At its core, this concise textbook presents standard material for a first course in complex analysis at the advanced undergraduate level. This distinctive text will prove most rewarding for students who have a genuine passion for mathematics as well as certain mathematical maturity. Primarily aimed at undergraduates with working knowledge of real analysis and metric spaces, this book can also be used to instruct a graduate course. The text uses a conversational style with topics purposefully apportioned into 21 lectures, providing a suitable format for either independent study or lecture-based teaching. Instructors are invited to rearrange the order of topics according to their own vision. A clear and rigorous exposition is supported by engaging examples and exercises unique to each lecture; a large number of exercises contain useful calculation problems. Hints are given for a selection of the more difficult exercises. This text furnishes the reader with a means of learning complex analysis as well as a subtle introduction to careful mathematical reasoning. To guarantee a student’s progression, more advanced topics are spread out over several lectures. This text is based on a one-semester (12 week) undergraduate course in complex analysis that the author has taught at the Australian National University for over twenty years. Most of the principal facts are deduced from Cauchy’s Independence of Homotopy Theorem allowing us to obtain a clean derivation of Cauchy’s Integral Theorem and Cauchy’s Integral Formula. Setting the tone for the entire book, the material begins with a proof of the Fundamental Theorem of Algebra to demonstrate the power of complex numbers and concludes with a proof of another major milestone, the Riemann Mapping Theorem, which is rarely part of a one-semester undergraduate course.
This book looks at the mathematical foundations of the models currently in use. All existing books on bioinformatics are software-orientated and they concentrate on computer implementations of mathematical models of biology. This book is unique in the sense that it looks at the mathematical foundations of the models, which are crucial for correct interpretation of the outputs of the models.
In this monograph the author presents a coherent exposition of recent results on complete characterization of Kobayashi-hyperbolic manifolds with high-dimensional groups of holomorphic automorphisms. These classification results can be viewed as complex-geometric analogues of those known for Riemannian manifolds with high-dimensional isotropy groups that were extensively studied in the 1950s-70s.
We consider Levi non-degenerate tube hypersurfaces in complex linear space which are "spherical", that is, locally CR-equivalent to the real hyperquadric. Spherical hypersurfaces are characterized by the condition of the vanishing of the CR-curvature form, so such hypersurfaces are flat from the CR-geometric viewpoint. On the other hand, such hypersurfaces are of interest from the point of view of affine geometry. Thus our treatment of spherical tube hypersurfaces in this book is two-fold: CR-geometric and affine-geometric. Spherical tube hypersurfaces turn out to possess remarkable properties. For example, every such hypersurface is real-analytic and extends to a closed real-analytic spherical tube hypersurface in complex space. One of our main goals is to give an explicit affine classification of closed spherical tube hypersurfaces whenever possible. In this book we offer a comprehensive exposition of the theory of spherical tube hypersurfaces starting with the idea proposed in the pioneering work by P. Yang (1982) and ending with the new approach due to G. Fels and W. Kaup (2009).
At its core, this concise textbook presents standard material for a first course in complex analysis at the advanced undergraduate level. This distinctive text will prove most rewarding for students who have a genuine passion for mathematics as well as certain mathematical maturity. Primarily aimed at undergraduates with working knowledge of real analysis and metric spaces, this book can also be used to instruct a graduate course. The text uses a conversational style with topics purposefully apportioned into 21 lectures, providing a suitable format for either independent study or lecture-based teaching. Instructors are invited to rearrange the order of topics according to their own vision. A clear and rigorous exposition is supported by engaging examples and exercises unique to each lecture; a large number of exercises contain useful calculation problems. Hints are given for a selection of the more difficult exercises. This text furnishes the reader with a means of learning complex analysis as well as a subtle introduction to careful mathematical reasoning. To guarantee a student’s progression, more advanced topics are spread out over several lectures. This text is based on a one-semester (12 week) undergraduate course in complex analysis that the author has taught at the Australian National University for over twenty years. Most of the principal facts are deduced from Cauchy’s Independence of Homotopy Theorem allowing us to obtain a clean derivation of Cauchy’s Integral Theorem and Cauchy’s Integral Formula. Setting the tone for the entire book, the material begins with a proof of the Fundamental Theorem of Algebra to demonstrate the power of complex numbers and concludes with a proof of another major milestone, the Riemann Mapping Theorem, which is rarely part of a one-semester undergraduate course.
