A study of shock impacts and vibration dose values onboard highspeed marine craft

The shocks and impacts encountered on small high-speed craft exceed the limits set for safe working practice according to current standards. European legislation regarding the exposure to vibration will have far reaching effects on the operators of such craft with respect to the safety of their employees. This paper sets out to highlight the vibration dose values that can be expected during typical transits onboard high-speed craft and attempts to clarify some of the controversy currently surrounding vibration dose measurement in such circumstances. In order to relate vibration dosage to the impacts encountered and to boat motion, an algorithm was developed that identifies the timing and magnitude of impacts

Waveforms for Gravitational Radiation from Cosmic String Loops

We obtain general formulae for the plus- and cross- polarized waveforms of gravitational radiation emitted by a cosmic string loop in transverse, traceless (synchronous, harmonic) gauge. These equations are then specialized to the case of piecewise linear loops, and it is shown that the general waveform for such a loop is a piecewise linear function. We give several simple examples of the waveforms from such loops. We also discuss the relation between the gravitational radiation by a smooth loop and by a piecewise linear approximation to it.Comment: 16 pages, 6 figures, Revte

Dense H-free graphs are almost (Χ(H)-1)-partite

By using the Szemeredi Regularity Lemma, Alon and Sudakov recently extended the classical Andrasfai-Erdos-Sos theorem to cover general graphs. We prove, without using the Regularity Lemma, that the following stronger statement is true. Given any (r+1)-partite graph H whose smallest part has t vertices, there exists a constant C such that for any given ε>0 and sufficiently large n the following is true. Whenever G is an n-vertex graph with minimum degree δ(G)≥(1 − 3/3r−1 + ε)n, either G contains H, or we can delete f(n,H)≤Cn2−1/t edges from G to obtain an r-partite graph. Further, we are able to determine the correct order of magnitude of f(n,H) in terms of the Zarankiewicz extremal function