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On Riemann-Finsler geometry

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Chinese Science Bulletin 1998年第6期43卷 447-450页

作者： mo xiaohuan school of mathematical sciences, peking university,{2., China school of mathematical {2. Peking University Beijing China

The history of Finsler geometry is reviewed and briefly recent development in Finsler geometry and its application is completed systematically. Furthermore, an interesting open problem has been proposed in this field.

关键词： Finsler space Chern connection Hilbert form Minkowski potential projective sphere bundle.

Recent developments and some open problems in Finsler geometry

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Chinese Science Bulletin 2001年第13期46卷 1059-1061页

作者： mo xiaohuan & SHEN Zhongmin1. {2. of {2. sciences, peking university, beijing 100871, China 2. Department of Mathematics, IUPUI 402.N. Blackford Street, Indianapolis, IN 462.2.32.6, USA school of mathematical {2. Peking University Beijing China Department of Mathematics IUPUI Indianapolis USA

Finsler geometry is just Riemannian geometry without the quadratic restriction. Recent studies on Finsler geometry have taken on a new look. In this article, we will briefly discuss recent developments and some open p... 详细信息

关键词： Finsler geometry open problems recent development.

Some constructions of projectively flat Finsler metrics

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Science China Mathematics 2006年第5期49卷 703-714页

作者： mo xiaohuan, SHEN Zhongmin & YANG Chunhong LMAM, {2. of {2. sciences, peking university, beijing 100871, China Department of {2. sciences, Indiana university-Purdue university, Indianapolis, IN 462.2.32.6, USA Department of Mathematics, Inner mongolia university, Hohhot 01002., China LMAM School of Mathematical Sciences Peking University Beijing 100871 China Department of mathematical sciences Indiana University-Purdue University Indianapolis IN 46202-3216 USA Department of Mathematics Inner Mongolia University Hohhot 010021 China

In this paper, we find some solutions to a system of partial differential equations that characterize the projectively flat Finsler metrics. Further, we discover that some of these metrics actually have the zero flag ... 详细信息

关键词： Randers metric, (α,β)-metric, Finsler metric, projectively flat metric, Scurvature.

Efficient estimation for additive hazards regression with bivariate current status data

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Science China Mathematics 2012年第4期55卷 763-774页

作者： TONG XingWei 1,,HU Tao 2.& SUN JianGuo 3,4 1 school of mathematical {2.,beijing Normal university,beijing 100875,China 2.school of mathematical {2.,Capital Normal university,beijing 100048,China 3 school of Mathematics,Jilin university,Changchun 130012.China 4 Department of Statistics,university of Missouri,Columbia,mo 652.1,USA 1. school of mathematical {2. Beijing Normal University Beijing 100875 China2. School of Mathematical Sciences Capital Normal University Beijing 100048 China3. School of Mathematics Jilin University Changchun 130012 China4. Department of Statistics University of Missouri Columbia MO 65211 USA

This paper discusses efficient estimation for the additive hazards regression model when only bivariate current status data are available. Current status data occur in many fields including demographical studies and tumorigenicity experiments （Keiding, 1991; Sun, 2.06） and several approaches have been proposed for the additive hazards model with univariate current status data （Linet M., 1998; Martinussen and Scheike, 2.02.. For bivariate data, in addition to facing the same problems as those with univariate data, one needs to deal with the association or correlation between two related failure time variables of interest. For this, we employ the copula model and an efficient estimation procedure is developed for inference. Simulation studies are performed to evaluate the proposed estimates and suggest that the approach works well in practical situations. An illustrative example is provided.

关键词： bivariate current status data copula model counting processes efficient estimation joint survivalfunction

On the weak convergence of super-Brownian motion with immigration

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Science China Mathematics 2009年第9期52卷 1875-1886页

作者： ZHANG Mei school of mathematical {2., beijing Normal university, beijing 100875, China school of mathematical {2. Beijing Normal University Beijing 100875 China

We prove fluctuation limit theorems for the occupation times of super-Brownian motion with immigration. The weak convergence of the processes is established, which improves the results in references. The limiting proc... 详细信息

关键词： super-Brownian motion with immigration occupation time process central limit theorem tightness 60J80 60F05

Distributed Heterogeneous Multi-Agent Optimization with Stochastic Sub-Gradient

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Journal of Systems Science & Complexity 2024年第4期37卷 1470-1487页

作者： HU Haokun mo Lipo CAO Xianbing school of Mathematics and Statistics Central South UniversityChangsha 410083China school of Mathematics and Statistics Beijing Technology and Business UniversityBeijing 100048China Research Centre for Agri-Product Quality Traceability Beijing Technology and Business UniversityBeijing 100048China school of Computer and Artificial Intelligence Beijing Technology and Business UniversityBeijing 100048China China Food Flavor and Nutrition Health Innovation Center Beijing Technology and Business UniversityBeijing 100048China

This paper studies the optimization problem of heterogeneous networks under a timevarying *** agent only accesses to one local objective function,which is *** improved algorithm with noisy measurement of local objective functions' sub-gradients and additive noises among information exchanging between each pair of agents is designed to minimize the sum of objective functions of all *** weaken the effect of these noises,two step sizes are introduced in the control *** graph theory,stochastic analysis and martingale convergence theory,it is proved that if the sub-gradients are uniformly bounded,the sequence of digraphs is balanced and the union graph of all digraphs is joint strongly connected,then the designed control protocol can force all agents to find the global optimal point almost *** last,the authors give some numerical examples to verify the effectiveness of the stochastic sub-gradient algorithms.

