User riadh - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-20T06:24:57Z http://mathoverflow.net/feeds/user/26066 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/126169/injectivity-radius Injectivity radius Riadh 2013-04-01T10:42:52Z 2013-04-01T10:42:52Z <p>Dear members, If you don't mind I would like to ask the following question about the calculation of the injectivity radius on some space. Indeed, I almost determined the injectivity radius (local and global) of the space of matrices $diag(\lambda_{1},\lambda_{2},\ldots,\lambda_{m})V: \lambda_{1}\geq\lambda_{2}\geq\ldots\geq\lambda_{m}>0, \sum_{i=1}^{m}\lambda_i^2=1,V\in SO(m)$, is there any mean to deduce the injectivity radius of the space of matrices $diag(\lambda_{1},\lambda_{2},\ldots,\lambda_{m})V: \lambda_{1}>\lambda_{2}>\ldots>\lambda_{m}>0, \sum_{i=1}^{m}\lambda_i^2=1,V\in SO(m)$ Thank you for the help Riadh</p> http://mathoverflow.net/questions/124496/sub-series-of-the-exponential-serie sub series of the exponential serie Riadh 2013-03-14T10:24:19Z 2013-03-14T10:24:19Z <p>Dear members, If you don't mind I would like to ask about the limit of the series of the form $\sum_{n\geq0}\frac{1}{(kn)!}$ where k is a constant integer.</p> <p>Thannk you Riadh </p> http://mathoverflow.net/questions/120894/expression-of-the-restriction-of-the-laplace-beltrami-operator-to-a-submanifold Expression of the restriction of the Laplace-Beltrami operator to a submanifold Riadh 2013-02-05T18:33:54Z 2013-02-05T18:33:54Z <p>Hello everybody, Given the expression of the Laplace-Beltrami operator $\Delta_M$ on a Riemannian manifold $M$, is there any method for determining the expression of the Laplace-Beltrami operator $\Delta_N$ where $N$ is a submanifold of $M$. Actually I am interested in $N=S(Y,r)=( X\in M s.t. d(X,Y)=r)$ where $Y\in M$ and $r$ is constant. Thank you Riadh</p> http://mathoverflow.net/questions/118057/relation-between-singular-values-of-matrices-and-their-products Relation between singular values of matrices and their products Riadh 2013-01-04T15:02:57Z 2013-01-04T15:14:57Z <p>Hello everybody, Is there any explicit relation between the singular values $\lambda_X$ and $\lambda_Y$ of two same size matrices $X$ and $Y$, respectively, and the singular values $\lambda_{XY^t}$ of the matrix $XY^t$? Otherwise said, is there a function $f$ such that $\lambda_{XY^t}=f(\lambda_X , \lambda_Y)$?</p> <p>Thank you Riadh</p> http://mathoverflow.net/questions/105880/laplace-beltrami-operator-expression Laplace-Beltrami operator expression Riadh 2012-08-29T20:25:59Z 2012-08-29T21:12:57Z <p>In the book Shape and Shape Theory of Kendall in p.147 I found the following expression of the Laplace-Beltrami operator: $\sum_i\left({v_i^2-\nabla_{v_i}v_i}\right)$ where $v_i$ are orthonormal tangent vectors. So please what does the exponent 2 stands for?</p> <p>Thank you</p> http://mathoverflow.net/questions/118057/relation-between-singular-values-of-matrices-and-their-products/118059#118059 Comment by Riadh Riadh 2013-01-04T22:00:14Z 2013-01-04T22:00:14Z Thank you a lot for your help Riadh http://mathoverflow.net/questions/118057/relation-between-singular-values-of-matrices-and-their-products/118059#118059 Comment by Riadh Riadh 2013-01-04T16:00:03Z 2013-01-04T16:00:03Z Thank you Riadh http://mathoverflow.net/questions/105880/laplace-beltrami-operator-expression/105882#105882 Comment by Riadh Riadh 2012-08-30T15:04:09Z 2012-08-30T15:04:09Z Thank you Mr. Beno&#238;t for that consideration. Actually in the book shape and shape theory I'am supposed to know this definition of Laplace-Beltrami operator, yet I do not know it though I do know other commun definitions of the $\Delta$ operator. Actually up to now I assimilated $v_i^2$ to the directional derivative of $v_i$ in the direction of $v_i$, the problem is that when $v_i$ is a vector field, both directional derivative $v_i^2$ and the covariant derivative $\nabla_{v_i}v_i$ are identical and then $\sum_i\left(v_i^2-\nabla_{v_i}v_i\right)$ reduces to zero. Thank you again