ABSTRACT. In the article strongly nondegenerate (h, n)-quadrics all of whose linear automorphisms are of the form z ~ pz, to ~ I/~12,~, p E C \ {0} are considered. Quadrics all of whose linear automorphisms are of this form were called c-rigid by V. Beloshapka. The main result of the article is the following: any c-rigid strongly nondegenerate (h, n)-quadric has no nonlinear automorphisms. A table indicating the relationship between linear and nonlinear automorphisms for (h, n)-quedrics is presented.
We have carried out pseudopotential calculations of the effect of mixing in semiconductor superlattices between bulk states derived from the conduction band minimum at thecentreof the bulk Brillouinzoneand thoseoftheXminimaat thezone edges. Wepresent a systematic account of (i) the strength of this coupling in GaAh4I.4~ superlattices as a function of the layer widths, (ii) the variation as a function of layer width of the magnitude of the energy gap that occurs when the levels derived from different bulk valleys cross, (iii) the changeoftheoscillatorstrengthofthe transitionacross thesuperlattice gapasafunction of the separation of the interacting levels, and (iv) the magnitude of the effect of strain on valley mixing.
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