This book looks at the mathematical foundations of the models currently in use. All existing books on bioinformatics are software-orientated and they concentrate on computer implementations of mathematical models of biology. This book is unique in the sense that it looks at the mathematical foundations of the models, which are crucial for correct interpretation of the outputs of the models.
We consider Levi non-degenerate tube hypersurfaces in complex linear space which are "spherical", that is, locally CR-equivalent to the real hyperquadric. Spherical hypersurfaces are characterized by the condition of the vanishing of the CR-curvature form, so such hypersurfaces are flat from the CR-geometric viewpoint. On the other hand, such hypersurfaces are of interest from the point of view of affine geometry. Thus our treatment of spherical tube hypersurfaces in this book is two-fold: CR-geometric and affine-geometric. Spherical tube hypersurfaces turn out to possess remarkable properties. For example, every such hypersurface is real-analytic and extends to a closed real-analytic spherical tube hypersurface in complex space. One of our main goals is to give an explicit affine classification of closed spherical tube hypersurfaces whenever possible. In this book we offer a comprehensive exposition of the theory of spherical tube hypersurfaces starting with the idea proposed in the pioneering work by P. Yang (1982) and ending with the new approach due to G. Fels and W. Kaup (2009).
In this monograph the author presents a coherent exposition of recent results on complete characterization of Kobayashi-hyperbolic manifolds with high-dimensional groups of holomorphic automorphisms. These classification results can be viewed as complex-geometric analogues of those known for Riemannian manifolds with high-dimensional isotropy groups that were extensively studied in the 1950s-70s.
This book contains a systematic study of ecological communities of two or three interacting populations. Starting from the Lotka-Volterra system, various regulating factors are considered, such as rates of birth and death, predation and competition. The different factors can have a stabilizing or a destabilizing effect on the community, and their interplay leads to increasingly complicated behavior. Studying and understanding this path to greater dynamical complexity of ecological systems constitutes the backbone of this book. On the mathematical side, the tool of choice is the qualitative theory of dynamical systems — most importantly bifurcation theory, which describes the dependence of a system on the parameters. This approach allows one to find general patterns of behavior that are expected to be observed in ecological models. Of special interest is the reaction of a given model to disturbances of its present state, as well as to changes in the external conditions. This leads to the general idea of “dangerous boundaries” in the state and parameter space of an ecological system. The study of these boundaries allows one to analyze and predict qualitative and often sudden changes of the dynamics — a much-needed tool, given the increasing antropogenic load on the biosphere.As a spin-off from this approach, the book can be used as a guided tour of bifurcation theory from the viewpoint of application. The interested reader will find a wealth of intriguing examples of how known bifurcations occur in applications. The book can in fact be seen as bridging the gap between mathematical biology and bifurcation theory.
