Finite element derivative superconvergent points for the Poisson equation under local rectangular mesh (in the two dimensional case) and local brick mesh (in the three dimensional situation) are investigated. All superconvergent points for the finite element space of any order that is contained in the tensor-product space and contains the intermediate family can be predicted. In case of the ser...

The construction presented in this paper can be briefly described as follows: starting from any “finite-dimensional” Markov transition function pt, on a measurable state space (E,B), we construct a strong Markov process on a certain “intrinsic” state space that is, in fact, a closed subset of a finite dimensional Euclidean space R. Of course we must explain the meaning of finite-dimensionality ...

We prove that a locally finite dimensional shift-invariant linear space of distributions must be a linear subspace of some shift-invariant space generated by finitely many compactly supported distributions. If the locally finite dimensional shift-invariant space is a subspace of the Hölder continuous space C or the fractional Sobolev space L , then the superspace can be chosen to be C or L , re...

A classical linear programming approach to optimization of flow or transportation in a discrete graph is extended to hybrid systems. The problem is finite dimensional if the state space is discrete and finite, but becomes infinite dimensional for a continuous or hybrid state space. It is shown how strict lower bounds on the optimal loss function can be computed by gridding the continuous state ...