Problem 8 To refine the results in Chapter 4, and to prove that f_\alpha(x)=\sum_{n=0}^{\infty}2^{-n\alpha}e^{2\pi i 2^n x}\\is nowhere differentiable even in the case \alpha = 1, we need to consider a variant of the delayed means \Delta_N, which in turn will be ...
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Today I hear every language as if it were the only one, and when I hear of one that is dying, it overwhelms me as though it were the death of the Earth. - Elias Canetti When I use a word [...] it means just what I choose it to mean – neither more nor less. - Humpty ...
As part of our project, we carried out asurvey of people in the street, and the thing that came up over and over againis that people don't think it's easy enough to recycle theirwaste. One problem is that there aren't enoughdrop- out sites, that is, the places where the public ...
Human rights should not be used as a pretext to suppress other countries. The US should immediately stop and redress its erroneous approach of politicizing and weaponizing human rights and applying double standard, and immediately lift all illegal unilateral sanctions and embargo on countries like Cub...
Samuel's photographs became a lasting tribute, an artistictransportation[5] of Victoria Foil's legacy into the hearts and minds of the city's inhabitants. They served as a reminder that history is not just a collection of facts but a tapestry of individual stories that shape the present. ...
Total cell counts were recorded as the sum of cell counts from the bottom of the upper and lower chambers. The cell migration index was calculated as the total area of migrating cells in the upper and lower chambers of the corresponding group divided by that of the WT CM group. Plasmid ...
If we can do as mentioned above, there can be no doubt (that)从句 例:如果我们能做到如上所述,毫无疑问地,我们就能精通英语。 If we can do as mentioned above, there can be no doubt that we can master English. 49. 因此,这就是…的原因。 Thus, this is the reason why .. 例:因此,这...
To understand the two proofs, I wrote them out using subscript notation and sum/product notation. It would be a useful exercise to try to really understand the proofs without using any modern notation. The right notation takes care of a lot for us, which we would otherwise have to k...