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12:06 AM
SE, Twitter, Facebook, Blog, Website... I am all over the place.
Like a suicide bomber.
 
Sounds exhausting.
 
Hardly.
 
I don't think this is an issue, but I AM allowed to print everything published on arXiv, right?
 
that would take a lot of paper. also they do look out for mass downloading.
 
But they look out for mass downloading mainly because of robots.
 
12:12 AM
There's this set of notes that like 800 pages long. I just want to print that one.
That's okay right?
 
Good night.
 
thats great. copyright law is really weird so i got worried
 
@JonasTeuwen Good night.
 
good night
 
12:13 AM
@acassatt9 From wikipedia:
Files on arXiv can have a number of different copyright statuses:[18]

Some are public domain, in which case they will have a statement saying so.
Some are available under either the Creative Commons 3.0 Attribution-Share alike license or the Creative Commons 3.0 Attribution-non-commercial-Share Alike license.
Some are copyright to the publisher, but the author has the right to distribute them and has given arXiv a non-exclusive irrevocable license to distribute them.
 
if arXiv has a distribution license, that means I can print them out on my own since I was distributed them in pdf form, yes?
 
IANAL, but I am sure there should be no problem about it.
 
Well I'm contacting a printing & binding service to print and bind the article, so I don't want them to freak out because it's from a academic publishing website.
 
Ohh. In that case, I cannot help you because I am not even a US citizen.
 
haha
 
12:49 AM
zzzzZZzZZzZzZz
 
1:09 AM
Hey @Charlie
 
@math101 hey
 
So you are a mystery? lol
 
@math101 yes I am :)
 
1:57 AM
hey! i'm trying to find out if there are methods to have a runge kutta method yield same results on different timescales. e.g. stepping 1+1+1+1 or stepping 3+0.1+0.9 usually gives different results.
i'm quite sure the problem is known, i just have no idea how to phrase it properly
 
2:20 AM
@anon is ghost in the shell good?
 
"good"?
 
yes, good
 
you're asking someone who has a gits avatar. what could you hope to gain from asking me?
yes, I like the series and movies. not the manga.
 
is it famous?
 
yes
 
user19161
2:24 AM
I am now back to "blue". Today is a very sad day...
 
...
 
what is the character you have in the picture?@anon
 
lol
 
its mem right?
 
yes
 
user19161
2:26 AM
Haha, my god laughs.
 
what?
@anon is it the laughing man?
 
@Khromonkey he worships anon
 
It's not really a character, it's a sex doll from the second movie poster.
nope, laughing man (aka aoi) is a different avatar I have.
although it's debatable if the anonymous author of the email with the criticism of the murai vaccine is the true "laughing man" - this individual is only mentioned once in the entire series, in passing, though
 
is the laughing man the villain?
 
antagonist, sure. (in the first season) villain is presumptuous a word to throw around.
 
2:30 AM
Who is the major antagonist?
the Puppet Master?
 
user19161
@charlie I hope you are not upset by us. We did not mean to ignore you. I just don't feel like replying to every occurrence of hi in a chat room.
 
ok
 
in the first movie, the puppet master (aka project 2501) is the antagonist. in the second movie, it's the sex dolls (they become sentient and revolt). in the third movie, it is a different kind of "puppet master," and it is at first unknown if Motoko (usually the protagonist) is in this case the antagonist.
in the first season, it's apparently the laughing man, but then it is revealed there are actual villainous elements behind the micromachine therapy approval. in the second season, it is apparently a team of revolutionaries, then just one of the revolutionaries, then it is revealed there is an actual villain mastermind behind the scenes.
(I should have said criticism of the micromachine therapy approval decision over the murai vaccine earlier, not "criticism of the murai vaccine")
 
nice
well, good night all
 
user19161
@Khromonkey Good night.
 
user19161
2:37 AM
@anon Did you watch the movie series Death Note?
 
movie series? I watched the anime series and the manga, both good.
I have not seen the live-action movies.
 
user19161
I watched them all, the movies.
 
