Geophysical and television logging trials in horizontal boreholes for probing ahead of tunnels

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E11 must be a symmetry of strings and branes

We construct the non-linear realisation of the semi-direct product of E11 and its vector representation in five and eleven dimensions and find the dynamical equations it predicts at low levels. Restricting these results to contain only the usual fields of supergravity and the generalised space-time to be the usual space-time we find the equations of motion of the five and eleven dimensional maximal supergravity theories. Since this non-linear realisation contains effects that are beyond the supergravity approximation and are thought to be present in an underlying theory we conclude that the low energy effective action of string and branes must possess an E11 symmetry.Comment: 17 pages, The eleven dimensional results are given in more detail and are shown to be uniquely determined. Typographical and transcription errors are also correcte

Generalised vielbeins and non-linear realisations

We briefly review why the non-linear realisation of the semi-direct product of a group with one of its representations leads to a field theory defined on a generalised space-time equipped with a generalised vielbein. We give formulae, which only involve matrix multiplication, for the generalised vielbein, the Cartan forms and their transformations. We consider the generalised space-time introduced in 2003 in the context of the non-linear realisation of the semi-direct product of E(11) and its first fundamental representation. For this latter theory we give explicit expressions for the generalised vielbein up to and including the levels associated with the dual graviton in four, five and eleven dimensions and for the IIB theory in ten dimensions. We also compute the generalised vielbein, up to the analogous level, for the non-linear realisation of the semi-direct product of very extended SL(2) with its first fundamental representation, which is a theory associated with gravity in four dimensions.Comment: 42 page

The X-ray eclipse of OY Car resolved with XMM-Newton: X-ray emission from the polar regions of the white dwarf

We present the XMM-Newton X-ray eclipse lightcurve of the dwarf nova OY Car. The eclipse ingress and egress are well resolved for the first time in any dwarf nova placing strong constraints on the size and location of the X-ray emitting region. We find good fits to a simple linear eclipse model, giving ingress/egress durations of 30+/-3 sec. Remarkably this is shorter than the ingress/egress duration of the sharp eclipse in the optical as measured by Wood et al. (1989) and ascribed to the white dwarf (43+/-2 sec). We also find that the X-ray eclipse is narrower than the optical eclipse by 14+/-2 sec, which is precisely the difference required to align the second and third contact points of the X-ray and optical eclipses. We discuss these results and conclude that X-ray emission in OY Car most likely arises from the polar regions of the white dwarf. Our data were originally reported by Ramsay et al (2001), but they did not make a quantitative measurement of eclipse parameters. We have also corrected important timing anomalies present in the data available at that time.Comment: 6 pages, 5 figures; accepted for publication in MNRA

On hamiltonian colorings of block graphs

A hamiltonian coloring c of a graph G of order p is an assignment of colors to the vertices of G such that $D(u,v)+|c(u)-c(v)|\geq p-1$ for every two distinct vertices u and v of G, where D(u,v) denoted the detour distance between u and v. The value hc(c) of a hamiltonian coloring c is the maximum color assigned to a vertex of G. The hamiltonian chromatic number, denoted by hc(G), is the min{hc(c)} taken over all hamiltonian coloring c of G. In this paper, we present a lower bound for the hamiltonian chromatic number of block graphs and give a sufficient condition to achieve the lower bound. We characterize symmetric block graphs achieving this lower bound. We present two algorithms for optimal hamiltonian coloring of symmetric block graphs.Comment: 12 pages, 1 figure. A conference version appeared in the proceedings of WALCOM 201

Chiral Green's Functions in Superconformal Field Theory

By solving the Ward identities in a superconformal field theory we find the unique three-point Green's functions composed of chiral superfields for N = 1,2,3,4 supersymmetry. We show that the N=1 four-point function with R-charge equal to one is uniquely determined by the Ward identities up to the specification of four constants. We discuss why chiral Green's functions above three-points, with total R-charge greater than N, are not uniquely determined.Comment: 32 pages, no figures, LaTeX2e forma