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global Zero-relaxation Limit Problem of the Electro-diffusion Model Arising in Electro-Hydrodynamics

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Acta Mathematicae Applicatae Sinica 2024年第1期40卷 241-268页

作者： Ming-hua yang Si-ming Huang jin-yi Sun Department of Mathematics Jiangxi University of Finance and EconomicsNanchang330032China school of Public Administration Guangdong University of Foreign StudiesGuangzhou510006China College of Mathematics and statistics Northwest Normal UniversityLanzhou730070China

In this paper,we study a global zero-relaxation limit problem of the electro-diffusion model arising in electro-hydrodynamics which is the coupled Planck-Nernst-Poisson and Navier-Stokes *** is,the paper deals with a singular limit problem of{u^(∈)_(t)+u^(∈)·▽u^(∈)-Δu^(∈)+▽P^(∈)=Δφ^(∈)▽φ^(∈),in R^(3)×(0,∞),▽·u^(∈)=0,in R^(3)×(0,∞),n^(∈)_(t)+u^(∈)·▽n^(∈)-Δn^(∈)=-▽·(n^(∈)▽φ^(∈)),in R^(3)×(0,∞),ct+u^(∈)·▽c^(∈)-Δc^(∈)=▽·(c^(∈)▽φ^(∈)),in R^(3)×(0,∞),∈^(-1)φ^(∈)_(t)=Δφ^(∈)-n^(∈)+c^(∈),in R^(3)×(0,∞),(u^(∈),n^(∈),c^(∈),φ^(∈))|t=0=(u0,n0,c0,φ0),in R^(3) involving with a positive,large parameter^(∈).The present work show a case that(u^(∈),n^(∈),c^(∈))stabilizes to(u^(∞),n∞,c∞):=(u,n,c)uniformly with respect to the time variable as^(∈)→+∞with respect to the strong topology in a certain Fourier-Herz space.

关键词： fourier-Herz space littlewood-Paley decomposition stability limit dissipative system

gradient-based algorithms for multi-objective bi-level optimization

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Science china Mathematics 2024年第6期67卷 1419-1438页

作者： Xinmin yang Wei Yao Haian Yin Shangzhi Zeng jin Zhang National Center for Applied Mathematics in Chongqing Chongqing401331China school of Mathematical Sciences Chongqing Normal UniversityChongqing401331China Department of Mathematics Southern University of Science and TechnologyShenzhen518055China National Center for Applied Mathematics Shenzhen Shenzhen518000China Department of Mathematics and statistics University of VictoriaVictoriaBCV8W 2Y2Canada

Multi-objective bi-level optimization(MOBLO)addresses nested multi-objective optimization problems common in a range of ***,its multi-objective and hierarchical bi-level nature makes it notably ***-based MOBLO algorithms have recently grown in popularity,as they effectively solve crucial machine learning problems like meta-learning,neural architecture search,and reinforcement ***,these algorithms depend on solving a sequence of approximation subproblems with high accuracy,resulting in adverse time and memory complexity that lowers their numerical *** address this issue,we propose a gradient-based algorithm for MOBLO,called gMOBA,which has fewer hyperparameters to tune,making it both simple and ***,we demonstrate the theoretical validity by accomplishing the desirable Pareto *** experiments confirm the practical efficiency of the proposed method and verify the theoretical *** accelerate the convergence of gMOBA,we introduce a beneficial L2O(learning to optimize)neural network(called L2O-gMOBA)implemented as the initialization phase of our gMOBA *** results of numerical experiments are presented to illustrate the performance of L2O-gMOBA.

关键词： multi-objective bi-level optimization convergence analysis Pareto stationary learning to optimize

Almost sure central limit theorems for random functions

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Science china Mathematics 2006年第12期49卷 1788-1799页

作者： LU Chuanrong, QIU jin & XU Jianjun school of Mathematics and statistics, Zhejiang university of Finance and Economics, Hangzhou 310018, china Department of Mathematics, Zhejiang university, Hangzhou 310028, china 1. school of Mathematics and statistics Zhejiang University of Finance and Economics Hangzhou 310018 China 2. Department of Mathematics Zhejiang University Hangzhou 310028 China

