In this paper we consider the notion of commutation for a pair of continuous and convex Hamiltonians, given in terms of commutation of their Lax– Oleinik semigroups. This is equivalent to the solvability of an associated multi– time Hamilton–Jacobi equation. We examine the weak KAM theoretic aspects of the commutation property and show that the two Hamiltonians have the same weak KAM solutions ...

In any cable or power line communications, impulse noise is known to be the most difficult noise to filter. In particular, non periodic asynchronous impulse noise is impossible to predict. Under such noise conditions, the OFDM symbol generally used in PLC is corrupted. To overcome this problem, the signal-to-noise ratio is generally improved by detecting and/or filtering the noise. This leads h...

The commutation relations of composite fields are studied in the 3, 2 and 1 spatial dimensions. It is shown that the field of an atom consisting of a nucleus field and an electron field satisfies, in the space-like asymptotic limit, the canonical commutation relations within the sub-Fock space of the atom. The field-particle duality in the bound state is discussed from a statistical point of vi...

The commutation relations of the composite fields are studied in the 3, 2 and 1 space dimensions. It is shown that the field of an atom consisting of a nucleus and an electron fields satisfies, in the space-like asymptotic limit, the canonical commutation relations within the sub-Fock-space of the atom. The field-particle duality in the bound state is discussed from the statistics point of view...

Recent trends in Radio Telescopes deploy BLDC motors for their 2-axis rotation. BLDC motors implement electronic commutation by avoiding carbon brushes and mechanical commutation. Resolvers mounted on rotor shaft of BLDC motors form good sensor feedback and work in-conjunction with RDC and FPGA interface to implement speed and position control. Brushes in DC torque form an important source of a...

Based on the analysis of the principle of torque ripple with commutation time for brushless DC motor, this paper proposes a method to restrain commutation torque ripple. This method is an improved predictive current control. First, an expression is built about the torque ripple during commutation time. After analysis, the non-commutation phase current is related to torque ripple. Then, a kind o...

Non-equilibrium quantum field theory studies time dependence of processes which are not available for the S-matrix description. One of the new methods of investigation in non-equilibrium quantum theory is the stochastic limit method. This method is an extension of the works by Bogoliubov, van Hove and Prigogine and it permits to study not only the system but also the reservoir degrees of freedo...

Possible (algebraic) commutation relations in the Lagrangian quantum theory of free (scalar, spinor and vector) fields are considered from mathematical view-point. As sources of these relations are employed the Heisenberg equations/relations for the dynamical variables and a specific condition for uniqueness of the operators of the dynamical variables (with respect to some class of Lagrangians)...