalous kinetics, and the behavior of self-propelling particles.
This classic test first published in 1966 has withstood the test of time as a teaching aid for English-speaking singers, coaches, and accompanists, in order that their art may be more communicative to the public. This word-by-word translation allows the artist to properly interpret and express the feelings and emotions that the words require at the proper time.
90 haunting, evocative prints by first major Expressionist artist and one of the greatest graphic artists of his time: The Scream, Anxiety, Death Chamber, The Kiss, Madonna, On the Jetty, Picking Apples, Ibsen in the Cafe of the Grand Hotel, etc. Introduction by Alfred Werner.
Since the discovery of ferrocene and the sandwich-type complexes, the development of organometallic chemistry took its course like an avalanche and became one of the scientific success stories of the second half of the twentieth century. Based on this development, the traditional boundaries between inorganic and organic chemistry gradually disappeared and a rebirth of the nowadays highly important field of homogeneous catalysis occurred. It is fair to say that despite the fact that the key discovery, which sparked it all off, was made more than 50 years ago, organometallic chemistry remains a young and lively discipline.
In his book, the author, a physicist with more than 30 years experience in an International Research Centre, describes and analyses his “travels” in another reality, i.e. experiences in a not-everyday plane of consciousness. They are called “holotropic” i.e. aiming towards the “Whole“ and are in part comparable with near-death experiences and spontaneously occurred again and again (without the use of drugs!). The struggle between the author’s “physics conscience” and the recollections of that other reality is the theme that recurs throughout the book. Topics that are discussed include: *Creation, the Big Bang and the Higgs field *The position of women in the Bible and in contemporary society * Trinity, a concept common to all religions *Is God male or female, or...? A new view of God *Religion, Spirituality and Science *Space, Time and Matter. Physics and Mysticism. What is real? *Polarity, the driving force for all events on earth *Archetypes: Fertility, the Great Mother, Gaia and the New Energy *The global crisis: Imbalance between nature and technology; Egoism versus Altruism. By reading this book with the heart, the overwhelming beauty of the “higher worlds” will open step by step and the reader will behold the infinite splendour of eternal BEING.
The aim of this book is the pedagogical exploration of the basic principles of quantum-statistical thermodynamics as applied to various states of matter – ranging from rare gases to astrophysical matter with high-energy density. The reader will learn in this work that thermodynamics and quantum statistics are still the concepts on which even the most advanced research is operating - despite of a flood of modern concepts, classical entities like temperature, pressure, energy and entropy are shown to remain fundamental. The physics of gases, plasmas and high-energy density matter is still a growing field and even though solids and liquids dominate our daily life, more than 99 percent of the visible Universe is in the state of gases and plasmas and the overwhelming part of matter exists at extreme conditions connected with very large energy densities, such as in the interior of stars. This text, combining material from lectures and advanced seminars given by the authors over many decades, is a must-have introduction and reference for both newcomers and seasoned researchers alike.
Whether you're a seasoned randonneur or an armchair dreamer, this is the book for you. A fantastic, practical guide for any keen rider on how to complete 25 of the most famous rides across Europe.
The corporate history of BASF spans an era of German and international economic history that began with the rise of the 'new industries' as of the late nineteenth century and continues today in their confrontation with the new economy. This book examines BASF's corporate governance, financial system, industrial relations, system of qualification and relation to other companies. A corporate history of BASF promises more than an insight into the functioning of an industrial organisation. It also reveals the reasons for the extraordinary economic dynamics of the German empire and the enormous expansion of the world economy before World War I. BASF's history stands at the centre of Germany's wartime economy during two world wars and highlights both its strengths and weaknesses. Just as the IG Farben trust helped support Germany's course of politicoeconomic autarky after 1933, so it was that BASF helped facilitate West Germany's startlingly quick return to the world market. BASF has since been among the transnational companies whose efforts at the leading edge of economic and technological progress are paradigmatic for Germany's entry into the new economy of the twenty-first century.
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