@Khromonkey Good Night
Donald Duck gets embarrassed when loses his tshirt? He doesn't wear bottoms!
 
2:59 AM
@math101 hello.
 
hi, can you help me show that the ideals ( a + b sqrt(-5) ) and ( a - b sqrt ( - 5 ) ) only intersect at the ideal generated by their norm? i.e. when the conjugates are multiplied. I think this is true, and it's true at least in the case I have to prove ( a = 2, b = 1 ). But i'm having trouble with it
 
ideals of what
 
one generated by a + b sqrt( - 5 ) and the other generated by its conjugate a - b sqrt( - 5 ) , a and b are integers
I tried to work out equations by brute force but I end up with two equations and four variables
haha
no, it's not
but I am out of ideas
oh I think I can do something here
I can reduce the number of variables
but saying that if p = (a + b sqrt ( - 5 ) )* k1 = ( a - bsqrt(-5) )* k2
then norm ( k 1 ) = norm ( k 2 ) and k1 and k2 should be conjugate
or is a unit
 
i'm asking ideals of which ring
 
Z [ sqrt ( - 5 ) ]
sorry
 
3:15 AM
i mean, am i being silly here or can't you just map a + b sqrt(-5) to a - (-b) sqrt(-5)
 
what do you mean?
 
are you saying the ideals are { a + b sqrt(-5) : a,b in Z } and { a - b sqrt(-5) : a,b in Z } ?
 
the principal ideals generated by ( a + b sqrt( -5 ) ) and ( a - b sqrt(-5) )
so all R-multiples of those two conjugates
 
ah so a and b are fixed?
 
yea
 
3:23 AM
Slow night on Math.SE!
 
ah right ok. so you want to know how it can happen that $\left(c + d \sqrt(-5)\right)\left(a + b \sqrt(-5)\right)\in \langle a - b \sqrt{-5}$, thus $\left(c + d \sqrt(-5)\right)\left(a + b \sqrt(-5)\right)=\left(e + f\sqrt{-5}\right)\left(a + b \sqrt(-5)\right)$ for some $e$ and $f$.
 
sorry I can't parse latex in the chat
but yeah
 
you should get chatjax
 
just to make notation look nicer writing a + b sqrt( -5 ) as (a,b )
just when does (x,y) * ( a , b ) = (h,k ) *( a, -b )
should be only when (x,y) = (a, -b) and (h,k) = ( a,b )
 
anyhow expanding out we get $ac-5bd+(ad+bc)\sqrt{-5}=ae+5bf+(af-be)\sqrt{-5}$ whence $a(d-f)+b(c+e)=0$ and $a(c-e)-5b(d+f)=0$
then we can solve for $e$ and $f$ in terms of $a,b,c,d$
$e=\frac{a^2c+5b^2+10abd}{a^2+5b^2}$
 
3:31 AM
we have 2 equations and 4 variables
 
and $f=\frac{-2abc+a^2d+5b^2d}{a^2+5b^2}$
so we've got the bottom factoring to the norm you're talking about
 
@Elliot, what do you know about Dedekind domain?
 
well, I am trying to show that this ring is a dedekind domain actually
 
so because we're in $\mathbb{Z}$ and not in $\mathbb{Q}$ the top has to have a factor of $a^2+5b^2$
 
@Sanchez HI.
 
3:33 AM
hi @BenjaLim
 
@Elliot The intersection of two ideals is also their lcm.
 
what about c and d?
 
@Sanchez What do you think of Kempf's book on algebraic varieties?
 
this gives us the condition on $c$ and $d$
 
how do I know gcd's even exist in this ring?
 
3:34 AM
@BenjaLim, I didn't read it before, so I don'tk now.
@BenjaLim, and it's not gcd, rather it's lcm
 
@Elliot Unique factorization of ideals in a Dedekind domain.
 
