The main purpose of this paper is to use estimates for character sums and analytic methods to study the first power mean of the inversion of Dirichlet L-functions with the weight of general quadratic Gauss sums,and th...The main purpose of this paper is to use estimates for character sums and analytic methods to study the first power mean of the inversion of Dirichlet L-functions with the weight of general quadratic Gauss sums,and three asymptotic formulae are obtained.展开更多
The main purpose of this paper is to use elementary methods and properties of the classical Gauss sums to study the computational problem of one kind of fourth power mean of the generalized quadratic Gauss sums mod q ...The main purpose of this paper is to use elementary methods and properties of the classical Gauss sums to study the computational problem of one kind of fourth power mean of the generalized quadratic Gauss sums mod q （a positive odd number）, and give an exact computational formula for it.展开更多
A novel Krein space approach to robust H∞ filtering for linear uncertain systems is developed. The parameter uncertainty, entering into both states and measurement equations, satisfies an energy-type constraint. Then...A novel Krein space approach to robust H∞ filtering for linear uncertain systems is developed. The parameter uncertainty, entering into both states and measurement equations, satisfies an energy-type constraint. Then a Krein space approach is used to tackle the robust H∞ filtering problem. To this end, a new Krein space formal system is designed according to the original sum quadratic constraint （SQC） without introducing any nonzero factors into it and, consequently, the estimate recursion is obtained through the filter gain in Krein space. Finally, a numerical example is given to demonstrate the effectiveness of the proposed approach.展开更多
In this paper, a novel Krein space approach to robust estimation for uncertain systems with accumulated bias is proposed. The bias is impacted by system uncertainties and exists in both state transition and observer m...In this paper, a novel Krein space approach to robust estimation for uncertain systems with accumulated bias is proposed. The bias is impacted by system uncertainties and exists in both state transition and observer matrices. Initial conditions and cross-correlated uncertainty inputs are described by the sum quadratic constraint （SQC）. Without modifying the SQC, the minimal state of the SQC is obtained through Krein space method. The inertia condition for a minimum of a deterministic quadratic form is derived when the coefficient of observer uncertainty input is non-unit matrix. Recursions of Krein space state filtering and bias filtering are developed respectively. Since the cross correlation between uncertainties is considered, a cross correlation gain is introduced into the posteriori estimator. Finally, a numerical example illustrates the performance of the proposed filter.展开更多
文摘The main purpose of this paper is to use estimates for character sums and analytic methods to study the first power mean of the inversion of Dirichlet L-functions with the weight of general quadratic Gauss sums,and three asymptotic formulae are obtained.
基金Supported by the NSF of China(Grant No.11771351)
文摘The main purpose of this paper is to use elementary methods and properties of the classical Gauss sums to study the computational problem of one kind of fourth power mean of the generalized quadratic Gauss sums mod q （a positive odd number）, and give an exact computational formula for it.
基金supported by the National Natural Science Foundation of China (51179039)the Ph.D. Programs Foundation of Ministry of Education of China (20102304110021)
文摘A novel Krein space approach to robust H∞ filtering for linear uncertain systems is developed. The parameter uncertainty, entering into both states and measurement equations, satisfies an energy-type constraint. Then a Krein space approach is used to tackle the robust H∞ filtering problem. To this end, a new Krein space formal system is designed according to the original sum quadratic constraint （SQC） without introducing any nonzero factors into it and, consequently, the estimate recursion is obtained through the filter gain in Krein space. Finally, a numerical example is given to demonstrate the effectiveness of the proposed approach.
基金supported by the Fundamental Research Funds for the Central Universities(No.DL13BB14)
文摘In this paper, a novel Krein space approach to robust estimation for uncertain systems with accumulated bias is proposed. The bias is impacted by system uncertainties and exists in both state transition and observer matrices. Initial conditions and cross-correlated uncertainty inputs are described by the sum quadratic constraint （SQC）. Without modifying the SQC, the minimal state of the SQC is obtained through Krein space method. The inertia condition for a minimum of a deterministic quadratic form is derived when the coefficient of observer uncertainty input is non-unit matrix. Recursions of Krein space state filtering and bias filtering are developed respectively. Since the cross correlation between uncertainties is considered, a cross correlation gain is introduced into the posteriori estimator. Finally, a numerical example illustrates the performance of the proposed filter.
