Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the fina\ question. G. K. Chesterton. The Scandal of Father 'The Hermit Oad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gu\ik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.
Heterojunctions and Metal-Semiconductor Junctions discusses semiconductor-semiconductor heterojunctions and metal-semiconductor heterojunctions, which are of significant practical importance today and also of considerable scientific interest, with worthwhile problems still to be explored and understood. Many classes of heterojunctions are believed to have new and valuable applications. Although some aspects of heterojunction behavior remain areas for continued scientific and technological study, the main outlines of the subject are clear. This book comprises nine chapters, and begins with an introduction to semiconductor heterojunctions. Succeeding chapters then discuss semiconductor p-n heterojunction models and diode behavior; heterojunction transistors; isotype (n-n, p-p) heterojunctions; optical properties of heterojunctions and heterojunction lasers; metal-semiconductor barriers; metal-semiconductor junction behavior; high yield photoemissive cathodes; and fabrication of heterojunctions. This book will be of interest to practitioners in the fields of applied physics.
This important new book sets forth a comprehensive description of various mathematical aspects of problems originating in numerical solution of hyperbolic systems of partial differential equations. The authors present the material in the context of the important mechanical applications of such systems, including the Euler equations of gas dynamics, magnetohydrodynamics (MHD), shallow water, and solid dynamics equations. This treatment provides-for the first time in book form-a collection of recipes for applying higher-order non-oscillatory shock-capturing schemes to MHD modelling of physical phenomena. The authors also address a number of original "nonclassical" problems, such as shock wave propagation in rods and composite materials, ionization fronts in plasma, and electromagnetic shock waves in magnets. They show that if a small-scale, higher-order mathematical model results in oscillations of the discontinuity structure, the variety of admissible discontinuities can exhibit disperse behavior, including some with additional boundary conditions that do not follow from the hyperbolic conservation laws. Nonclassical problems are accompanied by a multiple nonuniqueness of solutions. The authors formulate several selection rules, which in some cases easily allow a correct, physically realizable choice. This work systematizes methods for overcoming the difficulties inherent in the solution of hyperbolic systems. Its unique focus on applications, both traditional and new, makes Mathematical Aspects of Numerical Solution of Hyperbolic Systems particularly valuable not only to those interested the development of numerical methods, but to physicists and engineers who strive to solve increasingly complicated nonlinear equations.
The Institute of Physics Conference Series is a leading International medium for the rapid publication of proceedings of major conferences and symposia reviewing new developments in physics and related areas. Volumes in the series comprise original refereed papers and are regarded as standard referee works. As such, they are an essential part of major libration collections worldwide. The twelfth conference on the Microscopy of Semiconducting Materials (MSM) was held at the University of Oxford, 25-29 March 2001. MSM conferences focus on recent international advances in semiconductor studies carried out by all forms of microscopy. The event was organized with scientific sponsorship by the Royal Microscopical Society, The Electron Microscopy and Analysis Group of the Institute of Physics and the Materials Research Society. With the continual shrinking of electronic device dimensions and accompanying enhancement in device performance, the understanding of semiconductor microscopic properties at the nanoscale (and even at the atomic scale) is increasingly critical for further progress to be achieved. This conference proceedings provides an overview of the latest instrumentation, analysis techniques and state-of-the-art advances in semiconducting materials science for solid state physicists, chemists, and materials scientists.
Completely updated edition, written by a close-knit author team Presents a unique approach to stroke - integrated clinical management that weaves together causation, presentation, diagnosis, management and rehabilitation Includes increased coverage of the statins due to clearer evidence of their effectiveness in preventing stroke Features important new evidence on the preventive effect of lowering blood pressure Contains a completely revised section on imaging Covers new advances in interventional radiology
Boolean valued analysis is a technique for studying properties of an arbitrary mathematical object by comparing its representations in two different set-theoretic models whose construction utilises principally distinct Boolean algebras. The use of two models for studying a single object is a characteristic of the so-called non-standard methods of analysis. Application of Boolean valued models to problems of analysis rests ultimately on the procedures of ascending and descending, the two natural functors acting between a new Boolean valued universe and the von Neumann universe. This book demonstrates the main advantages of Boolean valued analysis which provides the tools for transforming, for example, function spaces to subsets of the reals, operators to functionals, and vector-functions to numerical mappings. Boolean valued representations of algebraic systems, Banach spaces, and involutive algebras are examined thoroughly. Audience: This volume is intended for classical analysts seeking powerful new tools, and for model theorists in search of challenging applications of nonstandard models.
Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the fina\ question. G. K. Chesterton. The Scandal of Father 'The Hermit Oad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gu\ik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.
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