The study of the mapping class group Mod(S) is a classical topic that is experiencing a renaissance. It lies at the juncture of geometry, topology, and group theory. This book explains as many ...important theorems, examples, and techniques as possible, quickly and directly, while at the same time giving full details and keeping the text nearly self-contained. The book is suitable for graduate students.
"This new and expanded edition is intended to help candidates prepare for entrance examinations in mathematics and scientific subjects, including STEP (Sixth Term Examination Paper). STEP is an ...examination used by Cambridge Colleges for conditional offers in mathematics. They are also used by some other UK universities and many mathematics departments recommend that their applicants practice on the past papers even if they do not take the examination. Advanced Problems in Mathematics bridges the gap between school and university mathematics, and prepares students for an undergraduate mathematics course. The questions analysed in this book are all based on past STEP questions and each question is followed by a comment and a full solution. The comments direct the reader’s attention to key points and put the question in its true mathematical context. The solutions point students to the methodology required to address advanced mathematical problems critically and independently. This book is a must read for any student wishing to apply to scientific subjects at university level and for anyone interested in advanced mathematics. "This new and expanded edition is intended to help candidates prepare for entrance examinations in mathematics and scientific subjects, including STEP (Sixth Term Examination Paper). STEP is an examination used by Cambridge Colleges for conditional offers in mathematics. They are also used by some other UK universities and many mathematics departments recommend that their applicants practice on the past papers even if they do not take the examination. Advanced Problems in Mathematics bridges the gap between school and university mathematics, and prepares students for an undergraduate mathematics course. The questions analysed in this book are all based on past STEP questions and each question is followed by a comment and a full solution. The comments direct the reader’s attention to key points and put the question in its true mathematical context. The solutions point students to the methodology required to address advanced mathematical problems critically and independently. This book is a must read for any student wishing to apply to scientific subjects at university level and for anyone interested in advanced mathematics.
A Unified Summary of the Models and Optimization Methods Used in Computational LithographyOptical lithography is one of the most challenging areas of current integrated circuit manufacturing ...technology. The semiconductor industry is relying more on resolution enhancement techniques (RETs), since their implementation does not require significant changes in fabrication infrastructure. Computational Lithographyis the first book to address the computational optimization of RETs in optical lithography, providing an in-depth discussion of optimal optical proximity correction (OPC), phase shifting mask (PSM), and off-axis illumination (OAI) RET tools that use model-based mathematical optimization approaches.The book starts with an introduction to optical lithography systems, electric magnetic field principles, and the fundamentals of optimization from a mathematical point of view. It goes on to describe in detail different types of optimization algorithms to implement RETs. Most of the algorithms developed are based on the application of the OPC, PSM, and OAI approaches and their combinations. Algorithms for coherent illumination as well as partially coherent illumination systems are described, and numerous simulations are offered to illustrate the effectiveness of the algorithms. In addition, mathematical derivations of all optimization frameworks are presented.The accompanying MATLAB® software files for all the RET methods described in the book make it easy for readers to run and investigate the codes in order to understand and apply the optimization algorithms, as well as to design a set of optimal lithography masks. The codes may also be used by readers for their research and development activities in their academic or industrial organizations. An accompanying MATLAB® software guide is also included. An accompanying MATLAB® software guide is included, and readers can download the software to use with the guide at ftp://ftp.wiley.com/public/sci_tech_med/computational_lithography.Tailored for both entry-level and experienced readers, Computational Lithographyis meant for faculty, graduate students, and researchers, as well as scientists and engineers in industrial organizations whose research or career field is semiconductor IC fabrication, optical lithography, and RETs. Computational lithography draws from the rich theory of inverse problems, optics, optimization, and computational imaging; as such, the book is also directed to researchers and practitioners in these fields.
Robust optimization is still a relatively new approach to optimization problems affected by uncertainty, but it has already proved so useful in real applications that it is difficult to tackle such ...problems today without considering this powerful methodology. Written by the principal developers of robust optimization, and describing the main achievements of a decade of research, this is the first book to provide a comprehensive and up-to-date account of the subject. Robust optimization is designed to meet some major challenges associated with uncertainty-affected optimization problems: to operate under lack of full information on the nature of uncertainty; to model the problem in a form that can be solved efficiently; and to provide guarantees about the performance of the solution.
This work presents the KKL observer design for nonlinear time-varying discrete systems. We first give sufficient conditions on the existence of a sequence of functions (T_k) transforming the given ...system dynamics into an exponentially stable filter of the output in some other target coordinates, where an observer is directly designed. Then, we prove that under uniform Lipschitz backward distinguishability, the maps (T_k) become uniformly Lipschitz injective after a certain time if the target dynamics are pushed sufficiently fast. This leads to an arbitrarily fast discrete observer after a certain time, which exhibits similarities with the famous high-gain observer for continuous-time systems. Input-to-state stability of the estimation error with respect to uncertainties, input disturbances, and measurement noise is then shown. Next, under the milder backward distinguishability, we show the injectivity of the maps (T_k) after a certain time for a generic choice of the target filter dynamics. Examples including a discretized permanent magnet synchronous motor (PMSM) illustrate the proposed observer.
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