Mathematics - 2012-09-05 (page 2 of 4)

Nice work on the formatting :)

Haha. thanks.

@DantheMan What happened to the x in the denominator?

Michael Greinecker

2:34 PM

The last step?

Ahh yes.. that should be there

$10\sqrt{\frac{2}{5x}} = 10\sqrt{\frac{2(5x)}{5x(5x)}} = 10\sqrt{\frac{10x}{25x^2}} = 10\frac{\sqrt{10x}}{\sqrt{25x^2}} = 10\frac{\sqrt{10x}}{5x} = 5\frac{\sqrt{10x}}{2x}$

Good

That is correct?

no

10/5 = 2 in the last step.

5 mins ago, by Dan the Man

$10\sqrt{\frac{2}{5x}} = 10\sqrt{\frac{2(5x)}{5x(5x)}} = 10\sqrt{\frac{10x}{25x^2}} = 10\frac{\sqrt{10x}}{\sqrt{25x^2}} = 10\frac{\sqrt{10x}}{5x} = 5\frac{\sqrt{10x}}{2}$

and don't forget the x.

Ah right.

2:38 PM

Hi all

So... $2\frac{\sqrt{10x}}{x}$ ?

Hello Senior :-D

@JohnSenior Hello!

@DantheMan Yes.

@MichaelGreinecker Awesome.

2:39 PM

Hello everybody!

1 min ago, by Dan the Man

So... $2\frac{\sqrt{10x}}{x}$ ?

@DantheMan Remember to write x=/= 0

I have a question about parabolic PDE's: I don't know any process described by parabolic PDE where t can't be interpreted as time. Maybe somebody knows?

hi @anon

hello

I'm the only one who uses this laptop, yet Skype was installed on it 40 minutes ago without my knowledge. I feel something spooky is going on.

Haha

Does $\sqrt{\frac{5}{8y^3}} = \frac{\sqrt{10y}}{4y^2}$ ?

2:50 PM

@anon might be time to do a bit of investigating - like looking at logged-in users, processes running and IP addresses you are connected to ...

I second that.

@DantheMan yes

@anon Thanks

@anon what OS is your laptop running?

Windows 7. It appears I've actually had Skype for a couple months at least, it just got modified an hour ago and decided to start up.

2:59 PM

It might have just updated...

@anon that is a bit less spooky then :)

@anon You could always uninstall it.

Skype is a heinous program

blackhat.com/presentations/bh-europe-06/bh-eu-06-biondi/…

2

Actually kind of frightening, that.

@acedittutoring Welcome ace!

@Nimza Do you mean time as a physical parameter, or time as a non-spatial dimension in the equation?

3:09 PM

@EdGorcenski as physical parameter

It is sometimes possible to introduce a "time" variable that doesn't represent physical time.

in which process for example?

You can introduce a nuisance variable and evolve the solution of the PDE to stationarity w/r.t. that nuisance variable

even in Ricci flow t can be interpreted as time

For example, the Lagged Diffusivity method found in Vogel's Computational Inverse Methods book

3:10 PM

m

Alternatively, the construction of the binomial, Poisson, and negative binomial distributions from their probability generating functions introduces a time-like nuisance variable.

In fact, the lagged diffusivity algorithm is a great example

@EdGorcenski thank you. I'll look.

You can have a time-sampled signal with noise, 1-D or 2-D. The independent variable domain is physical time. However, the method doesn't care about physical time, and constructs a PDE that attempts to minimize the total variation. The method then evolves an approximation to the derivative of the signal, $u_t$, over a nuisance time variable; iteration stops when $u_t$ is nearly zero everywhere.

$\frac{4}{\sqrt{3} + \sqrt{2}} = 4\sqrt{3} - 4\sqrt{2}$?

Is the PDE parabolic? I have no idea. But -- there's no reason that I can see that you couldn't derive a similar formulation.

3:15 PM

@DantheMan yes

@anon Thanks

@EdGorcenski but I'm afraid you don't understand what I want. I want to find a physical process described by, say, heat equation, but where t is not a time or whatever like a time.... for example t is a space variable.

it is an additional question on entrance exam in graduate school

... $= 4(\sqrt{3} - \sqrt{2})$ ?

