1988, ISBN 0691084335, Volume no. 116., viii, 246

Book

1998, Canadian Mathematical Society series of monographs and advanced texts, ISBN 9780471128076, Volume 21, xi, 583

Book

1995, Lecture notes in mathematics, ISBN 9783540603115, Volume 1617., xi, 305

Book

1983, Lecture notes in mathematics, ISBN 0387122907, Volume 987, xi, 186

Book

Journal of Number Theory, ISSN 0022-314X, 08/2016, Volume 165, pp. 355 - 362

By using the properties of Gauss sums and the mean value theorem of the Dirichlet L-function, a hybrid mean value problem involving certain Hardy sum and...

Kloosterman sum | Hardy sum | Hybrid mean value | Gauss sum | EISENSTEIN | DEDEKIND | MATHEMATICS | SERIES | THETA-FUNCTIONS | Information science

Kloosterman sum | Hardy sum | Hybrid mean value | Gauss sum | EISENSTEIN | DEDEKIND | MATHEMATICS | SERIES | THETA-FUNCTIONS | Information science

Journal Article

IEEE Transactions on Neural Networks and Learning Systems, ISSN 2162-237X, 03/2017, Volume 28, Issue 3, pp. 714 - 725

H ∞ control is a powerful method to solve the disturbance attenuation problems that occur in some control systems. The design of such controllers relies on...

Algorithm design and analysis | zero-sum game (ZSG) | Heuristic algorithms | H ∞ control">H ∞ control | Adaptive dynamic programming (ADP) | Artificial neural networks | Games | Approximation algorithms | policy iteration (PI) | Mathematical model | Game theory | H8 control | COMPUTER SCIENCE, HARDWARE & ARCHITECTURE | APPROXIMATION | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | DISCRETE-TIME-SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC | H-infinity control | LEARNING ALGORITHM | POLICY UPDATE ALGORITHM | CRITIC DESIGNS | COMPUTER SCIENCE, THEORY & METHODS | EQUATION | STATE-FEEDBACK CONTROL | Computer simulation | Control systems design | Adaptive algorithms | Feasibility studies | Control systems | Theoretical analysis | Adaptive control | Gauss-Newton method | Optimization | Zero sum games | Neural networks | Least squares method | Newton methods | Disturbance | Attenuation | Electronic & video games | Dynamic programming | Internet | Iterative methods

Algorithm design and analysis | zero-sum game (ZSG) | Heuristic algorithms | H ∞ control">

Journal Article

Mathematical Programming, ISSN 0025-5610, 10/2013, Volume 141, Issue 1, pp. 349 - 382

We present in this paper alternating linearization algorithms based on an alternating direction augmented Lagrangian approach for minimizing the sum of two...

Alternating direction method | Primary 65K05 | Augmented Lagrangian method | Optimal gradient method | Variable splitting | Gauss-Seidel method | Theoretical, Mathematical and Computational Physics | Mathematics | Alternating linearization method | Mathematical Methods in Physics | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Convex optimization | 90C25 | Numerical Analysis | Peaceman-Rachford method | Secondary 68Q25 | Combinatorics | MATHEMATICS, APPLIED | SIGNAL RECOVERY | DECOMPOSITION | EQUATIONS | COMPUTER SCIENCE, SOFTWARE ENGINEERING | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MINIMIZATION | MONOTONE VARIATIONAL-INEQUALITIES | SPLITTING ALGORITHM | INVERSE PROBLEMS | CONSTRAINED OPTIMIZATION | SELECTION | OPERATORS | Methods | Management science | Algorithms | Studies | Splitting | Computation | Mathematical analysis | Mathematical models | Iterative methods | Optimization | Linearization

Alternating direction method | Primary 65K05 | Augmented Lagrangian method | Optimal gradient method | Variable splitting | Gauss-Seidel method | Theoretical, Mathematical and Computational Physics | Mathematics | Alternating linearization method | Mathematical Methods in Physics | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Convex optimization | 90C25 | Numerical Analysis | Peaceman-Rachford method | Secondary 68Q25 | Combinatorics | MATHEMATICS, APPLIED | SIGNAL RECOVERY | DECOMPOSITION | EQUATIONS | COMPUTER SCIENCE, SOFTWARE ENGINEERING | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MINIMIZATION | MONOTONE VARIATIONAL-INEQUALITIES | SPLITTING ALGORITHM | INVERSE PROBLEMS | CONSTRAINED OPTIMIZATION | SELECTION | OPERATORS | Methods | Management science | Algorithms | Studies | Splitting | Computation | Mathematical analysis | Mathematical models | Iterative methods | Optimization | Linearization

Journal Article

Statistics and Probability Letters, ISSN 0167-7152, 11/2017, Volume 130, pp. 57 - 62

Given , a sequence of real valued random variables, we define , , and define the by linear interpolation of (assuming for all ). In this note the convergence...

