{"title":"Eigenvalues and eigenvectors of semigroup generators obtained from diagonal generators by feedback","authors":"G. Weiss, Cheng-Zhong Xu","doi":"10.4310/CIS.2011.V11.N1.A5","DOIUrl":"https://doi.org/10.4310/CIS.2011.V11.N1.A5","url":null,"abstract":"We study infinite-dimensional well-posed linear systems with output feedback such that the closed-loop system is well-posed. The generator A of the open-loop system is assumed to be diagonal, i.e., the state space X (a Hilbert space) has a Riesz basis consisting of eigenvectors of A. We investigate when the closed-loop generator A is Riesz spectral, i.e, its generalized eigenvectors form a Riesz basis in X. We construct a new Riesz basis in X using the sequence of eigenvectors of A and the control operator B. If this new basis is, in a certain sense, close to a subset of the generalized eigenvectors of A , then we conclude that A is Riesz spectral. This approach leads to several results on Riesz spectralness of A where the closed-loop eigenvectors need not be computed. We illustrate the usefulness of our results through several examples concerning the stabilization of systems described by partial differential equations in one space dimension. For the systems in the examples we show that the closed-loop generator is Riesz spectral. Our method allows us to simplify long computations which were necessary otherwise.","PeriodicalId":45018,"journal":{"name":"Communications in Information and Systems","volume":"11 1","pages":"71-104"},"PeriodicalIF":0.9,"publicationDate":"2011-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70404843","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Avalanche: A Network Coding Analysis","authors":"R. Yeung","doi":"10.4310/CIS.2007.V7.N4.A3","DOIUrl":"https://doi.org/10.4310/CIS.2007.V7.N4.A3","url":null,"abstract":"In this paper, we study the application of random network coding in peer-to-peer (P2P) networks. The system we analyze is based on a prototype called Avalanche proposed in [8] for large scale content distribution on such networks. We present the necessary techniques for analyzing the system and show that random network coding provides the system with both maximum bandwidth efficiency and robustness. We also point out that the model for random network coding in P2P networks is very different from the one that has been studied extensively in the literature.","PeriodicalId":45018,"journal":{"name":"Communications in Information and Systems","volume":"7 1","pages":"353-358"},"PeriodicalIF":0.9,"publicationDate":"2007-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70404792","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Conformal Spherical Parametrization for High Genus Surfaces","authors":"X. Gu, Xin Li, S. Yau, W. Zeng","doi":"10.4310/CIS.2007.V7.N3.A4","DOIUrl":"https://doi.org/10.4310/CIS.2007.V7.N3.A4","url":null,"abstract":"Surface parameterization establishes bijective maps from a surface onto a topologically equivalent standard domain. It is well known that the spherical parameterization is limited to genus-zero surfaces. In this work, we design a new parameter domain, two-layered sphere, and present a framework for mapping high genus surfaces onto sphere. This setup allows us to transfer the existing applications based on general spherical parameterization to the field of high genus surfaces, such as remeshing, consistent parameterization, shape analysis, and so on. Our method is based on Riemann surface theory. We construct meromorphic functions on surfaces: for genus one surfaces, we apply Weierstrass P-functions; for high genus surfaces, we compute the quotient between two holomorphic one-forms. Our method of spherical parameterization is theoretically sound and practically efficient. It makes the subsequent applications on high genus surfaces very promising.","PeriodicalId":45018,"journal":{"name":"Communications in Information and Systems","volume":"93 1","pages":"273-286"},"PeriodicalIF":0.9,"publicationDate":"2007-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70404750","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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