User gstar2002 - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-21T07:42:11Z http://mathoverflow.net/feeds/user/19294 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/118169/is-there-a-relationship-between-entropy-of-a-fininte-distrete-probability-distrib Is there a relationship between Entropy of a fininte distrete probability distribution and the squre sum of the values of probability mass function of that distribution? gstar2002 2013-01-06T01:48:21Z 2013-01-08T16:54:50Z <p>Sorry for the long title. What I mean is that for two vectors (a_1,...,a_n) and (b_1,...,b_n) with the property $a_i,b_i \geq 0$ and $\sum a_i =\sum b_i =1$. </p> <p>If $-\sum a_ilog(a_i) > -\sum b_ilog(b_i)$ implies $\sum a_i^2 &lt; \sum b_i^2$ or something similar?</p> http://mathoverflow.net/questions/116708/do-the-eigenvectors-find-by-use-pca-on-a-set-of-data-point-a-good-replacement-fo Do the Eigenvectors find by use PCA on a set of data point, a good replacement for Random Projection when I later on use L1Magic to reconstruct the sparse vector? gstar2002 2012-12-18T14:45:39Z 2012-12-18T15:16:51Z <p>Concretely if I use the first k eigenvectors find by PCA with a point set A,to project another sparse vector b to k dimension subspace, then use L1-magic to recover b. Will this be better than a Random Projecton. L1-magic is a software tool for compress sensing. b is not a vector from A, but possibly have the same distribution of A.</p> http://mathoverflow.net/questions/112485/why-are-two-ranomly-choosed-vectors-in-high-dimension-space-likely-to-be-perpandi why are two ranomly choosed vectors in high dimension space likely to be perpandicular to each other? gstar2002 2012-11-15T14:19:38Z 2012-11-15T14:19:38Z <p>I once heard that if you ranomly choosed two vectors in high dimension space, it is very likely that they are perpandicular to each other? Can some give me an intuitive explaination for this? thanks.</p> http://mathoverflow.net/questions/111033/what-is-the-distribution-of-the-distance-between-a-specific-word-in-a-text-which What is the distribution of the distance between a specific word in a Text which is generated by a markov process? gstar2002 2012-10-29T22:10:40Z 2012-10-29T23:23:30Z <p>What is the distribution of the distance between a specific word in a Text which is generated by a markov process?</p> <p>For example for a text which is generated by a multinomial distribution over words, this distribution of distance will be a Geometric distribution. Thanks.</p> http://mathoverflow.net/questions/108646/is-is-preferable-to-use-a-difference-formula-of-higher-order-of-accuracy-for-spat Is is preferable to use a difference formula of higher order of accuracy for spatial derivatives to solve this IVP problem ? gstar2002 2012-10-02T15:35:39Z 2012-10-10T18:17:11Z <p>I want to numerically integrate the equation $\partial_t u= a(t) \partial_xu+b\partial_{xxx}u+c$ to get $u(t)$. Is is preferable to use a difference formula of higher order of accuracy for spatial derivatives? Thanks. I am using a Semi-Discretization method called Method of Lines (vertical) to treat this problem.</p> http://mathoverflow.net/questions/103137/problem-using-finite-difference-to-solve-a-initial-value-problem Problem using finite difference to solve a initial value problem gstar2002 2012-07-26T00:50:49Z 2012-08-01T00:30:09Z <p>Hallo, I tried to use 'finite difference' method to solve a Initial Value Problem(IVP). For the two boundaries I used periodical condtion and for the differential operators I used 4th degree center approximations. But as result, I got this thing. Where comes this strange oscillation What do you think could be the problem. Should I use a smaller x stepsize? Will use a forward approximation help? Thanks. Actually I am using matlab's odes15s.</p> <p>The strange thing is that, if I use a biger x stepsize, say 0.1, i will get a smooth result. With s stepsize 0.06, I will get the result showed in the picture. I tried ode45, which is based on an explicit Runge-Kutta (4,5) formula, the Dormand-Prince pair and ode23tb, which is an implementation of TR-BDF2. I got the same result.</p> <p>Thanks.</p> <p><a href="http://imgur.com/96eXy" rel="nofollow"><img src="http://i.imgur.com/96eXy.png" alt="" title="Hosted by imgur.com" /></a></p> <p>\begin{aligned} \dot{q} &amp; = -\frac{\partial (6*q^2/5*h)}{\partial x}-\frac{3*q}{h^2}+h*h'''-(1+10*cos(pi*t))*h*h'\ \end{aligned}</p> <p>\begin{aligned} \dot{h} &amp; = -\frac{\partial q}{\partial x} \end{aligned}</p> <p>\begin{aligned} h(t,0) = h(t,10),q(t,0) = q(t,10) \end{aligned}</p> <p>$h(0,x)$, $q(0,x)$ are known.