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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(lmam, 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.

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, school of mathematical sciences, peking university, beijing 100871, china school of mathematical sciences, Heilongjiang university, Harbin 150080, china school of mathematical sciences, Jilin university, Changchun 130012, china lmam School of Mathematical Sciences Peking University Beijing China school of mathematical sciences Heilongjiang University Harbin China school of mathematical sciences Jilin University 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-20M,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

Predicting Polymerase Ⅱ Core Promoters by Cooperating Transcription Factor Binding Sites in Eukaryotic Genes

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Acta Biochimica et Biophysica Sinica 2004年第4期36卷 250-258页

作者： Xiao-Tu ma, Min-Ping QIAN*, and Hai-Xu TANG1 school of mathematical sciences, peking university and Center for Theoretical Biology, peking university, beijing 100871, china 1Department of Computer Science and Engineering, university of California, San Diego, La Jolla CA 92093-0114, USA school of mathematical sciences Peking University and Center for Theoretical Biology Peking UniversityBeijing 100871 China Department of Computer Science and Engineering University of CaliforniaSan Diego La Jolla CA 92093-0114 USA

Several discriminate functions for predicting core promoters that based on the potential cooperation between transcription factor binding sites (TFBSs) are discussed. It is demonstrated that the promoter predicting accuracy is improved when the cooperation among TFBSs is taken into consideration. The core promoter region of a newly discovered gene CKLFSF1 is predicted to locate more than 1.5 kb far away from the 5' end of the transcript and in the last intron of its upstream gene, which is experimentally confirmed later. The core promoters of 3402 human RefSeq sequences, obtained by extending the mRNAs in human genome sequences, are predicted by our algorithm, and there are about 60% of the predicted core promoters locating within the ± 500 bp region relative to the annotated transcription start site.

关键词： promoter transcription factor binding site transcription start site gene finding

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 sciences 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

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 school of mathematical sciences & Laboratory of mathematics and Complex Systems Beijing Normal University Beijing 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

Petrogenesis and significance of the Hongshan syenitic pluton,South Taihang: zircon SHRIMP U-Pb age, chemical compositions and Sr-Nd isotopes

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Progress in Natural Science:materials International 2006年第2期16卷 192-200页

作者： ZHOU Ling and CHEN Bin (Key Laboratory of Orogenic Belts and Crustal Evolution, MOE, school of Earth and Space sciences, peking university, beijing 100871, china) Key Laboratory of Orogenic Belts and Crustal Evolution MOE School of Earth and Space Sciences Peking University Beijing 100871 China

The Hongshan syenitic pluton (South Taihang) is mainly made up of hornblende syenite and minor granite. SHRIMP zircon dating yields a U-Pb age of 135±2.7 ma for the emplacement of the pluton, while biotite Rb-Sr isotopic data give an isochron of 120. 3±2.4 ma. Hongshan syenites show low silica, high alkalis and LILE such as Sr, and exhibit negligible Eu anomalies or slightly positive anomalies in the REE patterns. The syenites show quite enriched isotopic compositions with Isr from 0.7052 to 0. 7102 and εNd(t) from -7.5 to - 11.1. Petrogenesis of the pluton can be that partial melting of an enriched lithospheric mantle gave birth to an alkali basaltic magma, which subsequently underplated in the lower crust and experienced a coupled fractionation of ferromagnesian phases like pyroxene and hornblende and minor ( china Plateau" in the Mesozoic.

关键词： syenite zircon SHRIMP Nd-Sr isotopes Taihang North china craton.

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 2school of mathematical sciences, peking university, beijing 100871, china Institute of Applied mathematics Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China school of mathematical sciences Peking University Beijing 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

Upper bound and formula for class numbers of abelian function fields

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Progress in Natural Science:materials International 2006年第3期16卷 321-323页

作者： ma Lianrong and ZHANG Xianke (Department of mathematical sciences, Tsinghua university, beijing 100084, china) Department of mathematical sciences Tsinghua University Beijing 100084 China

For any abelian function field K (i.e. any subfield of a cyclotomic function field L=k (∧P) over the rational function field k ) with conductor being an irreducible polynomial over a finite field of odd characteristic, by studying the Carlitz-module structure and the character group of K, an explicit upper bound and a calculating formula of the relative divisor class number h- (K) of K are given. Our calculated results of K develop Rosen’s recent results of L .

关键词： Carlitz module cyclotomic function field class number character abelian function field.