Recent content by JG89

To be specific, the compound the I am trying to crystallize is usually comprised of nearly opaque, pearly crystals. When it is in its base form, it is dissolved in diethyl ether, then precipitated in its hydrochloride form by adding an acetone/HCL acid solution (or by bubbling dry HCL gas...

Suppose I have a substance that has been crystallized. Now suppose I break down those crystals into powder, grains, etc. How can I reconstruct that powder into a crystal again? Do I just dissolve it into a solvent and then evaporate the solvent? Another quick question - is it possible to...

I am trying to recrystallizing lidocaine out of methanol. I created a saturated solution of lidocaine and hot methanol, waited for it to cool to room temperature, then threw it in a cool water bath. There was no recrystallization. I decided to evaporate the methanol to recover my lidocaine and...

Suppose I am trying to dissolve a compound into a minimal amount of solvent (let's assume that this compound is not pure and its impurity is not soluble in the solvent). So I have this compound in a glass and I slowly add the solvent, waiting until my compound is dissolved. How do I know that...

I have just taken a first year course in physics. But it wasn't a course that the physics majors were taking. It was an easier course, a level below. I guess I should just learn the physics then. I want to learn it, if possible, in such a way that it is a direct path to GR. I don't want to learn...

I want to study GR from a mathematical point of view but I know almost no physics. Is this possible? And what textbook would be more geared towards this? Also, what are the math prerequisites that I need? I have studied up to analysis on manifolds, some linear algebra and multi-linear...

Wow, I can't believe I wrote that. I was dead tired and my counter-example I was trying to type out was A = (0,1), B = [1,2]. But even that fails. My apologies, I'll try not to post when I'm half awake anymore lol.

The space has to be Hausdorff and B has to be open. A = (0,1) and B = [1,0] is a counter example to what you say

This particular derangement doesn't affect the sum when passing to the limit because \forall n \in \mathbb{N} , \sum_{k=0}^n a_k x^k = \sum_{k=0}^n a_{n-k} x^{n-k} . Thus \sum_{k=0}^{\infty} a_k x^k = \sum_{k=0}^{\infty} a_{n-k} x^{n-k}

Could you give some context behind the equations?

Wow, now I feel silly. I confused the hell outta myself, I should've known better. Thanks for the replies.

I know they're differentiating with respect to x, that's exactly what I have a problem with. As far as I know, the usual derivative of a map requires the domain to be a subset of \mathbb{R}^n , but the x that they are differentiating with respect to is a function, it's not a real number, or an...

They give a differential equation: x' = f_a(x) = ax(1-x) . In determining if the equilibrium points are sources or sinks, they say: We may also determine this information analytically. We have f'_a(x) = a - 2ax How can they differentiate with respect to x? x is a function, it doesn't...

The initial value for n doesn't matter. It's presumably not zero.

@Borg, thanks for those sources, I will check them out! @russ, I want to do day trading.I've scheduled a study date with my dad this Saturday, so I shall pick his brain like I never have before! Thanks guys!