On the noncommutative and nonassociative geometry of octonionic space time, modified dispersion relations and grand unification
The octonionic geometry (gravity) developed long ago by Oliveira and Marques, J. Math. Phys. 26, 3131 (1985) is extended to noncommutative and nonassociative space time coordinates associated with oct...
The octonionic geometry (gravity) developed long ago by Oliveira and Marques, J. Math. Phys. 26, 3131 (1985) is extended to noncommutative and nonassociative space time coordinates associated with oct...
Complex variables for separation of the Hamilton-Jacobi equation on real pseudo-Riemannian manifolds
In this paper the geometric theory of separation of variables for the time-independent Hamilton-Jacobi equation is extended to include the case of complex eigenvalues of a Killing tensor on pseudo-Rie...
In this paper the geometric theory of separation of variables for the time-independent Hamilton-Jacobi equation is extended to include the case of complex eigenvalues of a Killing tensor on pseudo-Rie...
Optimal shape of a blob
J. Math. Phys. 48, 073518 (2007); doi:10.1063/1.2752008
Published 27 July 2007
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This paper presents the solution to the following optimization problem: What is the shape of the two-dimensional region that minimizes the average Lp distance between all pairs of points if the area of this region is held fixed? Variational techniques are used to show that the boundary curve of the optimal region satisfies a nonlinear integral equation. The special case p=2 is elementary and for this case the integral equation reduces to a differential equation whose solution is a circle. Two nontrivial special cases, p=1 and p=![[infinity]](http://scitation.aip.org/stockgif3/infin.gif)
, have already been examined in the literature. For these two cases the integral equation reduces to nonlinear second-order differential equations, one of which contains a quadratic nonlinearity and the other a cubic nonlinearity.
©2007 American Institute of Physics
, have already been examined in the literature. For these two cases the integral equation reduces to nonlinear second-order differential equations, one of which contains a quadratic nonlinearity and the other a cubic nonlinearity.
©2007 American Institute of Physics
| History: | Received 20 January 2007; accepted 30 May 2007; published 27 July 2007 |
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http://link.aip.org/link/?JMAPAQ/48/073518/1 |
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