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incompleteness and Minimality of Exponential System

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Journal of Mathematical Research and Exposition 2011年第2期31卷 215-223页

作者： Si Yu KE Guan Tie DENG School of Mathematical Sciences and Key Laboratory of Mathematics and Complex System Ministry of Education Bcijing Normal University Beijing 100875 P. R. China

Necessary and sufficient conditions are obtained for the incompleteness and the minimality of the exponential system E（Λ,M） = {z l e λ n z ： l = 0,1,...,m n-1;n = 1,2,...} in the Banach space E 2 [σ] consisting of some analytic functions in a half *** the incompleteness holds,each function in the closure of the linear span of exponential system E（Λ,M） can be extended to an analytic function represented by a Taylor-Dirichlet ***,by the conformal mapping ζ = φ（z） = e z ,the similar results hold for the incompleteness and the minimality of the power function system F （Λ,M） = {（log ζ） l ζ λ n ： l = 0,1,...,m n-1;n = 1,2,...} in the Banach space F 2 [σ] consisting of some analytic functions in a sector.

关键词： incompleteness minimality exponential system

incompleteness of Complex Exponential System in L_α~p Space

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Journal of Mathematical Research and Exposition 2010年第6期30卷 1078-1082页

作者： Xie Quan FAN Guan Tie DENG Key Laboratory of Mathematics and Complex Systems Ministry of EducationChinaSchool of Mathematical SciencesBeijing Normal UniversityBeijing 100875P.R.China

A necessary and sufficient condition is obtained for the incompleteness of complex exponential system in the weighted Banach space Lαp = {f：∫＋∞∞ ｜f（t）e-α（t）｜pdt ＋∞},where 1 ≤ p ＋∞ and α（t） is a we... 详细信息

关键词： incompleteness exponential system approximation.

Incomplete multi-view clustering via local and global co-regularization

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Science China(Information Sciences) 2022年第5期65卷 96-111页

作者： Jiye LIANG Xiaolin LIU Liang BAI Fuyuan CAO Dianhui WANG Key Laboratory of Computational Intelligence and Chinese Information Processing of Ministry of Education School of Computer and Information Technology Shanxi University Artificial Intelligence Research Institute China University of Mining and Technology Department of Computer Science and Computer Engineering La Trobe University

The incompleteness of multi-view data is a phenomenon associated with real-world data mining applications, which brings a huge challenge for multi-view clustering. Although various types of clustering methods, which try to obtain a complete and consensus clustering result from a latent subspace, have been developed to overcome this problem, most methods excessively rely on views-public instances to bridge the connection with view-private instances. When lacking sufficient views-public instances, existing methods fail to transmit the information among incomplete views effectively. To overcome this limitation, we propose an incomplete multi-view clustering algorithm via local and global co-regularization(IMVC-LG). In this algorithm, we define a new objective function that is composed of two terms: local clustering from each view and global clustering from multiple views, which constrain each other to exploit the local clustering information from different incomplete views and determine a global consensus clustering result, ***, an iterative optimization method is proposed to minimize the objective function. Finally, we compare the proposed algorithm with other state-of-the-art incomplete multi-view clustering methods on several benchmark datasets to illustrate its effectiveness.

关键词： incompleteness multi-view clustering local clustering global clustering co-regularization

On the Closure of Complex Exponential System in Weighted Banach Space

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Journal of Mathematical Research and Exposition 2011年第6期31卷 1067-1073页

作者： Yun Xia LI Guan Tie DENG Department of Mathematics Chuxiong Normal UniversityYunnan 675000P.R.China School of Mathematical Sciences and Key Laboratory of Mathematics and Complex System Ministry of EducationBeijing Normal UniversityBeijing 100875P.R.China

In this paper,closure of the linear span on complex exponential system in weighted Banach space Lαp is *** function in the closure of complex exponential system can be extended to an entire function represented by Ta... 详细信息

关键词： incompleteness closure exponential system Taylor-Dirichlet series.

Effects　of　magnitude　accuracy　and　complete－ness　data　on　seismic　hazard　parameters

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Acta Seismologica Sinica(English Edition) 1996年第4期9卷 99-108页

作者：邵辉成谢家树王平王亚秀

This paper is aimed to solve the question that present seismic catalogs are incomplete. The authors improve the maximum likelihood method to estimate seismic hazard parameters, considering different accuracy and completeness. As an example, we calculated the seismic hazard parameters of Fen Wei Seismic Belt and South Shaanxi Region. And based on it, we use single parameter sensitivity analysis method and multi parameter sensitivity analysis method to analyse and discuss the sensitivity of parameters and the uncertainty of result.

关键词： incompleteness uncertainty the maximum likelihood method sensitivity.

Exponential Polynomial Approximation with Unrestricted Upper Density

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Journal of Mathematical Research and Exposition 2011年第2期31卷 353-358页

作者： Xiang Dong YANG Department of Mathematics Kunming University of Science and Technology Yunnan 650093 P. R. China

We take a new approach to obtaining necessary and sufficient conditions for the incompleteness of exponential polynomials in L p α ,where L p α is the weighted Banach space of complex continuous functions f defined on the real axis R satisfying ＋∞ ∞ ｜f（t）｜ p e -α（t） dt） 1/p ,1 p ∞,and α（t） is a nonnegative continuous function defined on the real axis *** this paper,the upper density of the sequence which forms the exponential polynomials is not required to be *** the study of weighted polynomial approximation,consideration of the case is new.

关键词： incompleteness Banach space exponential system

Pragmatic turn in biology: From biological molecules to genetic content operators

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World Journal of Biological Chemistry 2014年第3期5卷 279-285页

作者： Guenther Witzany Telos-Philosophische Praxis

Erwin Schrdinger‘s question "What is life?" received the answer for decades of "physics + chemistry". The concepts of Alain Turing and John von Neumann introduced a third term: "information". This led to the understanding of nucleic acid sequences as a natural code. Manfred Eigen adapted the concept of Hammings "sequence space". Similar to Hilbert space, in which every ontological entity could be defined by an unequivocal point in a mathematical axiomatic system, in the abstract "sequence space" concept each point represents a unique syntactic structure and the value of their separation represents their dissimilarity. In this concept molecular features of the genetic code evolve by means of self-organisation of matter. Biological selection determines the fittest types among varieties of replication errors of quasi-species. The quasi-species concept dominated evolution theory for many decades. In contrast to this, recent empirical data on the evolution of DNA and its forerunners, the RNA-world and viruses indicate cooperative agent-based interactions. Group behaviour of quasi-species consortia constitute de novo and arrange available genetic content for adaptational purposes within real-life contexts that determine epigenetic markings. This review focuses on some fundamental changes in biology, discarding its traditional status as a subdiscipline of physics and chemistry.

关键词： Life Information Quasi-species incompleteness theorem Genetic content operators