(which is what we wanted, right? to solve for the $c$ and $d$ so that it can be a part of the RHS)
 
@Sanchez can you have a look at it briefly for me please? My supervisor wants to start with that book.
 
oh, you mean gcd's of their ideals and not gcd's of the generators
 
yes of course :D
 
3:37 AM
I remember skimming that book in the past, should be fine, and at all rate just listen to your advisor.
 
@Elliot and what do you mean by <<ideal generated by their norm>> ?
@Sanchez the books has some heavy shit on cohomology in it of sheaves. I just thought a more classical approach would be better.
 
I mean the ideal generated by a+bsqrt(-5) * a - b sqrt(-5)
 
@BenjaLim, I disagree. Seeing cohomology asap is a good thing in my opinion.
 
@Elliot ah by $a^2 + 5b^2$.
 
yeah
 
3:39 AM
@Sanchez but he said he used it as a masters student at cambridge :D
@Sanchez my level is a lot lower than that.
 
@Elliot, another idea for your problem: Show that (a+b\sqrt{5}) + (a-b\sqrt{5}) = 1. Then you can find some c,d in your ring, c(a+b\sqrt{5}) + d(a-b\sqrt{5}) = 1.
If you have e(a+b\sqrt{5}) lying in (a-b\sqrt{5}), multiply $e$ to both sides of the last equation to show that e lies in (a-b\sqrt{5})
@BenjaLim, I disagree.
 
@Elliot Once you know that they are coprime their intersection is just their product and you are pretty much done.
 
yeah
right
 
@Sanchez I only know singular cohomology. And things like the cup product/ kunneth formula I'm not so sure about.
 
thank you
 
3:42 AM
@Elliot Here is an alternative way to show they are coprime.
 
@BenjaLim, it's gonna take you a while to cohomology anyway, don't worry.
You don't need much of those kunneth stuff
rather, it would be nice if you know some cech cohomology
 
@Sanchez Suppose we have a prime ideal $P$ of $\mathcal{O}_K$ that divides (a+b\sqrt{5}) and $(a - b\sqrt{5})$
 
I don't know if the sum of their ideals is the whole space though. doesn't look right.. unless a is a unit?
 
Now $P$ lies over some prime ideal $p \in \Bbb{Z}$.
 
oh wait, the intersection always lies in the product
 
3:45 AM
So taking norms we need $p$ or $p^2$ to divide $a^2 - 5b^2$ and $a^2 + 5b^2$
@Sanchez Hmmmm somehow people always advise to start with simple things like fulton/ shafarevich
@Sanchez You on the other hand were crazy to start with Hartshorne right away :D
 
I dun think shafarevich is simple at all
 
@Sanchez really?
 
You need to understand that the difference is in language (between shafarevich and hartshorne eg)
 
Hi, @Jason. I see you're "back from the black!"
 
Shafarevich develops much things even in book 1
 
3:48 AM
ok.
 
i think they talk about what non-singular means etc. (and the comm alg theorems there are the same as schemes anyway), they even talk about classification of singularities by dynkin diagrams
 
wowowowow
 
fulton covers a lot less than shafarevich
 
yes I agree
@Sanchez You see my original ideal was to use fulton first (only 100 pages) as a stepping stone to say geometry of schemes
 
reading rr is a good idea to be honest
so that life is more interesting than the study of linguistics
 
3:50 AM
rr?
 
riemann roch
 
Riemann Roch?
That is covered in Fulton too
 
yes, but i think it's beyond 100 pages
 
what is?
 
riemann roch
not in the first 100 pages i believe
 
3:51 AM
ah yes it's like 110
yeah
but when I said read 100 pages I meant the whole of Fulton
 
oh
is it that short?
 
I thought the whole of Fulton as 100 pages
 
hm
 
yes.
 
i thought it's like 150-200
 
3:52 AM
no
 
hm
 
@Sanchez anyway I have a quick question about units in real quadratic fields
@Sanchez We know that the units are $\{ \pm u^k\}$ where $u$ is a fundamental unit
now when they say $u$ is a fundamental unit, do they mean up to sign it is the smallest positive unit? @Sanchez ?
 
i think so
i'm not too sure how the terminologies go though
 
ok.
@Sanchez thanks. I should go now.
 
ttyl @BenjaLim
 
3:56 AM
@Sanchez I will inform you the thoughts of my supervisor.
 
