The Stokes operator is a differential-integral operator induced by the Stokes equations. In this paper, we analyze the Stokes operator from the point of view of the Helmholtz minimum dissipation principle. We show tha...The Stokes operator is a differential-integral operator induced by the Stokes equations. In this paper, we analyze the Stokes operator from the point of view of the Helmholtz minimum dissipation principle. We show that, through the Hodge orthogonal decomposition, a pair of bounded linear operators, a restriction operator and an extension operator, are induced from the divergence-free constraint. As a consequence, we use it to calculate the eigenvalues of the Stokes operator.展开更多
An open problem was proposed in [1](2.11.28): in induced spaces, can we express the interior (closure) of a fuzzy set A as the union of a family of fuzzy sets which take corresponding constant value on the interior (c...An open problem was proposed in [1](2.11.28): in induced spaces, can we express the interior (closure) of a fuzzy set A as the union of a family of fuzzy sets which take corresponding constant value on the interior (closure)of each level set of A?展开更多
This paper proposes a novel pair of induced IF covering approximation operators in an IF covering approximation space,and discusses some basic properties about definable IFSs.A measure is defined to describe the uncer...This paper proposes a novel pair of induced IF covering approximation operators in an IF covering approximation space,and discusses some basic properties about definable IFSs.A measure is defined to describe the uncertainty of IFSs in IF covering approximation spaces.Finally,we study the properties of reductions of an IF covering respectively based on induced IF covering approximation operators and IF covering approximation operators.展开更多
基金supported by the National Natural Science Foundation of China (No.10772103)the Shanghai Leading Academic Discipline Project (No.Y0103)
文摘The Stokes operator is a differential-integral operator induced by the Stokes equations. In this paper, we analyze the Stokes operator from the point of view of the Helmholtz minimum dissipation principle. We show that, through the Hodge orthogonal decomposition, a pair of bounded linear operators, a restriction operator and an extension operator, are induced from the divergence-free constraint. As a consequence, we use it to calculate the eigenvalues of the Stokes operator.
基金Project supported by the National Natural Science Foundation of China
文摘An open problem was proposed in [1](2.11.28): in induced spaces, can we express the interior (closure) of a fuzzy set A as the union of a family of fuzzy sets which take corresponding constant value on the interior (closure)of each level set of A?
基金supported by the National Natural Science Foundation of China(Nos.60773174 and 60963006)Hebei Province Science and Technology Research and Development Program(No.09276158).
文摘This paper proposes a novel pair of induced IF covering approximation operators in an IF covering approximation space,and discusses some basic properties about definable IFSs.A measure is defined to describe the uncertainty of IFSs in IF covering approximation spaces.Finally,we study the properties of reductions of an IF covering respectively based on induced IF covering approximation operators and IF covering approximation operators.
