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Robust and Optimal Control
by Da-Wei Gu Mi-Ching TsaiA Two-port Framework for Robust and Optimal Control introduces an alternative approach to robust and optimal controller synthesis procedures for linear, time-invariant systems, based on the two-port system widespread in electrical engineering. The novel use of the two-port system in this context allows straightforward engineering-oriented solution-finding procedures to be developed, requiring no mathematics beyond linear algebra. A chain-scattering description provides a unified framework for constructing the stabilizing controller set and for synthesizing H2 optimal and H8 sub-optimal controllers. Simple yet illustrative examples explain each step. A Two-port Framework for Robust and Optimal Controla features: Aaaaaaaaa a hands-on, tutorial-style presentation giving the reader the opportunity to repeat the designs presented and easily to modify them for their own programs;Aaaaaaaaa an abundance of examples illustrating the most important steps in robust and optimal design; andAaaaaaaaa end-of-chapter exercises. To further demonstrate the proposed approaches, in the last chapter an application case study is presented which demonstrates the use of the framework in a real-world control system design and helps the reader quickly move on with their own challenges. MATLAB- codes used in examples throughout the book and solutions to selected exercise questions are available for download. The text will have particular resonance for researchers in control with an electrical engineering background, who wish to avoid spending excessive time in learning complex mathematical, theoretical developments but need to know how to deal with robust and optimal control synthesis problems. Please see http: //km. emotors. ncku. edu. tw/class/hw1. html] for solutions to the exercises provided in this book. "
Robustness Theory and Application (Wiley Series in Probability and Statistics)
by Brenton R. ClarkeA preeminent expert in the field explores new and exciting methodologies in the ever-growing field of robust statistics Used to develop data analytical methods, which are resistant to outlying observations in the data, while capable of detecting outliers, robust statistics is extremely useful for solving an array of common problems, such as estimating location, scale, and regression parameters. Written by an internationally recognized expert in the field of robust statistics, this book addresses a range of well-established techniques while exploring, in depth, new and exciting methodologies. Local robustness and global robustness are discussed, and problems of non-identifiability and adaptive estimation are considered. Rather than attempt an exhaustive investigation of robustness, the author provides readers with a timely review of many of the most important problems in statistical inference involving robust estimation, along with a brief look at confidence intervals for location. Throughout, the author meticulously links research in maximum likelihood estimation with the more general M-estimation methodology. Specific applications and R and some MATLAB subroutines with accompanying data sets—available both in the text and online—are employed wherever appropriate. Providing invaluable insights and guidance, Robustness Theory and Application: Offers a balanced presentation of theory and applications within each topic-specific discussion Features solved examples throughout which help clarify complex and/or difficult concepts Meticulously links research in maximum likelihood type estimation with the more general M-estimation methodology Delves into new methodologies which have been developed over the past decade without stinting on coverage of “tried-and-true” methodologies Includes R and some MATLAB subroutines with accompanying data sets, which help illustrate the power of the methods described Robustness Theory and Application is an important resource for all statisticians interested in the topic of robust statistics. This book encompasses both past and present research, making it a valuable supplemental text for graduate-level courses in robustness.
Robustness and Complex Data Structures
by Sonja Kuhnt Roland Fried Claudia BeckerThis Festschrift in honour of Ursula Gather's 60th birthday deals with modern topics in the field of robust statistical methods, especially for time series and regression analysis, and with statistical methods for complex data structures. The individual contributions of leading experts provide a textbook-style overview of the topic, supplemented by current research results and questions. The statistical theory and methods in this volume aim at the analysis of data which deviate from classical stringent model assumptions, which contain outlying values and/or have a complex structure. Written for researchers as well as master and PhD students with a good knowledge of statistics.
Robustness in Econometrics
by Van-Nam Huynh Vladik Kreinovich Songsak SriboonchittaThis book presents recent research on robustness in econometrics. Robust data processing techniques - i. e. , techniques that yield results minimally affected by outliers - and their applications to real-life economic and financial situations are the main focus of this book. The book also discusses applications of more traditional statistical techniques to econometric problems. Econometrics is a branch of economics that uses mathematical (especially statistical) methods to analyze economic systems, to forecast economic and financial dynamics, and to develop strategies for achieving desirable economic performance. In day-by-day data, we often encounter outliers that do not reflect the long-term economic trends, e. g. , unexpected and abrupt fluctuations. As such, it is important to develop robust data processing techniques that can accommodate these fluctuations.
