Higher order integrability in generalized holonomy

Higher Order Integrability in Generalized Holonomy

Supersymmetric backgrounds in M-theory often involve four-form flux in addition to pure geometry. In such cases, the classification of supersymmetric vacua involves the notion of generalized holonomy taking values in SL(32,R), the Clifford group for eleven-dimensional spinors. Although previous investigations of generalized holonomy have focused on the curvature RMN (Ω) of the generalized SL(32...

Generalized Higher Order Spt-functions

We give a new generalization of the spt-function of G.E. Andrews, namely Sptj(n), and give its combinatorial interpretation in terms of successive lower-Durfee squares. We then generalize the higher order spt-function sptk(n), due to F.G. Garvan, to jsptk(n), thus providing a two-fold generalization of spt(n), and give its combinatorial interpretation.

Generalized higher order Stirling numbers

Integrability of the Higher-Order Nonlinear Schrödinger Equation Revisited

Only the known integrable cases of the Kodama-Hasegawa higherorder nonlinear Schrödinger equation pass the Painlevé test. Recent results of Ghosh and Nandy add no new integrable cases of this equation. Being a true high-technology application of a mathematical object, the optical soliton in fiber optical lines of communications is an ideal carrier of information because the integrability of its...

Generalized structure of higher order nonclassicality

A generalized notion of higher order nonclassicality (in terms of higher order moments) is introduced. Under this generalized framework of higher order nonclassicality, conditions of higher order squeezing and higher order subpoissonian photon statistics are derived. A simpler form of the Hong-Mandel higher order squeezing criterion is derived under this framework by using an operator ordering ...