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1. Gauss sums, Kloosterman sums, and monodromy groups
by Katz, Nicholas M
1988, ISBN 0691084335, Volume no. 116., viii, 246
Gaussian sums | Monodromy groups | Homology theory | Kloosterman sums
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2. Gauss and Jacobi sums
by Berndt, Bruce C., 1939 and Evans, Ronald J and Williams, Kenneth S
1998, Canadian Mathematical Society series of monographs and advanced texts, ISBN 9780471128076, Volume 21, xi, 583
Gaussian sums | Jacobi sums
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3. Sums and Gaussian vectors
by Yurinsky, Vadim
1995, Lecture notes in mathematics, ISBN 9783540603115, Volume 1617., xi, 305
Gaussian sums | Limit theorems (Probability theory)
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4. Gauss sums and p-adic division algebras
by Bushnell, Colin J. 1947- (Colin John) and Fröhlich, A. 1916- (Albrecht) and SpringerLink (Online service)
1983, Lecture notes in mathematics, ISBN 0387122907, Volume 987, xi, 186
Gaussian sums | Division algebras | Algebra
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5. Full Text Some identities involving certain Hardy sum and Kloosterman sum
by Peng, Wen and Zhang, Tianping
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
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6. Full Text Iterative Adaptive Dynamic Programming for Solving Unknown Nonlinear Zero-Sum Game Based on Online Data
by Yuanheng Zhu and Dongbin Zhao and Xiangjun Li
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
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7. Full Text Fast alternating linearization methods for minimizing the sum of two convex functions
by Goldfarb, Donald and Ma, Shiqian and Scheinberg, Katya
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
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8. Full Text Partial sum processes and continued fractions
by Athreya, Krishna B and Athreya, Jayadev S
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
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9. Full Text Sum capacity of the vector Gaussian broadcast channel and uplink-downlink duality
by Viswanath, P and Tse, D.N.C
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
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10. Full Text Equivariant Gauss sum of finite quadratic forms
by Ma, Shouhei
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
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11. Full Text The Gauss sums and Jacobi sums over Galois ring GR(p 2, r)
by Li, Jin and Zhu, ShiXin and Feng, KeQin
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
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12. Full Text Sum-Product Unmixing for Hyperspectral Analysis With Endmember Variability
by Puladas, Charan and Hossler, Katie and Ash, Joshua N
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
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13. Character sums with exponential functions and their applications
by Koni͡agin, S. V. (Sergeĭ Vladimirovich) and Shparlinski, Igor E
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
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14. Full Text The Gaussian-Lorentzian Sum, Product, and Convolution (Voigt) functions in the context of peak fitting X-ray photoelectron spectroscopy (XPS) narrow scans
by Jain, Varun and Biesinger, Mark C and Linford, Matthew R
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
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15. Full Text Some mixed character sum identities of Katz
by Evans, Ron
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
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16. Full Text The Gauss sums and Jacobi sums over Galois ring GR(p(2), r)
by Li, J and Zhu, SX and Feng, KQ
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
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17. Full Text On the classical Gauss sum and the recursive properties
by Bai, Hui and Hu, Jiayuan
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
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18. Full Text A new hybrid power mean involving the generalized quadratic Gauss sums and sums analogous to Kloosterman sums
by Lv, Xingxing and Zhang, Wenpeng
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
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19. Full Text An hybrid mean value of quadratic Gauss sums and a sum analogous to Kloosterman sums
by Pan, Xiaowei and Zhang, Han
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
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20. Full Text Character Sum Factorizations Yield Sequences With Ideal Two-Level Autocorrelation
by Arasu, K. T and Dillon, J. F and Player, K. J
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
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