In this paper, a system of differential equations determining timelike and spacelike ruled surfaces are established in the lines space, using the invariant quantities of a given geodesic curves on the surface in Lorentz space. The solution of the system of differential equations are obtained in spacial cases and as relation of this solutions are given corollaries. Mathematics Subject Classifica...

The idea that quantum gravity can be realized at the TeV scale is extremely attractive to theorists and experimentalists alike. This proposal leads to extra spacial dimensions large compared to the elec-troweak scale. Here we give a very systematic view of the foundations of the theories with large extra dimensions and their physical consequences .

We study finite blow-up solutions of the heat equation with nonlinear boundary conditions. We provide a sufficient condition for the single point blow-up at the origin and a precise spacial singularity of the blow-up profile. Mathematics subject classification (2010): 35K20, 35B44.

A mathematical driver model is given in the spacial equation form, which takes into account the previewed information of the path. Optimal control method is considered for the ideal no time-delay case and Lyapunov-Krasovskii functional approach is applied to deal with drivers’ reaction time-delay. For both cases, exponential stability is guaranteed for the closedloop system.