Robustness in Statistical Forecasting
by Yuriy KharinThis book offers solutions to such topical problems as developing mathematical models and descriptions of typical distortions in applied forecasting problems; evaluating robustness for traditional forecasting procedures under distortionism and more.
Rod & Staff Grade 1 Math
by Rod StaffThe Rod & Staff Grade 1 Math Student Book (Part 2) continues with Lessons 86-170. Like the Rod & Staff Grade 1 Math Student Book (Part 1), this book continues the mastery approach method when teaching mathematics.
Rods, Sets and Arrows: The Rise and Fall of Modern Mathematics in Belgium (History of Mathematics Education)
by Dirk De Bock Geert VanpaemelFor anyone interested in the history and effects of the introduction of so-called “Modern Mathematics” (or “Mathématique Moderne,” or “New Mathematics,” etc.) this book, by Dirk De Bock and Geert Vanpaemel, is essential reading. The two authors are experienced and highly qualified Belgian scholars and the book looks carefully at events relating to school mathematics for the period from the end of World War II to 2010. Initially the book focuses on events which helped to define the modern mathematics revolution in Belgium before and during the 1960s. The book does much more than that, however, for it traces the influence of these events on national and international debates during the early phases of the reform. By providing readers with translations into English of relevant sections of key Continental documents outlining the major ideas of leading Continental scholars who contributed to the “Mathématique Moderne” movement, this book makes available to a wide readership, the theoretical, social, and political backdrops of Continental new mathematics reforms. In particular, the book focuses on the contributions made by Belgians such as Paul Libois, Willy Servais, Frédérique Lenger, and Georges Papy. The influence of modern mathematics fell away rapidly in the 1970s, however, and the authors trace the rise and fall, from that time into the 21st century, of a number of other approaches to school mathematics—in Belgium, in other Western European nations, and in North America. In summary, this is an outstanding, landmark publication displaying the fruits of deep scholarship and careful research based on extensive analyses of primary sources.
Rogerson's Book of Numbers: The Culture of Numbers—from 1,001 Nights to the Seven Wonders of the World
by Barnaby RogersonTHE STORIES BEHIND OUR ICONIC NUMBERSRogerson's Book of Numbers is based on a numerical array of virtues, spiritual attributes, gods, devils, sacred cities, powers, calendars, heroes, saints, icons, and cultural symbols.It provides a dazzling mass of information for those intrigued by the many roles numbers play in folklore and popular culture, in music and poetry, and in the many religions, cultures, and belief systems of our world.The stories unfold from millions to zero: from the number of the beast (666) to the seven deadly sins; from the twelve signs of the zodiac to the four suits of a deck of cards. Along the way, author Barnaby Rogerson will show you why Genghis Khan built a city of 108 towers, how Dante forged his Divine Comedy on the number eleven, and why thirteen is so unlucky in the West whereas fourteen is the number to avoid in China.
Rogue Waves in Integrable Systems
by Bo Yang Jianke YangThis book offers a holistic picture of rogue waves in integrable systems. Rogue waves are a rare but extreme phenomenon that occur most famously in water, but also in other diverse contexts such as plasmas, optical fibers and Bose-Einstein condensates where, despite the seemingly disparate settings, a common theoretical basis exists. This book presents the physical derivations of the underlying integrable nonlinear partial differential equations, derives the explicit and compact rogue wave solutions in these integrable systems, and analyzes rogue wave patterns that arise in these solutions, for many integrable systems and in multiple physical contexts. Striking a balance between theory and experiment, the book also surveys recent experimental insights into rogue waves in water, optical fibers, plasma, and Bose-Einstein condensates. In taking integrable nonlinear wave systems as a starting point, this book will be of interest to a broad cross section of researchers and graduate students in physics and applied mathematics who encounter nonlinear waves.
Rosenbrock—Wanner–Type Methods: Theory and Applications (Mathematics Online First Collections)
by Andreas Bartel Michael Günther Matthias Ehrhardt Tim Jax Gerd SteinebachThis book discusses the development of the Rosenbrock—Wanner methods from the origins of the idea to current research with the stable and efficient numerical solution and differential-algebraic systems of equations, still in focus. The reader gets a comprehensive insight into the classical methods as well as into the development and properties of novel W-methods, two-step and exponential Rosenbrock methods. In addition, descriptive applications from the fields of water and hydrogen network simulation and visual computing are presented.
