In the light of the recent Lin, Lunin, Maldacena (LLM) results, we investigate 1/2-BPS geometries in minimal (and next to minimal) supergravity in D = 6 dimensions. In the case of minimal supergravity, solutions are given by fibrations of a two-torus T 2 specified by two harmonic functions. For a rectangular torus the two functions are related by a non-linear equation with rare solutions: AdS 3 × S 3 , the pp-wave and the multicenter string. "Bubbling", i.e. superpositions of droplets, is accommodated by allowing the complex structure of the T 2 to vary over the base. The analysis is repeated in the presence of a tensor multiplet and similar conclusions are reached, with generic solutions describing D1D5 (or their dual fundamental string-momentum) systems. In this framework, the profile of the dual fundamental string-momentum system is identified with the boundaries of the droplets in a two-dimensional plane.
We give a new low-temperature expansion variable for the king model. Expansions in the new variable, x = 1 -tanh(J/kT), then converge right up to the critical point. Power series in the new variable are derived, and then analysed by the Pade method and the method of N-point fits. For the spontaneous magnetization of the Ising model in three dimensions, we obtain p = 0.312 f 0.002 for the simple cubic lattice, = 0.3125 f 0.0015 for the body-centred cubic lattice, and /l = 0.312 f 0.004 for the face-centred cubic lattice. For the low-temperature susceptibility we obtain y' = 1.30 f 0.02, y' = 1.28 k 0.04, and y' = 1.29 k 0.04 for the simple cubic, bodycentred cubic and face-centred cubic lattices respectively. For the low-temperature specific heat we estimate & < a' < 0.2 for all three laticces. We conclude that p = &, that y' = must be favoured over y' = 14, and that c(' rr 4 for all three-dimensional lattices.
Examples are giren of the behaviour over several jears of the working standards of inductance and capacitance maintained at the National Physical Laboratory. The information is supplementary .to that contained in previous papers.
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