Results 21 to 30 of about 7,622 (261)
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
doaj +1 more source
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
doaj +1 more source
Proceedings of the American Mathematical Society, 1956 where p is an odd prime, has been proved in a variety of ways. In particular the proof in [3, p. 623 ] may be cited. We remark that Estermann [1 ] has recently given a simple proof of (1) that is valid for arbitrary odd p. In the present note we indicate a short proof of (1) that makes use of some familiar results from cyclotomy. Let E = e27riP and let
openaire +2 more sources
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
doaj +1 more source
Gauss sums and quantum mechanics [PDF]
Journal of Physics A: Mathematical and General, 2000 By adapting Feynman's sum over paths method to a quantum mechanical system whose phase space is a torus, a new proof of the Landsberg-Schaar identity for quadratic Gauss sums is given. In contrast to existing non-elementary proofs, which use infinite sums and a limiting process or contour integration, only finite sums are involved.
Armitage, Vernon, Rogers, Alice
openaire +2 more sources
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
doaj +1 more source
Gauss Quadrature for Integrals and Sums
International Journal of Pure and Applied Mathematics Research, 2023 Gauss quadrature integral approximation is extended to include integrals with a measure consisting of a continuous as well as a discrete component. That is, we give an approximation for the integral of a function plus its sum over a discrete weighted set.
openaire +2 more sources
Summation identities for the Kummer confluent hypergeometric function 1F1(a; b;z)
Kuwait Journal of Science, 2023 The role which hypergeometric functions have in the numerical and symbolic calculation, especially in the fields of applied mathematics and mathematical physics motivated research in this paper.
Gradimir V. Milovanović +2 more
doaj +1 more source
Upper bound estimate of incomplete Cochrane sum
Open Mathematics, 2017 By using the properties of Kloosterman sum and Dirichlet character, an optimal upper bound estimate of incomplete Cochrane sum is given.
Ma Yuankui, Peng Wen, Zhang Tianping
doaj +1 more source
SECOND MOMENTS IN THE GENERALIZED GAUSS CIRCLE PROBLEM
Forum of Mathematics, Sigma, 2018 The generalized Gauss circle problem concerns the lattice point discrepancy of large spheres. We study the Dirichlet series associated to $P_{k}(n)^{2}$, where $P_{k}(n)$ is the discrepancy between the volume of the $k$-dimensional sphere of radius ...
THOMAS A. HULSE +3 more
doaj +1 more source