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This book mainly deals with the Bochner-Riesz means of multiple Fourier integral and series on Euclidean spaces. It aims to give a systematical introduction to the fundamental theories of the Bochner-Riesz means and important achievements attained in the last 50 years. For the Bochner-Riesz means of multiple Fourier integral, it includes the Fefferman theorem which negates the Disc multiplier conjecture, the famous Carleson-Sjölin theorem, and Carbery-Rubio de Francia-Vega's work on almost everywhere convergence of the Bochner-Riesz means below the critical index. For the Bochner-Riesz means o
Fourier series. --- Euclidean algorithm. --- Algorithm of Euclid --- Continued division --- Division, Continued --- Euclid algorithm --- Euclidian algorithm --- Euclid's algorithm --- Algorithms --- Number theory --- Fourier integrals --- Series, Fourier --- Series, Trigonometric --- Trigonometric series --- Calculus --- Fourier analysis --- Harmonic analysis --- Harmonic functions --- Fourier series --- Euclidean algorithm --- Mathematical models.
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Spherical functions. --- Euclidean algorithm. --- Algorithm of Euclid --- Continued division --- Division, Continued --- Euclid algorithm --- Euclidian algorithm --- Euclid's algorithm --- Algorithms --- Number theory --- Functions, Spherical --- Spherical harmonics --- Transcendental functions --- Spheroidal functions --- Funcions esferoïdals --- Algorismes --- Algorisme d'Euclides --- Algoritmes --- Àlgebra --- Algorismes computacionals --- Algorismes genètics --- Anàlisi numèrica --- Funcions recursives --- Programació (Matemàtica) --- Programació (Ordinadors) --- Teoria de màquines --- Traducció automàtica --- Funcions harmòniques
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architectuur --- architecture [discipline] --- Architecture --- anno 2000-2099 --- 72.039 --- 72:681.3 --- Architectuur ; 21ste eeuw ; 2000-2010 --- Architectuur ; ontwerpanalyse ; vormanalyse ; 21ste eeuw --- Architectuur en technologie --- Architectuur en wiskunde ; architectuur en wetenschap --- Architectuur ; stedenbouw ; digitale ontwerpen --- Architectuur ; non standard --- 72.012/013 --- 51 --- 72.01 --- architectonisch ontwerp --- architectuur 21e eeuw --- vormanalyse --- -Euclidean algorithm --- 514.12 --- 72.013 --- 721.01 --- Algorithm of Euclid --- Continued division --- Division, Continued --- Euclid algorithm --- Euclidian algorithm --- Euclid's algorithm --- Algorithms --- Number theory --- Architecture, Western (Western countries) --- Building design --- Buildings --- Construction --- Western architecture (Western countries) --- Art --- Building --- Architectuurgeschiedenis ; 2000 - 2050 --- Architectuur en computerwetenschappen --- Architectonisch ontwerp --- Architectuurontwerp --- Ontwerp (architectuur) --- Digitale architectuur --- CAAD --- Computer aided architectural design --- Mathematica --- Wiskunde --- architectuurtheorie, ontwerp, vormgeving --- Mathematical models --- Euclidean and pseudo-Euclidean geometries. Analytic geometry --- Vormgeving in de architectuur: proporties; afmetingen; harmonische systemen; principes van eenheid, orde, symmetrie --- Architectuurontwerpen. Bouwplannen. Bouwprojecten --- Hedendaagse architectuur. Bouwkunst sinds 1960 --- Design and construction --- 72.039 Hedendaagse architectuur. Bouwkunst sinds 1960 --- 721.01 Architectuurontwerpen. Bouwplannen. Bouwprojecten --- 72.013 Vormgeving in de architectuur: proporties; afmetingen; harmonische systemen; principes van eenheid, orde, symmetrie --- 514.12 Euclidean and pseudo-Euclidean geometries. Analytic geometry --- Architecture, Primitive
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Evolving from an elementary discussion, this book develops the Euclidean algorithm to a very powerful tool to deal with general continued fractions, non-normal Padé tables, look-ahead algorithms for Hankel and Toeplitz matrices, and for Krylov subspace methods. It introduces the basics of fast algorithms for structured problems and shows how they deal with singular situations. Links are made with more applied subjects such as linear system theory and signal processing, and with more advanced topics and recent results such as general bi-orthogonal polynomials, minimal Padé approximation, poly
