kinthelt

I'm looking for a good book on graph theory whose definition of a path allows repeated vertices. Anyone have any suggestions?

John opened a checking account in a bank on day d_0 and deposited there x_0 dollars.
Then on d_1 he deposited x_1.
Then on d_2 he deposited x_2.
...

Is there a theory of this kind of stochastic processes?

E.g. if differences d_1 - d_0, d_2 - d_1, ... distributed exponentially (Poisson process) and x_0, x_1, x_2...
lognormally (or Gauss, or Bernoulli, or ...), what would be distribution of $ total on day d ?

Notes augmented

We've enhanced and de-bugged Notes. If you haven't tried it yet, now's the time! You can create a private note when you ban multiple users. You can also delete multiple notes at once. Lastly, paid users have the option to add a note (visible only to you) whenever you add or remove a friend (guaranteed to avoid embarrassing social mishaps). If you don't currently have a paid account, you can upgrade now! It only takes a few minutes and costs less than a bad shopping mall haircut (plus, it's way more fashionable)!

Product tweaks and bug kill

1. In another effort to zap spam, comments containing links from domains LiveJournal deems untrustworthy are now automatically screened
2. If you sign up to get notifications of the Writer's Block question of the day, you'll now see the daily question in the email notification, so you'll have a little extra time to ponder before you post. You can subscribe to Writers Block notifications here
3. The issue causing random comments to vanish has been fixed!
4. If you visit a LiveJournal page and get prompted to log in, you'll be returned to the same page after you sign in (Thanks, Dreamwidth)!
5. If you don't edit the timestamp for an entry at all, the entry timestamp will indicate the time the entry was posted instead of the time the Update Journal page was loaded
6. Comments with paddings/backgrounds render correctly within the comment box (and will no longer wrap outside the box and break frames/margins)

New FCK fixes rich text editor!

1. We've updated our RTE (Rich Text Editor) to FCKeditor version 2.6.5
2. When switching from the RTE to HTML editor, links for syndicated feeds are no longer broken
3. RTE now functions properly in Safari 4.0
4. An extra line/space will not be auto-inserted whenever you switch from RTE to HTML editor
5. The insert image link now works correctly in all browsers

LiveJournal Cares

We’re pleased to introduce you to lj_cares, a new LiveJournal community dedicated to raising awareness and funds for U.S. charitable organizations that improve the health and well-being of people around the world. Each month, we’ll spotlight a nonprofit that is making a significant global impact through medical research, public outreach, and/or humanitarian social programs. Charities will be selected in accordance with the U.S. calendar of national health observances based on a high rating (of over 60%) on Charity Navigator and global scope of impact.

In this, our inaugural month of November, we will celebrate national adoption month by offering a charitable virtual gift (priced at $2.99) to support Love Without Boundaries, an organization that saves the lives of orphans with life-threatening diseases and places them in loving homes around the world. LiveJournal will donate 100% of the proceeds from the sale of charitable vgifts (we'll cover the cost of credit card transaction fees). To learn more about Love Without Boundaries, please visit lj_cares and read about how they helped save Baby Kang and the Rainbow Twins from fatal illnesses, who are now thriving in nurturing families. You can purchase your Love Without Boundaries gifts in the Virtual Gift shop.

Papered in postcards

A couple of weeks ago, we asked you to send in postcards to surround us with LiveJournal community. Thanks for coming through! We've received postcards all the way from Germany, Finland, and Canada and from all over the US, including Texas, Florida, Alaska, Montana, Wyoming, Indiana, Hawaii, and Oklahoma just to name just a handful. We're thrilled with our improved decor.

Please keep the love coming for one more week by writing to Frank the Goat, Esq., c/o LiveJournal, Inc., 539 Bryant Street, Suite 210, San Francisco, CA 94107. Be sure to include your username, since we'll be drawing the names of ten random contributors next Thursday to win paid account credits!

