We analyze the space Sr m,m (T ) of bivariate functions that are piecewise polynomial of bi-degree 6 (m,m) and of smoothness r along the interior edges of a planar T-mesh T . We give new combinatorial lower and upper bounds for the dimension of this space by exploiting homological techniques. We relate this dimension to the weight of the maximal interior segments of the T-mesh, defined for an o...

In this paper we present a hybrid domain decomposition approach for the parallel solution of linear systems arising from a discontinuous Galerkin (DG) finite element approximation of initial boundary value problems. This approach allows a general decomposition of the space–time cylinder into finite elements, and is therefore applicable for adaptive refinements in space and time. 1 A Space–Time ...

We use Dirichlet form methods to construct and analyse a general class of reversible Markov processes with totally disconnected state spaces. We study in detail the special case of bipartiteMarkov chains. The latter processes have a state space consisting of an \interior" with a countable number of isolated points and a, typically uncountable, \boundary". The equilibrium measure assigns all of ...

We formalized the article “New concepts in the theory of topological space – supercondensed set, subcondensed set, and condensed set” by Yoshinori Isomichi [4]. First we defined supercondensed, subcondensed, and condensed sets and then gradually, defining other attributes such as regular open set or regular closed set, we formalized all the theorems and remarks that one can find in Isomichi’s a...

Schirmer proved that there is a class of smooth self-maps of the unit sphere in Euclidean n-space with the property that any smooth self-map of the unit ball that extends a map of that class must have at least one fixed point in the interior of the ball. We generalize Schirmer’s result by proving that a smooth self-map of Euclidean n-space that extends a self-map of the unit sphere of that clas...

“Habitat Interior Space Design” is a compulsory course for environmental design majors. Through this course, students can clarify the ideas and methods of living space scheme systematically master types, styles, ergonomics spaces; therefore, learning Habitat Design well requires to more basic principles practical projects. In paper, we will discuss significant changes that have occurred as resu...