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Random updates | Delta Epsilons
https://deltaepsilons.wordpress.com/2010/06/14/random-updates
Mathematical research and problem solving. June 14, 2010. Posted by Akhil Mathew in Uncategorized. It’s been another two months already since anyone last posted here, hasn’t it? So, first of all, Damien Jiang. Have each uploaded the papers resulting from our RSI projects to arXiv. I’ve been discussing the story of my project on representation theory and the mathematics around it on my personal blog. See in particular here. I don’t really know what’s going to become of this blog as we all now ...You are c...
Nim-Chomp | Delta Epsilons
https://deltaepsilons.wordpress.com/2010/08/19/nim-chomp
Mathematical research and problem solving. August 19, 2010. Posted by lumixedia in combinatorics. Tags: combinatorial game theory. Wow, I’m really not cut out for helping to maintain a blog, am I? So what finally prompted me to post was Dr. Khovanova’s description of the game of Nim-Chomp at her blog. Which she suggested I respond to. First let’s pretend the bottom left square is not actually poisoned. We can transform this easy-Nim-Chomp into regular Nim as follows: for a given position in easy-Nim-...
A Puzzle | Delta Epsilons
https://deltaepsilons.wordpress.com/2010/06/25/a-puzzle
Mathematical research and problem solving. June 25, 2010. Posted by genericme in Uncategorized. Consider a set of. Are drawn randomly at a time, with replacement. What is. The expected number of draws I have to make to have drawn all of the objects? I have yet to find a satisfactory closed-form expression for even. I obtain an ugly series in terms of Stirling numbers of the second kind. However, I suspect that. Is this a well-known problem? June 25, 2010. I don’t known what it is in general. June 25, 2010.
Intel day 4 | Delta Epsilons
https://deltaepsilons.wordpress.com/2010/03/14/intel-day-4
Mathematical research and problem solving. March 14, 2010. Posted by Akhil Mathew in General. The second mathematician asked me to give an overview of my project in detail, so I went into my usual spiel. She asked me a few questions along the way about how the results were proved. Finally, she asked where I was going to go to college. I said that I didn’t know yet. This was a somewhat longer interview. 1 somebody - March 19, 2010. Well done Akhil for your prize. March 20, 2010. March 24, 2010. You are co...
Is early specialization good? | Delta Epsilons
https://deltaepsilons.wordpress.com/2010/03/04/is-early-specialization-good
Mathematical research and problem solving. Is early specialization good? March 4, 2010. Posted by Akhil Mathew in General. Thomas Sauvaget asked a question. On MO on whether specializing early is a good thing. It got into an interesting discussion, which continues. On his blog. I have placed some of my own thoughts there, so I won’t ramble here. In an unrelated note, if you haven’t already seen it, you ought to watch the MAA’s great. Also, cf. this MO thread for some good alternatives. July 9, 2010.
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Reversed Gronwall-Bellman’s inequality | Ngô Quốc Anh
https://anhngq.wordpress.com/2015/01/24/reversed-gronwalls-inequality
January 24, 2015. Reversed Gronwall-Bellman’s inequality. Filed under: Uncategorized — Tags: Gronwall inequality. 8212; Ngô Quốc Anh @ 23:01. In 1943. A nonlinear generalization of the Gronwall Bellman inequality is known as Bihari’s inequality. First, we consider the Gronwall inequality. Bounds by integrals based on lower bound. Be real-valued continuous functions defined on. And satisfies the differential inequality. Is bounded by the solution of the corresponding differential equation. That is to say.
Conformal Changes of the Green function for the conformal Laplacian | Ngô Quốc Anh
https://anhngq.wordpress.com/2014/12/21/conformal-changes-of-the-green-function-for-the-conformal-laplacian
December 21, 2014. Conformal Changes of the Green function for the conformal Laplacian. Filed under: Uncategorized — Tags: conformal changes. 8212; Ngô Quốc Anh @ 11:00. Long time ago, I talked about conformal changes for various geometric quantities on a given Riemannian manifold. Frequently used in conformal geometry in general, or when solving the prescribed scalar curvature equation in particular, is the conformal Laplacian, defined as follows. Is the scalar curvature of the metric. Such that for any.
On the simplicity of the first eigenvalue of elliptic systems with locally integrable weight | Ngô Quốc Anh
https://anhngq.wordpress.com/2015/04/28/on-the-simplicity-of-the-first-eigenvalue-of-elliptic-systems-with-locally-integrable-weight
April 28, 2015. On the simplicity of the first eigenvalue of elliptic systems with locally integrable weight. Filed under: Uncategorized — Ngô Quốc Anh @ 0:52. Of interest in this note is the simplicity of the first eigenvalue of the following problem. A simple variational argument shows that. Exists and can be characterized by. Further arguments show that. Is achieved by some positive pair. In the sense that for any test pair. By the simplicity of. We mean the eigenspace associated with. I did not consi...
