If you roll a pair of fair dice (numbered 1 thru 6 on each die), what is the probability of getting a sum of 1? When a pair of dice is? rolled, what is the probability that the sum of the dice is 6?, given that the outcome is not ...
in lowest terms necessarily equals the largest prime factor of , that allows one to evaluate the left-hand side of(5)almost exactly (this expression either vanishes, or is the product of for some primes ranging up to the largest prime factor of ...
prismatic cohomology in coordinates can be computed using a “-derivative” operator that for instance applies to monomials by the formula where 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 is a review of the issue of randomness in quantum mechanics, with special emphasis on its ambiguity; for example, randomness has different antipodal relationships to determinism, computability, and compressibility. Following a (Wittgensteinian) philosophical discussion of randomness in general, I ar...
(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, ...
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), ...
from one microstate to the next is independent of time, or on the past history of the system. We make the key assumption that the counting measure on microstates is invariant, or equivalently that the sum of all the transition probabilities that lead one away from a given microstate equals ...
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 definition of multiplication, we can then extend the flat connection to the ...
However, not knowing the customs, the foreigner makes the mistake of mentioning eye color in his address, remarking “how unusual it is to see another blue-eyed person like myself in this region of the world”. What effect, if anything, does thisfaux pashave on the tribe?