Search

Bioproduction is unique in its heterogeneous growth, unsteady product value, and production-rate-dependent harvesting cost structure. This paper develops a stochastic model for the harvesting process of a bioproduction, uses it to optimize a tropical-fruit-production harvesting operation, and conducts a sensitivity analysis with respect to the parameters in the model.

A method has been developed by which the draft of tillage tools in any chosen soil and operating at any chosen velocity can be predicted by a single testing of a geometrically similar tool. Experimental results on side chisels are presented. Predicted draft generally is accurate to within 20% of actual prototype draft.

A group of 108 male adults was randomly subdivided into four experimental treatment groups in order to test the hypothesis that the treatments would affect their performance on a symbol substitution test (simple mental task). The treatments and the post treatment simple mental task were each administered for periods of ten minutes. An analysis of variance revealed no significant difference among the performance of the groups. However, strong trends in favor of the exercise and the rest groups over the classroom instruction and the immediate retest groups did develop.

Much current research is concerned with the fixed points of contractive mappings (mappings which shrink distance in some manner) from a metric space into itself. In this remark we shall point out that most mappings treated in the literature are very special in the sense that all these mappings satisfy a condition which is rather severe: every periodic point must necessarily be a fixed point.

In this paper, we study the semifree Z actions on homotopy sphere pairs. We show that in some cases the equivariant normal bundle to the fixed point set is equivariantly stably trivial. We compute the rank of the torsion free part of the group of semifree actions on homotopy sphere pairs in some cases. We also show that there exist infinitely many semifree Z4s actions on even dimensional homotopy sphere pairs. 0. Introduction. Let G be a compact Lie group. A differentiable group action of G on a differentiable manifold Mn is a homomorphism i/i: GDiff (M), where Diff (M) is the group of diffeomorphisms of M. Let Fk be the submanifold of fixed points. A group action is semifree if the only isotropy subgroups are the trivial subgroup and the group itself. Under these restrictions, the action is linear in some neighborhood of Fk in M' in the sense that there is an equivariant vector bundle v normal to Fk in M' such that the action restricts on each fiber of v to a linear automorphism. In this paper, we are only interested in the differentiable semifree actions on homotopy sphere pairs, namely, the actions on homotopy spheres such that the fixed point sets are homotopy spheres. The action G = S1 defines a complex structure on v (the action on v is just that induced by the complex multiplication). In [2], Browder proved that for a semifree S1 action on a homotopy sphere pair, the normal bundle of the fixed point set is stably trivial as a complex vector bundle. The first question which interests us is the following: Problem 1. Is it true that the equivariant normal bundle to the fixed point set of a semifree Zm action on a homotopy sphere pair is equivariantly stably trivial? If G = Sl or Zm, it is known (see [2], [6]) that there are infinitely many semifree G actions on odd dimensional homotopy sphere pairs. As to semifree S1 actions on even dimensional homotopy sphere pairs, there are only finitely many [3]. Received by the editors February 22, 1974 and, in revised form, July 9, 1974. AMS (MOS) subject classifications (1970). Primary 57E25, 57E30.