Recent content by Geomancer

I suspect your intuition is more at fault than you numerics. Consider the function f=1 for positive x, -1 for negative x. Then the sum of a left moving copy of f (or a close smooth approximation) and a right moving copy of -f will give the behavior you describe.

Thanks, gel. That construction is certainly much easier than mine (though they work the same way).

Note that every infinite discrete set admits a bounded incomplete metric. Given noncompact (X,p), find e s.t. the set of balls of radius e has no finite subcover. Let {Bi} (indexed by a set I) be a minimal subcover (note we use Zorn's lemma here. This is simply to make the proof cleaner.) Assign...

So it is. Silly me.

As usual the answer depends on what question you're asking. You can create an algebraically complete field containing the integers that is a proper subset of the complex numbers (indeed, a countable set, whereas the complex numbers are uncountable). Note though that your definition of a good...

Clear? Not at all. I can see this for separable Hilbert spaces--though often people prefer to look at them as related to spaces of functions R->C (or R->R). For other spaces, I'm having difficulty seeing what you mean at all.

These posts are written in a hurry. If anything needs clarification, please ask. Above, I used two facts implicitly: the result given as an excercise immediately below the red box in the scan, and the fact that (f*g)(T)=f(T)*g(T). These are both easy.

Your interpretation of p(T) is correct. Take note of this, since it's a rather useful technique. As for the least common multiple thing, how obvious it is depends on how much algebra you've been doing lately. Your text probably should have supplied a proof, unless they already have results to...

Try assuming the contrary: that the action is not transitive on V. Deduce that R is bipartite. Contradiction. Am I missing something?

There is a gizmo called "Euler MacLauren Summation" that allows one to rapidly approximate sums by integrals; this may get you where you want to go. I must note that the example formula you gave may be simple enough to allow exact results. I'll think about this.

Um, it looks like the book you linked to was just using the projection to parameterize the sphere, and thus the set of surface orientations. Of course, this parameterization will induce local coordinate systems for most places on suitably well-behaved surfaces (is this the ultimate goal? Google...

Just having a metric is a very weak condition--most of the topological spaces you encounter will be metrizable. Having a Reimannian metric provides a lot of structure in addition to the topology (which you get from any metric). In particular, it makes a manifold into a differentiable manifold...

It's a list of places I'm considering for graduate school (math PhD). I've previously discussed my situation http://https://www.physicsforums.com/showthread.php?t=271391" . On consideration, I probably should have posted in that thread. Mods, please feel free to move this there. Thanks...

Thanks again for the comments on my previous post. I've done some work narrowing the field of math schools. Note that since my previous post I've made a decision to weight schools in the south a bit more heavily than those in the north. Here is a list, along with my comments. AMS Group I...

Thanks for the replies, One of the things I worry about is ending up in a place where I get practically no outside mental stimulation. This was the case, for example, at my second undergrad institution, and I tend to perform badly under such conditions. Simultaneously, the suggestion to...