Conformal change of the Laplace-Beltrami operator | Ngô Quốc Anh
https://anhngq.wordpress.com/2014/12/31/conformal-change-of-the-laplace-beltrami-operator
December 31, 2014. Conformal change of the Laplace-Beltrami operator. Filed under: Uncategorized — Tags: conformal changes. 8212; Ngô Quốc Anh @ 23:55. Happy New Year 2015! In the last entry in 2014, I talk about conformal change of the Laplace-Beltrami operator. A Riemannian manifold of dimension. A conformal metric of. Recall the following formula for the Laplace-Beltrami operator. Calculated with respect to the metric. Is the determinant of. Then, it is natural to consider the relation between. Can yo...
The conditions (NN), (P), (NN+) and (P+) associated to the Paneitz operator for 3-manifolds | Ngô Quốc Anh
https://anhngq.wordpress.com/2015/02/22/the-conditions-nn-p-nn-and-p-associated-to-the-paneitz-operator-for-3-manifolds
February 22, 2015. The conditions (NN), (P), (NN ) and (P ) associated to the Paneitz operator for 3-manifolds. Filed under: Uncategorized — Tags: Q-curvature. 8212; Ngô Quốc Anh @ 18:54. Of recent interest is the prescribed Q-curvature on closed Riemannian manifolds since it involves high-order differential operators. In a previous post. I have talked about prescribed Q-curvature on 4-manifolds. Recall that for 4-manifolds, this question is equivalent to finding a conformal metric. That is to solving.
The failure of compact Rellich-Kondrachov embedding: Unbounded domains and critical exponents | Ngô Quốc Anh
https://anhngq.wordpress.com/2015/01/07/the-failure-of-compact-rellich-kondrachov-embedding-unbounded-domains-and-critical-exponents
January 7, 2015. The failure of compact Rellich-Kondrachov embedding: Unbounded domains and critical exponents. Filed under: Uncategorized — Ngô Quốc Anh @ 19:49. In a very old entry, I talked about an extension of Rellich-Kondrachov. Theorem for embeddings between Sobolev spaces. For the sake of convenience, here is the statement of this extension:. Extension of Rellich-Kondrachov for bounded domains). Let. Be an open, bounded Lipschitz domain, and let. 1 The case of unbounded domains. In such a way that.
MSRI Workshops | Ngô Quốc Anh
https://anhngq.wordpress.com/edocument/msri-workshops
Here you can find a list of workshops and summer schools concerning general relativity hosted by MSRI. Hot Topics: Black Holes in Relativity. September 14, 2009 – September 18, 2009. Https:/ www.msri.org/workshops/522. July 09, 2012 – July 20, 2012. Https:/ www.msri.org/summer schools/657. Connections for Women: Mathematical General Relativity. September 03, 2013 – September 04, 2013. Https:/ www.msri.org/workshops/690. Ever since the epic work of Yvonne Choquet-Bruhat on the well-posedness of Einstein&#...
An extension of the Rellich-Kondrachov theorem | Ngô Quốc Anh
https://anhngq.wordpress.com/2010/05/05/an-extension-of-the-rellich-kondrachov-theorem
May 5, 2010. An extension of the Rellich-Kondrachov theorem. 8212; Tags: Rellich-Kondrachov. 8212; Ngô Quốc Anh @ 14:00. In mathematics, the Rellich-Kondrachov theorem is a compact embedding. Theorem concerning Sobolev spaces. It is named after the Italian-Austrian mathematician Franz Rellich. Be an open, bounded Lipschitz domain, and let. Then the Sobolev space. Is continuously embedded in the. And is compactly embedded in. It is worth noticing from the theory of Sobolev spaces that. Our aim is to prove.
Prescribed Q-curvature on 4-manifolds | Ngô Quốc Anh
https://anhngq.wordpress.com/2011/01/27/prescribed-q-curvature-on-4-manifolds
January 27, 2011. Prescribed Q-curvature on 4-manifolds. 8212; Tags: Paneitz operator. 8212; Ngô Quốc Anh @ 3:40. Be a compact Riemannian. Manifold, and let. Denote the Ricci tensor and the scalar curvature of. A natural conformally invariant in dimension four is. Is commonly refered to the. Is commonly denoted by. The second elementary symmetric polynomial in its eigenvalues. Note that, under a conformal change of the metric. Denotes the Paneitz operator. For any conformal metric. Denotes the Weyl tensor.
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Delta Epsilons | Mathematical research and problem solving
Mathematical research and problem solving. Extensions of Line Bundles on the Projective Line. January 26, 2015. Posted by Dennis in algebraic geometry. The following is probably obvious to experts, as it is easy to find generalizations using google. However, this humble master’s student didn’t find this most basic case, so it’s probably worth writing down. We will be working over the projective line. Over a field. The basic question is that, since we know that there exist nontrivial. Edit: Sometime after...
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