A jump system is a set of lattice points satisfying a certain exchange axiom. This notion was introduced by Bouchet and Cunningham 2], as a common generalization of (among others) the sets of bases of a matroid and degree sequences of subgraphs of a graph. We prove, under additional assumptions, a min-max formula for the distance of a lattice point from a jump system. The conditions are met in ...

We develop wavelet methods for the multiresolution representation of parametric curves and surfaces. To support the representation, we construct a new family of compactly supported symmetric biorthogonal wavelets with interpolating scaling functions. The wavelets in these biorthogonal pairs have properties better suited for curves and surfaces than many commonly used lters. We also give example...

This paper proposes a simple intersection algorithm for two sorted integer sequences . Our algorithm is designed based on x-fast trie since it provides efficient find and successor operators. We present that our algorithm outperforms skip list based algorithm when one of the sets to be intersected is relatively ‘dense’ while the other one is (relatively) ‘sparse’. Finally, we propose some possi...

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...

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...

ARTICLE INFO ______________________________________________________________ ______________________ Introduction: The study was aimed to assess the presence of actual differences between the objective and the perceived magnitude of a curvature between patients affected by Peyronie’s disease (PD) and congenital penile curvature (CPC). Materials and Methods: Wee analysed a cohort of 88 consecutive...