Following Kolokoltsov’s work [1], we present an extension of mean-field control theory in quantum framework. In particular such is done naturally by considering the Belavkin filtering and a setting. this setting, dynamics described controlled equation McKean-Vlasov type. We prove well-posedness under imperfect measurement records. Furthermore, show purification assumption propagation chaos for ...

We investigate the exact results of the Navier-Stokes equations using the methods developed by Polyakov. It is shown that when the velocity field and the density are not independent, the Burgers equation is obtained leading to exact N-point generating functions of velocity field. Our results show that, has to be generelized the operator product expansion, proposed by Polyakov both in the absenc...

we investigate the exact renormalization group (RG) in Einstein gravity coupled to N-component scalar field, working in the effective average action formalism and background field method. The truncated evolution equation is obtained for the Newtonian and cosmological constants. We have shown that screening or antiscreening behaviour of the gravitational coupling depends cricially on the choice ...

where c represents the mass concentration evolving with time t > 0, κ is the chemical diffusion in units of m3.s−1, and v the velocity field. We note that this Fick’s equation is written in a general form, where x = (x1, ..., xn) is a variable in an n-dimensional space. Accordingly, sums stretch from i, j = 1, ...n (but applications are sought in 2d and 3d spaces), and t > 0 is the time variabl...

This paper develops a method for solving Einstein’s equation numerically on multicube representations of manifolds with arbitrary spatial topologies. This method is designed to provide a set of flexible, easy to use computational procedures that make it possible to explore the never before studied properties of solutions to Einstein’s equation on manifolds with arbitrary toplogical structures. ...

Let $Rin textbf{C}^{mtimes m}$ and $Sin textbf{C}^{ntimes n}$ be nontrivial involution matrices; i.e., $R=R^{-1}neq pm~I$ and $S=S^{-1}neq pm~I$. An $mtimes n$ complex matrix $A$ is said to be an $(R, S)$-symmetric ($(R, S)$-skew symmetric) matrix if $RAS =A$ ($ RAS =-A$). The $(R, S)$-symmetric and $(R, S)$-skew symmetric matrices have a number of special properties and widely used in eng...

Electromagnetic localization and existence of gap solitons in nonlinear metamaterials, which exhibit a stop band in their linear spectral response, is theoretically investigated. For a self-focusing Kerr nonlinearity, the equation for the electric field envelope with carrier frequency in the stop band where the magnetic permeability μ(ω) is positive and the dielectric permittivity ǫ(ω) is negat...

The equation of state for quark matter is derived for a nonlocal, chiral quark model within the mean field approximation. Special emphasis is on the occurrence of a diquark condensate which signals a phase transition to color superconductivity and its effects on the equation of state. We present a fit formula for ’Bag pressure’, which is a constant in case when the quark matter is not color sup...

Inflationary consistency equations relate the scalar and tensor perturbations. We elucidate the infinite hierarchy of consistency equations of single-field inflation, the first of which is the well-known relation A2T/A 2 S = −nT/2 between the amplitudes and the tensor spectral index. We write a general expression for all consistency equations both to first and second-order in the slow-roll expa...