Ordered algebraic structures --- Numerical approximation theory --- Computer science --- lineaire algebra --- Algebras, Linear --- Euclidean algorithm --- Orthogonal polynomials --- Padé approximant --- #TELE:SISTA --- 519.6 --- 681.3*G11 --- 681.3*G12 --- 681.3*G13 --- Algorithm of Euclid --- Continued division --- Division, Continued --- Euclid algorithm --- Euclidian algorithm --- Euclid's algorithm --- Algorithms --- Number theory --- Linear algebra --- Algebra, Universal --- Generalized spaces --- Mathematical analysis --- Calculus of operations --- Line geometry --- Topology --- 681.3*G13 Numerical linear algebra: conditioning; determinants; Eigenvalues; error analysis; linear systems; matrix inversion; pseudoinverses; sparse and very largesystems --- Numerical linear algebra: conditioning; determinants; Eigenvalues; error analysis; linear systems; matrix inversion; pseudoinverses; sparse and very largesystems --- 681.3*G12 Approximation: chebyshev; elementary function; least squares; linear approximation; minimax approximation and algorithms; nonlinear and rational approximation; spline and piecewise polynomial approximation (Numerical analysis) --- Approximation: chebyshev; elementary function; least squares; linear approximation; minimax approximation and algorithms; nonlinear and rational approximation; spline and piecewise polynomial approximation (Numerical analysis) --- 681.3*G11 Interpolation: difference formulas; extrapolation; smoothing; spline and piecewise polynomial interpolation (Numerical analysis) --- Interpolation: difference formulas; extrapolation; smoothing; spline and piecewise polynomial interpolation (Numerical analysis) --- 519.6 Computational mathematics. Numerical analysis. Computer programming --- Computational mathematics. Numerical analysis. Computer programming --- Fourier analysis --- Functions, Orthogonal --- Polynomials --- Approximant, Padé --- Approximation theory --- Continued fractions --- Power series --- Euclidean algorithm. --- Algebras, Linear. --- Padé approximant. --- Orthogonal polynomials. --- Padé approximant. --- Pade approximant.
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The first book to offer a comprehensive view of the LLL algorithm, this text surveys computational aspects of Euclidean lattices and their main applications. It includes many detailed motivations, explanations and examples.
Cryptography -- Mathematics. --- Euclidean algorithm. --- Integer programming. --- Lattice theory. --- Cryptography --- Lattice theory --- Integer programming --- Euclidean algorithm --- Mathematics --- Engineering & Applied Sciences --- Physical Sciences & Mathematics --- Computer Science --- Mathematical Theory --- Algorithms. --- Mathematics. --- Algorithm of Euclid --- Continued division --- Division, Continued --- Euclid algorithm --- Euclidian algorithm --- Euclid's algorithm --- Lattices (Mathematics) --- Space lattice (Mathematics) --- Structural analysis (Mathematics) --- Cryptanalysis --- Cryptology --- Secret writing --- Steganography --- Algorism --- Computer science. --- Data structures (Computer science). --- Data encryption (Computer science). --- Computer science --- Computer Science. --- Data Structures. --- Data Encryption. --- Mathematics of Computing. --- Data Structures, Cryptology and Information Theory. --- Algorithm Analysis and Problem Complexity. --- Algebra --- Arithmetic --- Foundations --- Algorithms --- Number theory --- Programming (Mathematics) --- Algebra, Abstract --- Algebra, Boolean --- Group theory --- Set theory --- Topology --- Transformations (Mathematics) --- Crystallography, Mathematical --- Signs and symbols --- Symbolism --- Writing --- Ciphers --- Data encryption (Computer science) --- Data structures (Computer scienc. --- Computer software. --- Cryptology. --- Data Structures and Information Theory. --- Informatics --- Science --- Data encoding (Computer science) --- Encryption of data (Computer science) --- Computer security --- Software, Computer --- Computer systems --- Computer science—Mathematics. --- Information structures (Computer science) --- Structures, Data (Computer science) --- Structures, Information (Computer science) --- Electronic data processing --- File organization (Computer science) --- Abstract data types (Computer science) --- Artificial intelligence --- Cryptography. --- Information theory. --- Data Science. --- Data processing. --- Communication theory --- Communication --- Cybernetics --- Computer mathematics
