Linear optical systems acting on photon number states produce many interesting evolutions, but cannot give all the allowed quantum operations input state. Using Toponogov's theorem from differential geometry, we propose an iterative method that, for any arbitrary operator $U$ $n$ photons in $m$ modes, returns $\widetilde{U}$ which can be implemented with linear optics. The approximation is loca...

In this article, Ritz approximation have been employed to obtain the numerical solutions of a class of the fractional optimal control problems based on the Caputo fractional derivative. Using polynomial basis functions, we obtain a system of nonlinear algebraic equations. This nonlinear system of equation is solved and the coefficients of basis polynomial are derived. The convergence of the num...

We consider the full information best choice problem from a sequence X1, . . . , Xn of independent random variables. Under the basic assumption of convergence of the corresponding imbedded point processes in the plane to a Poisson process we establish that the optimal choice problem can be approximated by the optimal choice problem in the limiting Poisson process. This allows to derive approxim...

A direct numerical solution of the radiative transfer equation is typically expensive, since the radiative intensity depends on time, space and direction. An expansion in the direction variables yields an equivalent system of infinitely many moments. A fundamental problem is how to truncate the system. Various closures have been presented in the literature. We formulate the method of optimal pr...

In this paper an approximation scheme is developed for the solution of the linear quadratic Gaussian (LQG) control on a finite time interval for hereditary systems with multiple noncommensurate delays and distributed delay. The solution here proposed is achieved by means of two approximating subspaces: the first one to approximate the Riccati equation for control and the second one to approxima...