@DantheMan You lost the 5.

@JohnJunior What 5?

3:18 PM

4 mins ago, by Dan the Man

$\frac{4}{\sqrt{3} + \sqrt{2}} = 4\sqrt{3} - 4\sqrt{2}$?

@JohnJunior There is no 5...??

@DantheMan In the denominator: 3+2=5

@Nimza For any physical process, you will always have a time dependence; unless you expect the solution to evolve instantly in time, there is no physical formulation that can completely ignore time.

@JohnJunior You can't add those.

Siamak.A.M

hi all

3:21 PM

hi

You could possibly frame a problem with respect to momentum, or velocity, perhaps a Lagrangian frame for a fluid mechanics problem... or is it Eulerian...

@EdGorcenski maybe it is bad to say "process". "Reality" maybe is better

You probably want to avoid stochastics, then?

yeah

something easy

Then you probably want to use some sort of flux as your time-like independent variable

3:23 PM

@JohnJunior right?

2 hours ago, by Dan the Man

Since $(\sqrt{a} + \sqrt{b})(\sqrt{a} - \sqrt{b}) = (\sqrt{a})^2 - (\sqrt{b})^2 = a -b$, the order of any two conjugates is rational if the radicals are of order 2.

Simple example: an equation that describes a relationship based on the number of people in a shopping mall

@JohnJunior You're talking about that?

That's good I think, which equation?

I dunno -- make one up!

3:25 PM

Lol

Heh)

Or, if you want something continuous, let x, y be your spatial variables

@DantheMan What did you multiply the numerator and denominator by?

and let t represent, i dunno, a height or something.

like z? but what will mean $u_{z} = \Delta u$?)

3:26 PM

not like z

:6036827 $\frac{4(\sqrt{3} - \sqrt{2})}{(\sqrt{3} + \sqrt{2})(\sqrt{3} - \sqrt{2})}$

@DantheMan Yes, you are correct, good job :)

@JohnJunior Thanks! :)

Say, "the severity of the common cold $u$ in the land of Narnia depends on the latitude and longitude of where the ill person lives. However, Narnia is a magical land, and is filled with dwarves underground, and gryphons high in the air. The severity of the cold can be lessened by changing one's altitude, $t$. Compute the severity of the cold, $u(x,y,t)$ as one changes his or her altitude in Narnia according to the following relation: $u_{xx}+5u_{xy}+u_{yy} = 0$"

2

Wow, where did you get this quote? I want to read such book)

3:32 PM

I just made it up.

heh) nice!

With all apologies to C.S. Lewis's Chronicles of Narnia

Haha nice.

user19161

@anon It might be pulled in together with other software or updates you installed.

How many roots does 64 have?

user19161

3:40 PM

@DantheMan What do you mean?

infinitely many, unless you want (say) positive integer n-th roots (n=integer), or positive integer square roots (n=2 fixed)

user19161

Yet another brilliant answer by the cool one.

Uhhhhh

Not sure.

user19161

If you are not sure, it is time to read your textbook again.

Like $2^6 , 8^2$

3:43 PM

$64=(\pm2)^6=4^3=(\pm8)^2=64^1$...

So those are positive integer roots?

Yio

Hey if I'm given a function f(x) (say a polynomial) and I nest it n time f(f(x)), f(f(f(x))),...

is there a general way of obtaining the closed from expressen in terms of n

?

Say f(x)=a+bx^2+cx^4, what is f(···f(f(x)))? (n-time iteration)

There is at least one way, but it is very drawn-out.

namely?

Plug and chug.

3:48 PM

you can't find a closed form for an expression involving the variable n with plug and chug :P

that would amout to "plug'n'chug"

user19161

@anon If f is a polynomial, there might be, I dunno.

Sure you could... if the original polynomial is order $p$, then each nesting should increase the resulting polynomial order by $p$, and $n$ nestings should result in a polynomial of order $np$...

example: $f(x) = ax+b$. $n = 3$.

okay, but youn guys don't know a theory build around it..