Rotating Machinery, Optical Methods & Scanning LDV Methods, Volume 6: Proceedings of the 39th IMAC, A Conference and Exposition on Structural Dynamics 2021 (Conference Proceedings of the Society for Experimental Mechanics Series)
by Dario Di Maio Javad BaqersadRotating Machinery, Optical Methods & Scanning LDV Methods, Volume 6: Proceedings of the 39th IMAC, A Conference and Exposition on Structural Dynamics, 2021, the sixth volume of nine from the Conference brings together contributions to this important area of research and engineering. The collection presents early findings and case studies on fundamental and applied aspects of Structural Health Monitoring, including papers on:Novel TechniquesOptical Methods,Scanning LDV MethodsPhotogrammetry & DICRotating Machinery
Rotation Sets and Complex Dynamics (Lecture Notes in Mathematics #2214)
by Saeed ZakeriThis monograph examines rotation sets under the multiplication by d (mod 1) map and their relation to degree d polynomial maps of the complex plane. These sets are higher-degree analogs of the corresponding sets under the angle-doubling map of the circle, which played a key role in Douady and Hubbard's work on the quadratic family and the Mandelbrot set. Presenting the first systematic study of rotation sets, treating both rational and irrational cases in a unified fashion, the text includes several new results on their structure, their gap dynamics, maximal and minimal sets, rigidity, and continuous dependence on parameters. This abstract material is supplemented by concrete examples which explain how rotation sets arise in the dynamical plane of complex polynomial maps and how suitable parameter spaces of such polynomials provide a complete catalog of all such sets of a given degree. As a main illustration, the link between rotation sets of degree 3 and one-dimensional families of cubic polynomials with a persistent indifferent fixed point is outlined. The monograph will benefit graduate students as well as researchers in the area of holomorphic dynamics and related fields.
Rotation Transforms for Computer Graphics
by John VinceRotation transforms are used everywhere in computer graphics from rotating pictures in editing software, to providing an arbitrary view of a 3D virtual environment. Although the former is a trivial operation, the latter can be a challenging task. Rotation Transforms for Computer Graphics covers a wide range of mathematical techniques used for rotating points and frames of reference in the plane and 3D space. It includes many worked examples and over 100 illustrations that make it essential reading for students, academics, researchers and professional practitioners. The book includes introductory chapters on complex numbers, matrices, quaternions and geometric algebra, and further chapters on how these techniques are employed in 2D and 3D computer graphics. In particular, matrix and bivector transforms are developed and evaluated to rotate points in a fixed frame of reference, and vice versa.
Rotations, Quaternions, and Double Groups
by Simon L. AltmannThis self-contained text presents a consistent description of the geometric and quaternionic treatment of rotation operators, employing methods that lead to a rigorous formulation and offering complete solutions to many illustrative problems.Geared toward upper-level undergraduates and graduate students, the book begins with chapters covering the fundamentals of symmetries, matrices, and groups, and it presents a primer on rotations and rotation matrices. Subsequent chapters explore rotations and angular momentum, tensor bases, the bilinear transformation, projective representations, and the geometry, topology, and algebra of rotations. Some familiarity with the basics of group theory is assumed, but the text assists students in developing the requisite mathematical tools as necessary.
Rough Draft Math: Revising to Learn
by Amanda JansenTalking and writing about unfinished ideas is vital to learning mathematics, but most students only speak up when they think they have the right answer - especially middle school and high school students. Amanda Jansen and her collaborating teachers have developed a breakthrough approach to address this challenge. Rough Draft Math: Revising to Learn, Jansen shares the power of infusing math class with the spirit of revision so that students feel comfortable thinking aloud as they problem-solve rather than talking only to perform right answers. Creating a Community of Learners: As part of the rough draft framework, a class of students becomes an equitable and inclusive community of thinkers, one where students feel safe to engage in discourse while developing mathematical competency and confidence Practical Application of Innovative Ideas: This book includes specific teaching techniques and a range of classroom vignettes showing rough draft math in action within a student-centered teaching approach. Children can develop solutions at their own pace and share thought processes behind their conclusions Classroom Tested: Jansen has developed the concept of rough draft math in collaboration with a diverse group of dynamic and reflective teachers. Rough Draft Math' provides a blueprint for educators to allow free-thinking discussion while maintaining the mathematical learning goalsRough Draft Math, Jansen shows how to create an energetic classroom culture where students readily participate and share their evolving understanding while engaging in math talk, collaborative problem solving, and ongoing revision of ideas. '
Rough Draft Math: Rough Draft Math: Revising To Learn
by Amanda JansenMany students, especially as they get older, only share their thinking in math class when they’re sure they have the right answer. This means that some students hardly talk at all. Yet, talking and writing about in-process and unfinished ideas are vital to learning mathematics. How can we meet this challenge? Amanda (Mandy) Jansen and her collaborating teachers have developed a breakthrough approach: expand the idea of 'rough drafts' to the mathematics classroom. In Rough Draft Math, Mandy shares the power of infusing math class with the spirit of revision so that students feel comfortable thinking aloud as they talk to learn through problem-solving rather than talking only to perform right answers. In the process, a class of students becomes a community of mathematical thinkers, and teachers gain access into their students’ ideas and understandings. Inside you’ll find the following: an exploration of what the idea of revision could mean for math teaching and learning classroom vignettes to see rough draft math in action specific teaching techniques to encourage and practice rough draft thinking voices of teachers and students in rough draft classrooms Mandy’s reflections about her own teaching as a work in progress In Rough Draft Math, Mandy shows how to create a classroom culture in which your students will feel more comfortable expressing their partial understandings and in-process thinking, and then continually revising that thinking as they build deep, conceptual understanding of mathematics.
