Search found 758 matches

by z4lis
Wed Nov 30, 2011 1:07 am UTC
Forum: Mathematics
Topic: Again with the measure theory.
Replies: 11
Views: 2070

Re: Again with the measure theory.

1 = \lim_{\epsilon\to 0} T(f_{t, \epsilon}) = \lim_{\epsilon\to 0} \int f_{t,\epsilon} g\ d\lambda = t\left(\int g\ d\lambda\right) I might be missing something, but it looks like you're assuming that f_{t, \epsilon} is approaching the constant function t as epsilon goes to zero, bu...
by z4lis
Tue Nov 29, 2011 4:43 pm UTC
Forum: Mathematics
Topic: How to model parallel linear transforms with matrices
Replies: 8
Views: 1511

Re: How to model parallel linear transforms with matrices

Would a block matrix work, then? That is, if you want to do two transformations A, B in parallel, then just use the matrix

[A 0]
[0 B]

where the zeros indicate appropriately sized zero matrices. If you had inputs x, y before, then the new input is the column vector [x,y]T
by z4lis
Tue Nov 29, 2011 4:25 am UTC
Forum: Mathematics
Topic: Quick help categorizing a network.
Replies: 6
Views: 1235

Re: Quick help categorizing a network.

It sounds like you just want a partition of the nodes. I suppose each node corresponds to some physical or virtual object that plays one of several animations? In that case, it doesn't seem like there's really a mathematical reason to think of the nodes as being the same, and you could just have a r...
by z4lis
Mon Nov 28, 2011 9:57 pm UTC
Forum: Mathematics
Topic: Again with the measure theory.
Replies: 11
Views: 2070

Re: Again with the measure theory.

Note: it's been a while since I did anything with measure theory, so verify anything I say carefully. #1: The hint is not a bad one at all. Guessing a solution and checking it's correct is a common and useful technique in mathematics. Deriving an answer from first principles might be hard, but if in...
by z4lis
Mon Nov 28, 2011 4:21 pm UTC
Forum: Mathematics
Topic: Quick help categorizing a network.
Replies: 6
Views: 1235

Re: Quick help categorizing a network.

What do you mean by the nodes have "hidden expressions"?
by z4lis
Mon Nov 21, 2011 5:54 am UTC
Forum: Mathematics
Topic: Questions about Manifolds
Replies: 15
Views: 1896

Re: Questions about Manifolds

The more I've thought about it, the more I think the idea will go through, and inductively, to boot. Try showing that given a quasilinear path, there is some open set U of the manifold such that the quasilinear path never enters it by induction.
by z4lis
Mon Nov 21, 2011 5:13 am UTC
Forum: Mathematics
Topic: Questions about Manifolds
Replies: 15
Views: 1896

Re: Questions about Manifolds

Marbas wrote:I have not, actually. Although I don't know how I'd start doing that.


It might not even work. It's just where I'd probably start heading if I was given the problem. Not put much thought into it.
by z4lis
Mon Nov 21, 2011 5:08 am UTC
Forum: Mathematics
Topic: Questions about Manifolds
Replies: 15
Views: 1896

Re: Questions about Manifolds

Just read about half of this thread and without putting too much thought into it... have you tried showing something slightly stronger, such as given a quasilinear path, there is some neighborhood that the path never enters?
by z4lis
Sun Nov 20, 2011 1:21 am UTC
Forum: Mathematics
Topic: Uneducated question about a metric
Replies: 2
Views: 801

Re: Uneducated question about a metric

It turns out to be a very interesting idea, that has been studied extensively:

http://en.wikipedia.org/wiki/Lp_space
by z4lis
Sat Nov 19, 2011 10:42 pm UTC
Forum: Mathematics
Topic: expression for the product of n rotation matrices
Replies: 16
Views: 2118

Re: expression for the product of n rotation matrices

I don't have the abstract algebra/group theory background to understand it in those terms. I have a sense of what you mean, but I'm still not clear on why the last part, "To show that f is injective is just to show that a nontrivial word in F_2 is not mapped to a trivial rotation in SO(3).&quo...
by z4lis
Fri Nov 18, 2011 7:58 am UTC
Forum: Mathematics
Topic: Desperately need statistics help
Replies: 5
Views: 1570

