A characteristic p analogue of plt singularities and adjoint by Takagi S.

By Takagi S.

We introduce a brand new version of tight closure and provides an interpretation of adjoint beliefs through this tight closure. As a corollary, we end up log pair (X, Δ) is plt if and provided that the modulo p relief of (X, Δ) is divisorially F-regular for all huge p ≫ zero. the following, divisorially F-regular pairs are a category of singularities in optimistic attribute brought by way of Hara and Watanabe (J Algebra Geom 11:363-392, 2002) when it comes to Frobenius splitting.

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For others, fragmentation is a harbinger of social polarization as the former mass audience is balkanized into isolated groups. It’s the prospect of balkanization that underlies some of the more dire predictions about digital media. In chapter 5, we’ll look at the “hard evidence”76 on audience behavior to assess the veracity these predictions. We’ll see that the growth in digital media outlets, each fighting for public attention, has indeed fragmented audiences across an ever-increasing number of outlets.

People who watch one crime drama tend to watch others. People who choose one situation comedy tend to choose others. 29 But these aren’t particularly powerful effects that suggest people have strong genre loyalties. Social media users also show some evidence of genre preferences. 30 Although that same study showed that an interest in other types of news—local, national, and international— was unrelated to Twitter adoption. There are many reasons why genre preferences might not be evident in actual program choices,31 but two are relevant here.

108 Elite influentials have some power to promote a message. A recommendation from Oprah or some other celebrity can certainly affect what people pay attention to. However, in these cases, it’s difficult to disentangle effects of opinion leadership from the influencer’s visibility in more traditional mass media. 110 But no one seems to do it with any regularity. ”112 But focusing on opinion leaders and the structure of social networks doesn’t tell us how the quality of the message itself affects the likelihood of a cascade.

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