The fractional supersymmetry chiral algebras, A (K) , in two-dimensional conformal field theory are extended Virasoro algebras with fractional spin currents J (K) . We show that associativity and closure of A (K) determines its structure constants in the case that the Virasoro algebra is extended by precisely one current.We compute the structure constants of the A (K) algebras explicitly and we show that correlators of J (K) 's satisfy non-Abelian braiding relations.

A perturbation model is developed for sound scattering by a poroelastic seafloor having roughness small compared to the acoustic wavelength. The sediment is assumed to be homogeneous and isotropic with wave propagation described by Biot’s equations. When applied to sandy sediments, the model predicts backscattering levels that are substantially lower than those of a fluid model having the same roughness, density, sound speed, and attenuation.

We construct the K = 8 fractional superconformal algebras. There are two such extended Virasoro algebras, one of which was constructed earlier, involving a fractional spin (equivalently, conformal dimension) 6 5 current. The new algebra involves two additional fractional spin currents with spin 13 5 . Both algebras are nonlocal and satisfy non-abelian braiding relations. The construction of the algebras uses the isomorphism between the Z 8 parafermion theory and the tensor product of two tricritical Ising models. For the special value of the central charge c = 52 55 , corresponding to the eighth member of the unitary minimal series, the 13 5 currents of the new algebra decouple, while two spin 23 5 currents (level-2 current algebra descendants of the 13 5 currents) emerge. In addition, it is shown that the K = 8 algebra involving the spin 13 5 currents at central charge c = 12 5 is the appropriate algebra for the construction of the K = 8 (four-dimensional) fractional superstring.

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Abstract— Efficient and very‐compact projectors embedded into mobile consumer‐electronic devices, such as handsets, media players, gaming consoles, and GPS units, will enable new consumer use and industry business models. A keystone component for such projectors is a green laser that is commensurately efficient and compact. A synthetic green‐laser architecture is described that can achieve efficiencies of 15%. The architecture consists of an infrared distributed Bragg reflector laser coupled into a second‐harmonic‐generation device for conversion to green.