关键词： Communication noises distributed stochastic optimization heterogeneous networks subgradient measurement noises

Distributed Region Tracking and Perimeter Surveillance for Second-Order Multi-Agent Systems in Star-Shaped Sets

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Journal of Systems Science & Complexity 2024年第5期37卷 1995-2020页

作者： SHANG Juan mo Lipo MI Rongxin CAO Xianbing school of Mathematics and Statistics Beijing Technology and Business UniversityBeijing 100048China The Department of Foundation Shijiazhuang Institute of Railway TechnologyShijiazhuang 050041China school of Computer and Artificial Intelligence Beijing Technology and Business UniversityBeijing 100048China Research Centre for Agri-Product Quality Traceability Beijing Technology and Business UniversityBeijing 100048China Coordination Center of China National Computer Network Emergency Response Technical TeamBeijing 100029China

This paper investigates region tracking and perimeter surveillance of second-order multiagent systems,where all agents move within a star-shaped ***,by coordination transformations,the region tracking problem is converted from the star-shaped sets to a circular *** authors employ communication and collaboration to complete region tracking and perimeter surveillance tasks,and then revert back to the star-shaped set by using inverse ***,the authors propose a distributed control strategy based on attractive and interaction potential functions,under which all agents can quickly track a given circular region and move around the ***,the authors validate the effectiveness and performance advantages of the proposed method through simulation experiments.

关键词： Distributed control multi-agent systems star-shaped sets target tracking

Navigation Finsler metrics on a gradient Ricci soliton

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Applied Mathematics(A Journal of Chinese Universities) 2024年第2期39卷 266-275页

作者： LI Ying mo Xiao-huan WANG Xiao-yang Department of Applied Mathematics Zhejiang University of TechnologyHangzhou 310023China Key Laboratory of Pure and Applied Mathematics School of Mathematical SciencesPeking UniversityBeijing 100871China school of Mathematics and Statistics Beijing Institute of TechnologyBeijing 100081China

In this paper,we study a class of Finsler metrics defined by a vector field on a gradient Ricci *** obtain a necessary and sufficient condition for these Finsler metrics on a compact gradient Ricci soliton to be of isotropic S-curvature by establishing a new integral *** we determine the Ricci curvature of navigation Finsler metrics of isotropic S-curvature on a gradient Ricci soliton generalizing result only known in the case when such soliton is of Einstein *** its application,we obtain the Ricci curvature of all navigation Finsler metrics of isotropic S-curvature on Gaussian shrinking soliton.

关键词： gradient Ricci soliton navigation Finsler metric isotropic S-curvature Ricci curvature Gaussian shrinking soliton

Prediction and validation of diffusive uptake rates for indoor volatile organic compounds in axial passive samplers

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Energy and Built Environment 2024年第1期5卷 24-31页

作者： Yan Wang Tao Yu Jinhan mo Department of Building Science Tsinghua UniversityBeijing 100084China beijing Key Laboratory of Indoor Air Quality Evaluation and Control Beijing 100084China Wuhan Second Ship Design and Research Institute Wuhan 430205China school of Energy and Power Engineering Beihang UniversityBeijing 100191China Key Laboratory of Eco Planning&Green Building Ministry of Education(Tsinghua University)Beijing 100084China

The diffusive uptake rate is essential for using passive samplers to measure indoor volatile organic compounds(VOCs).The traditional theoretical model of passive samplers requires available regression formulas of uptake rates and physicochemical properties of adsorbents to predict the uptake ***,it is difficult to obtain the uptake rates of different VOCs under different sampling periods,and it is also difficult to obtain the physical parameters of adsorbents accurately and *** study provides a reliable numerical prediction method of diffusive uptake rates of *** modeling was based on the standard automated thermal desorption(ATD)tubes packed with Tenax TA and the mass transfer process during *** experimental determinations of toluene uptake rate are carried out to verify the prediction *** uptake rates of typical indoor VOCs are obtained from the literature to calibrate the key apparent parameters in the model by statistical regression *** predicted model can provide the VOC diffusive uptake rates under different sampling duration with an average deviation of less than 5%.This study can provide the basis for fast and accurate prediction of diffusive uptake rates for various VOC pollutants in built environments.

关键词： Indoor air quality Diffusive uptake rate Prediction model Sampling Adsorption