Let {Xn,-∞< n <∞} be a sequence of independent identically distributed random variables with EX1 = 0, EX12 = 1 and let Sn =∑k=1∞Xk, and Tn = Tn(X1,…,Xn) be a random function such that Tn = ASn + Rn, where supn E|... 详细信息

Let {Xn,-∞2 = 1 and let Sn =∑k=1∞Xk, and Tn = Tn(X1,…,Xn) be a random function such that Tn = ASn + Rn, where supn E|Rn| 2)) a.s., or Rn = O(n1/2-2γ) a.s., 0 statistics, Von-Mises statistics, linear processes, moving average processes, error variance estimates in linear models, power sums, product-limit estimators of a continuous distribution, product-limit estimators of a quantile function, etc.

关键词： statistics,random function,almost sure central limit theorem,logarithm average.

Method of sequential mesh on Koopman-Darmois distributions

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Science china Mathematics 2010年第4期53卷 917-926页

作者： LI Yan & PU XiaoLong school of Finance and statistics,East china Normal university,Shanghai 200241,china 1. school of Finance and statistics East China Normal University Shanghai 200241 China

For costly and/or destructive tests,the sequential method with a proper maximum sample size is *** on Koopman-Darmois distributions,this paper proposes the method of sequential mesh,which has an acceptable maximum sample *** comparison with the popular truncated sequential probability ratio test,our method has the advantage of a smaller maximum sample size and is especially applicable for costly and/or destructive tests.

关键词： method of sequential mesh sequential probability ratio test (SPRT) Koopman-Darmois distributions maximum sample size

Predicting influenza-like illness trends based on sentinel surveillance data in china from 2011 to 2019:A modelling and comparative study

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Infectious Disease Modelling 2024年第3期9卷 816-827页

作者： Xingxing Zhang Liuyang yang Teng Chen Qing Wang jin yang Ting Zhang Jiao yang Hongqing Zhao Shengjie Lai Luzhao Feng Weizhong yang school of Population Medicine and Public Health Chinese Academy of Medical Sciences&Peking Union Medical CollegeBeijing100073China State Key Laboratory of Respiratory Health and Multimorbidity China Key Laboratory of Pathogen Infection Prevention and Control(Peking Union Medical College) Ministry of EducationChina National Key Laboratory of Intelligent Tracking and Forecasting for Infectious Diseases National Institute for Communicable Disease Control and PreventionChinese Center for Disease Control and PreventionChina Department of Management Science and Information System Faculty of Management and EconomicsKunming University of Science and TechnologyKunming650506China Department of Applied Mathematics&statistics Stony Brook UniversityStony BrookNY11794-3600USA WorldPop School of Geography and Environmental ScienceUniversity of SouthamptonSouthamptonSO171BJUK

Background Influenza is an acute respiratory infectious disease with a significant global disease ***,the coronavirus disease 2019 pandemic and its related non-pharmaceutical interventions(NPIs)have introduced uncertainty to the spread of ***,comparative studies on the performance of innovative models and approaches used for influenza prediction are ***,this study aimed to predict the trend of influenza-like illness(ILI)in settings with diverse climate characteristics in china based on sentinel surveillance data using three approaches and evaluate and compare their predictive *** The generalized additive model(gAM),deep learning hybrid model based on gate Recurrent Unit(gRU),and autoregressive moving average-generalized autoregressive conditional heteroscedasticity(ARMA—gARCH)model were established to predict the trends of ILI 1-,2-,3-,and 4-week-ahead in bei{2.g,Tianjin,Shanxi,Hubei,Chongqing,guangdong,Hainan,and the Hong Kong Special Administrative Region in china,based on sentinel surveillance data from 2011 to *** relevant metrics,namely,Mean Absolute Percentage Error(MAPE),Root Mean Squared Error(RMSE),and R squared,were calculated to evaluate and compare the goodness of fit and robustness of the three *** Considering the MAPE,RMSE,and R squared values,the ARMA—gARCH model performed best,while the gRU-based deep learning hybrid model exhibited moderate performance and gAM made predictions with the least accuracy in the eight settings in ***,the models’predictive performance declined as the weeks ahead ***,blocked cross-validation indicated that all models were robust to changes in data and had low risks of *** Our study suggested that the ARMA—gARCH model exhibited the best accuracy in predicting ILI trends in china compared to the gAM and gRU-based deep learning hybrid ***,in the future,the ARMA—gARCH model may be used

