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The maturing of the field of data mining has brought about an increased level of mathematical sophistication. Such disciplines like topology, combinatorics, partially ordered sets and their associated algebraic structures (lattices and Boolean algebras), and metric spaces are increasingly applied in data mining research. This book presents these mathematical foundations of data mining integrated with applications to provide the reader with a comprehensive reference. Mathematics is presented in a thorough and rigorous manner offering a detailed explanation of each topic, with applications to data mining such as frequent item sets, clustering, decision trees also being discussed. More than 400 exercises are included and they form an integral part of the material. Some of the exercises are in reality supplemental material and their solutions are included. The reader is assumed to have a knowledge of elementary analysis. Features and topics: • Study of functions and relations • Applications are provided throughout • Presents graphs and hypergraphs • Covers partially ordered sets, lattices and Boolean algebras • Finite partially ordered sets • Focuses on metric spaces • Includes combinatorics • Discusses the theory of the Vapnik-Chervonenkis dimension of collections of sets This wide-ranging, thoroughly detailed volume is self-contained and intended for researchers and graduate students, and will prove an invaluable reference tool.

Data mining. --- Partially ordered sets. --- Metric spaces. --- Set theory. --- Computer science. --- Computer science --- Computer mathematics. --- Computer Science. --- Data Mining and Knowledge Discovery. --- Mathematics of Computing. --- Discrete Mathematics in Computer Science. --- Computational Mathematics and Numerical Analysis. --- Informatics --- Science --- Algorithmic knowledge discovery --- Factual data analysis --- KDD (Information retrieval) --- Knowledge discovery in data --- Knowledge discovery in databases --- Mining, Data --- Database searching --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Mathematics. --- Mathematics --- Aggregates --- Classes (Mathematics) --- Ensembles (Mathematics) --- Mathematical sets --- Sets (Mathematics) --- Theory of sets --- Logic, Symbolic and mathematical --- Posets --- Sets, Partially ordered --- Ordered sets --- Spaces, Metric --- Generalized spaces --- Set theory --- Topology --- Computational complexity. --- Complexity, Computational --- Machine theory --- Computer science—Mathematics.

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Principles of Terahertz Science and Technology aims to elucidate the fundamentals of THz technology and science for potential new users. It surveys major techniques of generating, detecting, and manipulating THz waves and also discusses a number of essential processes where THz waves interact with physical, chemical, and biological systems. This book serves as an introduction to THz technology for new researchers in various fields. Many different disciplines, such as ultrafast spectroscopy, semiconductor device fabrication, bio-medical imaging and more, involve the recent development of THz technology. It is necessary to lay down a strong, common foundation among researchers, so that communication can proceed smoothly. Previous THz research activities have concentrated on generation and detection, but the focus has now shifted to practical applications of this technology, such as high-speed optoelectronic signal processing and molecular spectroscopy. Drawing upon years of practical experience and using numerous examples and illustrative applications Yun-Shik Lee discusses The major techniques of generating, detecting, and manipulating THz waves Essential processes where THz waves interact with physical, chemical, and biological systems Medical Applications of T-Ray Imaging including, optical properties of human tissue, cancer diagnostics, reflective imaging of skin burns and detection of dental caries Principles of Terahertz Science and Technology is an ideal book for applied physicists, microwave engineers, biomedical engineers, electrical engineers, and analytical chemists interested in the fundamentals and applications of THz engineering.

Electromagnetic interactions --Congresses. --- Nuclear physics --Congresses. --- Electrical & Computer Engineering --- Engineering & Applied Sciences --- Electrical Engineering --- Millimeter wave devices. --- Optoelectronic devices. --- Submillimeter waves. --- Terahertz technology. --- Wave guides. --- Waveguides --- Submillimeter radiation --- Submillimeter-terahertz radiation --- Terahertz radiation --- Waves, Submillimeter --- Photo electric devices --- Photo electronic devices --- Photoelectronic devices --- Théorie axiomatique des ensembles --- Théorie axiomatique des ensembles --- Engineering. --- Microwaves. --- Optical engineering. --- Electronics. --- Microelectronics. --- Electronics and Microelectronics, Instrumentation. --- Microwaves, RF and Optical Engineering. --- Classical Electrodynamics. --- Optics, Lasers, Photonics, Optical Devices. --- Electric conductors --- Electric waves --- Electromagnetic waves --- Gyrators --- Microwave transmission lines --- Radio --- Transducers --- High technology --- Electromagnetic devices --- Radiation --- Electronic apparatus and appliances --- Optical instruments --- Electrooptical devices --- Integrated optics --- Microwave devices --- Millimeter waves --- Equipment and supplies --- Game theory --- Negotiation --- Axiomatic set theory --- Mathematical models --- Théorie des jeux --- Electrical engineering --- Physical sciences --- Hertzian waves --- Geomagnetic micropulsations --- Radio waves --- Shortwave radio --- Optics. --- Electrodynamics. --- Lasers. --- Photonics. --- New optics --- Optics --- Light amplification by stimulated emission of radiation --- Masers, Optical --- Optical masers --- Light amplifiers --- Light sources --- Optoelectronic devices --- Nonlinear optics --- Optical parametric oscillators --- Dynamics --- Physics --- Light --- Mechanical engineering --- Microminiature electronic equipment --- Microminiaturization (Electronics) --- Electronics --- Microtechnology --- Semiconductors --- Miniature electronic equipment --- Negotiation - Mathematical models