Octahedron Subgroups and Subrings

On Zero Subrings and Periodic Subrings

We give new proofs of two theorems on rings in which every zero subring is finite; and we apply these theorems to obtain a necessary and sufficient condition for an infinite ring with periodic additive group to have an infinite periodic subring. 2000 Mathematics Subject Classification. 16N40, 16N60, 16P99. Let R be a ring and N its set of nilpotent elements; and call R reduced if N = {0}. Follo...

Additive Subrings and Degeneracy

Suppose M ≡ N . Recently, there has been much interest in the classification of groups. We show that ‖π‖ > ∅. In [31], the authors address the structure of manifolds under the additional assumption that xΩ = πV . Therefore in [31], the main result was the classification of non-elliptic monoids.

The Octahedron Abstract Domain

An interesting area in static analysis is the study of numerical properties. Complex properties can be analyzed using abstract interpretation, provided that an adequate abstract domain is defined. Each domain can represent and manipulate a family of properties, providing a different trade-off between the precision and complexity of the analysis. The contribution of this paper is a new numerical...

Octahedron Environment Maps

In this paper, we examine the octahedron as a parameterization scheme to represent environment maps in real-time rendering applications. We discuss two projection schemes and show two convenient unfold mappings to pack the platonic solid into quadratic or rectangular textures. We carry out an analysis and consider rendering performance for interactive applications as well as the quality of repr...

Arrays and the Octahedron Recurrence