A comprehensive introduction to various numerical methods used in computational finance today Quantitative skills are a prerequisite for anyone working in finance or beginning a career in the field, as well as risk managers. A thorough grounding in numerical methods is necessary, as is the ability to assess their quality, advantages, and limitations. This book offers a thorough introduction to each method, revealing the numerical traps that practitioners frequently fall into. Each method is referenced with practical, real-world examples in the areas of valuation, risk analysis, and calibration of specific financial instruments and models. It features a strong emphasis on robust schemes for the numerical treatment of problems within computational finance. Methods covered include PDE/PIDE using finite differences or finite elements, fast and stable solvers for sparse grid systems, stabilization and regularization techniques for inverse problems resulting from the calibration of financial models to market data, Monte Carlo and Quasi Monte Carlo techniques for simulating high dimensional systems, and local and global optimization tools to solve the minimization problem.
The finite element method is a powerful tool even for non-linear materials’ modeling. But commercial solutions are limited and many novel materials do not follow standard constitutive equations on a macroscopic scale. Thus, is it required that new constitutive equations are implemented into the finite element code. However, it is not sufficient to simply implement only the equations but also an appropriate integration algorithm for the constitutive equation must be provided. This book is restricted to one-dimensional plasticity in order to reduce and facilitate the mathematical formalism and theory and to concentrate on the basic ideas of elasto-plastic finite element procedures. A comprehensive set of completely solved problems is designed for the thorough understand of the presented theory. After working with this new book and reviewing the provided solved and supplementary problems, it should be much easier to study and understand the advanced theory and the respective text books.
This book presents the theory and applications of radiative transfer in the atmosphere. It is written for graduate students and researchers in the fields of meteorology and related sciences. The book begins with important basic definitions of the radiative transfer theory. It presents the hydrodynamic derivation of the radiative transfer equation and the principles of variance. The authors examine in detail various quasi-exact solutions of the radiative transfer equation and give a thorough treatment of the radiative perturbation theory. A rigorous treatment of Mie scattering is given, including Rayleigh scattering as a special case, and the important efficiency factors for extinction, scattering and absorption are derived. The fundamentals of remote sensing applications of radiative transfer are presented. Problems of varying degrees of difficulty are included at the end of each chapter, allowing readers to further their understanding of the materials covered in the book.
Two conferences, Logic and Its Applications in Algebra and Geometry and Combinatorial Set Theory, Excellent Classes, and Schanuel Conjecture, were held at the University of Michigan (Ann Arbor). These events brought together model theorists and set theorists working in these areas. This volume is the result of those meetings. It is suitable for graduate students and researchers working in mathematical logic.
This study is the first comprehensive analysis of the physical theory of the Islamic philosopher Avicenna (d. 1037). It seeks to understand his contribution against the developments within the preceding Greek and Arabic intellectual milieus, and to appreciate his philosophy as such by emphasising his independence as a critical and systematic thinker. Exploring Avicenna’s method of "teaching and learning," it investigates the implications of his account of the natural body as a three-dimensionally extended composite of matter and form, and examines his views on nature as a principle of motion and his analysis of its relation to soul. Moreover, it demonstrates how Avicenna defends the Aristotelian conception of place against the strident criticism of his predecessors, among other things, by disproving the existence of void and space. Finally, it sheds new light on Avicenna’s account of the essence and the existence of time. For the first time taking into account the entire range of Avicenna’s major writings, this study fills a gap in our understanding both of the history of natural philosophy in general and of the philosophy of Avicenna in particular. This monograph has been awarded the annual BRAIS – De Gruyter Prize (Kulturpreis Bayern) in the Study of Islam and the Muslim World and the Iran World Award for Book of the Year (2020).
Practical Optimization: Algorithms and Engineering Applications is a hands-on treatment of the subject of optimization. A comprehensive set of problems and exercises makes the book suitable for use in one or two semesters of a first-year graduate course or an advanced undergraduate course. Each half of the book contains a full semester’s worth of complementary yet stand-alone material. The practical orientation of the topics chosen and a wealth of useful examples also make the book suitable for practitioners in the field.