Re: Desperately need statistics help

First of all I'm not really sure if this falls under the No Homework rule since I'm obviously not asking anyone to DO my homework for me. I'm simply not getting what my professor wants me to do here. I'm sorry if this thread violates any rules. solve this statistical help for this question: "T...
by z4lis
Fri Nov 18, 2011 7:32 am UTC
Forum: Mathematics
Topic: The notation "a/bc"
Replies: 24
Views: 3392

Re: The notation "a/bc"

It is universally accepted, that's the entire point of the order of operations. The problem is that we get lazy and write a/bc when we should be writing either a÷bc or \frac{a}{bc} and make our intentions clear. In other words, typeset your equations with a vinculum or an obelus and nobody will nee...
by z4lis
Fri Nov 18, 2011 4:15 am UTC
Forum: Mathematics
Topic: The notation "a/bc"
Replies: 24
Views: 3392

Re: The notation "a/bc"

For what it's worth, all the students at my elementary/middle/high schools were taught that multiplication and division is resolved left-to-right. However, since that's certainly not universally accepted, it's best to use parentheses to be clear.
by z4lis
Fri Nov 18, 2011 4:08 am UTC
Forum: Mathematics
Topic: expression for the product of n rotation matrices
Replies: 16
Views: 2118

Re: expression for the product of n rotation matrices

Think about the algebra that is going on. On the one hand, we have F_2, the free group on two elements. This the the "source" of our paradoxical decomposition. What we want is some injective map f:F_2 ---> SO(3), the group of rotations. To get this injective map, we pick two rotations p,q ...
by z4lis
Thu Nov 17, 2011 1:57 am UTC
Forum: Mathematics
Topic: Quickie -- bounding factorials
Replies: 4
Views: 4011

Re: Quickie -- bounding factorials

I spent a horrifyingly long time before I decided to finally look at...

Spoiler:
the power series of e^x.
by z4lis
Sun Nov 13, 2011 2:14 pm UTC
Forum: Mathematics
Topic: Bayes Question
Replies: 3
Views: 880

Re: Bayes Question

You're right that there is no such thing as a "mammogram outcome in the absence of a 'cancer relationship'", but we don't need to know anything about the patient's cancer status to guess the odds of them having a positive mammogram. You can assess the probability P(A) of an event A without...
by z4lis
Thu Nov 10, 2011 3:22 pm UTC
Forum: Mathematics
Topic: expression for the product of n rotation matrices
Replies: 16
Views: 2118

Re: expression for the product of n rotation matrices

Linky.

The proof of what you're after begins on page 12.
by z4lis
Sat Nov 05, 2011 5:18 pm UTC
Forum: Mathematics
Topic: Interesting problems which require the triangle inequality
Replies: 10
Views: 2456

Re: Interesting problems which require the triangle inequali

Maybe have them prove that the shortest smooth curve between two points is a straight line?
by z4lis
Tue Oct 18, 2011 2:29 am UTC
Forum: Mathematics
Topic: dirac delta functions on TI 89
Replies: 7
Views: 5137

Re: dirac delta functions on TI 89

If it's absolutely necessary, you could look for some kind of exponential-ly bump function that approximates it and integrate using that.
by z4lis
Fri Sep 30, 2011 3:24 pm UTC
Forum: Mathematics
Topic: Interesting Quadratic Models
Replies: 7
Views: 1653

Re: Interesting Quadratic Models

Morse theory is totally a real-life application of quadratic models. :twisted: (I was going to suggest it as a possibility, and then I reread your original post!) Anyway, lots of physical systems have quadratic terms. For instance, the kinetic energy of classical mechanics has a quadratic term. It ...
by z4lis
Wed Sep 21, 2011 2:47 am UTC
Forum: Mathematics
Topic: Decomposition of a matrix in a certain way
Replies: 7
Views: 2103

Re: Decomposition of a matrix in a certain way

I have a matrix, C, which is size N x M. I want to tell if this matrix can be decomposed as the outer product of a size N vector, A, and size M vector, B. Basically I want to see if it's possible to find vectors A and B such that Outer(A, B) = C. I don't know what A or B are, only what C is. Is the...
by z4lis
Tue Sep 20, 2011 7:48 pm UTC
Forum: Mathematics
Topic: Should I major in Math?
Replies: 11
Views: 3522

Re: Should I major in Math?