Rough Fuzzy Image Analysis: Foundations and Methodologies (Chapman & Hall/CRC Mathematical and Computational Imaging Sciences Series)
by Sankar K. Pal James F. PetersFuzzy sets, near sets, and rough sets are useful and important stepping stones in a variety of approaches to image analysis. These three types of sets and their various hybridizations provide powerful frameworks for image analysis. Emphasizing the utility of fuzzy, near, and rough sets in image analysis, Rough Fuzzy Image Analysis: Foundations and
Rough Multiple Objective Decision Making
by Jiuping Xu Zhimiao TaoUnder intense scrutiny for the last few decades, Multiple Objective Decision Making (MODM) has been useful for dealing with the multiple-criteria decisions and planning problems associated with many important applications in fields including management science, engineering design, and transportation. Rough set theory has also proved to be an effect
Rough Sets
by Dominik Ślęzak Georg Peters Yiyu Yao Richard Weber Guoyin Wang Víctor Flores Fernando Gomide Andrzej Janusz Claudio Meneses Duoqian MiaoVolume XII of the Transactions on Rough Sets (TRS) includes articles that are part of a special issue on Rough Set Structuring of Knowledge. These articles are extended versions of papers accepted for presentation at the Rough Set and Knowledge Technology Conference (RSKT 2008) organized in Chengdu, China, in May 2008. In fact, this conference did not take place because of the earthquake that dramatically hit the Chengdu province just before the event. The editors selected some papers accepted for RSKT 2008 and invited their authors to submit extended versions to this issue. The 11 submissions received after this invitation were sent to reviewers and, ?nally, 8 papers were accepted for publication in the special issue. The editors of the special issue are particularly grateful to all the authors of submitted papers, and to the editors of Transactions on Rough Sets, JamesF. Peters and Andrzej Skowron, who provided friendly and valuable assistance in the reviewing process. Special thanks are due to the following reviewers: Mohua Banerjee, Anna Gomolinsk a, Ryszard Janicki, Julia Johnson, Maneesh Joshi, Jusheng Mi, Sonajharia Minz, Sushmita Mitra, Tuan Trung Nguyen, Georg Pe- ters, Andrzej Skowron, Genlou Sun, Marcin Szczuka, Dominik Sl, ezak, Guoyin Wang, Hai Wang, Marcin Wolski, Haiyi Zhang, Yan Zhao, William Zhu. Their laudable e?orts made possible a careful selection and revision of submitted manuscripts. "
Rough Sets
by Dominik Ślęzak Yiyu Yao Davide Ciucci Lech Polkowski Piotr Artiemjew Dun Liu Beata ZieloskoDecision trees and decision rule systems are widely used in different applications as algorithms for problem solving, as predictors, and as a way for knowledge representation. Reducts play key role in the problem of attribute (feature) selection. The aims of this book are (i) the consideration of the sets of decision trees, rules and reducts; (ii) study of relationships among these objects; (iii) design of algorithms for construction of trees, rules and reducts; and (iv) obtaining bounds on their complexity. Applications for supervised machine learning, discrete optimization, analysis of acyclic programs, fault diagnosis, and pattern recognition are considered also. This is a mixture of research monograph and lecture notes. It contains many unpublished results. However, proofs are carefully selected to be understandable for students. The results considered in this book can be useful for researchers in machine learning, data mining and knowledge discovery, especially for those who are working in rough set theory, test theory and logical analysis of data. The book can be used in the creation of courses for graduate students.
