Naive method: If you had the coordinates of a street intersection, and wanted to examine nearby streets, you would have to go through the millions of segments each time, and check each one for adjacency. If you only needed to do this once, it would not be a problem to have to do...
I do not have proofs of these results (though I think something similar to (i) can be found in Knapp’s book, and (ii) should basically follow by using a rational parameterisation of with nonlinear). Assuming these assertions, this would mean that there is a curve of the form that ca...
After some initial Taylor expansion, I was blocked from forming such a counterexample because an inspection of the leading Taylor coefficients required one to construct a continuous periodic function of mean zero that never vanished, which of course was impossible by the intermediate value theorem. I...
What do you mean by " An algorithm taking Theta(n log n) is far preferential since it takes at least n log n (Omega n log n) and no more than n log n (Big O n log n). ", as in, is it the exact complexity of a algorithm as you wrote said at least Omega(nlogn) and at...
f(x) ∈ Ɵ(justlikethis) mean f "grows exactly like" justlikethis f(x) ∈Ω(lowerbound) means f "grows no slower than" lowerbound big-O notation doesn't care about constant factors: the function 9x² is said to "grow exactly like" 10x². Neither does big-O asymptotic n...
Suppose first that there is no “Siegel zero”, by which we mean a quadratic character of some conductor with a zero with for some small absolute constant . In this case the Siegel-Walfisz bound (1) improves to a quasipolynomial bound To establish Theorem 1 in this case, it suffices ...