The arrangement of a nite collection of geometric objects is the decomposition of the space into connected cells induced by them. We survey combinatorial and algorithmic properties of arrangements of arcs in the plane and of surface patches in higher dimensions. We present many applications of arrangements to problems in motion planning, visualization, range searching, molecular modeling, and g...

We extend the Billera–Ehrenborg–Readdy map between the intersection lattice and face lattice of a central hyperplane arrangement to affine and toric hyperplane arrangements. For toric arrangements, we also generalize Zaslavsky’s fundamental results on the number of regions. Résumé. Nous étendons l’opérateur de Billera–Ehrenborg–Readdy entre la trellis d’intersection et la trellis de faces d’un ...

conclusions the essential principles of health in iranian medicine were not only stated in quran, but also were emphasized. results six major classifications such as “life environment”, “food”, spiritual status”, “physical activity”, “sleeping and awaking”, “excretion and retention”, and four minor classifications such as” climates”, “seasons”, “sexual intercourse” and “menstruation” were adopt...

The four methods of illumination in the use of slit-lamp biomicroscopy of the anterior segment, described first by Vogt, are equally useful in the posterior part of the eye. Examination of the ocular fundus is more difficult. In particular, photography of the central and peripheral parts of the fundus demands additional technical arrangements if all the appearances of biomicroscopy are to be re...

In this paper we introduce polynomials associated with uniform oriented matroids whose coefficients enumerate cells in the corresponding arrangements. These polynomials are quite useful in the study of many enumeration problems of combinatorial geometry, such as counting faces of polytopes, counting Radon partitions, counting k-sets, and so forth. We also describe some striking equations relati...

for more than three decades healthcare decentralization has been promoted in developing countries as a way of improving the financing and delivery of public healthcare. decision autonomy under healthcare decentralization would determine the role and scope of responsibility of local authorities. jalal mohammed, nicola north, and toni ashton analyze decision autonomy within decentralized services...