in this paper we study properties of symbols such that these belong to class of symbols sitting insidesm ρ,φ that we shall introduce as the following. so for because hypoelliptic pseudodifferential operatorsplays a key role in quantum mechanics we will investigate some properties of m−hypoelliptic pseudodifferential operators for which define base on this class of symbols. also we consider maxi...

We present an experimental demonstration of heralded single photons prepared in pure quantum states from a parametric down-conversion source. It is shown that, through controlling the modal structure of the photon pair emission, one can generate pairs in factorable states and thence eliminate the need for spectral filters in multiple-source interference schemes. Indistinguishable heralded photo...

It has recently been argued that there are no dynamic screening corrections to Salpeter’s enhancement factor in thermonuclear reactions, in the weak-screening limit. The arguments used were: 1) The Gibbs probability distribution is factorable into two parts, one of which, exp(−β∑ eiej/rij) (β = 1/kBT ), is independent of velocity space; and 2) The enhancement factor is w = 1 + βeZ1Z2〈φ〉 with 〈φ...

A perfectly one-factorable (P1F) regular graph is a graph admitting a partition of the edge-set into one-factors such that the union of any two of them is a Hamiltonian cycle. The case of cubic graphs is treated. The existence of a P1F cubic graph is guaranteed for each admissible value of the number of vertices. A description of this class was obtained by Kotzig in 1962. It is the purpose of t...

We address the generalization and transfer of sensorimotor programs in robot systems. We use a factorable control-based approach that provides a natural, discrete abstraction of the underlying continuous state/action space and thus allows for the application of learning algorithms that converge in practical amounts of time. We argue that our approach provides an efficient means for the adaptati...