Austerlitz, Wagram, Borodino, Trafalgar, Leipzig, Waterloo: these are the places most closely associated with the era of the Napoleonic Wars. But how did this period of nearly continuous conflict affect the world beyond Europe? The immensity of the fighting waged by France against England, Prussia, Austria, and Russia, and the immediate consequences of the tremors that spread throughout the world. In this ambitious and far-ranging work, Alexander Mikaberidze argues that the Napoleonic Wars can only be fully understood in an international perspective. France struggled for dominance not only on the plains of Europe but also in the Americas, West and South Africa, Ottoman Empire, Iran, India, Indonesia, the Philippines, Mediterranean Sea, and the Atlantic and Indian Oceans. Taking specific regions in turn, Mikaberidze discusses major political-military events around the world and situates geopolitical decision-making within its long- and short-term contexts. From the British expeditions to Argentina and South Africa to the Franco-Russian maneuvering in the Ottoman Empire, the effects of the French Revolution and Napoleonic Wars would shape international affairs well into the next century. In Egypt, the wars led to the rise of Mehmed Ali and the emergence of a powerful state; in North America, the period transformed and enlarged the newly established United States; and in South America, the Spanish colonial empire witnessed the start of national-liberation movements that ultimately ended imperial control. Skillfully narrated and deeply researched, here at last is the global history of the period, one that expands our view of the Napoleonic Wars and their role in laying the foundations of the modern world.
The celebrated Schur-Weyl duality gives rise to effective ways of constructing invariant polynomials on the classical Lie algebras. The emergence of the theory of quantum groups in the 1980s brought up special matrix techniques which allowed one to extend these constructions beyond polynomial invariants and produce new families of Casimir elements for finite-dimensional Lie algebras. Sugawara operators are analogs of Casimir elements for the affine Kac-Moody algebras. The goal of this book is to describe algebraic structures associated with the affine Lie algebras, including affine vertex algebras, Yangians, and classical -algebras, which have numerous ties with many areas of mathematics and mathematical physics, including modular forms, conformal field theory, and soliton equations. An affine version of the matrix technique is developed and used to explain the elegant constructions of Sugawara operators, which appeared in the last decade. An affine analogue of the Harish-Chandra isomorphism connects the Sugawara operators with the classical -algebras, which play the role of the Weyl group invariants in the finite-dimensional theory.
“Electrocrystallization is a particular case of a first order phase transition” and “Electrocrystallization is a particular case of electrochemical kinetics” are two statements that I have heard and read many times. I do not like them for a simple reason: it is annoying to see that the subject to which you have devoted more than 30 years of your life may be considered as a “particular case”. Therefore, I decided to write this book in which Electrocrystallization is the main subject. To become competent in the field of Electrocrystallization one should possess knowledge of Electrochemistry, Nucleation and Crystal Growth, which means knowledge of Physical Chemistry, Physics and Mathematics. That is certainly difficult and in most cases those who study Electrocrystallization are either more electrochemists, or more physical chemists, or more physicists, very often depending on whom has been their teacher. Of course, there are scientists who consider themselves equally good in all those fields. Very frequently they are, unfortunately, equally bad. The difference is essential but strange enough, it is sometimes not easy to realize the truth immediately.
This monograph presents a systematic analysis of bubble system mathematics, using the mechanics of two-phase systems in non-equilibrium as the scope of analysis. The author introduces the thermodynamic foundations of bubble systems, ranging from the fundamental starting points to current research challenges. This book addresses a range of topics, including description methods of multi-phase systems, boundary and initial conditions as well as coupling requirements at the phase boundary. Moreover, it presents a detailed study of the basic problems of bubble dynamics in a liquid mass: growth (dynamically and thermally controlled), collapse, bubble pulsations, bubble rise and breakup. Special emphasis is placed on bubble dynamics in turbulent flows. The analysis results are used to write integral equations governing the rate of vapor generation (condensation) in non-equilibrium flows, thus creating a basis for solving a number of practical problems. This book is the first to present a comprehensive theory of boiling shock with applications to problems of critical discharge and flashing under the fast decompression conditions. Reynolds’ analogy was the key to solving a number of problems in subcooled forced-flow boiling, the theoretical results of which led to easy-to-use design formulas. This book is primarily aimed at graduate and post-graduate students specializing in hydrodynamics or heat and mass transfer, as well as research expert focused on two-phase flow. It will also serve as a comprehensive reference book for designers working in the field of power and aerospace technology.
