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Uniqueness and local stability for the inverse scattering problem of determining the cavity

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Science china mathematics 2005年第8期48卷 1113-1123页

作者： FENG Lixin & ma Fuming lmam,{2., Peking University, beijing 100871, china{2., Heilongjiang University, Harbin 150080, china school of mathematical sciences, Jilin University, Changchun 130012. china 1. lmam School of Mathematical Sciences Peking University 100871 Beijing China 2. school of mathematical sciences Heilongjiang University 150080 Harbin China 3. school of mathematical sciences Jilin University 130012 Changchun China

Considering a time-harmonic electromagnetic plane wave incident on an arbitrarily shaped open cavity embedded in infinite ground plane, the physical process is modelled by maxwell's equations. We investigate the inverse problem of determining the shape of the open cavity from the information of the measured scattered field. Results on the uniqueness and the local stability of the inverse problem in the 2.dimensional TM (transverse magnetic) polarization are proved in this paper.

关键词： uniqueness, stability, maxwell's equations, inverse scattering problem.

Recommendation Method for Contrastive Enhancement of Neighborhood Information

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Computers, materials & Continua 2024年第1期78卷 453-472页

作者： Hairong Wang beijing Zhou Lisi Zhang He ma school of Computer Science and Engineering North Minzu UniversityNingxia750021China

Knowledge graph can assist in improving recommendation performance and is widely applied in various person-alized recommendation ***,existing knowledge-aware recommendation methods face challenges such as weak user-item interaction supervisory signals and noise in the knowledge *** tackle these issues,this paper proposes a neighbor information contrast-enhanced recommendation method by adding subtle noise to construct contrast views and employing contrastive learning to strengthen supervisory signals and reduce knowledge ***,first,this paper adopts heterogeneous propagation and knowledge-aware attention networks to obtain multi-order neighbor embedding of users and items,mining the high-order neighbor informa-tion of users and ***,in the neighbor information,this paper introduces weak noise following a uniform distribution to construct neighbor contrast views,effectively reducing the time overhead of view *** paper then performs contrastive learning between neighbor views to promote the uniformity of view information,adjusting the neighbor structure,and achieving the goal of reducing the knowledge noise in the knowledge ***,this paper introduces multi-task learning to mitigate the problem of weak supervisory *** validate the effectiveness of our method,experiments are conducted on theMovieLens-1M,MovieLens-2.M,Book-Crossing,and Last-FM *** results showthat compared to the best baselines,our method shows significant improvements in AUC and F1.

关键词： Contrastive learning knowledge graph recommendation method

Weyl transform associated with wavelets

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Progress in Natural Science:materials International 2003年第7期 19-22页

作者： ma ruiqin and PENG Lizhong({2., school of mathematical sciences, Peking University, beijing 100871, china) lmam School of Mathematical Sciences Peking University Beijing 100871 China

The Weyl transform on the admissible wavelet space is defined, which is associated with the dilation and translation. And the criteria of its boundedness and compactness on the Lp-spaces are given.

关键词： affine group dilation and translation admissible wavelet Weyl transform bonndeness compactness.

On notions of harmonicity for non-symmetric Dirichlet form

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Science china mathematics 2010年第6期53卷 1407-1420页

作者： ma ZhiMing1, ZHU RongChan1, & ZHU XiangChan2.1Institute of Applied mathematics, Academy of mathematics and Systems Science, Chinese Academy of sciences, beijing 100190, china 2.8} of mathematical sciences, Peking University, beijing 100871, china 1. Institute of Applied mathematics Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China2. School of Mathematical Sciences Peking University Beijing 100871 China

In this paper, we extend the equivalence of the analytic and probabilistic notions of harmonicity in the context of Hunt processes associated with non-symmetric Dirichlet forms on locally compact separable metric spaces. Extensions to the processes associated with semi-Dirichlet forms and nearly symmetric right processes on Lusin spaces including infinite dimensional spaces are mentioned at the end of this paper.

关键词： harmonic functions uniformly integrable martingale SPV integrable non-symmetric Dirichlet forms non-symmetric Beurling-Deny decomposition Hunt processes

TRANSPORTATION INEQUALITIES FOR WEAKLY DEPENDENT SEQUENCES

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Acta mathematica Scientia 2011年第4期31卷 1494-1502页

作者：马宇韬 school of mathematical{2. Beijing Normal University

In [3], they gave necessary and sufficient condition for T 1 C and then as applications T 1 C for weakly dependent sequences was established. In this note, based on Gozlan-L′eonard characterization for W 1 H -inequal... 详细信息

关键词： W 1 H inequality T p (C)-inequality weakly dependent sequences tensorization

Analytical model of vertical load acting on jacked pipe considering soil arching effect in cohesionless soil

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Underground Space 2024年第1期14卷 263-284页

作者： Yu Zhang Lianjin Tao Xu Zhao Jun Liu Weizhang Liao Fei Guo Xiaohui Yang ruiqin Zhong beijing Advanced Innovation Center for Future Urban Design Beijing University of Civil Engineering and ArchitectureBeijing 102627China The Key Laboratory of Urban Security and Disaster Engineering Ministry of EducationBeijing University of TechnologyBeijing 100024China beijing Municipal Construction Group Co. LtdBeijing 100045China beijing Municipal Engineering Institute Beijing 100037China

For the project of pipe jacking in cohesionless soil,it is key to determine the vertical load on jacked pipe so as to predict the jacking force *** this paper,a new parabolic soil arching model was proposed to calculate the vertical load on jacked *** proposed analytical model was composed of parabolic soil arching zone,parabola-typed collapse zone and friction arch *** with existing literature,the key parameters(i.e.,height of parabolic soil arching,horizontal pressure coefficient and width and height of friction arch)were *** addition,considering that the trajectory of major stress is parabola,the formula of horizontal pressure coefficient was deduced in the friction *** parabolic soil arching zone is assumed as a three-hinged arch with reasonable arch axis,and the formula of load transfer was derived considering the transition effect of parabolic soil *** results of experiment,theoretical models and numerical model were adopted to verify the proposed analytical ***,the influence of the key parameters on the vertical load on jacked pipe were also discussed in *** work provides a meaningful reference for evaluating the vertical load on jacked pipe for design of pipe jacking.