关键词： Influenza-like illness Influenza Sentinel surveillance china Predicting Modeling

Singular Integral Equations with Cosecant Kernel in Solutions with Singularities of High Order

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Wuhan university Journal of Natural Sciences 2005年第2期10卷 339-343页

作者： HAN Hui-li 1,2 ,DU jin-yuan 1,3 1. school of Mathematics and statistics, Wuhan university, Wuhan 430072, Hubei, china 2. school of Mathematics and Computer, Ningxia university, Yinchuan 750021, Ningxia, china 3. Department of Mathematics, Hubei Institute for Nationalities, Enshi 445000, Hubei, china Wuhan university School of Mathematics and Statistics Wuhan Hubei China (GRID:grid.49470.3e) (ISNI:***) Ningxia university School of Mathematics and Computer Yinchuan Ningxia China (GRID:grid.260987.2) (ISNI:***) Wuhan university School of Mathematics and Statistics Wuhan Hubei China (GRID:grid.49470.3e) (ISNI:***) Hubei Institute for Nationalities Department of Mathematies Enshi Hubei China (GRID:grid.34418.3a) (ISNI:***)

We have discussed and solved the boundary value problem with period 2aπ and the singular integral equation with kernel csc t-tv/a in solution having singularities of high order, where the smooth contour of integratio... 详细信息

关键词： boundary value problem singular integral equation the singularities of high order

On the Existence of (v,3×3,λ)-Splitting Balanced Incomplete Block Design with λ between 2 to 9

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Journal of Shanghai Jiaotong university(Science) 2008年第4期13卷 482-486页

作者：苏仁旺王金华 College of statistics and Mathematics Zhejiang Gongshang University school of Science Nantong University

Let （v, u × c,λ）-splitting BIBD denote a （v, u × c,λ）-splitting balanced incomplete block design of order v with block size u × c and index A. The necessary conditions for the existence of a （v, u × c,λ）-splitting BIBD are v ≥ uc, λ（v- 1） -- 0 0 mod （c（u- 1）） and Av（v- 1） - 0 mod （c^2u（u- 1））. In this paper, for 2 ≤λ≤ 9 the necessary conditions for the existence of a （v, 3 × 3, λ）-splitting BIBD are also sufficient with one possible exception for （v, λ） = （39, 9）.

关键词： Splitting balanced incomplete block design group-divisible design (gDD)

The twisted conical Kahler-Ricci solitons on Fano manifolds

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Science china Mathematics 2024年第5期67卷 1085-1102页

作者： Xishen jin Jiawei Liu school of Mathematics Renmin University of ChinaBeijing 100872China school of Mathematics and statistics Nanjing University of Science&TechnologyNanjing 210094China

In this paper,we show the relation between the existence of twisted conical K?hler-Ricci solitons and the greatest log Bakry-Emery-Ricci lower bound on Fano *** is based on our proofs of some openness theorems on the existence of twisted conical Kahler-Ricci solitons,which generalize Donaldson’s existence conjecture and the openness theorem of the conical K?hler-Einstein metrics to the conical soliton case.

关键词： greatest log Bakry-Emery-Ricci lower bound twisted conical Kahler-Ricci soliton twisted Kahler-Ricci soliton

Asymptotic distributions in the projection pursuit based canonical correlation analysis

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Science china Mathematics 2010年第2期53卷 485-498页

作者： jin Jiao & CUI HengJian Department of statistics and Financial Mathematics, school of Mathematical Sciences, beijing Normal university, Laboratory of Mathematics and Complex Systems (beijing Normal university), Ministry of Education, beijing 100875, china 1. Department of statistics and Financial Mathematics School of Mathematical Sciences Beijing Normal University Beijing 100875 China2. Ministry of Education Laboratory of Mathematics and Complex Systems (Beijing Normal University) Beijing 100875 China

In this paper, associations between two sets of random variables based on the projection pursuit (PP) method are studied. The asymptotic normal distributions of estimators of the PP based canonical correlations and we... 详细信息

关键词： asymptotic distribution canonical correlation analysis influence function robust statistics