Here a complication arises that does not have mean close to zero, and one has to subtract off some suitable approximant to before one would expect good Gowers norms bounds. For the prime number theorem one can just use the approximant , giving but even for the prime number theorem in ...
Theorem 1 There does not exist any algorithm which, given a dimension , a periodic subset of , and a finite subset of , determines in finite time whether there is a translational tiling of by . The caveat is that we have to work with periodic subsets of , rather than all of ; we ...
a收入分配差距不断拉大,贫富悬殊加剧,社会矛盾在聚集,在深化。 The division of income disparity enlarges unceasingly, the polarization of the rich and the poor intensifies, the society contradictory is gathering, is deepening.[translate] ai don't know what's your mean 我不知道什么是您的手段[transl...
called general relativity, that would describe wormholes with somewhat different properties. For instance, one of the big distinctions in the types of wormholes that are described are whether or not they are traversable — by that I mean, whether you can go from one end to another. ...
Today, continual is the more likely of the two to mean “recurring,” but it also continues to be used, as it has been since the 14th century, with the meaning “continuing without interruption.” The words’ relative frequencies over the last two hundred years are shown in a curve from...
You'll notice a staggering difference between the Qantas Frequent Flyer and AAdvantage rates, though it's worth noting that AA miles can't be redeemed for travel in the premium economy cabin. Click on the table below to enlarge the image. ...
Superstars such as Madonna, Sir Elton John and Stevie Wonder performed in order to highlight (强调) international poverty and debt.小题1:What does the author mean by saying “the Glastonbury Festival has gone from strength to strength”? A.The festival has achieved growing success. B.Great ...
However, if one adds the additional operation of order to the reals, giving it the language of an ordered field rather than just a field, then quantifier elimination is recovered (the class of quantifier-free definable sets now enlarges to match the class of definable sets, which in this ...
However, this weaker result already suffices for many applications, and does not need any result as deep as the mean value theorem. Proof: To simplify notation we allow implied constants to depend on . As before, we may assume that for some small constant depending only on . We may also...
However, if one adds the additional operation of order to the reals, giving it the language of an ordered field rather than just a field, then quantifier elimination is recovered (the class of quantifier-free definable sets now enlarges to match the class of definable sets, which in this ...