Continued Fractions | Partial Sum Processes | Gauss Measure | STATISTICS & PROBABILITY

Continued Fractions | Partial Sum Processes | Gauss Measure | STATISTICS & PROBABILITY

Journal Article

IEEE Transactions on Information Theory, ISSN 0018-9448, 08/2003, Volume 49, Issue 8, pp. 1912 - 1921

We characterize the sum capacity of the vector Gaussian broadcast channel by showing that the existing inner bound of Marton and the existing upper bound of...

Additive noise | Base stations | Upper bound | Transmitters | Transmitting antennas | Receiving antennas | Broadcasting | Downlink | Associate members | Antenna arrays | Broadcast channels | Wireless system | Multiple antennas | COMPUTER SCIENCE, INFORMATION SYSTEMS | wireless system | multiple antennas | broadcast channels | downlink | ENGINEERING, ELECTRICAL & ELECTRONIC | Research | Antennas (Electronics) | Theory | Information systems | Mathematical analysis | Receivers | Gaussian | Vectors (mathematics) | Joints | Channels

Additive noise | Base stations | Upper bound | Transmitters | Transmitting antennas | Receiving antennas | Broadcasting | Downlink | Associate members | Antenna arrays | Broadcast channels | Wireless system | Multiple antennas | COMPUTER SCIENCE, INFORMATION SYSTEMS | wireless system | multiple antennas | broadcast channels | downlink | ENGINEERING, ELECTRICAL & ELECTRONIC | Research | Antennas (Electronics) | Theory | Information systems | Mathematical analysis | Receivers | Gaussian | Vectors (mathematics) | Joints | Channels

Journal Article

Forum Mathematicum, ISSN 0933-7741, 07/2018, Volume 30, Issue 4, pp. 1029 - 1047

The classical quadratic Gauss sum can be thought of as an exponential sum attached to a quadratic form on a cyclic group. We introduce an equivariant version...

11F27 | finite orthogonal groups | Weil representation | 11L05 | 11E99 | finite quadratic forms | Gauss sum | MATHEMATICS | MATHEMATICS, APPLIED

11F27 | finite orthogonal groups | Weil representation | 11L05 | 11E99 | finite quadratic forms | Gauss sum | MATHEMATICS | MATHEMATICS, APPLIED

Journal Article

Science China Mathematics, ISSN 1674-7283, 7/2013, Volume 56, Issue 7, pp. 1457 - 1465

Galois rings and exponential sums over Galois rings have many applications in algebraic combinatorics, coding theory and cryptography. In this paper, we...

finite fields | Galois rings | Gauss sums | Mathematics | 11L07 | Applications of Mathematics | Jacobi sums | 11T23 | Cryptography

finite fields | Galois rings | Gauss sums | Mathematics | 11L07 | Applications of Mathematics | Jacobi sums | 11T23 | Cryptography

Journal Article

IEEE Geoscience and Remote Sensing Letters, ISSN 1545-598X, 12/2018, Volume 15, Issue 12, pp. 1917 - 1921

Models of endmember variability capture the notion that multiple spectra may represent a single class or material, and while these models are physically...