Photos of the week

We have more dazzling images posted by talented LiveJournal photographers from around the world. We're hoping to span the entire globe, so please continue posting and tagging. Of course, you can also sit back and enjoy the view at lj_photophile.

You can see a sample of this week's gorgeous photos and check out spotlight communities and awesome user content after the jump!

( Read more... )

Curtains

We thank you, once again, for joining us. See you next week!

A couple more questions

1. If T: H-->K has finite rank, then T*:K-->H has finite rank and dim(Im(T)) = dim(Im(T*)).

I'm not really sure how to approach this.. =/

2. Show that an idempotent operator is compact if and only if it has finite rank.

The "only if" is quite easy, because any finite rank operator is compact, but the other direction has me stuck



Thanks for any help!

Do you know about the new website for mathematicians? It's called mathoverflow, and was released less than a month ago. It's accessible mostly to people who have at least started math grad school (indeed having recently acquired that status, I only understand about a quarter of the questions in my field), but the idea is to post questions that should be interesting to other mathematicians, or to answer them. Read the FAQ and join. Or have you already?

EDIT@08:16 UTC/GMT. Wow. That was ugly. I expected it to go for 30 minutes and have maybe 1 minute of broken connectivity. Instead it lasted over 4 hours and we had 10 minutes of downtime directly related to the load balancer upgrades and then another 5-10 minutes of downtime when our primary Pingback database server crashed and the secondary couldn't take over; which could have been indirectly caused by the network upgrade missing a self-VIP.

Anyways, we're up, we're working, the load balancers are barely breaking a sweat right now and I need some food and a shot of whiskey. I don't even *like* whiskey!!

Thanks mhwest and dnewhall for helping out!

---

On Saturday the 14th at 4AM UTC/GMT we will be upgrading the operating system of our network load balancers to a newer version, one that will allow us to use both CPUs! Nifty, because multiprocessing is nice.

Since we have 2 load balancers, the plan is to upgrade 1 at a time, and there really should be very little impact to our website. Hopefully you won't notice a thing and I'll get to go back to the hotel and watch some wonderful late night infomercials.

We've got a lot of exciting projects coming up for 2010 and we're hoping that we'll be able to deliver them all to you, that you will find it useful/cool/lovely and then you will use the site even more. Behind-the-scenes work like this will give us the capacity to handle the anticipated traffic, so expect a few more maintenance windows especially in the beginning of next year as we've got some neat ideas to improve performance around here! We had the recent 30-45 minute outage yesterday due to one of our logging databases filling up disk space -- not so great design coupled with my human error in handling the initial problem -- and it looks like we're going to finally have some resources to eliminate stuff like that. I can't wait!

As usual, I will be updating status.livejournal.org before and after, just in case you are not able to reach our main website during the work.

Hi everyone,

I am seeking any reference material that eventually explains Hopf algebras. Really, I'd take anything that does a good job at explaining related topics starting with the definition of a module. I need something designed for a non-specialist.

Thanks in advance.

All right, so normally I wouldn't be posting like three questions at the same time, but I had swine flu this week (make sure you get the vaccine if you haven't already, because I promise you don't want the swine flu, it sucks) and couldn't go to class or meet with people. So with no further ado:

1) We're supposed to show that a simple Lie group is linear. In the hint sheet the professor gave us, he says, let C_g be the map that is conjugation by g, and let Ad(g) = T_1 C_g, the differential of this map. (I think this is called the adjoint representation or something.) I have no idea where this hint is going, and I don't see anything extra special about simple Lie groups that helps us buy this result, except perhaps that they are connected (because the identity component of a Lie group is a normal subgroup).

2) Next thing I'd like to show is that the differential of the inversion map (call it inv) is negative the identity. The hint sheet says to use the fact that exp is a homomorphism from lines through the origin in the Lie algebra to the Lie group. Certainly it's the case that exp(-v) = inv(exp(v)), and I think this is probably what we want, but I don't know how to get T_1 inv in there.

3) Last one for now I promise. Why would the differential of the determinant be trace?