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The Euclidean shortest path (ESP) problem asks the question: what is the path of minimum length connecting two points in a 2- or 3-dimensional space? Variants of this industrially-significant computational geometry problem also require the path to pass through specified areas and avoid defined obstacles. This unique text/reference reviews algorithms for the exact or approximate solution of shortest-path problems, with a specific focus on a class of algorithms called rubberband algorithms. Discussing each concept and algorithm in depth, the book includes mathematical proofs for many of the given statements. Suitable for a second- or third-year university algorithms course, the text enables readers to understand not only the algorithms and their pseudocodes, but also the correctness proofs, the analysis of time complexities, and other related topics. Topics and features: Provides theoretical and programming exercises at the end of each chapter Presents a thorough introduction to shortest paths in Euclidean geometry, and the class of algorithms called rubberband algorithms Discusses algorithms for calculating exact or approximate ESPs in the plane Examines the shortest paths on 3D surfaces, in simple polyhedrons and in cube-curves Describes the application of rubberband algorithms for solving art gallery problems, including the safari, zookeeper, watchman, and touring polygons route problems Includes lists of symbols and abbreviations, in addition to other appendices This hands-on guide will be of interest to undergraduate students in computer science, IT, mathematics, and engineering. Programmers, mathematicians, and engineers dealing with shortest-path problems in practical applications will also find the book a useful resource. Dr. Fajie Li is at Huaqiao University, Xiamen, Fujian, China. Prof. Dr. Reinhard Klette is at the Tamaki Innovation Campus of The University of Auckland.
Computational complexity. --- Computer aided design. --- Computer science. --- Computer science -- Mathematics. --- Computer software. --- Electronic data processing. --- Euclidean algorithm. --- Optical pattern recognition. --- Graph algorithms --- Mathematics --- Engineering & Applied Sciences --- Physical Sciences & Mathematics --- Algebra --- Computer Science --- Mathematical analysis. --- Algebraic spaces. --- Spaces, Algebraic --- 517.1 Mathematical analysis --- Mathematical analysis --- Algorithm of Euclid --- Continued division --- Division, Continued --- Euclid algorithm --- Euclidian algorithm --- Euclid's algorithm --- Algorithms. --- Numerical analysis. --- Computer science --- Pattern recognition. --- Computer-aided engineering. --- Computer Science. --- Algorithm Analysis and Problem Complexity. --- Numeric Computing. --- Pattern Recognition. --- Discrete Mathematics in Computer Science. --- Math Applications in Computer Science. --- Computer-Aided Engineering (CAD, CAE) and Design. --- Mathematics. --- Geometry, Algebraic --- Algorithms --- Number theory --- CAD (Computer-aided design) --- Computer-assisted design --- Computer-aided engineering --- Design --- Informatics --- Science --- Complexity, Computational --- Electronic data processing --- Machine theory --- Optical data processing --- Pattern perception --- Perceptrons --- Visual discrimination --- ADP (Data processing) --- Automatic data processing --- Data processing --- EDP (Data processing) --- IDP (Data processing) --- Integrated data processing --- Computers --- Office practice --- Software, Computer --- Computer systems --- Automation --- Computer science—Mathematics. --- CAE --- Engineering --- Design perception --- Pattern recognition --- Form perception --- Perception --- Figure-ground perception --- Algorism --- Arithmetic --- Foundations
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