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 contact is modeled by a general normal damped response condition and a friction law, which are nonmonotone, possibly multivalued and have the subdifferential form. 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.
关键词：
Root-square mean;arithmetic mean;Seiffert mean
摘要：
In this paper, we establish two new inequalities between the root-square, arithmetic, and Seiffert means. The achieved results are inspired by the paper of Seiffert (Die Wurzel, 29, 221-222, 1995), and the methods from Chu et al. (J. Math. Inequal., 4, 581-586, 2010). The inequalities we obtained improve the existing corresponding results and, in some sense, are optimal. Mathematics Subject Classification (2010): 26E60.
摘要：
The degree distance of a graph which is a degree analogue of the Wiener index of the graph. Let G = TUV C6[2p,q] be the carbon nanotubes covered by C6, formulas for calculating the degree distance of armchair polyhex nanotubes TUV C6[2p,q] are provided.
摘要：
Let G is a connected graph with vertex set V, then the eccentric connectivity index of G is defined as Σ v∈V(G) deg(v)ecc(v) where deg(v) is the degree of a vertex v and ecc(v) is its eccentricity. The nanostar dendrimer is part of a new group of macromolecules that appear to be photon funnels just like artificial antennas. We obtain exact formulas for calculating the eccentric connectivity index of dendrimer nanostars.
摘要：
Abstract: This paper is devoted to a class of inverse coefficient problems for a Parabolic Equation, We obtain an existence and uniqueness theorem of weak solutions. Using the theories of Schauder Fixed-Point Theorem, an existence theorem is established for the inverse coefficient problems solutions.#@#@#摘要: 研究了一类抛物型方程的反系数问题，利用变分方法获得了方程弱解的存在性与唯一性，利用Schauder不动点定理得到了反系数问题解的存在性。
期刊：
Ars Combinatoria,2011年102:161-172 ISSN：0381-7032
通讯作者：
Liu, W.
作者机构：
[Chen, S.] Department of Mathematics and Computer Science, Hunan City University, Yiyang, Hunan 413000, China;[Liu, W.] School of Sciences, Nantong University, Nantong, Jiangsu, 226007, China
通讯机构：
[Liu, W.] S;School of Sciences, , Nantong, Jiangsu, 226007, China
摘要：
The Merrifield-Simmons index of a graph G, denoted by i(G), is defined to be the total number of its independent sets, including the empty set. Let Θ(a1, a2, . . ., ak) denote the graph obtained by connecting two distinct vertices with k independent paths of lengths a1, a2, . . ., ak respectively, we named it as multi-bridge graphs for convenience. Tight upper and lower bounds for the Merrifield-Simmons index of Θ(a1, a2, . . ., a k) are established in this paper.
