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P-Distances, Q-Distances and a Generalized Ekeland's Variational Principle in uniform spaces

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Acta Mathematica Sinica,English Series 2012年第2期28卷 235-254页

作者： Jing Hui QIU Fei HE School of Mathematical Sciences Soochow UniversitySuzhou 215006 P.R.China School of Mathematical Sciences Inner Mongolia UniversityHohhot 010021P.R.China

In this paper, we attempt to give a unified approach to the existing several versions of Ekeland＇s variational principle. In the framework of uniiorm spaces, we introduce p-distances and more generally, q-distances. Then we introduce a new type of completeness for uniform spaces, i.e., sequential completeness with respect to a q-distance （particularly, a p-distance）, which is a very extensive concept of completeness. By using q-distances and the new type of completeness, we prove a generalized Takahashi＇s nonconvex minimization theorem, a generalized Ekeland＇s variational principle and a generalized Caristi＇s fixed point theorem. Moreover, we show that the above three theorems are equivalent to each other. From the generalized Ekeland＇s variational principle, we deduce a number of particular versions of Ekeland＇s principle, which include many known versions of the principle and their improvements.

关键词： Ekeland＇s variational principle Takahashi＇s nonconvex minimization theorem Caristi＇sfixed point theorem uniform space locally convex space p-distance q-distance

ALMOST PERIODICITY AND EQUICONTINUITY OF THE TOPOLOGICAL TRANSFORMATION GROUP

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Applied Mathematics(A Journal of Chinese Universities) 2006年第4期21卷 467-472页

作者： Li Zhicong Li Juntao School of Science Beijing University of Aeronautics and Astronautics Beijing 100083 China. College of Mathematics and Information Science Henan Normal University Henan 453007 China.

In this paper, a characterization of almost periodicity of topological transformation groups on uniform spaces is given. By searching the appropriate base for uniform structure, it is shown that the topological transf... 详细信息

关键词： uniform space topological transformation group equicontinuity almost periodicity compactly almost periodicity.

Speech emotion recognition based on statistical pitch model

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Chinese Journal of Acoustics 2006年第1期25卷 87-96页

作者： WANG Zhiping ZHAO Li ZOU Cairong Department of Radio Engineering Southeast University Nanjing 210096

A modified Parzen-window method, which keep high resolution in low frequencies and keep smoothness in high frequencies, is proposed to obtain statistical model. Then, a gender classification method utilizing the statistical model is proposed, which have a 98% accuracy of gender classification while long sentence is dealt with. By separation the male voice and female voice, the mean and standard deviation of speech training samples with different emotion are used to create the corresponding emotion models. Then the Bhattacharyya distance between the test sample and statistical models of pitch, are utilized for emotion recognition in speech. The normalization of pitch for the male voice and female voice are also considered, in order to illustrate them into a uniform space. Finally, the speech emotion recognition experiment based on K Nearest Neighbor shows that, the correct rate of 81% is achieved, where it is only 73.85% if the traditional parameters are utilized.

关键词： emotion recognition statistical models classification method standard deviation high frequencies low frequencies high resolution uniform space test sample