Comments on: The Sunday Function

By: ollie

ollie — Tue, 03 Mar 2009 10:59:12 +0000

Gavin: that is what as known as the “bump function” ; it is used in differential topology to “sew” things together.

By: Gavin Flower

Gavin Flower — Tue, 03 Mar 2009 08:28:17 +0000

My favourite is (does it have a name?):

f(x) = 1 /(1 – e(-1/x))

lim f(x) = 1
x -> 0+

lim f(x) = 0
x -> 0-

By: riemann

riemann — Mon, 02 Mar 2009 20:13:21 +0000

I think it’s borderline blasphemy to not mention Riemann-zeta function before any other function..

http://en.wikipedia.org/wiki/Riemann_zeta_function

By: Eunoia

Eunoia — Mon, 02 Mar 2009 19:48:22 +0000

And then there’s Ackermann’s function, which I covered on february 10th, and the devil’s staircase which I’ll cover sometime this month. The latter has a zero derivative almost everywhere, except at the cantor dust points where it is infinite. It climbs from 0 to 1 ONLY at the cantor points. Continuous but not differentiable

By: A Cold Walk, A Lamarckian Result, Conservative Lust for Porn and other topics « blueollie

Mon, 02 Mar 2009 14:07:36 +0000

[...] Cosmic variance has a thread on people’s favorite mathematical functions. Here is one of mine: for [...]

By: Count Iblis

Count Iblis — Mon, 02 Mar 2009 13:46:01 +0000

This is a must read for all physicists!

By: Matt Springer

Matt Springer — Mon, 02 Mar 2009 01:34:35 +0000

Glad you like it! I have to say it’s one of my favorite things to write – there’s no limit to the material, and it’s all fascinating.

By: ollie

ollie — Sun, 01 Mar 2009 22:48:37 +0000

Here is mine:

g(x) = exp(-1/x^2) for x not equal to zero
= 0 if x = 0

g is “C-infinity” in that it has derivatives of all orders everywhere but is not analytic at x = 0, which means it doesn’t have a Taylor series about x = 0 that is valid on any open interval containing zero.

This is the basic building block of the “bump function” that allows us to do “surgery” in differential topology but the stumbling block between extending results from smooth to analytic manifolds.

By: Robert Papesch

Robert Papesch — Sun, 01 Mar 2009 22:31:07 +0000

The cusp geometry is a weird function that loses stability and jumps between two solution sets. It's used in economics to model transitions from monopolism to competition in a market.

By: Ken Clark

Ken Clark — Sun, 01 Mar 2009 19:11:57 +0000

the writers over at Arcsecond posts physics problems occasionally too.