Correlation | spectral unmixing | Computational modeling | ultraspectral image | hyperspectral image | Libraries | Gauss–Markov model | Endmember variability | Computational complexity | Hyperspectral imaging | Gauss-Markov model | GEOCHEMISTRY & GEOPHYSICS | REMOTE SENSING | IMAGERY | MODELS | ALGORITHM | IMAGING SCIENCE & PHOTOGRAPHIC TECHNOLOGY | ENGINEERING, ELECTRICAL & ELECTRONIC | Statistical analysis | Methodology | Variability | Gaussian distribution | Spectra | Empirical analysis | Complexity | Algorithms | Gaussian process | Message passing | Computation | Computer applications | Models | Markov models | Mathematical models | Reflectance

Correlation | spectral unmixing | Computational modeling | ultraspectral image | hyperspectral image | Libraries | Gauss–Markov model | Endmember variability | Computational complexity | Hyperspectral imaging | Gauss-Markov model | GEOCHEMISTRY & GEOPHYSICS | REMOTE SENSING | IMAGERY | MODELS | ALGORITHM | IMAGING SCIENCE & PHOTOGRAPHIC TECHNOLOGY | ENGINEERING, ELECTRICAL & ELECTRONIC | Statistical analysis | Methodology | Variability | Gaussian distribution | Spectra | Empirical analysis | Complexity | Algorithms | Gaussian process | Message passing | Computation | Computer applications | Models | Markov models | Mathematical models | Reflectance

Journal Article

1999, Cambridge tracts in mathematics, ISBN 9780521642637, Volume 136., viii, 163

The theme of this book is the study of the distribution of integer powers modulo a prime number. It provides numerous new, sometimes quite unexpected, links...

Exponential sums

Exponential sums

Book

Applied Surface Science, ISSN 0169-4332, 07/2018, Volume 447, pp. 548 - 553

X-ray photoelectron spectroscopy (XPS) is arguably the most important vacuum technique for surface chemical analysis, and peak fitting is an indispensable part...

Lorentzian function | XPS | GLP | Gaussian function | Voigt function | GLS | X-ray spectroscopy

Lorentzian function | XPS | GLP | Gaussian function | Voigt function | GLS | X-ray spectroscopy

Journal Article

Journal of Number Theory, ISSN 0022-314X, 10/2017, Volume 179, pp. 17 - 32

A conjecture connected with quantum physics led N. Katz to discover some amazing mixed character sum identities over a field of elements, where is a power of a...

Quadratic transformations | Hasse–Davenport relation | Gauss sums | Hypergeometric [formula omitted] functions over finite fields | Quantum physics | Jacobi sums | Hypergeometric F12 functions over finite fields | MATHEMATICS | Hypergeometric F-2 functions over finite fields | Hasse-Davenport relation | Quantum theory

Quadratic transformations | Hasse–Davenport relation | Gauss sums | Hypergeometric [formula omitted] functions over finite fields | Quantum physics | Jacobi sums | Hypergeometric F12 functions over finite fields | MATHEMATICS | Hypergeometric F-2 functions over finite fields | Hasse-Davenport relation | Quantum theory

Journal Article

SCIENCE CHINA-MATHEMATICS, ISSN 1674-7283, 07/2013, Volume 56, Issue 7, pp. 1457 - 1465

Galois rings and exponential sums over Galois rings have many applications in algebraic combinatorics, coding theory and cryptography. In this paper, we...

MATHEMATICS | finite fields | MATHEMATICS, APPLIED | Galois rings | Gauss sums | DIFFERENCE SETS | Jacobi sums | Algebra | Coding | Mathematical analysis | China | Cryptography | Combinatorial analysis | Sums | Rings (mathematics) | Series (mathematics) | Astronomy

MATHEMATICS | finite fields | MATHEMATICS, APPLIED | Galois rings | Gauss sums | DIFFERENCE SETS | Jacobi sums | Algebra | Coding | Mathematical analysis | China | Cryptography | Combinatorial analysis | Sums | Rings (mathematics) | Series (mathematics) | Astronomy

Journal Article

Advances in Difference Equations, ISSN 1687-1839, 12/2018, Volume 2018, Issue 1, pp. 1 - 6

Let p be a prime with p≡1mod8 $p\equiv1\bmod8$, ψ be an eighth character modp, and τ(ψ) $\tau(\psi)$ denote the classical Gauss sum modp. The main purpose of...