Rough Sets: International Joint Conference, IJCRS 2017, Olsztyn, Poland, July 3–7, 2017, Proceedings, Part I (Lecture Notes in Computer Science #10313)
by Dominik Ślęzak Yiyu Yao Davide Ciucci Lech Polkowski Piotr Artiemjew Dun Liu Beata ZieloskoDecision trees and decision rule systems are widely used in different applications as algorithms for problem solving, as predictors, and as a way for knowledge representation. Reducts play key role in the problem of attribute (feature) selection. The aims of this book are (i) the consideration of the sets of decision trees, rules and reducts; (ii) study of relationships among these objects; (iii) design of algorithms for construction of trees, rules and reducts; and (iv) obtaining bounds on their complexity. Applications for supervised machine learning, discrete optimization, analysis of acyclic programs, fault diagnosis, and pattern recognition are considered also. This is a mixture of research monograph and lecture notes. It contains many unpublished results. However, proofs are carefully selected to be understandable for students. The results considered in this book can be useful for researchers in machine learning, data mining and knowledge discovery, especially for those who are working in rough set theory, test theory and logical analysis of data. The book can be used in the creation of courses for graduate students.
Rough Sets: International Joint Conference, IJCRS 2018, Quy Nhon, Vietnam, August 20-24, 2018, Proceedings (Lecture Notes in Computer Science #11103)
by Tianrui Li Hung Son Nguyen Quang-Thuy Ha Małgorzata Przybyła-KasperekThis LNAI 1103 constitutes the proceedings of the International Joint Conference on Rough Sets, IJCRS 2018, held in Quy Nhon, Vietnam, in August 2018.The 40 full papers presented together with 5 short papers were carefully reviewed and selected from 61 submissions. The IJCRS conferences aim at bringing together experts from universities and research centers as well as the industry representing fields of research in which theoretical and applicational aspects of rough set theory already find or may potentially find usage.
Rough Sets: International Joint Conference, IJCRS 2024, Halifax, NS, Canada, May 17–20, 2024, Proceedings, Part I (Lecture Notes in Computer Science #14839)
by Pawan Lingras Dominik Ślęzak Yan Zhang Chris Cornelis JingTao Yao Mengjun HuThis two-volume set LNAI 14839-14840 constitutes the refereed proceedings of the International Joint Conference on Rough Sets, IJCRS 2024, held in Halifax, NS, Canada, during May 17–20, 2024. The 43 full papers included in this book were carefully reviewed and selected from 56 submissions. They are organized in topical sections as follows: Part I: Rough Set Models and Foundations; Rule Induction and Machine Learning; Granular Computing; and Rough Set Applications. Part II: Three-Way Decision and Rough Sets; Three-Way Decision in Data Analytics; Three-Way Decision in Broad Senses; Rental Market Data Mining; and Applications of Deep Learning and Soft Computing.
Rough Sets: International Joint Conference, IJCRS 2024, Halifax, NS, Canada, May 17–20, 2024, Proceedings, Part II (Lecture Notes in Computer Science #14840)
by Pawan Lingras Dominik Ślęzak Yan Zhang Chris Cornelis JingTao Yao Mengjun HuThis two-volume set LNAI 14839-14840 constitutes the refereed proceedings of the International Joint Conference on Rough Sets, IJCRS 2024, held in Halifax, NS, Canada, during May 17–20, 2024. The 43 full papers included in this book were carefully reviewed and selected from 56 submissions. They are organized in topical sections as follows: Part I: Rough Set Models and Foundations; Rule Induction and Machine Learning; Granular Computing; and Rough Set Applications. part II: Three-Way Decision and Rough Sets; Three-Way Decision in Data Analytics; Three-Way Decision in Broad Senses; Rental Market Data Mining; and Applications of Deep Learning and Soft Computing.
Rough Sets: International Joint Conference, IJCRS 2025, Chongqing, China, May 11–13, 2025, Proceedings, Part I (Lecture Notes in Computer Science #15708)
by Richard Jensen Xinbo Gao Guoyin Wang Chris Cornelis JingTao Yao Shuyin Xia Qinghua Zhang Christopher HenryThis three-volume set LNAI 15708-15709-15110 constitutes the proceedings of the International Joint Conference on Rough Sets, IJCRS 2025, held in Chongqing, China, during May 11–13, 2025.The 90 full papers included in these volumes were carefully reviewed and selected from 187 submissions. They are organized in topical sections as follows:Part I: Rough Set Models and Foundations; Fuzzy Rough Sets and Rough Fuzzy Sets; and Granular Computing.Part II: Rough Set Applications; Feature Selection and Knowledge Discovery; and Cognitive Computing.Part III: Three-way Data Analytics and Decision; Medicine and Health Data Mining; and Applications of Deep Learning and Soft Computing.