That's cool.
 
Yo. I was able to show $\bf Q$ is dense in $\prod_{p<\infty}{\bf Q}_p$ and not dense in the adeles (either through continuity of the abs val product or a different 'directness' argument.) but I want to know if $\bf Q$ is closed in $\prod_{p\le\infty}{\bf Q}_p$ which is a stronger claim. (I don't think $\bf A$ is closed in the latter so we don't get it automatically.) Searching "approximation theorems" and variants involves heavy algebraic group stuff I am unable to follow for the most part.
(I am also unable to see if $\bf Q$ is dense in ${\bf R}\times\prod_{p\ne\ell}{\bf Q}_p$ for finite primes $\ell$.)
 
4:13 AM
@anon
?
 
yes?
 
The function that is at y=1 for all $ x \in R $
except for x=0 where y=0
Is it continuous at x=0?
 
no
 
I thought so too
Ok thanks
 
4:27 AM
hmmmm so if the limit exists then the function is continuous?
or is that not necessarily?
@anon what is ur say on the matter?
 
the limit does exist for your function at x=0; the limit is 1. review your definition of continuity.
 
ohhhh but what abt my statement above its incorrect right?
ohhhh I get it
 
user19161
@math101 It is wrong.
 
Thanks @JasonBourne :)
 
user19161
For a function to be continuous at a point, the function must be defined at the point, the limit must exist, and these two must agree.
 
4:38 AM
okkk get it
 
user19161
If the point is at the interior of an interval, you have the left hand and right hand limits which must exist and be equal for the limit to exist.
 
i see
 
user19161
If the point is at the endpoint of a closed interval, then the limit really is just the one-sided limit, assuming the function is defined only on that closed interval.
 
Thanks Gotcha
 
user19161
Limits are defined at limit points. However, continuity may be defined in terms of epsilons and deltas, so that at isolated points, continuity is automatic.
 
4:43 AM
Thanks @JasonBourne
 
@JasonBourne Limits are defined at limit points I don't know why.
 
user19161
@FrankScience What I mean is, to define a limit, you need to start with a limit point.
 
user19161
Of course, at limit points, the limit may not exist.
 
Well, I see.
 
user19161
One should check out the definitions of limit point and isolated point to make sure one really understands them.
 
4:56 AM
At first, I didn't realize that the uniqueness of limit is depended on whether $p$ is a limit point.
 
user19161
Why do they want people to do the site evaluation?
 
user19161
I just realised it by clicking on a few links.
 
user19161
So they throw a few random posts at you and ask you to evaluate the helpfulness of the site?
 
If $f$ is continuous on a closed set of metric space $X$. How can we prove that there's an continuous extension of $f$ onto $X$.
 
user19161
Isn't that what the upvotes and downvotes are for?
 
user19161
5:02 AM
Also, why do they bother to ask non-registered users to evaluate the helpfulness of a post by clicking yes or no?
 
user19161
Firstly people can click wrongly.
 
user19161
Secondly they might not know how the site really works.
 
user19161
How can Tom Dick or Harry evaluate the quality of my post?
 
w00t! I just got the Fanatic badge! (I'm a little crazy at 12:12am)
2
 
user19161
@anorton HAHA
 
9:26 AM
40
Q: Please add an "Über-Fanatic" badge!

EtherI have officially qualified for the mythical "Ãœber-Fanatic badge", having remained faithful and dedicated to the site for 365 consecutive days. Can we make this badge less mythical and more real?

 
10:04 AM
can anybody suggest me a good book (or any other resource) for theory on Linear Optimization Problems.
 
10:39 AM
 
@Novice @amWhy do you even........??????????????
 
