摘要：
We consider a mathematical model which describes the frictional contact between a deformable body and a foundation. The process is quasistatic, the material is assumed to be viscoelastic with long memory and the frictional contact is modelled with subdifferential boundary conditions. The mechanical damage of the material is described by the damage function, which is modelled by a nonlinear partial differential equation. We derive the variational formulation of the problem, which is a coupled system of a hemivariational inequality and a parabolic equation. Then we prove the existence of a unique weak solution to the model. The proof is based on arguments of abstract stationary inclusion and a fixed point theorem.
摘要：
In this paper we consider the bifurcation problem -div A(x,?u)=λa(x)|u|~(p-2)u+f(x,u,λ) in Ω with p>1.Under some proper assumptions on A(x,ξ),a(x)and f(x,u,λ),we show that the existence of an unbounded branch of positive solutions bifurcating from the principal eigenvalue of the problem-divA(x,?u)=λa(x)|u|~(p-2)u
作者机构：
[Li Junfeng] Hunan City Univ, Dept Math & Comp Sci, Yiyang 413000, Peoples R China.
通讯机构：
[Li Junfeng] H;Hunan City Univ, Dept Math & Comp Sci, Yiyang 413000, Peoples R China.
关键词：
Bloch type space;boundedness;compactness;composition operator
摘要：
For all 0 > p, q > ∞, let Cφ, denote the composition operator from q-Bloch spaces β~P to little p-Bloch spaces β_0~p on the unit ball of C~n. In this article, necessary and sufficient conditions for Cφ to be a bounded or compact operator are given.
关键词：
data compression;discrete cosine transforms;image coding;steganography;support vector machines
摘要：
A JPEG image steganalysis scheme based on joint discrete cosine transform (DCT) domain features is proposed. Intrinsic characteristics of DCT coefficients, such as histogram, intrablock correlation, and interblock correlation, are exploited to construct three feature sets. Support vector machine is utilized to learn and discriminate the difference of features between cover and stego images. First, the three feature sets are investigated separately to reveal their individual capability of attacking steganographic methods. Second, the feature sets are combined to form a joint feature set with better performance. Experimental results demonstrate that all three feature sets individually succeed in attacking the four typical steganographic tools to some extent, with the intrablock feature set performing the best. Furthermore, the comparison experiments show that the jointed feature set not only outperforms the three individual feature sets but also proves to be better than a previous state-of-the-art steganalysis method.
期刊：
MATCH-COMMUNICATIONS IN MATHEMATICAL AND IN COMPUTER CHEMISTRY,2010年64(3):767-782 ISSN：0340-6253
通讯作者：
Chen, Shubo
作者机构：
[Liu, Weijun; Chen, Shubo] Cent S Univ, Coll Math, Changsha 410075, Hunan, Peoples R China.;[Chen, Shubo] Hunan City Univ, Dept Math, Yiyang 413000, Hunan, Peoples R China.
通讯机构：
[Chen, Shubo] C;Cent S Univ, Coll Math, Changsha 410075, Hunan, Peoples R China.
摘要：
For a graph G = (V, E), the modified Schultz index of G is defined as S*(G) = Sigma({u,v}subset of V(G)) (d(G)(u).d(G)(v))d(G)(u,v) where d(G)(u) (or d(u)) is the degree of the vertex u of G, and d(G)(u, v) is the distance between u and v. Let B(n) be the set of bicyclic graph with n vertices. In this paper, we study the modified Schultz index of B(n), graphs in B(n) with the smallest modified Schultz index S*(C) are determined. The corresponding extremal graphs are characterized as well.
期刊：
Ars Combinatoria,2010年97:241-248 ISSN：0381-7032
通讯作者：
Chen, Shubo
作者机构：
[Chen, Shubo] Hunan City Univ, Dept Math & Comp Sci, Yiyang 413000, Hunan, Peoples R China.;[Chen, Shubo] Cent S Univ, Coll Math, Changsha 410075, Hunan, Peoples R China.;[Zhou, Houqing] Shaoyang Univ, Dept Math, Shaoyang 422000, Hunan, Peoples R China.
