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We examine recent claims for a considerable amount of leptogenesis, in some inflationary scenarios, through the gravitational anomaly in the lepton number current. We find that when the short distances contributions are properly included the amount of lepton number generated is actually much smaller.

We analyze the reduction to four dimensions of the R 4 terms which are part of the ten-dimensional string effective actions, both at tree level and one loop. We show that there are two independent combinations of R 4 present, at one loop, in the type IIA four dimensional effective action, which means they both have their origin in M-theory. The d = 4 heterotic effective action also has such terms. This contradicts the common belief that there is only one R 4 term in four-dimensional supergravity theories, given by the square of the Bel-Robinson tensor. In pure N = 1 supergravity this new R 4 combination cannot be directly supersymmetrized, but we show that, when coupled to a scalar chiral multiplet (violating the U(1) R-symmetry), it emerges in the action after elimination of the auxiliary fields.

To understand plasma phenomena which will occur in a wall-confined, shock-heated fusion system, experiments and computer simulations have been carried out. The thermonuclear fusion cycle, energy transfer from a 6 > 1 hot plasma to a wall, plasma confinement by means of walls and a magnetic dam, and some new strong shock wave physics results are described and reviewed.

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