most recent 30 from http://mathoverflow.net 2013-06-18T05:13:54Z http://mathoverflow.net/feeds/user/7228 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/68745/necessary-conditons-for-implicit-function LaLone 2011-06-24T15:43:24Z 2011-06-25T20:03:34Z

<p>The Inverse Function Theorem provides sufficient conditions to determine when a function is defined implicitly by a relation. I would like to know some ways to determine when no such function is defined.</p> <p>Below is a link to a specific example and conjecture. </p> <p><a href="http://math.stackexchange.com/questions/46750/how-to-prove-the-implicit-function-theorem-fails" rel="nofollow">http://math.stackexchange.com/questions/46750/how-to-prove-the-implicit-function-theorem-fails</a></p>

http://mathoverflow.net/questions/68254/mathematicians-working-on-social-choice-theory LaLone 2011-06-20T00:19:25Z 2011-06-20T14:58:52Z

<p>Can someone tell me which mathematicians are actively working on social choice theory, or point to a place where they may be listed?</p>

http://mathoverflow.net/questions/21486/good-economical-textbook-for-undergraduate-intro-to-diff-eq-for-engineers/31547#31547 LaLone 2010-07-12T13:28:34Z 2010-07-12T13:28:34Z

<p>If the students at your College/University own the Stewart Calculus book, chapters 9 and 17 are probably a good place to start. Or at least to suggest as a supplement to the primary text you choose.</p>

http://mathoverflow.net/questions/13011/probability-in-number-theory/30131#30131 LaLone 2010-07-01T02:39:46Z 2010-07-01T13:34:01Z

<p>I recently noticed a connection, while looking at a campy sort of problem.</p> <p>The problem goes like this A strange sort of prison has 1200 cells and 1200 guards (each numbered 1-1200). Whenever a guard turns his key in a lock it either locks the cell or unlocks the cell. Every night guard 1 goes through and turns his key in each cell, locking all of them. Then guard 2 turns his key in each cell that is divisible by 2 (which unlocks each of these) and so on until all the guards have gone through their round. So the question is at the end of the night how many cells are locked, which cells are they. </p> <p>So you can figure out pretty easily that if a cell has an even number of divisors then it will be unlocked at the end of the night. Whereas if the cell has an odd number of divisors then it will end up locked. You can use the tau function to think about when a number will have an even number of divisors and when it will have an odd number of divisors. (I won't ruin the solution for anyone) While I was working on this I noticed that the probability of an integer having an odd number of divisors decreases by a factor of 1/2 whenever a new prime factor is added to the prime factorization of the integer. In other words to compute the probability that an integer has an odd number of divisors you can raise 1/2 to the number of distinct primes in the prime factorization. </p> <p>Once you figure out which cells are locked at the end of the night this conclusion will probably seem pretty worthless but it got me interested in the connection between number theory and probability</p>

http://mathoverflow.net/questions/68745/necessary-conditons-for-implicit-function/68760#68760 LaLone 2011-06-25T02:06:18Z 2011-06-25T02:06:18Z

Yeah that result was mentioned I guess it was kind of assumed the variables are Real. I elaborated a little to say that this means you can't have x or y defined as functions of u and v in an open n-hood of any point (u,v) because the only point that's a candidate is (0,0) and even at this point any variation in u or v will no longer satisfy the system. What I'm curious about is if there are other ways to make conclusions like that.

http://mathoverflow.net/questions/68254/mathematicians-working-on-social-choice-theory LaLone 2011-06-20T12:33:29Z 2011-06-20T12:33:29Z

I did find a few related tags, fair division, game theory, mathematical economics.

http://mathoverflow.net/questions/68254/mathematicians-working-on-social-choice-theory LaLone 2011-06-20T12:28:57Z 2011-06-20T12:28:57Z

I think there is enough activity in the area to warrant some type of related tag on MO.

http://mathoverflow.net/questions/68254/mathematicians-working-on-social-choice-theory/68265#68265 LaLone 2011-06-20T12:13:11Z 2011-06-20T12:13:11Z

I agree this was a great answer, by looking at his webpage, list of visitors and publications I found several others working in this field. Thanks!