scholarly journals A New Gauss Sum and Its Recursion Properties

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Li Chen
Keyword(s):  
Gauss Sum ◽  
Order Linear ◽  
Analytic Methods ◽  
Linear Recursion

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.

scholarly journals The Generalized Quadratic Gauss Sum and Its Fourth Power Mean

Mathematics ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 258
Author(s):  
Shimeng Shen ◽  
Wenpeng Zhang
Keyword(s):  
Character Sums ◽  
Gauss Sums ◽  
Gauss Sum ◽  
Fourth Power ◽  
Power Mean ◽  
Analytic Methods ◽  
Fourth Power Mean

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 interesting computational formulae for it.

scholarly journals A Hybrid Power Mean Involving the Dedekind Sums and Cubic Gauss Sums

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Jiayuan Hu ◽  
Yu Zhan ◽  
Qin Si
Keyword(s):  
Gauss Sums ◽  
Gauss Sum ◽  
Dedekind Sums ◽  
Power Mean ◽  
Hybrid Power ◽  
Analytic Methods ◽  
Hybrid Power Mean

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.

Analytical Study on Big Data

2018 ◽  
Vol 8 (5) ◽  
pp. 75
Author(s):  
Vivek Raich ◽  
Pankaj Maurya
Keyword(s):  
Information Technology ◽  
Big Data ◽  
Decision Maker ◽  
Analytical Study ◽  
Large Data ◽  
Decision Makers ◽  
Continuous Increase ◽  
Analytic Methods ◽  
Data Store ◽  
Business Engineering

in the time of the Information Technology, the big data store is going on. Due to which, Huge amounts of data are available for decision makers, and this has resulted in the progress of information technology and its wide growth in many areas of business, engineering, medical, and scientific studies. Big data means that the size which is bigger in size, but there are several types, which are not easy to handle, technology is required to handle it. Due to continuous increase in the data in this way, it is important to study and manage these datasets by adjusting the requirements so that the necessary information can be obtained.The aim of this paper is to analyze some of the analytic methods and tools. Which can be applied to large data. In addition, the application of Big Data has been analyzed, using the Decision Maker working on big data and using enlightened information for different applications.

CONTINUOUS-TIME FRACTIONAL ORDER LINEAR SYSTEMS IDENTIFICATION USING CHEBYSHEV WAVELET

2020 ◽  
Vol 6 (8(77)) ◽  
pp. 23-28
Author(s):  
Shuen Wang ◽  
Ying Wang ◽  
Yinggan Tang
Keyword(s):  
Linear Systems ◽  
Fractional Order ◽  
Continuous Time ◽  
Fractional Integration ◽  
Operational Matrices ◽  
Computation Complexity ◽  
Order Linear ◽  
Fractional Integration Operator ◽  
Systems Identification ◽  
Chebyshev Wavelet

In this paper, the identification of continuous-time fractional order linear systems (FOLS) is investigated. In order to identify the differentiation or- ders as well as parameters and reduce the computation complexity, a novel identification method based on Chebyshev wavelet is proposed. Firstly, the Chebyshev wavelet operational matrices for fractional integration operator is derived. Then, the FOLS is converted to an algebraic equation by using the the Chebyshev wavelet operational matrices. Finally, the parameters and differentiation orders are estimated by minimizing the error between the output of real system and that of identified systems. Experimental results show the effectiveness of the proposed method.

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