A copper theft investigation puts Arizona and the Apache Tribal Police on the trail of a deadly conspiracy in this borderland mystery thriller. Sgt. Bren Allred has seen all manner of criminality in beautiful Graham County, Arizona. He has managed to keep the worst of it from his wife, Monica, who is having a troubled pregnancy. But it will be difficult to keep the devils at bay as a new kind of trouble erupts across the region . . . When deputies Sanchez and Haley go undercover to investigate a rash of copper theft, they unwittingly stumble across a shadowy spy network. Meanwhile, Apache Police Sgt. Al Victor is confronted by a murder case involving a diplomat as he grapples with the ever-present problem of alcohol on the reservation.
Written by leading Russian scientists, including Nobel laureate, A.M. Prokhorov (1916-2002), this first book on this important technology allows an understanding of the physics of atomic vapor laser isotope separation and new photochemical methods of laser isotope separation. One entire chapter is devoted to chemical reactions of atoms in excited states, while further chapters deal with the separation of isotopes by one photon isotope-selective and coherent isotope-selective two photon excitation of atoms. A final chapter looks at the prospects for the industrial production of isotope products by laser isotope separation. The whole is rounded off by six appendices.
Principles of Bioenergetics summarizes one of the quickly growing branches of modern biochemistry. Bioenergetics concerns energy transductions occurring in living systems and this book pays special attention to molecular mechanisms of these processes. The main subject of the book is the "energy coupling membrane" which refers to inner membranes of intracellular organelles, for example, mitochondria and chloroplasts. Cellular cytoplasmic membranes where respiratory and photosynthetic energy transducers, as well as ion-transporting ATP-synthases (ATPases) are also part of this membrane. Significant attention is paid to the alternative function of mitochondria as generators of reactive oxygen species (ROS) that mediate programmed death of cells (apoptosis and necrosis) and organisms (phenoptosis). The latter process is considered as a key mechanism of aging which may be suppressed by mitochondria-targeted antioxidants.
After decades of research and development, emission detectors have recently become the most successful instrumentation used in modern fundamental experiments searching for cold dark matter, and are also considered for neutrino coherent scattering and magnetic momentum neutrino measurement. This book is the first monograph exclusively dedicated to emission detectors. Properties of two-phase working media based on noble gases, saturated hydrocarbon, ion crystals and semiconductors are reviewed.
This volume details the technical features and operational performance of the Soviet Su-25 'Frogfoot', which proved itself as a durable and versatile attack aircraft in a variety of theatres such as Afghanistan, Georgia and Ossetia. Today it is widely accepted as the true successor to the types of specialised ground--attack aircraft that emerged during World War II. This book illuminates the service history of the 'Frogfoot' in over 30 years of combat using first-hand accounts and revealing archive photographs. The awkward-looking Su-25 has often been underrated, but the faithful 'Frogfoot' is now slated to remain in service with most of its current operators across the globe until at least 2020. This study explores the successes of the 'Frogfoot' in full, demonstrating its strengths as a formidably armed, armoured and very agile attack aircraft.
The Yangians and twisted Yangians are remarkable associative algebras taking their origins from the work of St. Petersburg's school of mathematical physics in the 1980s. This book is an introduction to the theory of Yangians and twisted Yangians, with a particular emphasis on the relationship with the classical matrix Lie algebras.
Russia played a decisive role in the Napoleonic wars and the success in the struggle against France allowed Russian leaders to profoundly influence the course of European history. Over the last 200 years, the Napoleonic era has been discussed and analysed in numerous studies, but many fail to fully portray the Russian side of events due to the relative scarcity of Russian sources in English. Only a handful of Russian memoirs have been translated, while dozens remain unknown outside Russia. This book seeks to fill this gap by providing, in English, previously unavailable memoirs of Russian participants. Defeat at Leipzig in 1813 had driven Napoleon back across the borders of France, and in January 1814 the Russians, Austrians, Prussians and their other German allies stood poised to cross the Rhine. But the French Emperor was far from beaten, and the ensuing campaign saw desperate fighting, with the outcome very much in the balance. This book is the first to bring together dozens of letter, diaries and memoirs of Russian participants of the 1814 Campaign. Reading these documents we see both what Russian officers and soldiers experienced during the final months of the three-year-long campaign as well as their joy at defeating Russia’s most dangerous enemy. We follow them not only through the heat of battle but also on delightful tours of Paris which they describe as the pleasure and entertainment capital of the world.
