Results 71 to 80 of about 884,151 (313)
Artificial Intelligence as the Next Visionary in Liquid Crystal Research
Advanced Functional Materials, EarlyView.The functions of AI in the research laboratory are becoming increasingly sophisticated, allowing the entire process of hypothesis formulation, material design, synthesis, experimental design, and reiterative testing to be automated. In our work, we conceive how the incorporation of AI in the laboratory environment will transform the role and ...
Mert O. Astam +2 more
wiley +1 more source
The hybrid mean value of Dedekind sums and two-term exponential sums
Open Mathematics, 2016 In this paper, we use the mean value theorem of Dirichlet L-functions, the properties of Gauss sums and Dedekind sums to study the hybrid mean value problem involving Dedekind sums and the two-term exponential sums, and give an interesting identity and ...
Leran Chang, Xiaoxue Li
doaj +1 more source
New identities involving Hardy sums $S_3(h, k)$ and general Kloosterman sums
AIMS Mathematics, 2021 The main purpose of this paper is to obtain some exact computational formulas or upper bounds for hybrid mean value involving Hardy sums $S_{3}(h, p)$ and general Kloosterman sums $K(r, l, \lambda; p)$.
Wenjia Guo, Yuankui Ma, Tianping Zhang
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Advanced Materials, EarlyView.Metasurface‐engineered NC‐TENG arrays integrate tactile pressure mapping, non‐contact gesture sensing, and acoustic signal readouts in one ultrathin module, and outperforms pristine PDMS in terms of electrical output and real‐time spatial mapping for next‐gen wearables.
Injamamul Arief +12 more
wiley +1 more source
Products related to Gauss sums.
Journal für die reine und angewandte Mathematik (Crelles Journal), 1974 Let \(m\geq 2\) be an integer, let \(p\) be a prime with \(p\equiv 1\pmod m\) and let \(\rho\) be a primitive \(m\)-th root of unity. Then \(p\) splits completely in the cyclotomic field \(\mathbb Q(\rho)\) and, if we pick \(\mathfrak p\) to be one of the prime divisors of \(p\) in \(\mathbb Q(\rho)\) we define a character \(\chi\) of order \(m\) on \(\
openaire +1 more source
On the General Dedekind Sums and Two-Term Exponential Sums
The Scientific World Journal, 2014 We use the analytic methods and the properties of Gauss sums to study the computational problem of one kind hybrid mean value involving the general Dedekind sums and the two-term exponential sums, and give an interesting computational formula for it.
Junli Zhang, Wenpeng Zhang
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On a Certain Quadratic Character Sums of Ternary Symmetry Polynomials modp
Journal of Mathematics, 2021 In this article, we are using the elementary methods and the properties of the classical Gauss sums to study the calculating problem of a certain quadratic character sums of a ternary symmetry polynomials modulo p and obtain some interesting identities ...
Yuanyuan Meng
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Advanced Materials Interfaces, EarlyView.This study investigates the thermochromic properties of VO2 deposited on aluminum doped zinc oxide precoated fused silica with Al2O3, TiO2, and WO3 as interface layers. The results indicate that the metal‐to‐insulator transition is highly influenced by the grains formed at the interface.
Eduard Llorens Balada, Eugen Stamate
wiley +1 more source
Acta Arithmetica, 1996 For a multiplicative character \(\chi\) and a nontrivial additive character \(\lambda\) of the finite field with \(q\) elements (\(q\) is a power of an odd prime), the Gauss sums \[ \sum\lambda(\text{tr }g) \quad\text{over }g\in SO^+(2n,q) \] and \[ \sum\chi(\text{det }g) \lambda(\text{tr }g) \quad\text{over }g\in O^+(2n,q) \] are considered.
Kim, Dae San, Lee, In-Sok
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On the high-th mean of one special character sums modulo a prime
AIMS Mathematics, 2023 Using the elementary method of the classical Gauss sums and the properties of character sums, we study a linear recurrence formula about the form $ G\left(n\right) = 1+\sum_{a = 1}^{p-1}\left(\frac{a^2+n\bar{a}^2}{p}\right) $ and about the mean value of $
Yan Ma, Di Han
doaj +1 more source