User quimey vivas - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-20T11:41:31Z http://mathoverflow.net/feeds/user/2245 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/18100/theorems-with-unexpected-conclusions/18115#18115 Answer by Quimey Vivas for Theorems with unexpected conclusions Quimey Vivas 2010-03-13T22:36:28Z 2010-03-13T22:36:28Z <p>I like <a href="http://en.wikipedia.org/wiki/Sharkovsky%27s_theorem" rel="nofollow">Sharkovskii's theorem</a>. It says that there is an explicit ordering of the natural numbers such that if $f:\mathbb{R}\rightarrow \mathbb{R}$ has a periodic point of least period m and m precedes n in the above ordering, then f has also a periodic point of least period n.</p> http://mathoverflow.net/questions/17901/existence-of-antiderivatives-of-nasty-but-elementary-functions/17903#17903 Answer by Quimey Vivas for existence of antiderivatives of nasty but elementary functions Quimey Vivas 2010-03-11T19:47:58Z 2010-03-12T12:24:42Z <p>I haven't a concrete example but there is a <a href="http://en.wikipedia.org/wiki/Darboux%27s_theorem_%28analysis%29" rel="nofollow">theorem</a> that says that the derivative of a function has the intermediate value property. This fact makes me think that could be a elementary function without antiderivative.</p> <p>EDIT:</p> <p>I am going to be more explicit:</p> <p>If f is a elementary function, it is defined in the interval (a,b), and it is the derivative of another function (not necessary an elementary function) then f satisfies the intermediate value property inside (a,b).</p> http://mathoverflow.net/questions/17519/how-to-compute-the-number-of-regular-spheres-needed-to-fill-a-rectangular-space/17522#17522 Answer by Quimey Vivas for How to compute the number of regular spheres needed to fill a rectangular space Quimey Vivas 2010-03-08T21:14:51Z 2010-03-08T21:14:51Z <p>Maybe this is useful: <a href="http://en.wikipedia.org/wiki/Sphere_packing" rel="nofollow"> Sphere Packing </a></p> http://mathoverflow.net/questions/17048/compute-the-centroid-of-a-3d-planar-polygon/17118#17118 Answer by Quimey Vivas for Compute the Centroid of a 3D Planar Polygon Quimey Vivas 2010-03-04T18:35:39Z 2010-03-04T18:35:39Z <p>These formulas could be deduced using <a href="http://en.wikipedia.org/wiki/Green_theorem" rel="nofollow"> Green's theorem </a>. For example the formula used to compute the polygon's area is proved using the vector field F=(-y/2,x/2).</p> <p>Maybe you can do the same in the space using analogous vector fields and <a href="http://en.wikipedia.org/wiki/Stokes_theorem" rel="nofollow"> Stokes' theorem </a>.</p> http://mathoverflow.net/questions/17901/existence-of-antiderivatives-of-nasty-but-elementary-functions/17903#17903 Comment by Quimey Vivas Quimey Vivas 2010-03-12T12:33:01Z 2010-03-12T12:33:01Z I want to say that there is a necessary condition in order to be the derivative of a derivable function defined in the interval (a,b). This condition is the intermediate value condition. I never use what you say, maybe I just misstated because I am not a native English speaker. I don't understand what is wrong in my post. Could you be more explicit please?