We obtain the Killing equations and the corresponding infinitesimal isometries for the ten dimensional space generated by a large number of coincident D3-branes. In a convenient limit this space becomes an AdS5 × S 5 which is relevant for the AdS/CFT correspondence. In this case, using Poincaré coordinates, we also write down the Killing equations and infinitesimal isometries. Then we obtain a ...

We consider " cosmologically symmetric " (i.e. solutions with homogeneity and isotropy along three spatial dimensions) five-dimensional spacetimes with a scalar field and a three-brane representing our universe. We write Einstein's equations in a conformal gauge, using light-cone coordinates. We obtain explicit solutions: a. assuming proportionality between the scalar field and the logarithm of...

In this work we examine noncommutativity of position coordinates in classical symplectic mechanics and its quantisation. In coordinates {q i , p k } the canonical symplectic two-form is ω 0 = dq i ∧ dp i. It is well known in symplectic mechanics [5, 6, 7] that the interaction of a charged particle with a magnetic field can be described without a choice of a potential in a Lagrangian formalism. ...

In this paper, after defining pure proportional navigation guidance in the 3-dimensional state from a new point of view, range estimation for passive homing missiles isexplained. Modeling has been performed by using line of sight coordinates with a particulardefinition. To obtain convergent estimates of those state variables involved particularly inrange channel and unavailable from IR trackers...

We present a numerical method, based on a three-dimensional finite volume wave-propagation algorithm, for solving the Vlasov equation in a full six-dimensional (three spatial coordinates, three velocity coordinates) case in length scales comparable to the size of the Earth’s magnetosphere. The method uses Strang splitting to separate propagation in spatial and velocity coordinates, and is secon...