11:06 AM
hi there
 
 
2 hours later…
12:57 PM
hello
@AkramHassan, yo uthere
 
1:13 PM
@user58512 Hey why do you ask about adeles and ideles?
 
@BenjaLim, I resolved it with Sanchez
 
@user58512 Have you studied algebraic number theory?
 
a bit
 
Well why not study it properly before learning about advanced topics? @user58512
 
yes @user58512
 
1:17 PM
@user58512 and what do you mean by you resolved it with sanchez?
 
Good day everybody!
 
hello
 
@user58512 hi
 
@user58512 what did you resolve with sanchez?
 
my question
 
1:20 PM
what do you mean by " what do they look like" ?
@user58512 I can't even picture say what a prime ideal lying over $2$ looks like.
@Tobias Hey. As a graduate student you must have studied algebraic geometry yes?
 
@BenjaLim yes
 
@Tobias which book did you start out with? Are you familiar with Kempf's algebraic curves?
 
no
I started out with some lecture notes written by the lecturer (this was a very basic course that only looked at curves in P^2)
 
right.
@Tobias Because my lecturer wants to being with Kempf's algebraic curves. I on the other hand suggested the more basic Fulton.
 
not familiar with Fulton's book on the introductory stuff
I am taking a course at the moment using his book on intersection theory
 
1:25 PM
ok wow that is quite advanced.
 
for the more advanced stuff, I first learned it from Humphreys and Springers books on linear algebraic groups
 
@Tobias isn't chapter 3 of the intersection theory book on k - theory?
@Tobias I've only looked once at the intersection theory book, the appendix that was for a combinatorial formula.
 
then from Mumford and then Hartshorne when I needed some more background
then from Jantzens representation of algebraic groups for the functorial approach
 
ok.
@Tobias your algebraic geometry is pretty advanced :D
 
@BenjaLim we have only just gotten to the definition of intersection product. Not sure about the later chapters
@BenjaLim not really. I mainly know the stuff needed to study algebraic groups
 
1:28 PM
@Tobias I remember being introduced to stiefel - whitney classes at the end of algebraic topology last sem
@Tobias have you studied GIT?
 
GIT?
 
geometric invariant theory
 
ahh, no, I haven't studied that
 
ok I thought that was related to stuff concerning algebraic groups.
 
my angle on all of this stuff is very algebraic
 
1:30 PM
well I am sure GIT is algebraic too no?
 
I don't really know anything about it
it might well be
 
@Tobias ok.
@Tobias I should go now to finish up some problems. TTYL :D
 
user19161
@BenjaLim I prefer geometric integration theory.
 
2:01 PM
O, load the mobile version
Why am I not getting a mobile version?
 
@skullpatrol remind me next year
 
oh @anon your avatar has changed
 
@eugene nice name
 
thanks i guess.
 
One of my favorite actors is Eugene
 
2:17 PM
I just noticed his name is "ramanujan-dirac" math.stackexchange.com/questions/278470/…
 
@BenjaLim What??????
 
2:32 PM
@amWhy You changed into a keyboard before valentines?
 
@OrangeHarvester I'll put on some hearts closer to valentine's day: enlarge the icon, you'll see the center key is "?" - fits my user...and I like the blue ;-)
 
@amWhy Ohh nice! btw, it that is actually the e key. ;-)
 
@OrangeHarvester hehehehe
 
@amWhy if I may ask, are you a graduate student?
 
@OrangeHarvester Yes, currently sort of on a year's "sabbatical" - ABD
 
2:37 PM
@orange you could use this as gravatar, it would be funny
 
@amWhy Okay, ABD means all but dissertion right?
 
@OrangeHarvester Yes...I've got funding/fellowship this year to research, so no need to "teach"
 
@amWhy Cool. What is your research field?
@Charlie Hahaha.
 
Hehehe
 
Good morning/evening/night
 
2:45 PM
Hi.
 
@Khromonkey buenos dias
 
guten tag
 
Bonjour
 
Pourjour
 
Haha
@Khromonkey ¿Como estás?
 
