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Some comparison theorems for the spectral radius of double splittings of different matrices under suitable conditions are presented, which are superior to the corresponding results in the recent paper by Miao and Zheng (2009). Some comparison theorems between the spectral radius of single and double splittings of matrices are established and are applied to the Jacobi and Gauss-Seidel double SOR method. [ABSTRACT FROM AUTHOR]

Consider the surjective, continuous map ƒ : X → X and the continuous map f of K(X) induced by ƒ, where ƒ is a compact metric space and K(X) is the space of all nonempty compact subsets of ƒ endowed with the Hausdorff metric. In this paper, we give a short proof that if ƒ is Li-Yoke sensitive, then ƒ is Li-Yorke sensitive. Furthermore, we give an example showing that Li-Yorke sensitivity of ƒ does not imply Li-Yorke sensitivity of ƒ. [ABSTRACT FROM AUTHOR]

This paper concerns the regularity criterion of theweak solutions to the three-dimensional (3D) micropolar fluid equations in terms of the pressure. It is proved that if one of the partial derivatives of pressure satisfies ∂3 π ε Lp(0, T; Lq(R³)) with 2/p + 3/q ≤ 2, 3 < q < ∞,1 < p < ∞, then the weak solution of the micropolar fluid equations becomes regular on (0, T). [ABSTRACT FROM AUTHOR]

Rough set theory is an efficient and essential tool for dealing with vagueness and granularity in information systems. Coveringbased rough set theory is proposed as a significant generalization of classical rough sets. Matroid theory is a vital structure with high applicability and borrows extensively fromlinear algebra and graph theory. In this paper, one type of covering-based approximations is studied from the viewpoint of Eulerian matroids. First, we explore the circuits of an Eulerian matroid from the perspective of coverings. Second, this type of covering-based approximations is represented by the circuits of Eulerian matroids. Moreover, the conditions under which the covering-based upper approximation operator is the closure operator of a matroid are presented. Finally, a matroidal structure of covering-based rough sets is constructed. These results show many potential connections between covering-based rough sets and matroids. [ABSTRACT FROM AUTHOR]

The Exp-function method combined with F-expansion method is employed to investigate the K(m,n) equation with t-dependent coefficients. The solitary wave solutions and periodic wave solutions to the equation are constructed analytically under certain circumstances. The results presented in this paper improve the previous results. [ABSTRACT FROM AUTHOR]

We use the geometric notion of a differential system describing surfaces of a constant negative curvature and describe a family of pseudospherical surfaces for the KdV-Burgers-Kuramoto and nonlinear Schrödinger equations with constant Gaussian curvature -1. Travelling wave solutions for the above equations are obtained by using a sech-tanh method and Wu's elimination method. [ABSTRACT FROM AUTHOR]