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COADJOINT ORBITS FOR THE CENTRAL EXTENSION OF Diff^+(S^1) AND THEIR representatives

Acta Mathematica Scientia 2004年第2期24卷 185-205页

作者：戴佳玲 Doug pickrell Department of Mathematics the University of ArizonaTucsonAZ85721USA

According to Kirillov's idea, the irreducible unitary representations of a Lie group G roughly correspond to the coadjoint orbits (?).In the forward direction one applies the methods of geometric quantization to produce a representation, and in the reverse direction one computes a transform of the character of a representation, to obtain a coadjoint orbit. The method of orbits in the representations of Lie groups suggests the detailed study of coadjoint orbits of a Lie group G in the space (?)~* dual to the Lie algebra (?) of G. In this paper, two primary goals are achieved: one is to completely classify the smooth coadjoint orbits of Virasoro group for nonzero central charge c; the other is to find representatives for coadjoint orbits. These questions have been considered previously by Segal, Kirillov, and Witten, but their results are not quite complete. To accomplish this, the authors start by describing the coadjoint action of D-the Lie group of all orientation preserving diffeomorphisms on the circle S^1, and its central extension (?), then the authors will give a complete classification of smooth coadjoint orbits. In fact, they can be parameterized by a subspace Of conjugacy classes of (?)(1,1). Finally, the authors will show how to find representatives f coadjoint orbits by analyzing the vector fields stabilizing the orbits, and describe the amazing connection between the characteristic (trace) of conjugacy classes of (?)(1, 1) and that of vector fields stabilizing orbits.

关键词： Coadjoint representations coadjoint orbits stabilizers vector fields representatives

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District Partisan Homogeneity, Communications, and the Electoral Motive: An Analysis of the Facebook Posts of Members of the U.S. House of representatives

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Social Networking 2017年第2期6卷 148-163页

作者： Scot Schraufnagel Quan Li Adam Schuster Department of Political Science Northern Illinois University DeKalb Illinois USA College of Political Science and Public Administration Wuhan University Wuhan China Northern Illinois University DeKalb Illinois USA

The research examines the way in which members of the U.S. House of Representative represent themselves on the social network site Facebook. Each member’s activity is observed on seven different occasions and the frequency and substantive character of posts made during the second half of 2013 are established. The focus is on position-taking posts versus posts which mention the district the member serves in. Our expectation is that members from electorally safe districts will be more likely to advertise their policy positions while members from marginal districts will be more inclined to advertise their district connections. We control for minority party status, gender, and ideological extremism among other concerns and learn electoral safety is a good predictor of both “position-taking” and “district mentions”. Consistent with an electoral motive, we also find members from the minority party less likely to take positions on the issues of the day and more likely to mention the district they serve in.

关键词： U.S. House of representatives Facebook Posts Electoral Motives Credit Claiming

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Vice-President Xie meets with representatives of US organizations attending forum

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Voice of Friendship 2019年第2期 57-57页

作者： Zhang Yang 不详

Vice-President Xie Yuan met with representatives of Sister Cities International and the US-China Friendship Association from the United States,who were in Beijing to attend the Subnational Cooperation Themed Forum of ... 详细信息

关键词： Vice-President representatives organizations

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Clustering Gene Expression Data Through Modified Agglomerative M-CURE Hierarchical Algorithm

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Computer Systems Science & Engineering 2022年第6期41卷 1027-1041页

作者： E.Kavitha R.Tamilarasan N.Poonguzhali M.K.Jayanthi Kannan A Constituent College of Anna University University College of EngineeringVillupuram605103India A Constituent College of Anna University University College of EngineeringPattukkottai614701India Department of Computer Science and Engineering Manakula Vinayagar Institute of TechnologyPuducherry605107India Department of Computer Science Engineering Faculty of Engineering and TechnologyJAIN(Deemed-To-Be University)Bangalore562112India

Gene expression refers to the process in which the gene information isused in the functional gene product synthesis. They basically encode the proteinswhich in turn dictate the functionality of the cell. The first step in gene expressionstudy involves the clustering usage. This is due to the reason that biological networks are very complex and the genes volume increases the comprehending challenges along with the data interpretation which itself inhibit vagueness, noise andimprecision. For a biological system to function, the essential cellular moleculesmust interact with its surrounding including RNA, DNA, metabolites and proteins. Clustering methods will help to expose the structures and the patterns inthe original data for taking further decisions. The traditional clustering techniquesinvolve hierarchical, model based, partitioning, density based, grid based and softclustering methods. Though many of these methods provide a reliable output inclustering, they fail to incorporate huge data of gene expressions. Also, thereare statistical issues along with choosing the right method and the choice of dissimilarity matrix when dealing with gene expression data. We propose to use amodified clustering algorithm using representatives (M-CURE) in this workwhich is more robust to outliers as compared to K-means clustering and also ableto find clusters with size variances.

关键词： Clustering gene identifiers representatives dimension reduction

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MOURNING FOR VICTIMS

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Beijing Review 2017年第51期60卷 3-5页

About 10,000 representatives of all walks of life pay silent tribute at a national memorial ceremony to mark the 80th anniversary of the Nanjing Massacre, in Nanjing east China＇s Jiangsu Province, on December 13.

关键词： MOURNING FOR VICTIMS representatives of all walks

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