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Construction of periodic wavelet frames with dilation matrix

Frontiers of Mathematics in China 2014年第1期9卷 111-134页

作者： Dayong LU Dengfeng LI Institute of Applied Mathematics School of Mathematics and Information Sciences Henan University Kaifeng 475001 China School of Mathematics and Computer Science Wuhan Textile University Wuhan 430200 China

An important tool for the construction of periodic wavelet frame with the help of extension principles was presented in the Fourier domain by Zhang and Saito [Appl. Comput. Harmon. Anal., 2008, 125： 68-186]. We extend their results to the dilation matrix cases in two aspects. We first show that the periodization of any wavelet frame constructed by the unitary extension principle formulated by Ron and Shen is still a periodic wavelet frame under weaker conditions than that given by Zhang and Saito, and then prove that the periodization of those generated by the mixed extension principle is also a periodic wavelet frame if the scaling functions have compact supports.

关键词： Periodic wavelet frames extension principle matrix dilation function periodization

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Linguistic dynamic systems based on computing with words and their stabilities

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Science in China(Series F) 2009年第5期52卷 780-796页

作者： MO Hong WANG FeiYue College of Electric and Information Engineering Changsha University of Science and Technology Changsha 410004 China Key Laboratory of Complex Systems and Intelligent Science Institute of Automation Chinese Academy of Science Beijing 100080 China

Linguistic dynamic systems （LDS） are the systems based on computing with words （CW） instead of computing with numbers or symbols. In this paper, LDS are divided into two types： type-I LDS being converted from conventional dynamical systems （CDS） by using extension principle and type-II LDS by using fuzzy logic rules. For type-I LDS, the method of endograph is provided to discuss the stabilities of type-I LDS and two cases of stabilities of logistic mappings： one is the states being abstracted and the other is parameters also being abstracted. For type-Ⅱ LDS, the method of degree of match is used to discuss the dynamical behavior of arbitrary initial words under fuzzy rule.

关键词： computing with words (CW) extension principle stability fuzzy rule degree of match

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General Schemes of Iterative Optimization with Applications to Optimal Control Problems

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Journal of the Operations Research Society of China 2016年第2期4卷 223-232页

作者： Oles Vladimirovich Fesko Vladimir Iosifovich Gurman Irina Viktorovna Rasina East China Normal University Shanghai 200241China Ailamazyan Program Systems Institute Russian Academy of SciencesPereslavl-Zalesskii 152021Russia Trapeznikov Institute of Control Sciences Russian Academy of SciencesMoscow 117997Russia

A general(abstract)scheme of iterative improvement and optimization on the base of extension,localization principles which would help to generate new concrete methods and algorithms for new problems is *** to optimal... 详细信息

关键词： Iterative optimization Optimal control extension principle Localization principle

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Construction of Multivariate Tight Framelet Packets Associated with Dilation Matrix

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Analysis in Theory and Applications 2015年第2期31卷 109-122页

作者： Firdous A.Shah Abdullah Department of Mathematics University of Kashmir Department of Mathematics ZHDC University of Delhi

In this paper, we present a method for constructing multivariate tight framelet packets associated with an arbitrary dilation matrix using unitary extension principles. We also prove how to construct various tight fra... 详细信息

关键词： Wavelet tight frame framelet packet matrix dilation extension principle Fouriertransform.

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Initial and Stopping Condition in Possibility Principal Factor Rotation

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Journal of Applied Mathematics and Physics 2023年第5期11卷 1482-1486页

作者： Houju Hori Jr. Chief in Nara Community Tsubakikishi Shrine Nara Japan

Uemura [1] discovered the mapping formula for Type 1 Vague events and presented an alternative problem as an example of its application. Since it is well known that the alternative problem leads to sequential Bayesian inference, the flow of subsequent research was to make the mapping formula multidimensional, to introduce the concept of time, and to derive a Markov (decision) process. Furthermore, we formulated stochastic differential equations to derive them [2]. This paper refers to type 2 vague events based on a second-order mapping equation. This quadratic mapping formula gives a certain rotation named as possibility principal factor rotation by transforming a non-mapping function by a relation between two mapping functions. In addition, the derivation of the Type 2 Complex Markov process and the initial and stopping conditions in this rotation are mentioned. .

关键词： extension principle Vague Event Type 2 Possibility Different Equation Possibility Principal Factor Analysis Initial and Stopping Condition

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Intuitionistic Fuzzy Riemann Integral

Intuitionistic Fuzzy Riemann Integral

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2009中国控制与决策会议

作者： Minghu Ha~11,Lanzhen Yang ~1 1.College of Mathematics and Computer Sciences,Hebei University,Baoding,071002,China

＜正＞This paper discusses multi-variable extension principles of intuitionistic fuzzy sets,and presents three types of intuitionistic fuzzy Riemann integral,which is a generalization of fuzzy Riemann integral.

关键词： Intuitionistic Fuzzy Set extension principle Multi-Variable extension principle Intuitionistic Fuzzy Riemann Integral

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