Er, coefficients, I should say, not polynomial order

3:51 PM

you can't plug and chug an indefinite number of times though, and a closed-form expression here would mean an expression that depends on n

How do I write $abc$ in $\LaTeX$ with a curved line over $ab$ and a curved line under $bc$?

user19161

@anon I am surprised none of the latex guys answered you yet.

$f(f(x)) = a(ax+b)+b = a^2x+(a+1)b$
$f(f(f(x))) = a^2(ax+b)+(a+1)b = a^3x+(a^2+a+1)b = a^nx+(a^n-1)/(a-1)b$

overset/underset/tilde?

(guess)

plug'n'chug reminds me of another question I have: can one say that regular automata and in turn the turing machine were invented for the purpose of solving the Entscheidungsproblem? Historically.

I hereby coin the term "axiom schema of stupid questions"

(not implying that the above question would be stupid)

4:07 PM

$\sqrt[3]{x} - m = n$
$x = n^3 + 3n^2m + 3nm^2 + m^3$ ?

@anon: hi, do you have a personal webpage for academical purposes?

@DantheMan yes @Ilya no (why?)

academical vs. academic, what is right?

Thanks

academic

4:09 PM

@anon: just thought, that it's time for me to have one

user19161

Yes, remember to put your pic there too.

which pic, my MSE Rama-blue gravatar?

user19161

No, your face.

heh..

haha

user19161

4:10 PM

What is Rama blue?

@WillHunting well, that's for sure, don't worry

@WillHunting see the first picture here

user19161

@Ilya One look at your face costs 10 dollars, I know.

@Will: huh, that was before the 2008's crysis

user19161

@Ilya You are some god? I did not know.

now it's $100

@WillHunting you're a human, you're not supposed to know everything

user19161

4:12 PM

Those who see the proof see me.

which drugs?

user19161

Because I am the proof.

that should be something heavier than marijuana

I know its effect, its different

hm...

Somebody solve this. $\sqrt{y^2 - 8} + y = 4$

You should take a crack at it first.

4:21 PM

I have been for the past 15 minutes

What did you try?

square both sides, simplify, square again...

it's not working

try subtracting $y$ from both sides and then squaring

k

MaoYiyi

I know this is not the site for latex; however, I was wondering how does one put the box with the points, after the question, on the right side of the paper in latex?

I did try searching tex.stackexchange.com but can't find anything

4:24 PM

googling gives me paultaylor.eu/proofs/QEDdoc.pdf

@anon $y=3$ ?

yup

Yes!

@DantheMan You can always check it by substituting y=3 back into the original equation.

@JohnJunior Yeah. It worked.

$\sqrt{-9} + \sqrt{-36} = 9i$ ?

user19161

4:29 PM

@JohnJunior Though there might be other solutions, not saying so for this case.

@WillHunting Yeah

MaoYiyi

found it.

@DantheMan Back into the original equation.

@JohnJunior yes

11 mins ago, by Dan the Man

Somebody solve this. $\sqrt{y^2 - 8} + y = 4$

y=3

4:33 PM

$1+3=4$

4=4 True

$\checkmark$

Yes, it is :)

4:49 PM

do what extend do mathematicans consider computer science part of math?

"To what extent", Do you mean?

@NickKidman To what extent do computer scientists consider math a part of computer science?

Jayesh Badwaik

@NickKidman Depends on the purpose.

@JohnJunior haha

;-)

4:56 PM

I think they would consider it a part of math, though at least non-CS mathematicians might consider analysis, geometry, topology, algebra etc. to be "purer" subjects, although CS is related to asymptotics and logic (the latter is certainly pure). Algorithmic thinking and computing solutions are necessary in many higher areas of mathematics so there is exposure.

hi @JohnSenior

@JohnJunior Hi there

@JohnSenior How's the record breaking rainy days of England?

@JohnJunior not sure - but it is the wettest summer out of the last 100 or so :(

although last 2 days have been very pleasant and sunny

this is pretty arbitrary

Fundamental theorem

The fundamental theorem of a field of mathematics is the theorem considered central to that field. The naming of such a theorem is not necessarily based on how often it is used or the difficulty of its proofs. For example, the fundamental theorem of calculus gives the relationship between differential calculus and integral calculus, which are two distinct branches that were not obviously related. The names are mostly traditional, so that for example the fundamental theorem of arithmetic is basic to what would now be called number theory. The mathematical literature sometimes refers to t...

