CHANGES IN U.V. SURVIVAL CURVES OF ESCHERICHIA COLl B/r CONCOMITANT WITH CHANGES IN GROWTH CONDITIONS

Abstract— For E. coli B/r u.v.-irradiated while in logarithmic growth, the nature of the dose-response curve was strongly dependent on both pre- and post-irradiation conditions of growth. Survival curves for cells grown in nutrient medium, or minimal medium with glucose, and plated immediately after irradiation, demonstrated an initial insensitive or 'shoulder' region provided the plating medium was such that no derepression was required of operons controlling inducible enzyme systems. If, however, such derepression was called for, survival curves were of exponential form. Delay in plating resulted in the return of the survival curve to the shouldered form even when 'shift-down' media were used.
Of those cells grown before u.v.-irradiation in minimal media and plated thereafter with the same sugar as carbon source, only those grown with glucose (or lactose) demonstrated the shouldered survival curve.     

ASSOCIATED FORMS OF BINARY QUARTICS AND TERNARY CUBICS

Let \( {\mathcal{Q}}_n^d \) be the vector space of forms of degree d?≥?3 on ? ⁿ , with n?≥?2. The object of our study is the map Φ, introduced in earlier articles by M. Eastwood and the first two authors, that assigns every nondegenerate form in \( {\mathcal{Q}}_n^d \) the so-called associated form, which is an element of \( {{\mathcal{Q}}_n^d}^{\left(d-2\right)*} \). We focus on two cases: those of binary quartics (n?=?2, d?=?4) and ternary cubics (n?=?3, d?=?3). In these situations the map Φ induces a rational equivariant involution on the projective space ?\( \left({\mathcal{Q}}_n^d\right) \), which is in fact the only nontrivial rational equivariant involution on ?\( \left({\mathcal{Q}}_n^d\right) \). In particular, there exists an equivariant involution on the space of elliptic curves with nonvanishing j-invariant. In the present paper, we give a simple interpretation of this involution in terms of projective duality. Furthermore, we express it via classical contravariants.     

RECASTING RESULTS IN EQUIVARIANT GEOMETRY

Using the language of stacks, we recast and generalize a selection of results in equivariant geometry.