In this paper we investigate the combinatorial complexity of an algorithm to determine the geometry and the topology related to an arrangement of hyperplanes in multi-dimensional Euclidean space from the “probing” on the arrangement. The “probing” by a flat means the operation from which we can obtain the intersection of the flat and the arrangement. For a finite set H of hyperplanes in Ed, we ...

In this article, we examine sets of lines in PG(d,F) meeting each hyperplane in a generator set of points. We prove that such a set has to contain at least b1.5dc lines if the field F has at least b1.5dc elements, and at least 2d− 1 lines if the field F is algebraically closed. We show that suitable 2d − 1 lines constitute such a set (if |F| > 2d − 1), proving that the lower bound is tight over...

drous Rochelle salt, and the third we tentatively suggest corresponds to solid complex. At all events, the tie-lines show no indication of running to the sodium hydroxide comer. For the reason previously given, it cannot be expected that the tie-lines should intersect in a point. The appearance of the solid phase a t this stage is remarkable. It swells in bulk so as to occupy almost the total v...

BACKGROUND The contour length of the circular chromosome of bacteria is greater than a millimeter but must be accommodated within a cell that is only a few micrometers in length. Bacteria do not have nucleosomes and little is known about the arrangement of the chromosome inside a prokaryotic cell. RESULTS We have investigated the arrangement of chromosomal DNA within the bacterium Bacillus su...