5:15 PM

This is pretty practical.

2

How do you post like that?

[text](link)

There's some magic in the chat server that recognizes chat posts that consist solely of links to Wikipedia, or to an SE site, or (I think) some other places. Overuse of this feature tends to be discouraged in this room.

Yeah. But how @NickKidman did.

Ahhh

ok

k

How do you quote someone?

@DantheMan Not exactly quote, but press the bent arrow that appears to the far right of their post (only visible when you mouse over the post), and your next one will be linked to it.

5:26 PM

Yeah I know... That's for replying. But how do you quote someone?

I've seen @JohnJunior do it.

@DantheMan Hover over their post, on the right

There's a little arrow-y thingie

Just to the right of the star.

That's for replying...

3 mins ago, by Henning Makholm

@DantheMan Not exactly quote, but press the bent arrow that appears to the far right of their post (only visible when you mouse over the post), and your next one will be linked to it.

Aha!

Like that.

Ah sweet!

cool. thanks.

5:39 PM

Lol

@JohnJunior: The poker theorem isn't practical at all - as far as I can see

@NickKidman It is if you play.

If you say so

It just says "play the odds."

@HenningMakholm: Can one say that regular automata and in turn the turing machine were invented for the purpose of solving the Entscheidungsproblem? Historically.

5:43 PM

It's not practical in that it is not constructive; it is practical in that it is useful in comforting yourself when you do the right thing and lose anyway

That^ is gambling.

Gustavo Bandeira

:6038886

2 mins ago, by John Junior

That^ is gambling.

Yay! I got it too!

Q: Why did my friend lose all his money?

Congratulations :-D

Gustavo Bandeira

PRO!

You guys discussing about poker, it kinda reminder me this:

25

Not sure if this is a question for math.se or stats.se, but here we go: Our MUD (Multi-User-Dungeon, a sort of textbased world of warcraft) has a casino where players can play a simple roulette. My friend has devised this algorithm, which he himself calls genius: Bet 1 gold If you win, bet 1 ...

The last clause should read "continue doubling until you win or have no money". — Chris Eagle Aug 28 at 8:31

@ChrisEagle It's plausible: $2 \cdot 0 =0$. One can easily double poorness. Doubling richness is the challenging step. — Gustavo Bandeira Aug 28 at 18:07

@NickKidman The Turing machine was definitely invented particularly in connection with the Entscheidungsproblem -- at least as far as the title of Turing's original article tells. It's not clear to me that finite automata have a direct connection, though.

(Except insofar as everything related to computability descends at least morally from the Entscheidungsproblem).

5:50 PM

@JohnJunior That's why I stick to craps.

Can one sum up, in short terms, how the grammatical features of the connectives (not, and,...) which are used to make up a sequence (which is the input of the machine) is recognized by the machine? I mean it has to in some way, otherwise one couldnt even make an Entscheidung regarding the Entscheindungsproblem, no?

I understand how a string of 0's and 1's get recognized by a regular automat, but the formulas of first order logic say relate to the symbols left and right

@EdGorcenski Whatever you gamble on always remember: "Luck never made a man wise."

3

maybe the is clear if one understands turning machines properly - does the reader know all connectives of the input and does it make "where to go"-decissions based on that

fun fact, the guy I was sitting next to in school got rich with poker right after we left school (with 19)

@NickKidman In general this is the problem of parsing the input -- computer science has a lot to say about that. The syntax of formal logic is usually chosen simple enough to be, handled by a recursive-descent parser, though.

parsing is basically about algorithms which take strings and put them apart in a systematic manner, right

Gustavo Bandeira

5:56 PM

@NickKidman Nice class: He got rich with poker, you got rich as an Australian actress, singer, film producer,[1] and humanitarian AND A RAPPER!!!!

I'm also a rapper

@NickKidman The machine then has to build an internal representation of the input somehow. Usually how one thinks about this is to imagine one is programming a machine that feels more like an actual computer (such as a RAM), and then appeal to a general theorem that a Turing machine can simulate any RAM.