Some sharp upper bounds of Laplacian spectral radius of trees in terms of order,diameter,pendant vertex number,covering number,edge covering number or total independence number are given.And the ninth to thirteenth la...Some sharp upper bounds of Laplacian spectral radius of trees in terms of order,diameter,pendant vertex number,covering number,edge covering number or total independence number are given.And the ninth to thirteenth largest values of Laplacian spectral radius over the class of trees on a given order are also given.展开更多
With the aid of symbolic computation, we present the symmetry transformations of the (2+1)-dimensionalCaudrey-Dodd Gibbon-Kotera-Sawada equation with Lou's direct method that is based on Lax pairs. Moreover, witht...With the aid of symbolic computation, we present the symmetry transformations of the (2+1)-dimensionalCaudrey-Dodd Gibbon-Kotera-Sawada equation with Lou's direct method that is based on Lax pairs. Moreover, withthe symmetry transformations we obtain the Lie point symmetries of the CDGKS equation, and reduce the equation withthe obtained symmetries. As a result, three independent reductions are presented and some group-invariant solutions ofthe equation are given.展开更多
Making use of the direct method proposed by Lou et al. and symbolic computation, finite symmetry transformation groups for a (2+ l)-dimensional cubic nonlinear Schrodinger (NLS) equation and its corresponding cyl...Making use of the direct method proposed by Lou et al. and symbolic computation, finite symmetry transformation groups for a (2+ l)-dimensional cubic nonlinear Schrodinger (NLS) equation and its corresponding cylindrical NLS equations are presented. Nine related linear independent infinitesimal generators can be obtained from the finite symmetry transformation groups by restricting the arbitrary constants in infinitesimal forms. Some exact solutions are derived from a simple travelling wave solution.展开更多
A novel histogram descriptor for global feature extraction and description was presented. Three elementary primitives for a 2×2 pixel grid were defined. The complex primitives were computed by matrix transforms. ...A novel histogram descriptor for global feature extraction and description was presented. Three elementary primitives for a 2×2 pixel grid were defined. The complex primitives were computed by matrix transforms. These primitives and equivalence class were used for an image to compute the feature image that consisted of three elementary primitives. Histogram was used for the transformed image to extract and describe the features. Furthermore, comparisons were made among the novel histogram descriptor, the gray histogram and the edge histogram with regard to feature vector dimension and retrieval performance. The experimental results show that the novel histogram can not only reduce the effect of noise and illumination change, but also compute the feature vector of lower dimension. Furthermore, the system using the novel histogram has better retrieval performance.展开更多
In this paper, we consider a system of (2+2)-dimensional nonlinear models by using CK direct method and Hereman-Nuseir method generated by the Janlent-Miodek Hierarchy. We construct some new multiple kink and singu...In this paper, we consider a system of (2+2)-dimensional nonlinear models by using CK direct method and Hereman-Nuseir method generated by the Janlent-Miodek Hierarchy. We construct some new multiple kink and singular kink solutions of (2+1)-Dimensional Nonlinear Models with the aid of symbolic computation.展开更多
基金Supported by National Natural Science Foundation of China(10871204)
文摘Some sharp upper bounds of Laplacian spectral radius of trees in terms of order,diameter,pendant vertex number,covering number,edge covering number or total independence number are given.And the ninth to thirteenth largest values of Laplacian spectral radius over the class of trees on a given order are also given.
基金Supported by the Natural Key Basic Research Project of China under Grant No. 2004CB318000the 'Math + X' Key Project and Science Foundation of Dalian University of Technology under Grant No. SFDUT0808
文摘With the aid of symbolic computation, we present the symmetry transformations of the (2+1)-dimensionalCaudrey-Dodd Gibbon-Kotera-Sawada equation with Lou's direct method that is based on Lax pairs. Moreover, withthe symmetry transformations we obtain the Lie point symmetries of the CDGKS equation, and reduce the equation withthe obtained symmetries. As a result, three independent reductions are presented and some group-invariant solutions ofthe equation are given.
基金The project supported by K.C. Wong Magna Fund in Ningbo University, National Natural Science Foundation of China under Grant Nos. 10747141 and 10735030;Zhejiang Provincial Natural Science Foundations of China under Grant No. 605408;Ningbo Natural Science Foundation under Grant Nos. 2007A610049 and 2006A610093;National Basic Research Program of China (973 Program 2007CB814800);Program for Changjiang Scholars and Innovative Research Team in University (IRTO734)
文摘Making use of the direct method proposed by Lou et al. and symbolic computation, finite symmetry transformation groups for a (2+ l)-dimensional cubic nonlinear Schrodinger (NLS) equation and its corresponding cylindrical NLS equations are presented. Nine related linear independent infinitesimal generators can be obtained from the finite symmetry transformation groups by restricting the arbitrary constants in infinitesimal forms. Some exact solutions are derived from a simple travelling wave solution.
基金Project(60873010) supported by the National Natural Science Foundation of ChinaProjects(N090504005, N090604012, N090104001) supported by the Fundamental Research Funds for the Central UniversitiesProject(NCET-05-0288) supported by Program for New Century Excellent Talents in University
文摘A novel histogram descriptor for global feature extraction and description was presented. Three elementary primitives for a 2×2 pixel grid were defined. The complex primitives were computed by matrix transforms. These primitives and equivalence class were used for an image to compute the feature image that consisted of three elementary primitives. Histogram was used for the transformed image to extract and describe the features. Furthermore, comparisons were made among the novel histogram descriptor, the gray histogram and the edge histogram with regard to feature vector dimension and retrieval performance. The experimental results show that the novel histogram can not only reduce the effect of noise and illumination change, but also compute the feature vector of lower dimension. Furthermore, the system using the novel histogram has better retrieval performance.
基金Supported by the National Natural Science Foundation of China under Grant No. 10647112the Fundamental Research Funds for the Central Universities
文摘In this paper, we consider a system of (2+2)-dimensional nonlinear models by using CK direct method and Hereman-Nuseir method generated by the Janlent-Miodek Hierarchy. We construct some new multiple kink and singular kink solutions of (2+1)-Dimensional Nonlinear Models with the aid of symbolic computation.