通讯机构：
[Chen, Shubo] H;Hunan City Univ, Dept Math & Comp Sci, Yiyang 413000, Hunan, Peoples R China.
摘要：
The Zagreb indices are topological indices of graphs, which defined as, Mi(G) = Σv⋯V(G) (d(v))2, M2(G) = Σuv⋯V(G) (d(u)d(v)). In this paper, we determine the upper and lower bounds for the Zagreb indices of unicyclic graphs in terms of their order and girth. In each case, we characterize the extremal graphs.
作者机构：
[Xiao, Cui'e] Cent S Univ, Sch Math Sci & Comp Technol, Changsha 410075, Hunan, Peoples R China.;[Liu, Zhenhai] Guangxi Univ Nationalities, Sch Math & Comp Sci, Nanning 530006, Peoples R China.;[Xiao, Cui'e] Hunan City Univ, Dept Math & Computat Sci, Yiyang 413000, Peoples R China.
通讯机构：
[Liu, Zhenhai] G;Guangxi Univ Nationalities, Sch Math & Comp Sci, Nanning 530006, Peoples R China.
关键词：
Elliptic hemivariational inequality;Inverse coefficient problem;Existence of quasisolution
摘要：
This paper is devoted to a class of inverse coefficient problems for nonlinear elliptic hemivariational inequalities. The unknown coefficient of elliptic hemivariational inequalities depends on the gradient of the solution and belongs to a set of admissible coefficients. It is shown that the nonlinear elliptic hemivariational inequalities are uniquely solvable for the given class of coefficients. The result of existence of quasisolutions of the inverse problems is obtained.
作者机构：
[Qi, Liqun] Hong Kong Polytech Univ, Dept Appl Math, Kowloon, Hong Kong, Peoples R China.;[Wang, Fei] Hunan City Univ, Dept Math, Yiyang, Hunan, Peoples R China.;[Wang, Yiju] Qufu Normal Univ, Sch Operat Res & Management Sci, Rizhao 276800, Shandong, Peoples R China.
通讯机构：
[Qi, Liqun] H;Hong Kong Polytech Univ, Dept Appl Math, Kowloon, Hong Kong, Peoples R China.
摘要：
As a global polynomial optimization problem, the best rank-one approximation to higher order tensors has extensive engineering and statistical applications. Different from traditional optimization solution methods, in this paper, we propose some Z-eigenvalue methods for solving this problem. We first propose a direct Z-eigenvalue method for this problem when the dimension is two. In multidimensional case, by a conventional descent optimization method, we may find a local minimizer of this problem. Then, by using orthogonal transformations, we convert the underlying supersymmetric tensor to a pseudo-canonical form, which has the same E-eigenvalues and some zero entries. Based upon these, we propose a direct orthogonal transformation Z-eigenvalue method for this problem in the case of order three and dimension three. In the case of order three and higher dimension, we propose a heuristic orthogonal transformation Z-eigenvalue method by improving the local minimum with the lower-dimensional Z-eigenvalue methods, and a heuristic cross-hill Z-eigenvalue method by using the two-dimensional Z-eigenvalue method to find more local minimizers. Numerical experiments show that our methods are efficient and promising.
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.
期刊：
PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY,2008年51(2):407-419 ISSN：0013-0915
通讯作者：
Liu, Zhenhai
作者机构：
[Liu, Zhenhai] Cent S Univ, Dept Math, Changsha 410075, Hunan, Peoples R China.;[Liu, Guifang] Hunan City Univ, Dept Math, Yiyang 413049, Hunan, Peoples R China.
通讯机构：
[Liu, Zhenhai] C;Cent S Univ, Dept Math, Changsha 410075, Hunan, Peoples R China.
关键词：
Primary 35B34;47J20;49J40;65N25;elliptic hemivariational inequality;generalized Clarke subdifferential;pseudo-monotone operator;existence of solutions
摘要：
This paper is devoted to the Dirichlet problem for quasilinear elliptic hemivariational inequalities at resonance as well as at non-resonance. Using Clarke's notion of the generalized gradient and the property of the first eigenfunction, we also build a Landesman-Lazer theory in the non-smooth framework of quasilinear elliptic hemivariational inequalities.
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.