I've never done amazingly in AMC's, and I've never gotten higher than a 2 on the AIME, making really dumb mistakes on simple problems along the way. This is pretty irrelevant. I never did particularly well in mathematics competitions either, but I seem to be doing just fine in my undergraduate prog...
by z4lis
Thu Sep 15, 2011 8:52 pm UTC
Forum: Mathematics
Topic: Help with a simple proof
Replies: 27
Views: 2496

Re: Help with a simple proof

so I think I got it, and if so, the stupidity i feel will be frustrating =_= anyhow, compare x^n/(a-x) to just x^n. integrate x^n from 0->1 and you end up with 1/(n+1). The limit of that quantity as n->inf is 0. Since that approaches 0, so does the original integral, since the original integrand x^...
by z4lis
Wed Sep 14, 2011 7:15 pm UTC
Forum: Mathematics
Topic: Help with a simple proof
Replies: 27
Views: 2496

Re: Help with a simple proof

z4lis: that's where i'm getting stuck. I'm sure I'm overlooking something real simple but I can't think of how to deal with that integral. It's not something as simple as finding an antiderivative, is it? Ah, alright. Often, when you're trying to prove stuff with limits, finding exact formulas isn'...
by z4lis
Wed Sep 14, 2011 6:30 pm UTC
Forum: Mathematics
Topic: Help with a simple proof
Replies: 27
Views: 2496

Re: Help with a simple proof

Could you prove that [math]\lim_{n \rightarrow \infty} \int_0^{1-t} \frac{x^n}{a -x } dx = 0[/math] for 0 < t < 1? Once you do that, how can you combine that with the previous stuff to get the whole thing?
by z4lis
Wed Sep 14, 2011 4:05 pm UTC
Forum: Mathematics
Topic: Help with a simple proof
Replies: 27
Views: 2496

Re: Help with a simple proof

Given that, all I can think of doing is splitting the integral into two, one from 0->(1-t) then add to it the integral from (1-t)->1. With this, for the case where a=2, the first integral gives you ln(2/1+t) and the second gives you ln(1/1-t), at which point if you take the limit where t->0, you en...
by z4lis
Wed Sep 14, 2011 2:55 pm UTC
Forum: Mathematics
Topic: Help with a simple proof
Replies: 27
Views: 2496

Re: Help with a simple proof

Since with a larger n, I_n always gets smaller, then as n->infinity, I_n approaches 0. That all makes sense to me and without further doubt proves what I need, but I feel as if that's just not a mathematically rigorous way to prove it. Certainly I_n monotonically decreasing doesn't mean they go to ...
by z4lis
Sun Sep 11, 2011 1:02 pm UTC
Forum: Mathematics
Topic: Matrices with Continuous Indices
Replies: 7
Views: 2476

Re: Matrices with Continuous Indices

I have no idea if it's relevant to what you're saying, but in my PDE class the analogs between matrices and integral kernels was stressed a bit. If you have a function K(x,y) and define g(x) = \int K(x,y) f(y) dy, this is quite similar to matrix multiplication: v(...
by z4lis
Sun Sep 11, 2011 12:54 pm UTC
Forum: Mathematics
Topic: Elliptic geometry or Hyperbolic geometry
Replies: 10
Views: 1593

Re: Elliptic geometry or Hyperbolic geometry

Yes, I'll take semi-Riemannian geometry for 500.

Mmm. Having your cake while eating and baking it. Enjoy only having a single index for your manifolds, peasants!
by z4lis
Fri Sep 09, 2011 8:27 pm UTC
Forum: Mathematics
Topic: A simple Differential Geometry problem
Replies: 11
Views: 2190

Re: A simple Differential Geometry problem

So, it turns out I answered my own question in the OP. It is possible to use the chain rule to show that DF(x) is nonsingular. Then you simply use the fact that it is impossible to have a nonsingular matrix from R^n to R^m when m<n. Z4lis: Uhh...nothing yet. D: Ah, so not that far into it just yet....
by z4lis
Fri Sep 09, 2011 1:30 pm UTC
Forum: Mathematics
Topic: A simple Differential Geometry problem
Replies: 11
Views: 2190

Re: A simple Differential Geometry problem

If a function is a diffeomorphism, what could you say about the induced function on the tangent space?
by z4lis
Thu Sep 08, 2011 2:26 am UTC
Forum: Mathematics
Topic: Ten repeating numbers in Pi
Replies: 21
Views: 7262

Re: Ten repeating numbers in Pi

Isn't it a theorem that every finite string of digits appears somewhere in pi?

