Multilinear Calderón Zygmund operators on variable exponent Morrey spaces over domains

The boundedness of multilinear singular integrals of Calderón-Zygmund type on product of variable exponent Lebesgue spaces over both bounded and unbounded domains are obtained. Further more, the boundedness for this type multilinear operators on product of variable exponent Morrey spaces over domains is shown in the paper.     

Generalized graph entropies

This article deals with generalized entropies for graphs. These entropies result from applying information measures to a graph using various schemes for defining probability distributions over the elements (e.g., vertices) of the graph. We introduce a new class of generalized measures, develop their properties, compute the measures for selected graphs, and briefly discuss potential applications to classification and clustering problems. © 2011 Wiley Periodicals, Inc. Complexity, 17,45–50, 2011     

A two‐level finite element method for the stationary Navier‐Stokes equations based on a stabilized local projection

In this article, we propose a two‐level finite element method to analyze the approximate solutions of the stationary Navier‐Stokes equations based on a stabilized local projection. The local projection allows to circumvent the Babuska‐Brezzi condition by using equal‐order finite element pairs. The local projection can be used to stabilize high equal‐order finite element pairs. The proposed method combines the local projection stabilization method and the two‐level method under the assumption of the uniqueness condition. The two‐level method consists of solving a nonlinear equation on the coarse mesh and solving a linear equation on fine mesh. The nonlinear equation is solved by the one‐step Newtonian iteration method. In the rest of this article, we show the error analysis of the lowest equal‐order finite element pair and provide convergence rate of approximate solutions. Furthermore, the numerical illustrations coincide with the theoretical analysis expectations. From the view of computational time, the results show that the two‐level method is effective to solve the stationary Navier‐Stokes equations. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2011     

On distorted probabilities and m-separable fuzzy measures

Fuzzy measures are used in conjunction with fuzzy integrals for aggregation. Their role in the aggregation is to permit the user to express the importance of the information sources (either criteria or experts). Due to the fact that fuzzy measures are set functions, the definition of such measures requires the definition of 2ⁿ parameters, where n is the number of information sources. To make the definition easier, several families of fuzzy measures have been defined in the literature.In this paper m-separable fuzzy measures are introduced. We present some results on this type of measures and we relate them to some of the previous existing ones. We study generating functions for m-separable fuzzy measures and some properties related to these generating functions.     

QUASI-DIAGONALIZATION FOR A SINGULARLY PERTURBED DIFFERENTIAL SYSTEM WITH TWO PARAMETERS

By two successive linear transformations,a singularly perturbed differential system with two parameters is quasi-diagonalized. The method of variation of constants and the principle of contraction map are used to prove the existence of the transformations.     

Symmetry and Uniqueness of Solutions of an Integral System

In this paper, we study the positive solutions for a class of integral systems and prove that all the solutions are radially symmetric and monotonically decreasing about some point. Moreover, we also obtain the uniqueness result for a special case. We use a new type of moving plane method introduced by Chen-Li-Ou [1]. Our new ingredient is the use of Hardy-Littlewood-Sobolev inequality instead of Maximum Principle.     

Decay of Solutions to a 2D Schroedinger Equation

Let u ∈ C（1R, H1） be the solution to the initial value problem for a 2D semilinear Schr6dinger equation with exponential type nonlinearity, given in [1]. We prove that the Lr norms of u decay as t→±∞, provided that r〉2.     

Seiberg-Witten Like Monopole Equations on R5

We give an analogy of Seiberg-Witten monopole equations on flat Euclidian space R5. For this we used an irreducible representation of complex Clifford algebra Cl5. For the curvature equation we use a kind of self-duality notion of a 2-form on R5 which is given in [1].     

Global Strong Solutions for the Viscous,Micropolar, Compressible Flow

In this paper, we consider the viscous, micropolar, compressible flow in one dimension. We give the proof of existence and uniqueness of strong solutions for the initial boundary problem that vacuum can be allowed initially.     

Very Singular Similarity Solutions and Hermitian Spectral Theory for Semilinear Odd-order PDEs

Asymptotic large- and short-time behavior of solutions of the linear dispersion equation μt = Uxxx in IR× IR＋, and its （2k＋l）th-order extensions are studied. Such a refined scattering is based on a ＂Hermitian＂ spectral theory for a pair {B,B＊} of non self-adjoint rescaled operators