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The Generalized Quadratic Gauss Sum and Its Fourth Power Mean
Mathematics, 2019 In this article, our main purpose is to introduce a new and generalized quadratic Gauss sum. By using analytic methods, the properties of classical Gauss sums, and character sums, we consider the calculating problem of its fourth power mean and give two ...
Wenpeng Zhang, Shimeng Shen
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A New Gauss Sum and Its Recursion Properties
Journal of Mathematics, 2021 In this paper, we introduce a new Gauss sum, and then we use the elementary and analytic methods to study its various properties and prove several interesting three-order linear recursion formulae for it.
Li Chen
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On the Hybrid Power Mean Involving the Character Sums and Dedekind Sums
Journal of Mathematics, 2021 The main purpose of this paper is to use the elementary and analytic methods, the properties of Gauss sums, and character sums to study the computational problem of a certain hybrid power mean involving the Dedekind sums and a character sum analogous to ...
Xiaoling Xu
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A Hybrid Power Mean Involving the Dedekind Sums and Cubic Gauss Sums
Journal of Mathematics, 2021 The main purpose of this paper is using analytic methods and the properties of the Dedekind sums to study one kind hybrid power mean calculating problem involving the Dedekind sums and cubic Gauss sum and give some interesting calculating formulae for it.
Jiayuan Hu, Yu Zhan, Qin Si
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The quantum-mechanical Coulomb propagator in an L2 function representation
Scientific Reports, 2021 The quantum-mechanical Coulomb propagator is represented in a square-integrable basis of Sturmian functions. Herein, the Stieltjes integral containing the Coulomb spectral function as a weight is evaluated.
Rolf Gersbacher, John T. Broad
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A new iteration method for solving space fractional coupled nonlinear Schrödinger equations [PDF]
Iranian Journal of Numerical Analysis and Optimization, 2022 A linearly implicit difference scheme for the space fractional coupled nonlinear Schrödinger equation is proposed. The resulting coefficient matrix of the discretized linear system consists of the sum of a complex scaled identity and a symmetric positive ...
H. Aslani +2 more
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A Two-Filter Approach for State Estimation Utilizing Quantized Output Data
Sensors, 2021 Filtering and smoothing algorithms are key tools to develop decision-making strategies and parameter identification techniques in different areas of research, such as economics, financial data analysis, communications, and control systems.
Angel L. Cedeño +4 more
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A note on two-term exponential sum and the reciprocal of the quartic Gauss sums
Advances in Difference Equations, 2021 The main purpose of this article is by using the properties of the fourth character modulo a prime p and the analytic methods to study the calculating problem of a certain hybrid power mean involving the two-term exponential sums and the reciprocal of ...
Wenpeng Zhang, Xingxing Lv
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On the classical Gauss sum and the recursive properties
Advances in Difference Equations, 2018 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 this paper is using the analytic method and the properties of the classical Gauss sum to study ...
Hui Bai, Jiayuan Hu
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IEEE Access, 2020 In multi-agent networked systems, parameter estimation problems arising in many practical applications are often required to solve Non-Linear Least Squares (NLLS) problems with the usual objective function (i.e., sum of squared residuals).
Mou Wu +3 more
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