2:51 PM
todo tranquilo mi valedor
 
Bueno
 
como sigue la chamba?
 
hi everyone
 
@Khromonkey what?
 
3:00 PM
how's your job or studies going
 
user19161
Hi @cha
 
@JasonBourne hi Jasbear
@Khromonkey good, good
@Khromonkey you said you like to watch novels
 
@Charlie watch novels?
 
that was chokadkaakan, but I do like to read novels also
 
What is watching novels? Documentaries?
 
3:07 PM
@Khromonkey I mean "telenovelas"
 
oh, no, they suck
 
@Khromonkey haha the mexican one are famous here, I watched some of them
 
what?? Don't you wanna vomit and cry?
 
@Charlie What is the difference between a soap opera and a normal TV show? Or, for that purpose, the difference between a telenovela and a TV show?
 
why is zeta(r) = O(1 + 1/(r-1))? r real > 1
 
3:12 PM
@OrangeHarvester well the telenovela usually is like a romance book divided in chapter, we watch them, each "episide" depends in tge prevus and there are no seasons. The go on air mostly everyday for 3 minth, approx
 
@Charlie okay. but tv shows are the same too, divided into episodes which many times depend on previous ones.
 
@OrangeHarvester try this
 
@Charlie I still cannot see the difference. But this line is interesting "On the other hand, Ugly Betty has already proven to be a success story on ABC, although the network dropped the idea of the show as a telenovela and developed it as a standard weekly series". Why would timing of 'release' make a difference to the genre? Seems more like a marketing thing than actual genre difference.
 
@OrangeHarvester if you could watch one you would see. We can miss many epiaodes and still understand whats going on, telenovelas are slow some are mushy, the story is often the same
 
Can someone please tell me how this partial fraction decomposition was done? Specifically, the last two fractions; I don't understand why that is a correct decomposition.
 
3:25 PM
@Charlie Yes. I understand that too. :-) Sorry, I cannot see any difference. May be I am just dumb witted in this respect.
 
@PaulManta, it's just a guess
 
@PaulManta Partial fraction decomposition is just a method to get a current fraction as a sum of fractions with desired denominators. May be in this context, the desired denomiators are what are shown by the decomposition.
I think the decomposition is related to laplace transform, but I am not sure how this decomposition is going to be useful there.
 
@OrangeHarvester Thanks! Yes, it is related to the Laplace transform.
To see if I got this right, the simple fractions can be of any form as long as the the degree(nominator) >= degree(denominator) - 1?
 
@PaulManta Actually, you have a typo there.
It should be degree(numerator)< degree of (denonimator)
 
3:48 PM
@Theorem any problem for today?
 
@Charlie : i have so many :D
what are u interested in
ring theory , functional analysis
 
Hehehe
 
anyone who knows some of the basics about weyl's algebra ?
 
Sorry, no
 
@Charlie : same here , i have to learn it
 
3:54 PM
@Theorem are you graduate student?
 
@Charlie : not yet
graduate student means the one who has started with phd right ? i often get confused
i mean phd courses or so
 
@Theorem do you mean Weyl algebras or do you refer to some book about algebra by Weyl?
 
@Tobias : yes , some source where its discussed nicely .
nicely in the sense not very advanced , where things are skipped superfast
:P
 
that was not really a yes/no question, but I assume you mean the first one then
 
@Theorem so you are undergraduate?
 
3:58 PM
the distinction between undergraduate and graduate is not always the relevant one for people outside the US
 
@Charlie : to apply for phd i have another 1.5 years left , so i guess i am an undergraduate student.
@Tobias : Yes , thats why its often difficult to distinguish
 
Interesting
 
@Theorem I don't really know anything about the
Weyl algebras
 
@Tobias : are u from US ?
 
I have seen them mentioned in various talks, but that is about it
no, from Denmark
visiting the US at the moment
 
3:59 PM
can u tell me what it means to be a graduate student ?
 

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