Rational polynomial | The classical Gauss sum | Mathematics | Second-order linear recursive formula | Ordinary Differential Equations | Functional Analysis | Eighth character | Analysis | Difference and Functional Equations | 11L05 | Analytic method | Mathematics, general | Partial Differential Equations | MATHEMATICS | MATHEMATICS, APPLIED | Polynomials

Rational polynomial | The classical Gauss sum | Mathematics | Second-order linear recursive formula | Ordinary Differential Equations | Functional Analysis | Eighth character | Analysis | Difference and Functional Equations | 11L05 | Analytic method | Mathematics, general | Partial Differential Equations | MATHEMATICS | MATHEMATICS, APPLIED | Polynomials

Journal Article

Lithuanian Mathematical Journal, ISSN 0363-1672, 7/2017, Volume 57, Issue 3, pp. 359 - 366

The main purpose of this paper is using the analytic method and properties of the classical quadratic Gauss sums to study the computational problem of a hybrid...

Ordinary Differential Equations | generalized quadraticGauss sums | hybrid powermean | generalizedKloosterman sums | computational formula | 11L05 | Mathematics, general | Probability Theory and Stochastic Processes | Mathematics | Actuarial Sciences | Number Theory | MATHEMATICS | generalized Kloosterman sums | hybrid power mean | generalized quadratic Gauss sums | BOUNDS | Computation | Sums

Ordinary Differential Equations | generalized quadraticGauss sums | hybrid powermean | generalizedKloosterman sums | computational formula | 11L05 | Mathematics, general | Probability Theory and Stochastic Processes | Mathematics | Actuarial Sciences | Number Theory | MATHEMATICS | generalized Kloosterman sums | hybrid power mean | generalized quadratic Gauss sums | BOUNDS | Computation | Sums

Journal Article

Journal of Inequalities and Applications, ISSN 1025-5834, 12/2014, Volume 2014, Issue 1, pp. 1 - 8

The main purpose of this paper is, using the analytic methods and the properties of character sums, to study the computational problem of one kind of hybrid...

hybrid mean value | quadratic Gauss sums | Analysis | identity | Mathematics, general | Mathematics | Applications of Mathematics | a sum analogous to Kloosterman sums | Quadratic Gauss sums | Identity | A sum analogous to Kloosterman sums | Hybrid mean value | POLYNOMIALS | MATHEMATICS | EXPONENTIAL-SUMS | MATHEMATICS, APPLIED | DIRICHLET CHARACTERS | Computation | Mathematical analysis | Inequalities | Sums

hybrid mean value | quadratic Gauss sums | Analysis | identity | Mathematics, general | Mathematics | Applications of Mathematics | a sum analogous to Kloosterman sums | Quadratic Gauss sums | Identity | A sum analogous to Kloosterman sums | Hybrid mean value | POLYNOMIALS | MATHEMATICS | EXPONENTIAL-SUMS | MATHEMATICS, APPLIED | DIRICHLET CHARACTERS | Computation | Mathematical analysis | Inequalities | Sums

Journal Article

IEEE Transactions on Information Theory, ISSN 0018-9448, 06/2015, Volume 61, Issue 6, pp. 3276 - 3304

We give a new existence criterion for p-ary sequences which have ideal two-level autocorrelation; and we use it to obtain four general families of such...

Context | Correlation | Fourier transforms | Additives | Convolution | relative difference set | ideal two-level autocorrelation | Polynomials | p-ary sequence | character sum | Stickelberger congruence | Gauss sum | p-Ary sequence | Character sum | SINGER PARAMETERS | COMPUTER SCIENCE, INFORMATION SYSTEMS | CYCLIC DIFFERENCE SETS | FAMILY | ENGINEERING, ELECTRICAL & ELECTRONIC | Sequences (Mathematics) | Coding theory | Research | Correlation (Statistics) | Factorials | Mathematical research | Electronics | Mathematics | Normal distribution | Correlation analysis

Context | Correlation | Fourier transforms | Additives | Convolution | relative difference set | ideal two-level autocorrelation | Polynomials | p-ary sequence | character sum | Stickelberger congruence | Gauss sum | p-Ary sequence | Character sum | SINGER PARAMETERS | COMPUTER SCIENCE, INFORMATION SYSTEMS | CYCLIC DIFFERENCE SETS | FAMILY | ENGINEERING, ELECTRICAL & ELECTRONIC | Sequences (Mathematics) | Coding theory | Research | Correlation (Statistics) | Factorials | Mathematical research | Electronics | Mathematics | Normal distribution | Correlation analysis

Journal Article

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