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#1 Help Me ! » hard non contracting grammar » 2011-06-02 13:52:27

nha
Replies: 0

Hi,
Don't worry about it. I worked it out.

#2 Help Me ! » Poset Hasse Diagram » 2011-03-26 14:44:58

nha
Replies: 0

nvm. I got it.

#3 Help Me ! » Equivalence Classes » 2011-03-26 12:56:50

nha
Replies: 0

never mind, thanks.

#4 Help Me ! » finite intersection » 2011-03-13 13:18:50

nha
Replies: 1

Hey, I am really stuck on a question so if anyone can help me I would be very grateful.

Show that the set of finite unions of closed intervals

in
has the f.i.p.


I know that for a collection of sets to have the finite intersection property means that each nonempty finite sub-collection of these sets has a nonempty intersection.

I really need help on this question, analysis is killing me.

Thanks in advance for any help.

#5 Re: Help Me ! » all trees planar? » 2010-10-12 22:23:41

nha
boy15 wrote:

Ok, I might be getting somewhere.

A graph is planar if it can be drawn without edges that intersect within a plane. I believe this is true for all trees, right?

Do I use Euler's formula: v-e+f=2 where for a tree, f=1?

Yes, for a tree, f=1 and remember that for any tree the number of edges is 1 less than the number of vertices, so you have:

v=v, e=v-1 and f=1

so: v-e+f=v-(v-1)+1=2

So all trees are planar.

#6 Re: Help Me ! » exact solution to heat equation » 2010-10-11 14:34:57

nha
bobbym wrote:

Hi boy15;

boy15 wrote:

bobbym should be able to help you.

If you meant that sarcastically then I have to swallow it because I have been known to mess up.
If you really meant that, then boy do I wish that were true.
Truth is I am not even sure how solve the recurrence. I should know but I am drawing a blank with it.

Sorry nha, no help yet.

I am sure he really meant it since you help almost everyone on here! smile

Well, how would I evaluate:

, 
where
.

I know I need to use:

for all n

and

but I can't seem to get much.

#7 Re: Help Me ! » exact solution to heat equation » 2010-10-11 02:21:23

nha

Am I supposed to find

which gives the exact solution at points on the grid, and that
and
. I can't find what
is.

All I have is:

,   
where
.

I still need some help.

Thanks

#8 Help Me ! » exact solution to heat equation » 2010-10-10 17:54:56

nha
Replies: 5

Hey everyone, I need a little help with this question.

Relevant equations:


The question:

Let

and
, given the initial condition
, what is the exact solution at points on the grid?

So I have worked out

and
, and then worked out
.

I am just unsure what the exact solution is, since I don't know k.

Can someone help me with the exact solution.

Thanks

#9 Re: Help Me ! » convert from spherical coordinates » 2010-10-10 11:31:03

nha
bobbym wrote:

You can help me then. You have solved the simultaneous equations correctly.

How did you get ( 1 , π / 6 )?

Spherical coordinates refer to an angle inscribed on a circle of unit length don't they, so in polar it would be (1, pi/6)? Or is this totally wrong?

#10 Re: Help Me ! » convert from spherical coordinates » 2010-10-10 11:09:04

nha
bobbym wrote:

Hi;

You have lost me! How can we assume if we have one term in one system that we can get all three in another?

Yeah that makes sense but I don't see anything wrong with my working. I think it may be wrong but I can't see the error. It should be in the form (x,y,z), so I think the way you did it here is correct:

bobbym wrote:

For spherical to cartesian:

Just plug in

The rest you just leave as they are.

What about cylindrical coordinates? Do I use:


#11 Re: Help Me ! » convert from spherical coordinates » 2010-10-10 10:34:49

nha

This is my attempt to convert to Cartesian.
The polar coordinates of

are
. Using
and
to get
for the Cartesian coordinates, but I am unsure if this is correct. And I still can't seem to get an answer for the cylindrical coordinates.

#12 Re: Help Me ! » convert from spherical coordinates » 2010-10-10 01:38:26

nha
bobbym wrote:

You want to convert spherical to cartesian and cylindrical?

Yes, but with it just being phi I am having some trouble.

#13 Re: Help Me ! » coordinate transformation double integral » 2010-10-10 01:34:18

nha
bobbym wrote:

Yes, that is what I mean, sorry a typo. I adjusted the above post.
You will now get a different answer for the next integration.

You should get 2e^2 - 4e as the answer instead of -2e

Yes, thanks again bobbym.

#14 Help Me ! » convert from spherical coordinates » 2010-10-10 01:25:26

nha
Replies: 9

Hey all, I really need some help on this one, I just can seem to find a connection anywhere between formulas for each coordinate system.

