The relationship between Strebel boundary dilatation of a quasisymmetric function h of the unit circle and the dilatation indicated by the change in the modules of the quadrilaterals with vertices on the circle intrig...The relationship between Strebel boundary dilatation of a quasisymmetric function h of the unit circle and the dilatation indicated by the change in the modules of the quadrilaterals with vertices on the circle intrigues many mathematicians. It had been a conjecture for some time that the dilatations Ko（h） and K1（h） of h are equal before Anderson and Hinkkanen disproved this by constructing concrete counterexamples. The independent work of Wu and of Yang completely characterizes the condition for Ko（h） = K1 （h） when h has no substantial boundary point. In this paper, we give a necessary and sufficient condition to determine the equality for h admitting a substantial boundary point.展开更多
Due to the advancements in remote sensing technologies,the generation of hyperspectral imagery(HSI)gets significantly increased.Accurate classification of HSI becomes a critical process in the domain of hyperspectral ...Due to the advancements in remote sensing technologies,the generation of hyperspectral imagery(HSI)gets significantly increased.Accurate classification of HSI becomes a critical process in the domain of hyperspectral data analysis.The massive availability of spectral and spatial details of HSI has offered a great opportunity to efficiently illustrate and recognize ground materials.Presently,deep learning(DL)models particularly,convolutional neural networks(CNNs)become useful for HSI classification owing to the effective feature representation and high performance.In this view,this paper introduces a new DL based Xception model for HSI analysis and classification,called Xcep-HSIC model.Initially,the presented model utilizes a feature relation map learning(FRML)to identify the relationship among the hyperspectral features and explore many features for improved classifier results.Next,the DL based Xception model is applied as a feature extractor to derive a useful set of features from the FRML map.In addition,kernel extreme learning machine(KELM)optimized by quantum-behaved particle swarm optimization(QPSO)is employed as a classification model,to identify the different set of class labels.An extensive set of simulations takes place on two benchmarks HSI dataset,namely Indian Pines and Pavia University dataset.The obtained results ensured the effective performance of the XcepHSIC technique over the existing methods by attaining a maximum accuracy of 94.32%and 92.67%on the applied India Pines and Pavia University dataset respectively.展开更多
For every torsion free Fuchsian group F with Poincaré’s -operator norm ║г║=1, it is proved that there exists an extremal Beltrami differential of F which is also extremal under its own boundary correspondence...For every torsion free Fuchsian group F with Poincaré’s -operator norm ║г║=1, it is proved that there exists an extremal Beltrami differential of F which is also extremal under its own boundary correspondence. It is also proved that the imbedding of the Teichmüller space T(Γ) into the universal Teichmüller space T is not a global isometry unless Γ is an elementary group.展开更多
An explicit example of a Reich sequence for a uniquely extremal quasiconformal mapping in a borderline case between uniqueness and non-uniqueness is given.
Let S be a Riemann surface with genus p and n punctures. Assume that 3p- 3 ＋ n 〉 0 and n 〉 1. Let a be a puncture of S and let S = S∪{α}. Then all mapping classes in the mapping class group Mods that fixes the pu...Let S be a Riemann surface with genus p and n punctures. Assume that 3p- 3 ＋ n 〉 0 and n 〉 1. Let a be a puncture of S and let S = S∪{α}. Then all mapping classes in the mapping class group Mods that fixes the puncture a can be projected to mapping classes of Mod$ under the forgetful map. In this paper the author studies the mapping classes in Mods that can be projected to a given hyperbolic mapping class in Mode.展开更多
This paper studies extremal quasiconformal mappings. Some properties of the variability set are obtained and the Hamilton sequences which are induced by point shift differentials are also discussed.
