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A Class of Robust Independence Tests Based on Weighted Integrals of Empirical Characteristic Functions
《Acta Mathematica Sinica,English Series》2024年第12期2921-2952,共32页Feng ZOU Chang Liang ZOU Heng Jian CUI 
supported by National Natural Science Foundation of China(NNSFC)(Grant No.12201317);China Postdoctoral Science Foundation(Grant No.2022M721716),Changliang Zou’s research was supported by the National Key R&D Program of China(Grant Nos.2022YFA1003703,2022YFA1003800);the National Natural Science Foundation of China(Grant Nos.11925106,12231011,11931001,12226007,12326325);Cui’s research was supported by NNSFC(Grant Nos.12031016 and 11971324)。
In this paper,we propose a class of robust independence tests for two random vectors based on weighted integrals of empirical characteristic functions.By letting weight functions be probability density functions of a ...
关键词：Asymptotic properties DATA-DRIVEN robust independence tests special distributions weighted integrals 
Discontinuities of Banana Integrals in Dispersion Relation Representation
《Chinese Physics Letters》2024年第11期12-16,共5页Xu-Liang Chen Peng-Fei Yang Wei Chen 
supported by the National Natural Science Foundation of China(Grant No.12175318);the Natural Science Foundation of Guangdong Province of China(Grant No.2022A1515011922).
We derive the discontinuities of banana integrals using the dispersion relation iteratively,and find a series of identities between the parameterized discontinuities of banana integrals(p-DOBIs).Similar to elliptic in...
关键词：DISPERSION INTEGRALS enable 
Optimized numerical density functional theory calculation of rotationally symmetric jellium model systems
《Chinese Physics B》2024年第10期349-355,共7页Guangdi Zhang Li Mao Hongxing Xu 
supported by the National Key Research and Development Program of China(Grant No.2020YFA0211303);the National Natural Science Foundation of China(Grant No.91850207);the numerical calculations in this paper have been done on the supercomputing system in the Supercomputing Center of Wuhan University.
In real space density functional theory calculations,the effective potential depends on the electron density,requiring self-consistent iterations,and numerous integrals at each step,making the process time-consuming.I...
关键词：density functional theory basis set integrals precomputation nanorod 
Boundary Points,Minimal L^(2)Integrals and Concavity PropertyⅢ—Linearity on Riemann Surfaces and Fibrations over Open Riemann Surfaces
《Acta Mathematica Sinica,English Series》2024年第9期2091-2152,共62页Qi An GUAN Zhi Tong MI Zheng YUAN 
supported by National Key R&D Program of China(Grant No.2021YFA1003100);supported by NSFC(Grant Nos.11825101,11522101 and 11431013);supported by the Talent Fund of Beijing Jiaotong University;supported by China Postdoctoral Science Foundation(Grant Nos.BX20230402 and 2023M743719)。
In this article,we consider a modified version of minimal L^(2) integrals on sublevel sets of plurisubharmonic functions related to modules at boundary points,and obtain a concavity property of the modified version.As...
关键词：Minimal L^(2)integrals plurisubharmonic functions boundary points weakly pseudoconvex Kähler manifold 
Boundary points, minimal L^(2) integrals and concavity property Ⅱ: Weakly pseudoconvex Kähler manifolds
《Science China Mathematics》2024年第7期1665-1718,共54页Qi’an Guan Zhitong Mi Zheng Yuan 
supported by National Key R&D Program of China (Grant No. 2021YFA1003100);supported by National Natural Science Foundation of China (Grant Nos. 11825101, 11522101, and 11431013);supported by the Talent Fund of Beijing Jiaotong University;supported by China Postdoctoral Science Foundation (Grant Nos. BX20230402 and 2023M743719)。
In this paper, we consider minimal L^(2) integrals on the sublevel sets of plurisubharmonic functions on weakly pseudoconvex K?hler manifolds with Lebesgue measurable gain related to modules at boundary points of the ...
关键词：minimal L^(2)integrals plurisubharmonic functions boundary points weakly pseudoconvex K?hler manifold 
Concavity Property of Minimal L^(2)Integrals with Lebesgue Measurable GainⅣ:Product of Open Riemann Surfaces
《Peking Mathematical Journal》2024年第1期91-154,共64页Qi’an Guan Zheng Yuan 
supported by National Key R&D Program of China 2021YFA1003100,NSFC-11825101,NSFC-11522101 and NSFC-11431013.
In this article,we present characterizations of the concavity property of minimal L^(2)integrals degenerating to linearity in the case of products of analytic subsets on products of open Riemann surfaces.As applicatio...
关键词：Plurisubharmonic function Multiplier ideal sheaf Minimal L^(2)integral CONCAVITY Optimal L^(2)extension theorem 
Equivariant Tautological Integrals on Flag Varieties
《Chinese Annals of Mathematics,Series B》2024年第3期463-486,共24页Xiaobo ZHUANG 
supported by the National Natural Science Foundation of China(No.11901528);Zhejiang Provincial Natural Science Foundation of China(No.LQ19A010011);the Fundamental Research Funds of Zhejiang Sci-Tech University(No.2021Q045).
The author apples the Atiyah-Bott-Berline-Vergne formula to the equivariant tautological integrals over flag varieties of types A,B,C,D,and recovers the formulas expressing the integrals as iterated residues at infini...
关键词：LOCALIZATION Flag variety RESIDUE 
Moderate Deviations for Parameter Estimation in the Fractional Ornstein–Uhlenbeck Processes with Periodic Mean
《Acta Mathematica Sinica,English Series》2024年第5期1308-1324,共17页Hui JIANG Shi Min LI Wei Gang WANG 
supported by the Natural Science Foundation of Jiangsu Province of China(Grant No.BK20231435);Fundamental Research Funds for the Central Universities(Grant No.NS2022069);supported by Natural Science Foundation of Zhejiang Province(Grant No.LY19A010004)。
In this paper,we study the asymptotic properties for the drift parameter estimators in the fractional Ornstein-Uhlenbeck process with periodic mean function and long range dependence.The Cremér-type moderate deviatio...
关键词：Cramér-type moderate deviation fractional Ornstein-Uhlenbeck process parameter estimation multiple Wiener-Ito integrals 
The Stability of the Gauss-Laguerre Rule for Cauchy P.V. Integrals on the Half Line
《American Journal of Computational Mathematics》2023年第4期505-511,共7页Maria Rosaria Capobianco Giuliana Criscuolo 
In this paper, the authors give a different and more precise analysis of the stability of the classical Gauss-Laguerre quadrature rule for the Cauchy P.V. integrals on the half line. Moreover, in order to obtain this ...
关键词：Gauss Quadrature Exponential Weights Cauchy P.V. Integrals Stability 
Fourier coefficients of restrictions of eigenfunctions
《Science China Mathematics》2023年第8期1849-1878,共30页Emmett L.Wyman Yakun Xi Steve Zelditch 
supported by National Science Foundation of USA (Grant Nos.DMS-1810747 and DMS-1502632);supported by National Natural Science Foundation of China (Grant No.12171424)。
Let{e_(j)}be an orthonormal basis of Laplace eigenfunctions of a compact Riemannian manifold(M,g).Let H■M be a submanifold and{ψ_(k)}be an orthonormal basis of Laplace eigenfunctions of H with the induced metric.We ...
关键词：EIGENFUNCTIONS period integrals Kuznecov formula 
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