Since their first occurrence in 2008, a rapid increase of new psychoactive substances (NPS) on the recreational drug market has been observed. One class NPS are synthetic opioids, which poses health risk due to high affinity and potency most these compounds for opioid receptors. Four receptor subtypes known, mü-opioid (MOR), delta-opioid (DOR), kappa-opioid (KOR) nociceptin receptor, G protein-...

An analysis of the Kimura 3ST model of DNA sequence evolution is given on the basis of its continuous Lie symmetries. The rate matrix commutes with a U(1)×U(1)×U(1) phase subgroup of the group GL(4) of 4× 4 invertible complex matrices acting on a linear space spanned by the 4 nucleic acid base letters. The diagonal ‘branching operator’ representing speciation is defined, and shown to intertwine...

The symmetry reduction of the equation u 0 +∇ u − 4 5 ∇u = 0 to ordinary differential equations with respect to all subalgebras of rank three of the algebra A E (1) ⊕ AC (3) is carried out. New invariant solutions are constructed for this equation.

Motivated by D-brane scenarios, we consider a non-supersymmetric model based on the gauge symmetry U (3) C ×U (3) L ×U (3) R which is equivalent to the SU (3) 3 " trinification " model supplemented by three U (1)s. Two U (1) combinations are anomalous while the third U (1) Z ′ is anomaly free and contributes to the hypercharge generator. This hypercharge embedding correspods to sin 2 θ W = 6 19...