This is the second of a series of two papers where decoupling of unphysical states in the minimal pure spinor formalism is investigated. The multi-loop amplitude prescription for the minimal pure spinor superstring formulated in hep-th/0406055 involves the insertion of picture changing operators in the path integral. In the first paper it was shown that these operators are not BRST closed insid...

Apraxia of speech (AOS) is the impairment of motor programming. However, the exact nature of this deficit remains unclear. In particular, AOS without other speech-language deficit is called pure AOS, but it is very rare. When diagnosing AOS, the characteristic of articulation is considered a crucial criterion, which has been proposed for differentiating AOS from phonological and dysarthric diso...

A recently introduced model describing the folding of the triangular lattice is generalized allowing for defects in the lattice and written as an Ising model with nearest– neighbor and plaquette interactions on the honeycomb lattice. Its phase diagram is determined in the hexagon approximation of the cluster variation method and the crossover from the pure Ising to the pure folding model is inv...

A recently introduced model describing the folding of the triangular lattice is generalized allowing for defects in the lattice and written as an Ising model with nearest– neighbor and plaquette interactions on the honeycomb lattice. Its phase diagram is determined in the hexagon approximation of the cluster variation method and the crossover from the pure Ising to the pure folding model is inv...

Exact solutions of traveling wave are acquired by employ a relatively new technique which is called standard tanh method for nonlinear diffusion–convection equation. The applied the first time finding travelling equation , where n and m, integers, order (m=4, n=7) (m=5, n=9). Analytical equations obtained as polynomial in tanh(x), plots exact given. results compared with F-Expansion to validate...

We derive a hierarchy of stochastic evolution equations for pure states (quantum trajectories) for open quantum system dynamics with non-Markovian structured environments. This hierarchy of pure states (HOPS) is generally applicable and provides the exact reduced density operator as an ensemble average over normalized states. The corresponding nonlinear equations are presented. We demonstrate t...

We report Monte Carlo simulations that show both vapor-liquid and closed-loop liquid-liquid equilibrium in a pure substance, for a model fluid that forms orientation-dependent intermolecular bonds. This is the first time that direct evidence of liquid-liquid immiscibility in a pure fluid has been found using exact methods. Because the model is formulated in terms of a tetrahedrally coordinated ...