The automatic generation of dynamic or complex audio signals has a wide range of applications, from sound effects design to virtual instrument implementation. Techniques for the creation of content in these domains typically involve searching though large input spaces in order to find combinations that produce interesting results. These input spaces can be viewed as all the possible input signa...

§1. Geometry of finite type and review of CR-extension theory . . . . .2. §2. Identification of CR vector fields and of Segre varieties . . . . . . . . . .4. §3. Segre varieties and extrinsic complexification . . . . . . . . . . . . . . . . . . . .10. §4. Segre sets and iterated complexifications . . . . . . . . . . . . . . . . . . . . . . . . .12. §5. Segre varieties and conjugate Segre variet...

We show that the complexification (Ã, τ̃) of a real locally pseudoconvex (locally absorbingly pseudoconvex, locally multiplicatively pseudoconvex, and exponentially galbed) algebra (A,τ) is a complex locally pseudoconvex (resp., locally absorbingly pseudoconvex, locally multiplicatively pseudoconvex, and exponentially galbed) algebra and all elements in the complexification (Ã, τ̃) of a commutati...

We show that a natural complexification and a mild generalization of the idea of completeness guarantee geodesic completeness of CliftonPohl torus; we explicitely compute all of its geodesics.

We show that a natural complexification and a mild generalization of the idea of completeness guarantee geodesic completeness of CliftonPohl torus; we explicitely compute all of its geodesics.