A simple proof is presented for the min-max theorem of Lovv asz on cacti. Instead of using the result of Lovv asz on matroid parity, we shall apply twice the (conceptionally simpler) matroid intersection theorem.

Just as the Bernstein basis and Be Âzier points give us tools to manipulate polynomials, the Poisson basis and control points provide a new framework for investigating analytic functions. Using the Poisson representation, two different subdivision algorithms for analytic functions can be derived as extensions of the Be Âzier polynomial subdivision algorithm. The ®rst procedure generates an appr...

Weighted finite-state machines with n tapes describe n-ary rational string relations. The join n-ary relation is very important regarding to applications. It is shown how to compute it via a more simple operation, the auto-intersection. Join and auto-intersection generally do not preserve rationality. We define a class of triples 〈A, i, j〉 such that the auto-intersection of the machine A w.r.t....

The outline analyzes the principal difficulties, which emerge at the applying of the modern quantum theory based on the Copenhagen School concept to phenomena developed in the range close to 10 cm (the point of intersection of the three fundamental interactions). It is shown that at this scale, the interaction of a moving particle with space plays an essential role and just space assigns wave a...

Let B be a finite collection of geometric (not necessarily convex) bodies in the plane. Clearly, this class of geometric objects naturally generalizes the class of disks, lines, ellipsoids, and even convex polygons. We consider geometric intersection graphs GB where each body of the collection B is represented by a vertex, and two vertices of GB are adjacent if the intersection of the correspon...

Our contribution is twofold. Firstly, for a system of uncertain linear equations where the uncertainties are column-wise and reside in general convex sets, we show that the intersection of the set of possible solutions and any orthant is convex. We derive a convex representation of this intersection. Secondly, to obtain centered solutions for systems of uncertain linear equations, we compute th...

The intersection between objects relates to a class of problems where either precise intersection is required or imprecise intersection is acceptable. The calculation of intersection between two 2D/3D objects is a computation-intensive process. For qualitative spatio-temporal reasoning, it is sufficient to know the existence of intersection instead of the precise intersection. In order to ident...

Molecular fragmentation into three products poses an analytical challenge to theory and experiment alike. We used translational spectroscopy and high-level ab initio calculations to explore the highly debated three-body dissociation of sym-triazine to three hydrogen cyanide molecules. Dissociation was induced by charge exchange between the sym-triazine radical cation and cesium. Calculated stat...

The question of how government agencies can acquire actionable, useful information about legitimate but unknown targets without intruding upon the electronic activity of innocent parties is extremely important. We address this question by providing experimental evidence that actionable, useful information can indeed be obtained in a manner that preserves the privacy of innocent parties and that...