Search found 532 matches

by scarletmanuka
Thu Nov 01, 2007 4:19 am UTC
Forum: Mathematics
Topic: Sudoku?
Replies: 10
Views: 1670

Re: Sudoku?

If you have enough information so that there is only one solution, then by definition you can deduce all the remaining values (in some sequence) without guessing. The chain of deductions required to fill in the next value might be long, but the length required to make you start guessing instead of a...
by scarletmanuka
Wed Oct 31, 2007 6:23 am UTC
Forum: Mathematics
Topic: limit of a function defined in terms of another function
Replies: 18
Views: 2188

Re: limit of a function defined in terms of another function

I'm surprised that nobody has yet mentioned the logistic map f(x) = kx (1-x) where k in (0, 4] is a parameter that controls how chaotic the solutions are. For k<=1 the only fixed point is 0; for 1 < k <= 3 there is another fixed point at 1 - 1 / k ; for 3 < k <= 1+sqrt(6) (approx. 3.4495) f n (x) co...
by scarletmanuka
Wed Oct 31, 2007 5:03 am UTC
Forum: Mathematics
Topic: I should know this...gah!
Replies: 10
Views: 1606

Re: I should know this...gah!

MrDelirious wrote:
ikerous wrote:A=64*Sin(theta)(1 + cos(theta))

d'oh. I must need sleep. Should that 64 drop out? Otherwise, I get:

dA/d(theta) = 64*cos(theta) * (1+cos(theta)) + sin(theta) * (64sin(theta))
= 64cos2(theta) +cos(theta) + 64sin2(theta)

I think you mean
= 64cos2(theta) + 64cos(theta) + 64sin2(theta)
by scarletmanuka
Wed Oct 31, 2007 1:29 am UTC
Forum: Mathematics
Topic: I can haz integration halp plz?
Replies: 11
Views: 1290

Re: I can haz integration halp plz?

I'm not quite sure what you mean by the first part of your question. For the second part, I have to agree. In general this will give you a second-order ODE which you will have to try and solve, most likely by variation of parameters or some such technique.
by scarletmanuka
Wed Oct 31, 2007 1:20 am UTC
Forum: Mathematics
Topic: I can haz integration halp plz?
Replies: 11
Views: 1290

Re: I can haz integration halp plz?

The difference is that if you have F'(y) = f(y) and G'(x) = g(x), the chain rule says d / dx (F(y)) = F'(y) dy / dx = f(y) dy / dx so we can say that f(y) dy = g(x) dx => f(y) dy / dx = g(x) => d / dx (F(y)) = g(x) => F(y) = G(x). This doesn't work with higher derivatives because the second derivati...
by scarletmanuka
Wed Oct 31, 2007 1:04 am UTC
Forum: Mathematics
Topic: I can haz integration halp plz?
Replies: 11
Views: 1290

Re: I can haz integration halp plz?

Unfortunately not. :( Consider a simple example: F(x, t) = t = m ( d2x / dt2 ) Solving this as a constant coefficient second order ODE gives us x(t) = t 3 / (6m) + At + B for arbitrary constants A and B. Separating and integrating twice would give us int(int(m dx) dx) = int(int(t dt) dt) => m x 2 /2...
by scarletmanuka
Wed Oct 31, 2007 12:56 am UTC
Forum: Mathematics
Topic: I can haz integration halp plz?
Replies: 11
Views: 1290

Re: I can haz integration halp plz?

If you separate variables as suggested, you will get an equation relating v and x. If you want to get x(t), this will be a differential equation which you will have to solve somehow. The third one actually looks to be the easiest: m dv / dt = f(t) g(v) obviously separates to give you int(m dv / g(v)...
by scarletmanuka
Mon Oct 29, 2007 11:56 pm UTC
Forum: Mathematics
Topic: Paging Problem
Replies: 6
Views: 1309

Re: Paging Problem

In that case, surely the adversary can just request each available page in turn and screw you no matter what? (Assuming there are more pages than will fit into the cache, which is a rather weak assumption - if there aren't then it's pretty easy to spot an optimal paging algorithm 8)) In that case th...
by scarletmanuka
Mon Oct 29, 2007 8:49 am UTC
Forum: Mathematics
Topic: Paging Problem
Replies: 6
Views: 1309

Re: Paging Problem

It depends on whether the page requests are really being generated by an adversary or not, and if the adversary is expected to have knowledge of your paging algorithm. If you have an adversary who knows your paging algorithm and is trying to make you look bad, go with the random page option. If you ...
by scarletmanuka
Mon Oct 29, 2007 8:29 am UTC
Forum: Mathematics
Topic: (anything)^0?
Replies: 30
Views: 5177

Re: (anything)^0?

antonfire wrote:Jerry Bona wrote:
The Axiom of Choice is obviously true; the Well Ordering Principle is obviously false; and who can tell about Zorn's Lemma?

That is an awesome quote. I love it! :lol:
by scarletmanuka
Mon Oct 29, 2007 8:03 am UTC
Forum: General
Topic: Who the dickens are you?
Replies: 10922
Views: 2419794

Re: POST HERE FIRST - INTRO THREAD THE THIRD

Snap! I'm Sacha, also from Perth, Western Australia. I eventually managed to snarf a PhD in maths and now work as a data architect at a mortgage aggregator. I'm married with three kids and don't usually get very much sleep. :o
by scarletmanuka
Wed Oct 17, 2007 4:31 am UTC
Forum: Individual XKCD Comic Threads
Topic: 0330: "Indecision"
Replies: 196
Views: 35159

Re: Indecision Discussion

So how does "Wait, I think there's a rule about this" in the first panel fit in with "I did not know that rule / Me neither" in the last panel?

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