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On the Fourth Moment of Coefficients of Symmetric Square L-Function

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Chinese Annals of Mathematics,Series B 2012年第6期33卷 877-888页

作者： Huixue lao School of Mathematical Sciences Shandong Normal University

t Let f（z） be a holomorphic Hecke eigencuspform of weight k for the full mod- ular group. Let Af（n） be the nth normalized Fourier coefficient of f（z）. Suppose that L（sym2f, s） is the symmetric square L-function associated with f（z）, and Asym2f（n） de- notes the nth coefficient L（sym2f, s）. In this paper, it is proved that where P2 （t） is a polynomial in t of degree 2. Similarly, it is obtained that where P2（t） is a polynomial in t of degree 2.

关键词： Fourier coefficient of cusp form Symmetric power L-function Rankin-Selberg L-function

On the Distribution of Integral Ideals and Hecke Grssencharacters

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Chinese Annals of Mathematics,Series B 2010年第3期31卷 385-392页

作者： Huixue lao School of Mathematical Sciences Shandong Normal University Jinan 250014 China.

The author uses analytic methods to study the distribution of integral ideals and Hecke Grossencharacters in algebraic number fields. Nowak＇s results on the distribution of integral ideals, and Chandrasekharan and G... 详细信息

关键词： Dedekind zeta-function Integral ideal Grossencharacters

Exponential Sums over Primes Formed with Coefficients of Primitive Cusp Forms

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Acta Mathematica Sinica,English Series 2009年第4期25卷 687-692页

作者： Hui Xue lao Department of Mathematics Shandong Normal University Ji'nan 250014 P. R. China School of Mathematics Shandong University Ji'nan 250100 P. R. China

Let Af（n） be the coefficient of the logarithmic derivative for the Hecke L-function. In this paper we study the cancellation of the function Ay（n） twisted with an additive character e（α√n）, α 〉0, i.e. Ef（x... 详细信息

关键词： Fourier coefficient of cusp forms exponential sums Hecke L-function

The Cancellation of Fourier Coefficients of Cusp Forms over Different Sparse Sequences

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Acta Mathematica Sinica,English Series 2013年第10期29卷 1963-1972页

作者： Hui Xue lao Department of Mathematics Shandong Normal University

Abstract Let λf（n） be the n-th normalized Fourier coefficient of a holomorphic Hecke eigenform f（z） ∈ Sk（F）, In this paper, we established nontrivial estimates for ∑n≤x λf（n^i）λf（n^j）,where 1≤ij≤4.

关键词： Fourier coefficients cusp forms L-function sparse sequence

Integral mean square estimation for the error term related to n xλ2(n2)

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Science China Mathematics 2015年第10期58卷 2125-2132页

作者： lao HuiXue SANKARANARAYANAN Ayyadurai School of Mathematical Sciences Shandong Normal University School of Mathematics Tata Institute of Fundamental Research

Let λf(n) be the n-th normalized Fourier coefficient of a holomorphic Hecke eigenform f(z) ∈Sk(Γ).We establish that, for any ε > 0,1/Xintegral from n=1 to x|sum λ~2f^((n^2)) from n≤x to - c_2x|2dx ?ε X154/101+... 详细信息

关键词： holomorphic cusp forms symmetric power L-function Rankin-Selberg L-function

Design and Myoelectric Control of an Anthropomorphic Prosthetic Hand

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Journal of Bionic Engineering 2017年第1期14卷 47-59页

作者： Nianfeng Wang Kunyi lao Xianmin Zhang Guangdong Province Key Laboratory of Precision Equipment and Manufacturing Technology South China University of Technology Guangzhou 510640 China

This paper presents an anthropomorphic prosthetic hand using flexure hinges, which is controlled by the surface electromyography （sEMG） signals from 2 electrodes only. The prosthetic hand has compact structure with 5 fingers and 4 Degree of Freedoms （DoFs） driven by 4 independent actuators. Helical springs are used as elastic joints and the joints of each finger are coupled by tendons. The myoelectric control system which can classify 8 prehensile hand gestures is built. Pattern recognition is employed where Mean Absolute Value （MAV）, Variance （VAR）, the fourth-order Autoregressive （AR） coefficient and Sample Entropy （SE） are chosen as the optimal feature set and Linear Discriminant Analysis （LDA） is utilized to reduce the dimension. A decision of hand gestures is generated by LDA classifier after the current projected feature set and the previous one are ＂pre-smoothed＂, and then the final decision is obtained when the current decision and previous decisions are ＂post-smoothed＂ from the decisions flow. The prosthetic hand can perform prehensile postures for activities of daily living and carry objects under the control of EMG signals.

