Nonempirical quantum chemical ST0-3G calculations were performed for cluster models of two oxygen-bridged T0 4 tetrahedra (T = Si, Al). The models are based on [(H0)3T0T(0H)3]"structures and, in case of Al-containing models (n = 1,2), their electric neutrality is ensured by adding positive point charges. The calculations suggest the occurrence of X4.I — O —Al^ pairings provided certain electric...

We report a new type of Hamiltonian equations and maximum principle for the optimal control of a Goursat system when the underlying domain of 2-D "time" is not rectangular and has non-smooth boundary. The resulting Hamiltonian equations form a system of impulsive hyperbolic partial differential equations, with the impulses induced by the conditions on the costate at points of discontinuity on t...

The reductions of the Heun equation to the hypergeometric equation by rational changes of its independent variable are classified. Heun-to-hypergeometric transformations are analogous to the classical hypergeometric identities (i.e., hypergeometric-to-hypergeometric transformations) of Goursat. However, a transformation is possible only if the singular point location parameter and normalized ac...

This paper develops a constructive method for finding a nilpotent basis for a special class of smooth nonholonomic distributions. The main tool is the use of the Goursat normal form theorem which arises in the study of exterior differential systems. The results are applied to the problem of finding a set of nilpotent input vector fields for a nonholonomic control system, which can then used to ...