</p> http://mathoverflow.net/questions/97771/what-is-the-relation-between-vector-space-and-the-defination-of-vector-in-physics what is the relation between vector space and the defination of vector in physics. gstar2002 2012-05-23T15:33:16Z 2012-05-23T15:33:16Z <p>In physics book there are some wired definition of vector in terms of how the quantity behave under rotation of axes[Kundu P26]. Are they trying to define vector space in term of the results of special kind of map or some thing like that? or we are talking about different things? Thanks. </p> <p>Kundu, Pijush K., and Ira M. Cohen. Fluid Mechanics, Second Edition. 2nd ed. Academic Press, 2001.</p> http://mathoverflow.net/questions/118169/is-there-a-relationship-between-entropy-of-a-fininte-distrete-probability-distrib/118373#118373 Comment by gstar2002 gstar2002 2013-01-15T22:11:30Z 2013-01-15T22:11:30Z @ R W, first off, thanks a lot for the very informative reply! But I still have one more question, what do you mean by &quot;naturally defined infinitesimal limits &quot;? do you mean n go to infinite? http://mathoverflow.net/questions/118169/is-there-a-relationship-between-entropy-of-a-fininte-distrete-probability-distrib Comment by gstar2002 gstar2002 2013-01-06T21:51:34Z 2013-01-06T21:51:34Z and I think for the case n = 2, it is true. http://mathoverflow.net/questions/118169/is-there-a-relationship-between-entropy-of-a-fininte-distrete-probability-distrib Comment by gstar2002 gstar2002 2013-01-06T10:42:59Z 2013-01-06T10:42:59Z @Anthony I am not sure, if it can be ture under this specific condiction. http://mathoverflow.net/questions/116708/do-the-eigenvectors-find-by-use-pca-on-a-set-of-data-point-a-good-replacement-fo Comment by gstar2002 gstar2002 2012-12-18T15:51:55Z 2012-12-18T15:51:55Z @Steve Hi Steve I changed my question a little, hope than will help. http://mathoverflow.net/questions/112485/why-are-two-ranomly-choosed-vectors-in-high-dimension-space-likely-to-be-perpandi Comment by gstar2002 gstar2002 2012-11-15T15:33:35Z 2012-11-15T15:33:35Z hi, @Speyer you are right, that is exactly what am thinking about. Can you give a tip where can I find the exact calculating for the problem. http://mathoverflow.net/questions/108646/is-is-preferable-to-use-a-difference-formula-of-higher-order-of-accuracy-for-spat/109314#109314 Comment by gstar2002 gstar2002 2012-10-29T20:28:51Z 2012-10-29T20:28:51Z The acture system is more complicated, but I think the Fourier method is applicable. http://mathoverflow.net/questions/108646/is-is-preferable-to-use-a-difference-formula-of-higher-order-of-accuracy-for-spat/109314#109314 Comment by gstar2002 gstar2002 2012-10-29T20:00:19Z 2012-10-29T20:00:19Z Thanks David. I decided to use MOL to solve the problem. But I will try to use the Fourier method, if I have one more chance. http://mathoverflow.net/questions/108646/is-is-preferable-to-use-a-difference-formula-of-higher-order-of-accuracy-for-spat Comment by gstar2002 gstar2002 2012-10-04T15:25:47Z 2012-10-04T15:25:47Z hi, @tom-dickens it is a equation resulting from fluid dynamics. http://mathoverflow.net/questions/103137/problem-using-finite-difference-to-solve-a-initial-value-problem Comment by gstar2002 gstar2002 2012-08-01T11:35:11Z 2012-08-01T11:35:11Z what I am plotting here is the height of the fluid surface. It is h in the equation. http://mathoverflow.net/questions/103137/problem-using-finite-difference-to-solve-a-initial-value-problem Comment by gstar2002 gstar2002 2012-08-01T08:49:54Z 2012-08-01T08:49:54Z It is a model of faraday instability in thin fluid film http://mathoverflow.net/questions/103137/problem-using-finite-difference-to-solve-a-initial-value-problem Comment by gstar2002 gstar2002 2012-08-01T00:18:21Z 2012-08-01T00:18:21Z @Ryan, I edit my question. I hope that will turn it to a suitable question here. thanks http://mathoverflow.net/questions/103137/problem-using-finite-difference-to-solve-a-initial-value-problem Comment by gstar2002 gstar2002 2012-07-26T10:57:05Z 2012-07-26T10:57:05Z I am asking about the theoretical reason. The ODE have up to third degree differential operators in it and it is nonlinear. http://mathoverflow.net/questions/97771/what-is-the-relation-between-vector-space-and-the-defination-of-vector-in-physics Comment by gstar2002 gstar2002 2012-05-23T17:05:27Z 2012-05-23T17:05:27Z OK. I am not sure if this is off topic. I think it should be a part of Mathematical physics. I do not think i should post on physicsoverflow, physicists are less interested in those abstract math thing.