The main aim of this new book is to summarise the knowledge on the metabolic transformation of carnosine in excitable tissues of animals and human beings and to analyse the nature of its biological activity. At the beginning of monograph, the short history of the problem is stated. Distribution of carnosine in tissues, its appearance in ontogeny of vertebrates and correlation between carnosine content and functional activity of tissues are discussed. Chemical properties of carnosine and its natural derivatives and their ability to bind heavy metals and protons in water solution are documented. Special attention is paid to free radical quenching ability and to anti-glycating action. Biological activity of carnosine and carnosine containing compounds was tested using biological models of several levels of complexity, starting from individual enzymes and acellular mixtures and finishing to living cells and survival animals. Effects of carnosine on the whole animals under ischemic, hypoxic and other extreme conditions are described. In conclusion, the ability of carnosine to protect brain and muscular tissues from oxidative injury during exhausting exercise, extreme loading or neurodegenerative diseases is demonstrated. Based on these properties, carnosine is postulated to be a potent protector of human beings from oxidative stress.
In a definitive new account of the Soviet Union at war, Alexander Hill charts the development, successes and failures of the Red Army from the industrialisation of the Soviet Union in the late 1920s through to the end of the Great Patriotic War in May 1945. Setting military strategy and operations within a broader context that includes national mobilisation on a staggering scale, the book presents a comprehensive account of the origins and course of the war from the perspective of this key Allied power. Drawing on the latest archival research and a wealth of eyewitness testimony, Hill portrays the Red Army at war from the perspective of senior leaders and men and women at the front line to reveal how the Red Army triumphed over the forces of Nazi Germany and her allies on the Eastern Front, and why it did so at such great cost.
The Russian Officer Corps of The Revolutionary and Napoleonic Wars, 1795–1815 features more than 800 detailed biographies of the commanders of that era. Foreword by Professor Donald H. Horward, Institute on Napoleon and the French Revolution, Florida State University Based upon years of research in Russian archives, historian Alexander Mikaberidze’s biographies include the subject’s place of birth, family history, educational background, a detailed description of his military service, his awards and promotions, wounds, transfers, commands, and other related information, including the date and place of his death and internment, if known. In addition, an introductory chapter presents in meticulous detail the organization of the Russian military, how it was trained, the educational and cultural background of the officer corps, its awards and their history and meaning, and much more. This outstanding overview is supported and enhanced by three dozen charts, tables, and graphics that illustrate the rich history of the Russian officer corps. This study also includes an annotated bibliography to help guide students of the period through the available Russian sources. Stunning in its scope and depth of coverage, The Russian Officer Corps is essential reading for historians, scholars, genealogists, hobbyists, war gamers, and anyone working or studying late eighteenth and early nineteenth-century European history. Every student of the Revolutionary and Napoleonic Wars, as well as every academic library, will find this impressive reference work of this momentous period of history absolutely indispensable.
This proceedings volume is devoted to a wide variety of items, both in theory and experiment, of particle physics such as tests of the Standard Model and beyond, physics at the future accelerators, neutrino and astroparticle physics, heavy quark physics, non-perturbative QCD, quantum gravity effects and cosmology. It is important that the papers in this volume reveal the present status and new developments in the above-mentioned items on the eve of a new era that starts with the Large Hadron Collider (LHC).