关键词： electromyography anthropomorphic prosthetic hand myoelectric control pattern recognition prehensile gestures

Depth distortion correction for consumer-grade depth cameras in crop reconstruction

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Information Processing in Agriculture 2023年第4期10卷 523-534页

作者： Cailian lao Yu Feng Han Yang Key Laboratory of Modern Precision Agriculture System Integration Research Ministry of EducationChina Agricultural UniversityBeijing 100083PR China Key Laboratory of Agricultural Information Acquisition Technology Ministry of Agriculture and Rural AffairsChina Agricultural UniversityBeijing 100083PR China

Modern consumer-grade RGB-D cameras provide intensive depth estimation and high frame *** have been widely used in ***,depth anamorphose occurswhen using the RGB-D *** order to address this issue,this paper proposes a novel approach to correct the distorted depth images that fit the relationship between the true distances and the depth values from depth *** study considers the structured light camera ASUS Xtion PRO LIVE as example to develop a system for obtaining a series of depth images at different distances from the target plane.A comparison analysis is conducted between the images before and after correction to evaluate the performance of the distortion *** point cloud image of corrected maize leaves is well coincident with the original *** approach improves the accuracy of depth measurement and optimizes the subsequent use of the depth camera in crop reconstruction and phenotyping studies.

关键词： RGB-D camera Structured light Distortion Depth correction Point cloud

Firepower distribution method of anti-ship missile based on coupled path planning

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Journal of Systems Engineering and Electronics 2022年第4期33卷 1010-1024页

作者： LIU Gang AN Zhibiao lao Songyang LI Wu School of Information Science and Engineering Hunan Institute of Science and TechnologyYueyang 414006China College of Systems Engineering National University of Defense TechnologyChangsha 410000China

Anti-ship missile coordinated attack mission planning is a complex multi-objective optimization problem with multiple combinations of platforms, strong decision-making constraints,and tightly coupled links. To avoid the coupling disorder between path planning and firepower distribution and improve the efficiency of coordinated attack mission planning, a firepower distribution model under the conditions of path planning is established from the perspective of decoupling optimization and the algorithm is implemented. First, we establish reference coordinate system of firepower distribution to clarify the reference direction of firepower distribution and divide the area of firepower distribution;then, we construct an index table of membership of firepower distribution to obtain alternative firepower distribution plans;finally, the fitness function of firepower distribution is established based on damage income, missile loss,ratio of efficiency and cost of firepower distribution, and the mean square deviation of the number of missiles used, and the alternatives are sorted to obtain the optimal firepower distribution plan. According to two simulation experiments, the method in this paper can effectively solve the many-to-many firepower distribution problem of coupled path planning. Under the premise of ensuring that no path crossing occurs, the optimal global solution can be obtained, and the operability and timeliness are good.

关键词： anti-ship missile path planning firepower distribution cooperation weapon-target assignment(WTA) coupled

On the mean-square of the error term related ton ∑_（n≤x）λ~2（nj）

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Science China Mathematics 2011年第5期54卷 855-864页

作者： lao HuiXue SANKARANARAYANAN Ayyadurai Department of Mathematics Shandong Normal University Jinan 250014 China School of Mathematics Tata Institute of Fundamental Research Homi Bhabha Road Mumbai 400005 India

We prove a non-trivial upper bound for the quantity ∫X2|X ∑_(n≤x)λ~2(nj)-c(j-1)x| 2dx for j=2, 3, 4.

关键词： Rankin-Selberg zeta-function symmetric square L-functions mean-value theorems