Recent content by Prez Cannady

Just so I'm clear: 1. faculty -> factorial 2. distribution law -> distributive law Is that correct?

Indeed. Was just curious if there was a name for it or if I'm just writing down n^2 and (n + 1)^2 in a needlessly complicated fashion.

Was fooling around and wrote down these two equations today that appear to work. I'm not all that bright and I'm positive these either have some proof or restate some conjecture--probably something in a textbook. Could somebody help me out? \forall n \in \mathbb{N}_0\smallsetminus\{0\} n^2 =...

We have direct mass models of stellar motion inside of galaxies (basically, find a happy medium between a sphere and a disc). And of course dark matter corrections to explain the deviation between model and observation. Is there any pattern at all to the motion of extragalactic stars passing...

Okay, so first of all it seems the action is *not* the expression, but just the integral in the exponent of e. That's good to know.

Sweet. I have Zee.

Summary:: Pretty sure they have something to do with path integrals, or what not. But obviously it's hard to *search* for this stuff. Basically, I'm looking for a textbook, any textbook--physics, mathematics, etc.--that deals with integrals that look something like this (mistakes are mine): S...

Answer is probably not, but is there some connection between the inhomogeneous wave equation with a constant term and the spacetime interval in Minkowski space? $$ 1) ~~ \nabla^2 u - \frac{1}{c^2} \frac{\partial^2 u}{\partial t^2} = \sum_{i=0}^2 \frac{\partial^2 u}{\partial x_i^2} -...

Then let me phrase my question this way, and narrowly. Is there a name for functions that take vectors as arguments and perform non-linear operations on the argument's coefficients? And a method analogous to multiplying square matrices against vectors when performing linear transformations...

"This reference?"

I'm interested in ##V \rightarrow W## nonlinear transformations on vector spaces (where neither need be the same dimension). I've plenty of multivariable calc texts, but none seem to spend any time on this. I've fewer linear algebra texts, but hopes of finding even an honorable mention were in vain.

I'm having trouble finding textbook material on nonlinear functions on vectors. Just as I could define a function ##f## such that: $$f(x) = cos(x)$$ I'd like to write something like: $$f(\vec{x}) = \begin{pmatrix} f_1(x_1) \\ f_2(x_2) \\ ... \\ f_n(x_n) \end{pmatrix} $$ where ##f_i## is...

Depending on the source, I'll often see EFE written as either covariantly: $$R_{\mu\nu} - \frac{1}{2}Rg_{\mu\nu} = 8 \pi GT_{\mu\nu}$$ or contravariantly $$R^{\alpha\beta} - \frac{1}{2}Rg^{\alpha\beta} = 8 \pi GT^{\alpha\beta}$$ Physically, historically, and/or pragmatically, is there a...

Yeah. Dimensionally they agree because ##\theta## is dimensionless, but they're not equivalent. Thanks.

Parameterized, I think not. A contradiction: $$ \theta = sin(t) $$ $$ \frac{d\theta}{dt} = cos(t) $$ $$ \frac{d^2\theta}{dt^2} = -sin(t) $$ $$ \left(\frac{d\theta}{dt}\right)^2 = (cos(t))^2 $$