This book presents various examples of how advanced fluorescence and spectroscopic analytical methods can be used in combination with computer data processing to address different biochemical questions. The main focus is on evolutionary biochemistry and the description of biochemical and metabolic issues; specifically, the use of pulse amplitude modulated fluorescence (PAM) for the functional analysis of the cellular state, as well as results obtained by means of the derivative spectroscopy method characterizing structural reorganization of a cell under the influence of external factors, are discussed. The topics presented here will be of interest to biologists, geneticists, biophysicists and biochemists, as well as experts in analytical chemistry, pharmaceutical chemistry and radio chemistry and radio activation studies with protonen and alpha-particles. It also offers a valuable resource for advanced undergraduate and graduate students in biological, physical and chemical disciplines whose work involves derivative spectrophotometry and PAM-fluorescence.
It was a greatest pleasure for me to learn that Springer-Verlag wished to produce a second edition of my book. In this connection, Dr. H. Lotsch asked me to send hirn a list of misprints, mistakes, and inaccuracies that had been noticed in the first edition and to make corresponding corrections without disturbing the layout or the typo graphy too much. I accepted this opportunity with alacrity and, moreover, found some free places in the text where I was able to insert some concise, up-to-date information about new lasing compounds and stimulated emission channels. It was also possible to increase the number of reference citations. The reader of the second edition hence has access to more complete data on insulating laser crystals. However, sections on laser-crystal physics have not been updated, because a satisfactory de scription of the progress made in the last ten years in this field would have required the sections to be extended enormously or even a new book to be written. Moscow, July 1989 ALEXANDER A. KAMINSKII Preface to the First Edition The greatest reward for an author is the feeling of satisfaction he gets when it becomes c1ear to hirn that readers find his work useful. After my book appeared in the USSR in 1975 I received many letters from fellow physicists inc1uding colleagues from Western European countries and the USA.
Partition functions arise in combinatorics and related problems of statistical physics as they encode in a succinct way the combinatorial structure of complicated systems. The main focus of the book is on efficient ways to compute (approximate) various partition functions, such as permanents, hafnians and their higher-dimensional versions, graph and hypergraph matching polynomials, the independence polynomial of a graph and partition functions enumerating 0-1 and integer points in polyhedra, which allows one to make algorithmic advances in otherwise intractable problems. The book unifies various, often quite recent, results scattered in the literature, concentrating on the three main approaches: scaling, interpolation and correlation decay. The prerequisites include moderate amounts of real and complex analysis and linear algebra, making the book accessible to advanced math and physics undergraduates.
Schumann resonance has been studied for more than half a century. The field became popular among researchers of the terrestrial environment using natural sources of electromagnetic radiation—lightning strokes, primarily—and now many Schumann observatories have been established around the world. A huge number of publications can be found in the literature, the most recent collection of which was presented in a special Schumann resonance section of the journal Radio Science in 2007. The massive publications, however, impede finding information about how to organize measurements and start observations of global electromagnetic resonance. Relevant information is scattered throughout many publications, which are not always available. The goal of this book is to collect all necessary data in a single edition in order to describe the demands of the necessary equipment and the field-site as well as the impact of industrial and natural interference, and to demonstrate typical results and obstacles often met in measurements. The authors not only provide representative results but also describe unusual radio signals in the extremely low-frequency (ELF) band and discuss signals in the adjacent frequency ranges.
A review of modern approaches existing nowadays in ecological modelling of forest ecosystems in boreal and temperate forests. The book contains data on contemporary approaches in intensively developed simulation modelling of forest stands, soils and whole ecosystems as well; an analysis of existing spatial forest models and their significance and development; and a comprehensive discussion of theoretical (analytical) models of forest communities. The idea of a system of forest models for more effective solving of different theoretical and practical problems is also discussed. This work is particularly useful in its critical reviewing of modern achievements in forest ecosystem modelling and its discussion of more promising trends of forest modelling with an increase of their practical significance in the near future.
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