Convert

from spherical coordinates in to both cartesian coordinates and cylindrical coordinates.

Can anyone help me at all?

Thanks again.

#15 Re: Help Me ! » coordinate transformation double integral » 2010-10-10 01:23:14

nha
bobbym wrote:

Oh yeah, but I think you mean

as the u's cancel out on the first one. But thanks again bobbym.

#16 Re: Help Me ! » coordinate transformation double integral » 2010-10-10 01:13:58

nha
bobbym wrote:

That is not correct you did not do the first integration right. You integrated ok but your putting in of the limits of integration is wrong.

I don't see where I went wrong. sad

#17 Re: Help Me ! » coordinate transformation double integral » 2010-10-10 01:09:36

nha

The limits of integration, in terms of x and y are: y= 1, y= 2, and x= 1/y, x= y.

Since x= u/v and y= uv, those become uv= 1, uv= 2, and u/v= 1/uv, u/v= uv. The first two give v= 1/u and and v= 2/u while the last two reduce to u^2=1 and v^2=1.

Drawing those lines on a uv- graph, you can see that u= 1 and v= 1 intersect at (1, 1) on the graph of v= 1/u and intersect the graph of y= 2/v at u= 1, v= 2 and u= 2, v= 1. Essentially, then, the region you want to integrate over, in the uv-plane, is bounded by u= 1, v= 1, and v= 2/u. If u ranges from 1 to 2 then, for each u, v ranges from 1 to 2/u.

#18 Re: Help Me ! » coordinate transformation double integral » 2010-10-10 01:06:03

nha
bobbym wrote:

Assuming that everything is okay up to here do you want this integral done.

Something is still wrong here you have 2 integrals with different variables but only one variable in the integrand. Are you sure about your subs?

I think this is right:

#19 Re: Help Me ! » coordinate transformation double integral » 2010-10-10 00:40:27

nha
bobbym wrote:

Hi nha;

To show you what the answer to the inner integral looks like:

Before we work on getting this answer. I am not sure about your substitutions.
We might be working on the wrong integrals!

I think my substitutions were wrong, and I think the double integral is:

as I forgot to look at the domains of x and y and change u and v after considering the domains. I think this is right.

#20 Re: Help Me ! » coordinate transformation double integral » 2010-10-10 00:03:12

nha
bobbym wrote:

Hi;

What I am saying is that the inner integral can be done by parts or by a table lookup. The intervals of integration having variables is no problem at all. Is that what you mean by terminals the intervals?

If it is no trouble, could you show me some working out for what you mean, I don't understand. What I mean is how do I integrate the definite integral with terminals uv and 1/uv with respect to either du or dv?

#21 Re: Help Me ! » coordinate transformation double integral » 2010-10-09 23:53:24

nha
bobbym wrote:

Hi nha;

Is there some reason why you are not algebraically simplifying the inner integrand?

Hi bobbym, yes I know it simplifies down to a rather simple function but I am confused about the terminals uv and 1/uv after I integrate.

#22 Help Me ! » coordinate transformation double integral » 2010-10-09 23:31:07

nha
Replies: 16

Hey everyone, I am stuck on this question, I just can't get anymore done. Any help would be great.

Evaluate

by making the coordinate transformation
and
.

My working so far:

So:

But I don't get how to go from here, with the limits of one of the integrals having terminals with u and v in it.

If anyone can help that would be fantastic!

Thanks

#23 Re: Help Me ! » sequence question » 2010-09-12 17:25:45

nha
bobbym wrote:

Hi;

Sorry, a total hallucination. I am just not getting it right now. Are you sure that is the correct sequence?

That is how it is stated but I am starting to think that it might be a typo or a trick question. I can't seem to get it and neither can any of my friends.

#24 Re: Help Me ! » sequence question » 2010-09-12 17:03:18

nha
bobbym wrote:

My guess is the next one is 52. But it is just a guess based on a weak pattern.

Thanks again bobbym. How did you get 52, what weak pattern did you find? I couldn't find any sort of pattern.

#25 Re: Help Me ! » sequence question » 2010-09-12 16:34:01

nha
bobbym wrote:

Hi nha;

And it gets worse. There are an infinite amount of functions that can go through those set of points. Picking the next two numbers is actually mathematically impossible. Even a set that looks like this { 1,2,3,4,5,6,7,...}, humans guess 8 and because the questioner is also a human they are marked right. Actually the next number could be -12364 or anything else. Point is I could fit a different function to those points that would always produce a different 8th number. Still we try to guess at the simplest form that the questioner meant.

Hi bobbym
Cool, thanks for that. What do you think would be the next number after 30 and why? This is annoying me.

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