摘要：
The modified Schultz index of a graph is defined as S*(G) = Σ{u, v}⊂V(G)(d(u)·d(v))dG(u, v) where d(u) (or d(v)) is the degree of the vertex u (or v), and dG(u, v) is the distance between u and v. Explicit formulas for calculating the modified Schultz index of Zig-zag polyhex nanotubes are provided in this paper.
摘要：
For a graph G = (V, E), the modified Schultz index of G is defined as S*(G) = Σ{u, v}⊂V(G) (d(u)·d(v))dG(u, v) where d(u) (or d(v)) is the degree of the vertex u (or v) of G, and dG(u, v) is the distance between u and v. Explicit formulas for calculating the modified Schultz index of armchair polyhex nanotubes are provided in this paper.
摘要：
In this paper, we deal with a class of inequality problems for dynamic frictional contact between a piezoelectric body and a foundation. The model consists of a system of the hemivariational inequality of hyperbolic type for the displacement, the time dependent elliptic equation for the electric potential. The friction condition is described to be the Clarke subdifferential relations of nonmonotone and multivalued character in the tangential directions on the boundary. The existence of a weak solution to the model is proved by embedding the problem into a class of second-order evolution inclusions, and by applying a surjectivity result for multivalued operators.
期刊：
Journal of Computational and Theoretical Nanoscience,2009年6(3):662-666 ISSN：1546-1955
通讯作者：
Chen, Shubo
作者机构：
[Xiao, Zhengming] Hunan Univ Technol, Zhuzhou 412008, Hunan, Peoples R China.;[Li, Junfeng; Chen, Shubo] Hunan City Univ, Dept Math & Comp Sci, Yiyang 413000, Hunan, Peoples R China.
通讯机构：
[Chen, Shubo] H;Hunan City Univ, Dept Math & Comp Sci, Yiyang 413000, Hunan, Peoples R China.
关键词：
Distance;Modified Schultz index;Nanotube;Schultz index
摘要：
The modified Schultz index of a graph G is defined as S*(G) = Σ{u, v⊂V(G)(d(u)·d(v))dG(u, v) where d(u) (or d(v)) is the degree of the vertex u (or v), and dG (u, v) is the distance between u and v. Explicit formulas for calculating the modified Schultz index of nanotubes covered by C4 are provided in this report.
摘要：
Learning-based image steganalysis is an effective and universal approach to cope with the following two difficulties: unknown statistics and steganographic algorithms. A crucial part of the learning-based process is the selection of low-dimensional features, which strongly impacts the accuracy of classification. A novel principal feature selection and fusion (PFSF) method is presented to reduce features, and then it is applied to image steganalysis. First, we analyze the multicollinearity among features to eliminate redundant features. Next, we implement the linear transform based on principal components analysis (PCA) and use Savage decision-making to eliminate insignificant features. Last, in order to further reduce features, we fuse the selected features, followed by selecting the principal features from the fused features to form a new feature set. The advantage of the proposed method is that it needs the cover images only, without requiring the availability of the stego-images in the process of the features selection. Moreover, the proposed method greatly reduces the computational time. Our method has been tested on two feature sets from Moulin's and Fridrich's features. The experimental results show that our method not only reduces the feature number by 90%, but also provides more reliable detection results than the previous steganalysis methods do.
摘要：
In this paper, we present an eigenvalue method for testing positive definiteness of a multivariate form. This problem plays an important role in the stability study of nonlinear autonomous systems via Lyapunov's direct method in automatic control. At first we apply the D'Andrea-Dickenstein version of the classical Macaulay formulas of the resultant to compute the symmetric hyperdeterminant of an even order supersymmetric tensor. By using the supersymmetry property, we give detailed computation procedures for the Bezoutians and specified ordering of monomials in this approach. We then use these formulas to calculate the characteristic polynomial of a fourth order three dimensional supersymmetric tensor and give an eigenvalue method for testing positive definiteness of a quartic form of three variables. Some numerical results of this method are reported.
摘要：
The PI index is a graph invariant defined as the summation of the sums of n(eu)(e vertical bar G) and n(ev)(e vertical bar G) over all the edges e = uv of a connected graph G, i.e., PI(G) = Sigma(e epsilon E(G))[n(eu)(e vertical bar G) + n(ev)(e vertical bar G)], where n(eu)(e vertical bar G), where n(eu)(e vertical bar G) is the number of edges of G lying closer to u than to v and n(eu)(e vertical bar G) is the number of edges of G lying closer to v than to u. An efficient formula for calculating the PI index of polyomino chains is given, and the bounds for the PI index of polyomino chains are established. (C) 2008 Elsevier Ltd. All rights reserved.
期刊：
Applied Mathematics and Computation,2006年177(1):105-110 ISSN：0096-3003
通讯作者：
Li, Fan-Liang
作者机构：
[Li, Fan-Liang] Hunan City Coll, Dept Math & Computat Sci, Yi Yang 413000, Peoples R China.;Hunan Univ, Coll Math & Econometr, Changsha 410082, Peoples R China.
通讯机构：
[Li, Fan-Liang] H;Hunan City Coll, Dept Math & Computat Sci, Yi Yang 413000, Peoples R China.
关键词：
skew-centrosymmetric matrix;left and right inverse eigenvalue;optimal approximation;EIGENVALUE PROBLEMS
摘要：
The left and right inverse eigenvalue problem of skew-centrosymmetric matrices and its optimal approximation are considered. New necessary and sufficient conditions for the solvability of the problem are derived, the general expression of the solution is given. The optimal approximate solution and some numerical experiments are also provided.
作者机构：
[黄新] Department of Mathematics and Computer Science, Hunan City College, Yiyang 413000, China;[邓迎春] College of Mathematics and Computer Science, Hunan Normal University, Changsha 410081, China;[陈内萍] Department of Information, Hunan Business College, Changsha 410205, China
作者机构：
[胡锡炎; 张磊; 李范良] Coll. of Math. and Econ., Hu'nan Univ., Changsha 410082, China;[李范良] Dept. of Math. and Comp., Hu'nan City Coll., Yiyang 413000, China
通讯机构：
Coll. of Math. and Econ., Hu'nan Univ., China
作者机构：
[李俊锋] Department of Mathematics and Computer Science, Hunan City University, Yiyang 413000, China;[杨棣] Department of Computer Science, Kunming University of Science and Technology, Kunming 650093, China
作者机构：
[李天然] Department of Mathematics, Hunan City College, Yiyang, 413000, China;[陈传淼] Institute of Computation, Hunan Normal University, Changsha, 410081, China
作者机构：
[Zhang, ZZ] Hunan City Univ, Dept Math, Yiyang, Peoples R China.;Cent S Univ, Sch Math Sci, Changsha, Peoples R China.;Hunan Univ, Fac Math & Econometr, Changsha, Peoples R China.
通讯机构：
[Zhang, ZZ] H;Hunan City Univ, Dept Math, Yiyang, Peoples R China.
作者机构：
[邓汉元] Department of Mathematics, Mathematics/Computer Sciencs College, Hunan Normal University, Changsha 410081, China;[夏方礼] Department of Mathematics, Yiyang Teacher's College, Yiyang 413049, China;[夏建业] Department of Basic Sciences, Guangzhou Financial College, Guangzhou 510521, China
