Extension of weakly and strongly F-regular rings by flat maps

Let (R,m) -> (S,n) be a flat local homomorphism of excellent local rings. We investigate the conditions under which the weak or strong F-regularity of R passes to S. We show that is suffices that the closed fiber S/mS be Gorenstein and either F-finite (if R and S have a common test element), or F-rational (otherwise)

The vanishing of Tor_1^R(R^+,k) implies that R is regular

Let (R,m,k) be an excellent local ring of positive prime characteristic. We show that if Tor_1^R(R^+,k) = 0 then R is regular. This improves a result of Schoutens, in which the additional hypothesis that R was an isolated singularity was required for the proof.Comment: 3 pages, to appear in Proceedings of the AM

Representational momentum and the human face : an empirical note

Recent evidence suggests that observers may anticipate the future emotional state of an actor when viewing dynamic expressions of emotion, consistent with the notion of representational momentum. The current paper presents data that conflicts with these previous studies, finding instead that memory for the final frame of an emotional video tends to be shifted back in the direction of the first frame. While simple methodological issues may explain this difference (e.g., the use of morph sequences in previous studies versus naturalistic expressions here) a more theoretically interesting possibility is also considered. Specifically, recent studies of ensemble representations have shown that observes can rapidly extract the average expression from a display of up to 20 faces. It is suggested that the need to predict versus the need to maintain a stable estimate of the current state often compete when we interact with dynamic stimuli. Our memory for the final expression on an emotional face may be particularly sensitive to task demands and response timing, thus coming to reflect different solutions to this anticipation-averaging conflict depending on the precise experimental scenario.peer-reviewe

The Gettier Problem

In this chapter, we will explore the luck at issue in Gettier-styled counterexamples and the subsequent problem it poses to any viable reductive analysis of knowledge. In the 1st section, we will consider the specific species of luck that is at issue in Gettier counterexamples, then, in the next section, I will briefly sketch a diagnosis of the Gettier Problem and try to explain why the relevant species of luck has proven to be extremely difficult to avoid. And finally, I will consider a prominent objection to the proposed diagnosis of the Problem