However, it turns out that by combining -adic control on in Proposition 4 with the trivial control on in Proposition 3, one can obtain Theorem 1 by an elementary argument that does not use any further properties of (other than the obvious fact that the are rational integers), with the in...
We could just say that we bound (k+1) by loglogn/log p p^{k/loglogn} — and then apply multiplicativity– But what does this bound mean? Why are bounding the divisors from a fixed prime factor in terms of a quantity that again involving the contribution from the prime factor ? 9Ye...
But what in reality does a “3D world” actually mean? It means that the space around us has three dimensions, and that the position of anything can be described by using three numbers, also referred to as parameters or coordinates. There are various ways to specify these three parameters,...
Plugging into (*)'s RHS, we get: Then we get 1 = 1, so (*) is true at n = 1.There; we've shown that (*) works in some particular, named place. But does it work anywhere else?Well, that was our problem in the first place: we already knew that (*) worked in a few ...
Before we do the proof, which is quite short, it’s important to point out that the target dimensioncdoes not depend on the original dimension! It only depends on the number of points in the dataset, and logarithmically so. That makes this lemma seem like pure magic, that you can take...
Newton's 2nd law provides information on what a force does. But if you are looking for a better mathematical definition of the effect of a force, I think you are better off defining the effect of a net force as the change in momentum of an object, or Fnet=dpdtFnet=dpdt where, for ...
An important point: const int *p does not mean the value you are referring to is constant!!. It means that you can't change it through that pointer (meaning, you can't assign $*p = ...`). The value itself may be changed in other ways. Eg int x = 5; const ...
the "aversion to inequality"; • Theil index (T) that gives equal weights across the distribution; • Mean logarithmic deviation (MLD), which is more sensitive to changes at the lower end of the distribution, while CV is more responsive to changes in the upper end of the distribution. ...
AGAlgebraic Geometry(branch of pure mathematics) AGAbout good(coin collectin, grade) AGAdvocate General(various nations) AGAngular AGAcid Gas AGAccess Grid AGAir Group(aircraft carriers) AGAnalysis Group(CEOS) AGAcapulco Gold(marijuana strain) ...
Given an abstract graph G, or a drawing thereof, it is not always obvious as to whether that graph is planar; just because the drawing that you currently possess of G contains crossings, does not necessarily mean that all drawings of G do. The wonderful little web game “Planarity” illust...