EDIT: Found this. http://mathoverflow.net/questions/18375 ... -digits-of

So it's just highly suspected that that's the case.
by z4lis
Sun Aug 28, 2011 12:34 pm UTC
Forum: Mathematics
Topic: Is this proof valid?
Replies: 9
Views: 1770

Re: Is this proof valid?

When trying to prove things, you should be checking to make sure your conclusions make sense. The simplest way to do this is to try some counterexamples. From f(x,n) = f(x,n+1) , you're concluding that f(x,n) = ke^x . But this is disproven by something as simple as f(x,n&...
by z4lis
Tue Aug 23, 2011 8:29 pm UTC
Forum: Mathematics
Topic: Cantor-Schroder-Bernstein
Replies: 6
Views: 1120

Re: Cantor-Schroder-Bernstein

I'll just toss in my two cents. We have f:A \rightarrow B and g:B \rightarrow A that are both injective. Now, we want to define a function h:A \rightarrow B that is bijective using information from both f and g. Right from the start, we see that there are some points in A that must use f to get to B...
by z4lis
Mon Aug 15, 2011 5:33 pm UTC
Forum: Mathematics
Topic: Minecraft Shorelines are loops?
Replies: 18
Views: 3117

Re: Minecraft Shorelines are loops?

But, what happens at exactly p=1/2? I get that above p=1/2 one component is almost certainly infinite and the others are finite, and at less than p=1/2 the other component is almost certainly infinite while the other is finite. At p=1/2, do we get "50% chance one is infinite, 50% chance the ot...
by z4lis
Sun Aug 14, 2011 7:15 pm UTC
Forum: Mathematics
Topic: Minecraft Shorelines are loops?
Replies: 18
Views: 3117

Re: Minecraft Shorelines are loops?

Could someone link the wikipedia article? I'm having trouble understanding the p=1/2 case. Clearly land and water must follow the same probabilities here. Can all land and all lakes be finite on a single map? Actually, I guess that they can be (like some sort of infinite bulls-eye pattern), but it ...
by z4lis
Fri Aug 12, 2011 8:02 pm UTC
Forum: Mathematics
Topic: Minecraft Shorelines are loops?
Replies: 18
Views: 3117

Re: Minecraft Shorelines are loops?

If, on a minecraft map, you pick a shoreline near your spawn point and start following it, what is the probability that you will end up back where you started? My intuition says it is 1, but I don't know how to prove it. (For this problem I think you can pretend a minecraft map is infinite, but I a...
by z4lis
Fri Aug 12, 2011 7:49 pm UTC
Forum: Mathematics
Topic: Possibly basic differentiation question
Replies: 4
Views: 918

Re: Possibly basic differentiation question

\partial_{t} = \epsilon \partial_{t1} + \epsilon^{2} \partial_{t2} I don't think this equation makes any sense at all, as written. From my experience, if you wrote something like that, then this would be indicating that \partial_t and the other partials are vectors in some tangent spaces. The troub...
by z4lis
Thu Aug 04, 2011 8:49 am UTC
Forum: Mathematics
Topic: Some Probability Theory Question
Replies: 0
Views: 780

Some Probability Theory Question

So I'm reading a book about random walks on graphs and related ideas, and my probability theory is not very good. I need a little help with verifying that I know what I'm doing for one equality stated in the text. Suppose we have some method of choosing a spanning tree of our graph randomly, spannin...
by z4lis
Fri Jul 15, 2011 4:38 pm UTC
Forum: Mathematics
Topic: Addition and "wrong addition" of fractions
Replies: 7
Views: 1484

Re: Addition and "wrong addition" of fractions

Well, to start, the operation isn't well defined. (a/b)*(c/d) = (a+c)/(b+d), but (a/b)*(2c/2d) = (a+2c)/(b + 2d). Those numbers usually aren't going to be the same.

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