For each we introduce a time cutoff supported on that equals on and obeys the usual derivative estimates in between (the time derivative of size for each ). Later we will prove the truncation estimate Assuming this estimate, then if we set , then using Lemma 9 in my paper and (6), ...
(When mass equals that of the ground state, there is an explicit example, built using the pseudoconformal transformation, which shows that solutions can blow up in finite time.) In fact we can show a slightly stronger statement: for spherically symmetric focusing solutions with arbitrary mass, ...
When the atoms are traveling straight down through empty space by their own weight, at quite indeterminate times and places they swerve ever so little from their course, just so much that you can call it a change of direction. If it were not for this swerve, everything would fall downwards...
A pair of fair dice is thrown, what is the probability that the sum of the two numbers is greater than 10? What is the probability of getting a sum 9 from two throws of a dice? What is the probability of getting a sum of 9 from two throw...
Answer to: If you toss two dice and add the numbers facing up, what is the probability that the sum of the dice equals 5 or the sum of the dice is...
the of and to a in that is was he for it with as his on be at by i this had not are but from or have an they which one you were all her she there would their we him been has when who will no more if out so up said what its about than into them can only other time new...
on a popular book on astronomy tentatively entitled “Climbing the cosmic distance ladder“, which was initially based on a public lecture I have given on this topic for many years, but which we have found to be a far richer story than what I was aware of when I first gave those lecture...
is the “-analogue” of (a polynomial in that equals in the limit ). (The -analogues become more complicated for more general forms than these.) In this more concrete setting, the fact that prismatic cohomology is independent of the choice of coordinates apparently becomes quite a non-trivial...
Let . Using the definition of multiplication, we can create a flat connection on the -simplex which equals on , is equivalent to on , and is equivalent to on . We then glue on the edge and extend the flat connection to be equivalent to on . Using Grothendieck’s axiom and the ...
This is because for a randomly chosen odd , the number of times that divides can be seen to have a geometric distribution of mean –it equals any given value with probability . Such a geometric random variable is twice as likely to be odd as to be even, which is what gives the above...