关键词： Jacked pipe Soil arching effect Theoretical model Parabolic soil arching model Vertical load

Birth-death processes on trees

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Science china mathematics 2010年第11期53卷 2993-3004页

作者： ma YuTao school of mathematical sciences & Laboratory of mathematics and Complex Systems, beijing Normal University, beijing 100875, china 1. school of mathematical sciences & Laboratory of mathematics and Complex Systems Beijing Normal University Beijing 100875 China

In this paper, we consider birth-death processes on a tree T and we are interested when it is regular, recurrent and ergodic (strongly, exponentially). By constructing two corresponding birth death processes on Z+, we obtain computable conditions sufficient or necessary for that (in many cases, these two conditions coincide). With the help of these constructions, we give explicit upper and lower bounds for the Dirichlet eigenvalue λ0. At last, some examples are investigated to justify our results.

关键词： birth-death process tree ergodicity Dirichlet eigenvalue

Paleoceanographic evolution recorded in the northern South china Sea since 4 ma

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Science china Earth sciences 2005年第12期48卷 2166-2173页

作者： HUANG Baoqi1,2. JIAN Zhimin2.& WANG Pinxian2.1. school of Earth and Space sciences, Peking University,{2., china 2. Laboratory of marine Geology, Tongji University, Shanghai 2.0092. china 1. school of Earth and Space sciences Peking University 100871 Beijing China 2. Laboratory of marine Geology Tongji University 200092 Shanghai China

Upper water structure over the last 4 million years in the northern South china Sea (SCS) was reconstructed by sea surface temperature (SST) and primary productivity estimated by changes in the abundance of planktonic foraminifer, planktonic foraminifer transfer function, and the accumulation rate of benthic foraminifera. Results of SST and primary productivity show that SST gradually decreased since 4 ma, but differential seasonal temperature and primary productivity increased in steps mainly at about 3.1, 2.7, 2.1, 1.6, 0.9 and 0.5 ma. Comparison with tectonics and orbital variations indicates that phased rising of the Tibet since 3.6 ma, closing of Panama and Indonesian seaways, and orbital changes were responsible for the changes of upper water structure in the SCS, respectively.

关键词： northern South china Sea, upper water structure, Late Pliocene, planktonic foraminifer, ODP 1146.

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Science china Earth sciences 2004年第10期47卷 896-911页

作者： ZHANG Changhou1,2. WU Ganguo1,2. WANG Genhou2. ZHANG Weijie2.& SONG Honglin2.1. Key Laboratory of Lithospheric Tectonics and Lithoprobing Technology, china University of Geosciences, Ministry of Education of china, beijing 100083, china 2. school of Earth sciences and Mineral Resources, china University of Geosciences, beijing 100083, china 1. Key Laboratory of Lithospheric Tectonics and Lithoprobing Technology China University of Geosciences Ministry of Education of China 100083 Beijing China 2. school of Earth sciences and Mineral Resources China University of Geosciences 100083 Beijing China

The northwest trending tectonic belt in the middle part of the Mesozoic intraplate Yanshan Orogenic Belt, northeast Hebei Province, is composed of thrusts, extensional faults, strike-slip faults and syntectonic sedimentations as well. The northeastward basement-involved major thrusting deformation occurred between 174ma and 168maBP and was followed by an intrusion of the granitic plutonic rocks. As a part of the post-thrusting extensional deformations a northwest extending volcano-sedimentation system of Late Jurassic and Early Cretaceous formed in the southwest side of the belt. These volcano-sedimentary sequences are divided into Tuchengzi Formation, Zhangjiakou Formation, Yixian Formation and Jiufotang Formation re- spectively. They are characterized by southeastward migration as a result of the increasing down-dip slip displacement along the major extensional fault toward the southeast of the belt. The provenance area of the Jiufotang Formation north to it experienced southwestward thrusting during and after its later sedimentation. The thrusting in this stage resulted in the formation of an asymmetric footwall syncline with vergence to SW in the Jiufotang Formation in the NE side of the basin. Finally a dextral strike-slip deformation occurred along the NW tectonic belt. The striking tectono-geomorphological features and present seismic activities along this belt indicate that it has been being active since Cenozoic era and is still in the active state at present. This northwest extending tectonic belt was following the same direction and location as the existing fault systems within the basement as revealed by former geological and geophysical studies. So it is reasonable to infer the Mesozoic deformation along this belt to be a result of reactivation of the basement structures in a favorable tectonic stress field. The reactivation of basement struc- tures might be taken as one of the mechanisms of intraplate deformation and orogeny.

关键词： Yanshan Orogenic Belt, northwest extending tectonic complex, thrust system, geochronology.