Earth scientists have been concerned with the problem of disposal of radioactive wastes since 1955 when the National .Academy of Sciences gathered 65 scientists in Princeton, N.J., to consider the geological, biological, physical, and chemical aspects of waste containment. Investigations during the 1950's and early 1960's examined the feasibility of disposal of liquid high-level wastes in deep geologic basins and in salt mines. Scientists since then, sponsored largely by the U.S. Atomic Energy Commission and later by the U.S. Energy Research and Development Administration, carefully considered salt deposits as a repository for solidified high-level wastes. Within the past few years, in response to growing pressures for a resolution of the problem of disposing of the wastes, earth scientists at various universities and government laboratories, as well as at the U.S. Geological Survey (USGS), also began an intensive examination of the problem. As a result of this expanded examination, modified concepts of geologic disposal have evolved, and aspects of some older concepts have been questioned. Some of these changes in outlook and philosophy as perceived by USGS scientists are described in this Circular. Because the authors are confident that acceptable geologic repositories can be constructed, this paper should not be construed as an attempt to discredit the concept of geologic containment or the work done in the 1960's and early 1970's. However, the earth-science problems associated with disposal of radioactive wastes are not simple, nor are they completely understood. The many weaknesses in geologic knowledge noted in this report warrant a conservative approach to the development of geologic repositories in any medium. Increased participation in this problem by earth scientists of various disciplines appears necessary before final decisions are made to use repositories. Basic philosophical, as well as technological, issues remain to be resolved.

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We provide results on the smoothness of normalisers in connected reductive algebraic groups G over fields k of positive characteristic p. Specifically we we give bounds on p which guarantee that normalisers of subalgebras of g in G are smooth, i.e. so that the Lie algebras of these normalisers coincide with the infinitesimal normalisers.One of our main tools is to exploit cohomology vanishing of small dimensional modules. Along the way, we obtain complete reducibility results for small dimensional modules in the spirit of similar results due to Jantzen, Guralnick, Serre and Bendel-Nakano-Pillen.

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