Bike and Integrals · [Jun 19, 05:49 AM]
My good friend tells me that it is hard for her to see why so many small bad things happen to me all the time while seemingly those around me seem to get all of their things fixed and made better all the time when they are around me? Perhaps I am a Karma machine of the second type?
Last week, I borrowed Lorenza’s bike [that’s Professor Viola] to use and get used to for going around in the incredibly small yet hilly town of Hanover. I had it aired and nice and took it for a couple of rides but realized that I needed a seat cushion. So I ordered a seat cushion and a bike lube from amazon and voila... when they arrived in mail my front bike tire is magically punctured! [I won’t mention the IRS, my house catching fire, etc.]
Now I am stuck with one problem to solve, for which I also offer a prize:
Suppose a function $\theta(t)$ has finite derivative and $\theta(0)=0$. I also know that \[\int_0^T e^{-i\theta(t)}dt=0\] and \[\int_0^T t e^{-i\theta(t)}dt=0.\] I need to show that somehow, $\theta(T)=0$ or something similar. Any hint will get you an acknowledgment in an upcoming paper. Direct solutions might land you a third author sweet spot on it. Or you could reverse engineer this puzzle to write the paper yourself!
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