Negotiations among nations on policies to promote international economic integration have widened in recent years to cover new issues; for example, foreign direct investment rules, policies to promote competition, the international movement of labor, the environment and monetary union. In these negotiations, a consensus among the parties negotiating is usually lacking and many of these negotiat...
Abstract : Let be a 2nd order ODE. By Cartan equivalence method, we will study the local equivalence problem under the transformations group of time-fixed coordinates. We are going to solve this problem by an applicable method which has been recognized by R. Gardner, and classify them.
Abstract- Kernel trick and projection to tangent spaces are two choices for linearizing the data points lying on Riemannian manifolds. These approaches are used to provide the prerequisites for applying standard machine learning methods on Riemannian manifolds. Classical kernels implicitly project data to high dimensional feature space without considering the intrinsic geometry of data points. ...
Here, we investigate the possible optical anisotropy of vacuum due to gravitational field. In doing this, we provide sufficient evidence from direct coordinate integration of the null-geodesic equations obtained from the Lagrangian method, as well as ray-tracing equations obtained from the Plebanski’s equivalent medium theory. All calculations are done for the Schwarzschild geometry, which resu...
Reverse subdivision aims at constructing a coarser representation of an object given by a fine polygon mesh. In this paper, we first derive a mask for reverse Loop subdivision that can be applied to both regular and extraordinary vertices. The mask is parameterized, and thus can also be used in reversing variants of Loop subdivision, such as those proposed by Warren and Litke. We apply this mas...
Michael R. Douglas,
Bobby S. Acharya,
Simon K. Donaldson,
Viacheslav V. Nikulin,
Robert C. Myers,
An overview of the geometry of string theory, which sets the various contributions to this proceedings in this context.