let $k$ be a positive integer. a subset $s$ of $v(g)$ in a graph $g$ is a $k$-tuple total dominating set of $g$ if every vertex of $g$ has at least $k$ neighbors in $s$. the $k$-tuple total domination number $gamma _{times k,t}(g)$ of $g$ is the minimum cardinality of a $k$-tuple total dominating set of $g$. if$v(g)=v^{0}={v_{1}^{0},v_{2}^{0},ldots ,v_{n}^{0}}$ and $e(g)=e_{0}$, then for any in...

Multiresolution methods for representing data at multiple levels of detail are widely used for large-scale twoand three-dimensional data sets. We present a four-dimensional multiresolution approach for time-varying volume data. This approach supports a hierarchy with spatial and temporal scalability. The hierarchical data organization is based on subdivision. The -subdivision scheme only double...

Due to their simplicity and flexibility, polygonal meshes are about to become the standard representation for surface geometry in computer graphics applications. Some algorithms in the context of multiresolution representation and modeling can be performed much more efficiently and robustly if the underlying surface tesselations have the special subdivision connectivity. In this paper, we propo...

In this paper we present a new framework, based on subdivision surface approximation, for efficient compression and coding of 3D models represented by polygonal meshes. Our algorithm fits the input 3D model with a piecewise smooth subdivision surface represented by a coarse control polyhedron, near optimal in terms of control points number and connectivity. Our algorithm, which remains independ...

In this paper we present a new framework, based on subdivision surface fitting, for high rate compression and coding of 3D models. Our algorithm fits the input 3D model, represented by a polygonal mesh, with a piecewise smooth subdivision surface represented by a coarse control polyhedron. Our fitting scheme, particularly suited for meshes issued from mechanical or CAD parts, aims at getting cl...

Space partitioning techniques are well known especially because of their use in computer graphics, especially within ray-tracing acceleration techniques. The primary aim of those techniques is to enable fast test whether a geometric object resides at least partially within the given area. There are many modifications that proved the applicability despite of high memory requirements of complexit...

In 1985, Mader conjectured the existence of a function f such that every digraph with minimum out-degree at least f(k) contains a subdivision of the transitive tournament of order k. This conjecture is still completely open, as the existence of f(5) remains unknown. In this paper, we show that if D is an oriented path, or an in-arborescence (i.e., a tree with all edges oriented towards the root...

Since 2004 the European Directive 2001/20/EC concerning the implementation of good clinical practice in the conduct of clinical trials on medicinal products has become operative in Italy (Decreto legislativo 24 giugno 2003, n. 211). It is therefore the intention of the Ministry of Health to obtain through an intelligent application of the recent national decree clear indications on how to condu...