Müller cells make up just 0.005% of the cells in our central nervous system. They do not belong to the more esteemed family of neuronal cells but to the glia, a family of cells that until recently were seen as mere filling material between the neurons. Now, however, all that has changed. Sharing the insights of more than a quarter century of research into Müller cells, Drs. Andreas Reichenbach and Andreas Bringmann of Leipzig University make a compelling case for the central role Müller cells play. Everyone agrees that the eye is a very special and versatile sense organ, yet it has turned out in recent years that Müller cells are peculiar and multipotent glial cells. In the retina of most vertebrates and even of many mammals, Müller cells are the only type of (macro- ) glial cells; thus, they are responsible for a wealth of neuron-supportive functions that, in the brain, rely upon a division of labour among astrocytes, oligodendrocytes, and ependymal cells. Even beyond such a role in the central nervous system as "model glia", Müller cells are adapted to several exciting roles in support of vision. They deliver the light stimuli to the photoreceptor cells in the inverted vertebrate retina, aid the processing of visual information, and are responsible for the homeostatic maintenance of the retinal extracellular milieu. In Müller Cells in the Healthy and Diseased Retina, aimed not just at neurobiologists but at anyone concerned with retinal degeneration, every angle of Müller cells is covered, from an introduction to their basic properties, through their roles as 'light cables' and 'shock absorbers', to the part they play in diseases and disorders of the eye. Once these have all been covered in detail, the authors move on to discuss the future direction of research into these small but potent cellular phenomena. About the Authors Dr. Andreas Reichenbach was born in 1950 in Leipzig, Germany. He studied medicine and specialized as a physiologist, working on the mammalian retina. Since 1984, he has focused his efforts - and those of a growing number of fellows in his team - on Müller cell research. He has held a professorship at Leipzig University since 1994. After studying biology, Dr. Andreas Bringmann (* 1960) worked in the field of systemic neurophysiology until he was inspired in 1996 by Andreas Reichenbach to research the most interesting cell, the Müller cell. He is now in the Department of Ophthalmology of the University of Leipzig where he is the head of the Basic Research Laboratory
This study investigates the distribution of linguistic and specifically structural diversity in Northeast Asia (NEA), defined as the region north of the Yellow River and east of the Yenisei. In particular, it analyzes what is called the grammar of questions (GQ), i.e., those aspects of any given language that are specialized for asking questions or regularly combine with these. The bulk of the study is a bottom-up description and comparison of GQs in the languages of NEA. The addition of the phrase and beyond to the title of this study serves two purposes. First, languages such as Turkish and Chuvash are included, despite the fact that they are spoken outside of NEA, since they have ties to (or even originated in) the region. Second, despite its focus on one area, the typology is intended to be applicable to other languages as well. Therefore, it makes extensive use of data from languages outside of NEA. The restriction to one category is necessary for reasons of space and clarity, and the process of zooming in on one region allows a higher resolution and historical accuracy than is usually the case in linguistic typology. The discussion mentions over 450 languages and dialects from NEA and beyond and gives about 900 glossed examples. The aim is to achieve both a cross-linguistically plausible typology and a maximal resolution of the linguistic diversity of Northeast Asia.
Island phenomena are a central topic in generative grammar, especially because of principled exceptions to these general extraction constraints. This volume investigates exceptional extractions from phrasal adjunct islands. It argues, based on experimental studies, that several factors identified in the previous literature are uninformative about locality conditions because they show effects in both extraction and non-extraction sentence forms. The volume develops a multifactorial model to account for these effects without appealing to universal extraction conditions and argues that the relative acceptability of the underlying proposition determines acceptability across sentence types.
Develops a unified mathematical framework for treating a wide variety of diffusion-related periodic phenomena in such areas as heat transfer, electrical conduction, and light scattering. Deriving and using Green functions in one and higher dimensions to provide a unified approach, the author develops the properties of diffusion-wave fields first for the well-studied case of thermal-wave fields and then applies the methods to nonthermal fields.
This book addresses fault detection and isolation topics from a computational perspective. Unlike most existing literature, it bridges the gap between the existing well-developed theoretical results and the realm of reliable computational synthesis procedures. The model-based approach to fault detection and diagnosis has been the subject of ongoing research for the past few decades. While the theoretical aspects of fault diagnosis on the basis of linear models are well understood, most of the computational methods proposed for the synthesis of fault detection and isolation filters are not satisfactory from a numerical standpoint. Several features make this book unique in the fault detection literature: Solution of standard synthesis problems in the most general setting, for both continuous- and discrete-time systems, regardless of whether they are proper or not; consequently, the proposed synthesis procedures can solve a specific problem whenever a solution exists Emphasis on the best numerical algorithms to solve the synthesis problems for linear systems in generalized state-space form (also known as descriptor systems) Development of general synthesis procedures relying on new computational paradigms, such as factorization-based design based on filter updating techniques and nullspace-based synthesis Availability of a comprehensive set of free accompanying software tools for descriptor systems, which allows readers to easily implement all synthesis procedures presented in the book and ensures that all results are reproducible This book is primarily intended for researchers and advanced graduate students in the areas of fault diagnosis and fault-tolerant control. It will also appeal to mathematicians with an interest in control-oriented numerics.
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