Thanks for your help. I'm going to go hang my head in manifolds-induced shame now.

I'm re-taking the Math GRE tomorrow morning (ugh), and I want to take a couple peppermints. Does anyone know if small things such as this are permitted? I can't seem to find an answer to this specific question...


Edit: Well, I definitely did better this time, that much is for sure. I still don't really understand why graduate schools care if I can do 3 hours worth of hero-level integration, though....

The empire strikes back

In recent weeks, we've taken huge steps towards blocking spam accounts on LiveJournal. In fact, we've suspended as many as 30,000 accounts in a single day! We've implemented several pre-emptive measures to prevent the creation of spam accounts, and we've honed our detection of suspicious content. Spam bots are a crafty lot, so we'll continue to refine our tactics and keep up the good fight to keep you safe from spam attacks on LiveJournal.

RSS feeds again

If you're addicted to xkcd_rss, icanhaschzbrgr, or other syndicated feeds, we're pleased to report that we've resolved the update error that was mucking up your RSS feeds. While content was being pulled correctly, it wasn't being posted to the feeds themselves. Late last week, we finally nailed down what we hope was the root problem, so content should post properly. We thank you for your patience.

Wii have killer CSI Deadly Intent contests!

c_s_i

If you're a gamer who loves CSI, have Wii got news for you! c_s_i is sponsoring killer contests. Simply post a question to a member of the CSI crew. The winner will get a free copy of CSI: Deadly Intent for Nintendo Wii (with a retail value of $39.99) and get their question answered by a member of the CSI writing team! There's also a fantastic monthly contest. To enter, join c_s_i, play the online version of CSI: Deadly Intent, and respond to a two-part query for a chance to win a Wii! Entries will be judged on composition and originality. Sorry, but you must be a U.S. resident and over 18 years old to participate. Check out the rules here.

Enveloped in postcards

Last week, we asked you to send in postcards to help us decorate our drab concrete walls. Here's a photo of the results so far! Thank you so much and please keep them coming! You can mail them to Frank the Goat, Esq., c/o LiveJournal, Inc., 539 Bryant Street, Suite 210, San Francisco, CA 94107. Be sure to include your username, since we'll be giving ten random users paid account credits.

Photos of the week

If you haven't visited our new LiveJournal photo community, you're in for an amazing visual trip. LiveJournal users from around the world will take you on a scenic journey to everywhere. Post your own pictures or kick back and enjoy at lj_photophile. You can view some of this week's awesome photos after the jump. Please start tagging with geographic location, since we'd like to track all the places around the world represented in this community. Keep on commenting too!
( Read more... )

Ok, so I'm pretty much finished with my PhD and have started to look for postdoc positions. So far I've looked at mathjobs.org and EIMS and will contact people in my field (harmonic analysis and operator theory) and ask them to inform me if any kind of postdoc jobs open up (this is for the departments that aren't advertising an open postdoc position, though I'll directly email people of interest who are in departments that are advertising, just to inform them that I'm applying.)

So the question is, where else should I look for postdoc jobs (or really just academic jobs in general) to apply to?

I've seen the result all over the place, but no proof: The L^p-norm of a function f approaches the L-infty norm of f as p approaches infinity. Any illuminating clues?


EDIT: We assume f is in L^p and L^infty, so that it's in L^q for all q > p.

Two question:

1. Let B(H,K) denote the space of bounded linear operators H --> K. Show B(H,K) is complete under the operator norm ||T|| = sup{ ||Th|| : h in H and ||h||≤1 }.

I seem to really struggle with this operator norm guy. Obviously I want to start with a Cauchy sequence of operators and show that it converges to some operator in the space.... But I'm just not clear on how to do all that


2. Let g be in L^1(R). The operator L: L^2(R) --> L^2(R) defined by Lf(x) = ∫ g(x-y)f(y)dy is a bounded linear operator.


My initial thought is to try to realize g(x-y) as the kernel of some integral operator, but I'm not sure how to go about doing that exactly.

Any thoughts?


Thanks