LetT be the universal Teichmüller space viewed as the set of all normalized quasisymmetric homeomorphism of the unit circleS 1=?Δ. Denote byV h [z 0] the variability set ofz 0 with respect toh∈T. The following ...LetT be the universal Teichmüller space viewed as the set of all normalized quasisymmetric homeomorphism of the unit circleS 1=?Δ. Denote byV h [z 0] the variability set ofz 0 with respect toh∈T. The following is proved: Leth 0 be a point ofT. Suppose thatμ 0 is an arbitrarily given extremal Beltrami differential ofh 0 andf 0: μ→μ is a quasiconformal mapping with the Beltrami coefficientμ 0 andf 01s=h 0. Then there are a sequenceh n of points inT and a sequencew n of points in Δ withh n ∈(Δ?V h [z 0]) andw n →f 0(z 0) andh n →h 0 andn∞ such that the point shift differentials determined byh n asw n form a Hamilton sequence ofμ 0.展开更多
基金Supported by the National Natural Science Foundation of China(10671174, 10401036)a Foundation for the Author of National Excellent Doctoral Dissertation of China(200518)
文摘The relationship between Strebel boundary dilatation of a quasisymmetric function h of the unit circle and the dilatation indicated by the change in the modules of the quadrilaterals with vertices on the circle intrigues many mathematicians. It had been a conjecture for some time that the dilatations Ko（h） and K1（h） of h are equal before Anderson and Hinkkanen disproved this by constructing concrete counterexamples. The independent work of Wu and of Yang completely characterizes the condition for Ko（h） = K1 （h） when h has no substantial boundary point. In this paper, we give a necessary and sufficient condition to determine the equality for h admitting a substantial boundary point.
文摘Due to the advancements in remote sensing technologies,the generation of hyperspectral imagery(HSI)gets significantly increased.Accurate classification of HSI becomes a critical process in the domain of hyperspectral data analysis.The massive availability of spectral and spatial details of HSI has offered a great opportunity to efficiently illustrate and recognize ground materials.Presently,deep learning(DL)models particularly,convolutional neural networks(CNNs)become useful for HSI classification owing to the effective feature representation and high performance.In this view,this paper introduces a new DL based Xception model for HSI analysis and classification,called Xcep-HSIC model.Initially,the presented model utilizes a feature relation map learning(FRML)to identify the relationship among the hyperspectral features and explore many features for improved classifier results.Next,the DL based Xception model is applied as a feature extractor to derive a useful set of features from the FRML map.In addition,kernel extreme learning machine(KELM)optimized by quantum-behaved particle swarm optimization(QPSO)is employed as a classification model,to identify the different set of class labels.An extensive set of simulations takes place on two benchmarks HSI dataset,namely Indian Pines and Pavia University dataset.The obtained results ensured the effective performance of the XcepHSIC technique over the existing methods by attaining a maximum accuracy of 94.32%and 92.67%on the applied India Pines and Pavia University dataset respectively.
文摘For every torsion free Fuchsian group F with Poincaré’s -operator norm ║г║=1, it is proved that there exists an extremal Beltrami differential of F which is also extremal under its own boundary correspondence. It is also proved that the imbedding of the Teichmüller space T(Γ) into the universal Teichmüller space T is not a global isometry unless Γ is an elementary group.
文摘An explicit example of a Reich sequence for a uniquely extremal quasiconformal mapping in a borderline case between uniqueness and non-uniqueness is given.
文摘Let S be a Riemann surface with genus p and n punctures. Assume that 3p- 3 ＋ n 〉 0 and n 〉 1. Let a be a puncture of S and let S = S∪{α}. Then all mapping classes in the mapping class group Mods that fixes the puncture a can be projected to mapping classes of Mod$ under the forgetful map. In this paper the author studies the mapping classes in Mods that can be projected to a given hyperbolic mapping class in Mode.
基金Project supported by the National Natural Science Foundation of China (No.10171003, No.10231040) the Doctoral Education Program Foundation of China.
文摘This paper studies extremal quasiconformal mappings. Some properties of the variability set are obtained and the Hamilton sequences which are induced by point shift differentials are also discussed.
基金Project supported by the National Natural Science Foundation of China (Grant No. 19531060)the Doctoral Education Program Foundation of China
文摘LetT be the universal Teichmüller space viewed as the set of all normalized quasisymmetric homeomorphism of the unit circleS 1=?Δ. Denote byV h [z 0] the variability set ofz 0 with respect toh∈T. The following is proved: Leth 0 be a point ofT. Suppose thatμ 0 is an arbitrarily given extremal Beltrami differential ofh 0 andf 0: μ→μ is a quasiconformal mapping with the Beltrami coefficientμ 0 andf 01s=h 0. Then there are a sequenceh n of points inT and a sequencew n of points in Δ withh n ∈(Δ?V h [z 0]) andw n →f 0(z 0) andh n →h 0 andn∞ such that the point shift differentials determined byh n asw n form a Hamilton sequence ofμ 0.
