A map on the space of rational functions

We describe dynamical properties of a map $\mathfrak{F}$ defined on the space of rational functions. The fixed points of $\mathfrak{F}$ are classified and the long time behavior of a subclass is described in terms of Eulerian polynomials

Production mechanisms and single-spin asymmetry for kaons in high energy hadron-hadron collisions

Direct consequences on kaon production of the picture proposed in a recent Letter and subsequent publications are discussed. Further evidence supporting the proposed picture is obtained. Comparison with the data for the inclusive cross sections in unpolarized reactions is made. Quantitative results for the left-right asymmetry in single-spin processes are presented.Comment: 10 pages, 2 Postscript figure

\bar u - \bar d asymmetry - a few remarks

We make a few remarks on possible sources of uncertainties of the $\bar d - \bar u$ asymmetry obtained by different methods and comment on its possible verification in the future. In addition we comment on its present understanding.Comment: 3 pages, a talk at the 7th International Workshop on Deep Inelastic Scattering and QCD (DIS99), Zeuthen, April 199

Characterization of the Vertices and Extreme Directions of the Negative Cycles Polyhedron and Hardness of Generating Vertices of 0/1-Polyhedra

Given a graph $G=(V,E)$ and a weight function on the edges w:E\mapsto\RR, we consider the polyhedron $P(G,w)$ of negative-weight flows on $G$, and get a complete characterization of the vertices and extreme directions of $P(G,w)$. As a corollary, we show that, unless $P=NP$, there is no output polynomial-time algorithm to generate all the vertices of a 0/1-polyhedron. This strengthens the NP-hardness result of Khachiyan et al. (2006) for non 0/1-polyhedra, and comes in contrast with the polynomiality of vertex enumeration for 0/1-polytopes \cite{BL98} [Bussieck and L\"ubbecke (1998)]

A Map on the Space of Rational Functions

We describe dynamical properties of a map defined on the space of rational functions. The fixed points of F are classified and the long time behavior of a subclass is described in terms of Eulerian polynomials

Implementation status of mandatory inspection of sprayers in Romania

To harmonize the Romanian legislation on plant protection to the European legislation the Directive 128/2009 has been transposed into national legislation by Government Emergency Ordinance 34/2012 on establishing the institutional framework for action to the sustainable use of pesticides in Romania.National Action Plan approved by Decision 683/2013, on reducing the risks associated with the use of plant protection products is the strategic document regarding the continuous improvement of the use of plant protection products and contains quantitative targets, measures and timetables to reduce risks and the effects of using plant protection products on the environment and human health

An Efficient Implementation of a Quasi-polynomial Algorithm for Generating Hypergraph Transversals

Given a finite set V, and a hypergraph , the hypergraph transversal problem calls for enumerating all minimal hitting sets (transversals) for . This problem plays an important role in practical applications as many other problems were shown to be polynomially equivalent to it. Fredman and Khachiyan (1996) gave an incremental quasi-polynomial time algorithm for solving the hypergraph transversal problem [9]. In this paper, we present an efficient implementation of this algorithm. While we show that our implementation achieves the same bound on the running time as in [9], practical experience with this implementation shows that it can be substantially faster. We also show that a slight modification of the algorithm in [9] can be used to give a stronger bound on the running time