Bimodal spectrum wave conditions, known as crossing seas, can produce extreme waves which are hostile to humans during oceanic activities. This study reports some new findings of the probability in deep random seas response variation spectral bandwidth through fully non-linear numerical simulations. Two issues addressed, namely (i) impacts on changes statistics, i.e., kurtosis and crest exceeda...

5 Given n red and n blue points in general position in the plane, it is well-known 6 that there is a perfect matching formed by non-crossing line segments. We charac-7 terize the bichromatic point sets which admit exactly one non-crossing matching. 8 We give several geometric descriptions of such sets, and find an O(n log n) algorithm 9 that checks whether a given bichromatic set has this prope...

Consider a bipartite graph; letÕs suppose we draw the origin nodes and the destination nodes arranged in two columns, and the edges as straight line segments. A non crossing matching is a subset of edges such that no two of them intersect. Several algorithms for the problem of finding the non crossing matching of maximum cardinality are proposed. Moreover an extension to weighted graphs is cons...

The graph theoretic problem of crossing numbers has been around for over 60 years, but still very little is known about this simple, yet intricate nonplanarity measure. The question is easy to state: Given a graph, draw it in the plane with the minimum number of edge crossings. A lot of research has been devoted to giving an answer to this question, not only by graph theoreticians, but also by ...

We study bijections { Set partitions of type X } −̃→ { Set partitions of type X } for X ∈ {A,B,C,D}, which preserve openers and closers. In types A, B, and C, they interchange • either the number of crossings and of nestings, • or the cardinalities of a maximal crossing and of a maximal nesting. In type D, the results are obtained only in the case of non-crossing and nonnesting set partitions. I...

The expected value for the weighted crossing number of a randomly weighted graph is studied. A variation of the Crossing Lemma for expectations is proved. We focus on the case where the edge-weights are independent random variables that are uniformly distributed on [0, 1].

When patients with left-sided neglect are asked to bisect horizontal lines, they tend to place their marks to the right of the line's objective mid-point. However, when asked to bisect short lines they are either more accurate or paradoxically cross over and place their marks to the left of the objective mid-point. Previous explanations of the cross over phenomenon have considered specific aber...

There is a considerable interest in the possibility of crossing over autologous and directed donor blood to other patients. The practicality and safety of this approach depends on the possibility of disease transmission in these groups versus those of the usual homologous donors. A review of the current literature as to the incidence of infectious disease markers shows that the total number of ...