The perturbed Kaup-Kupershmidt equation is investigated in terms of the approximate symmetry perturbationmethod and the approximate direct method.The similarity reduction solutions of different orders are obtainedfor ...The perturbed Kaup-Kupershmidt equation is investigated in terms of the approximate symmetry perturbationmethod and the approximate direct method.The similarity reduction solutions of different orders are obtainedfor both methods, series reduction solutions are consequently derived.Higher order similarity reduction equations arelinear variable coefficients ordinary differential equations.By comparison, it is find that the results generated from theapproximate direct method are more general than the results generated from the approximate symmetry perturbationmethod.展开更多
In this paper,the authors study the persistence approximation property for quantitative K-theory of filtered L^(p)operator algebras.Moreover,they define quantitative assembly maps for L^(p)operator algebras when p∈[1...In this paper,the authors study the persistence approximation property for quantitative K-theory of filtered L^(p)operator algebras.Moreover,they define quantitative assembly maps for L^(p)operator algebras when p∈[1,∞).Finally,in the case of L^(p)crossed products and L^(p)Roe algebras,sufficient conditions for the persistence approximation property are found.This allows to give some applications involving the L^(p)(coarse)Baum-Connes conjecture.展开更多
An unsupervised learning algorithm, named soft spectral clustering ensemble （SSCE）, is proposed in this paper. Until now many proposed ensemble algorithms cannot be used on image data, even images of a mere 256 &#...An unsupervised learning algorithm, named soft spectral clustering ensemble （SSCE）, is proposed in this paper. Until now many proposed ensemble algorithms cannot be used on image data, even images of a mere 256 × 256 pixels are too expensive in computational cost and storage. The proposed method is suitable for performing image segmentation and can, to some degree, solve some open problems of spectral clustering （SC）. In this paper, a random scaling parameter and Nystrǒm approximation are applied to generate the individual spectral clusters for ensemble learning. We slightly modify the standard SC algorithm to aquire a soft partition and then map it via a centralized logcontrast transform to relax the constraint of probability data, the sum of which is one. All mapped data are concatenated to form the new features for each instance. Principal component analysis （PCA） is used to reduce the dimension of the new features. The final aggregated result can be achieved by clustering dimension-reduced data. Experimental results, on UCI data and different image types, show that the proposed algorithm is more efficient compared with some existing consensus functions.展开更多
In this paper, we consider the relations among L-fuzzy sets, rough sets and n-ary polygroup theory. Some properties of （normal） TL-fuzzy n-ary subpolygroups of an n-ary polygroup are first obtained. Using the concep...In this paper, we consider the relations among L-fuzzy sets, rough sets and n-ary polygroup theory. Some properties of （normal） TL-fuzzy n-ary subpolygroups of an n-ary polygroup are first obtained. Using the concept of L-fuzzy sets, the notion of ~）-lower and T-upper L-fuzzy rough approximation operators with respect to an L-fuzzy set is introduced and some related properties are presented. Then a new algebraic structure called （normal） TL-fuzzy rough n-ary polygroup is defined and investigated. Also, the （strong） homomorphism of θ-lower and T-upper L-fuzzy rough approximation operators is studied.展开更多
基金Supported by the National Natural Science Foundation of China under Grant Nos.10735030,10475055,10675065,and 90503006National Basic Research Program of China (973 Program 2007CB814800)
文摘The perturbed Kaup-Kupershmidt equation is investigated in terms of the approximate symmetry perturbationmethod and the approximate direct method.The similarity reduction solutions of different orders are obtainedfor both methods, series reduction solutions are consequently derived.Higher order similarity reduction equations arelinear variable coefficients ordinary differential equations.By comparison, it is find that the results generated from theapproximate direct method are more general than the results generated from the approximate symmetry perturbationmethod.
基金supported by the National Natural Science Foundation of China(Nos.12271165,12171156,12301154)the Science and Technology Commission of Shanghai Municipality(No.22DZ2229014).
文摘In this paper,the authors study the persistence approximation property for quantitative K-theory of filtered L^(p)operator algebras.Moreover,they define quantitative assembly maps for L^(p)operator algebras when p∈[1,∞).Finally,in the case of L^(p)crossed products and L^(p)Roe algebras,sufficient conditions for the persistence approximation property are found.This allows to give some applications involving the L^(p)(coarse)Baum-Connes conjecture.
文摘An unsupervised learning algorithm, named soft spectral clustering ensemble （SSCE）, is proposed in this paper. Until now many proposed ensemble algorithms cannot be used on image data, even images of a mere 256 × 256 pixels are too expensive in computational cost and storage. The proposed method is suitable for performing image segmentation and can, to some degree, solve some open problems of spectral clustering （SC）. In this paper, a random scaling parameter and Nystrǒm approximation are applied to generate the individual spectral clusters for ensemble learning. We slightly modify the standard SC algorithm to aquire a soft partition and then map it via a centralized logcontrast transform to relax the constraint of probability data, the sum of which is one. All mapped data are concatenated to form the new features for each instance. Principal component analysis （PCA） is used to reduce the dimension of the new features. The final aggregated result can be achieved by clustering dimension-reduced data. Experimental results, on UCI data and different image types, show that the proposed algorithm is more efficient compared with some existing consensus functions.
基金The second author is supported by National Natural Science Foundation of China （Grant Nos. 60774049, 60875034）, Natural Science Foundation of Education Committee of Hubei Province, China （Grant Nos. D20092901, Q20092907, D20082903, B200529001） and Natural Science Foundation of Hubei Province, China （Grant No. 2008CDB341）
文摘In this paper, we consider the relations among L-fuzzy sets, rough sets and n-ary polygroup theory. Some properties of （normal） TL-fuzzy n-ary subpolygroups of an n-ary polygroup are first obtained. Using the concept of L-fuzzy sets, the notion of ~）-lower and T-upper L-fuzzy rough approximation operators with respect to an L-fuzzy set is introduced and some related properties are presented. Then a new algebraic structure called （normal） TL-fuzzy rough n-ary polygroup is defined and investigated. Also, the （strong） homomorphism of θ-lower and T-upper L-fuzzy rough approximation operators is studied.
