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...

The growing size of the multiprocessor system increases its vulnerability to component failures. It is crucial to locate and to replace the faulty processors to maintain a system’s high reliability. The fault diagnosis is the process of identifying faulty processors in a system through testing. In this paper, we show that the largest connected component of the survival graph contains almost all...

We study the Optimal Linear Arrangement (OLA) problem of Halin graphs, one of the simplest classes of non-outerplanar graphs. We present several properties of OLA of general Halin graphs. We prove a lower bound on the cost of OLA of any Halin graph, and define classes of Halin graphs for which the cost of OLA matches this lower bound. We show for these classes of Halin graphs, OLA can be comput...