892 reputation
114
bio website joshphysics.com
location Los Angeles
age 28
visits member for 1 year, 9 months
seen 16 hours ago

New project: phermi.com

Let me know if you know of any hard physics problems with clever solutions. (email listed to the left)

Personal website: joshphysics.com

Currently a lecturer at the UCLA Department of Physics and Astronomy.

Ph.D. theoretical high energy physics, UCLA.

BA/BS in physics/math, UC Berkeley.


Mar
7
revised Inverse function with Dirac Delta
added 77 characters in body
Feb
24
comment $g''(t_0)$ where $g(t) = f(t, 1-t) , t_0 = 0$
@user129120 Your guess is as good as mine.
Feb
24
answered $g''(t_0)$ where $g(t) = f(t, 1-t) , t_0 = 0$
Feb
17
comment Inverse function with Dirac Delta
@Garrett See math.ucsd.edu/~wgarner/math4c/textbook/chapter2/…, for example. Notice also that saying "the" function $f(x) = x^2$ is misleading. One needs to both specify the domain of the function, and what it does to each element of the domain. If we define $f$ as the function whose domain is $[0,\infty)$ and for which $f(x) = x^2$ for all $x\in [0,\infty)$, then $f$ is invertible. But if we extend its domain to $(-\infty, \infty)$, then it is not invertible.
Feb
8
accepted Cochains: terminology
Feb
8
comment Cochains: terminology
@TedShifrin I most certainly will, especially since you're the second person who's suggested that to me, the first being a math grad student. I as a theoretical physics grad just learning this stuff, I really appreciate your help.
Feb
8
comment Cochains: terminology
@OlivierBégassat Thanks again.
Feb
8
comment Cochains: terminology
Thanks very much for this Olivier. Would you mind pointing me to a reference that discusses this stuff; I would very much appreciate it.
Feb
8
comment Cochains: terminology
@TedShifrin As a matter of terminology, would you happen to know if elements of $\mathrm{Hom}(M,\mathbb R)$ are ever referred to as cochains when $M$ is the $\mathbb Z$-module of chains? The $k$-form example you gave is precisely what I had in mind when I wrote this question; such objects arise naturally in physics (especially thermodynamics when modeling heat). By the way, I'm a fan of "multivariable mathematics," so I was, I must admit, somewhat star-struck when I saw your answer.
Feb
8
revised Cochains: terminology
edited body
Feb
8
comment Disprove a linear mapping
@SergioParreiras See the earlier version. For some reason, the OP removed the definition of $g$.
Feb
8
comment Disprove a linear mapping
@Slavica Yep. Sure thing.
Feb
8
comment Disprove a linear mapping
@Slavica What do you mean by a "general" disproof? This demonstrates that the statement "$g$ is linear" is false, because it is not the case that $g(\alpha x) = \alpha g(x)$ for all $\alpha$ and $x$. It's not as though "falsness" has multiple degrees.
Feb
8
answered Disprove a linear mapping
Feb
8
asked Cochains: terminology
Feb
7
comment Translations in two dimensions - Group theory
@user35952 Unfortunately I think not.
Feb
7
comment Translations in two dimensions - Group theory
@user35952 Yes it's a circle too. It's a circle with the same radius but whose center is at $(-a,-b)$. We could only have said that the equation for the circle was preserved in form (at least if we're using standard terminology) if there were some $R$, say, for which the transformed equation were $x^2+y^2 = R^2$; that equation has the same form. So, for example, a scaling $x\mapsto \alpha x, y\mapsto\alpha y$ would preserve the form of the equation for a circle at the origin because the new equation would be $x^2 + y^2 = (r/\alpha)^2$. Are thinking of a different notion of "preserve."
Feb
7
comment Translations in two dimensions - Group theory
@user35952 Well let's see. A circle is described by the equation $x^2 + y^2 = r^2$, and if we translate $x\mapsto x+a$, $y\mapsto y+b$, then we get $(x+a)^2 + (y+b)^2 = r^2$ which is certainly not an equation of the same form. In fact, the only such equation that will have the same form is the equation for any line in the direction of the translation $(a,b)$ itself.
Feb
7
comment Translations in two dimensions - Group theory
+1: I had forgotten about this way of packaging things; very slick.
Feb
7
comment Translations in two dimensions - Group theory
@user35952 I don't quite understand what you mean. Could you be more specific about what sorts of "equations" you're referring to?