For any interpolatory ternary subdivision scheme with two-ring stencils for a regular triangular or quadrilateral mesh, in this paper we show that the critical Hölder smoothness exponent of its basis function cannot exceed log3 11(≈ 2.18266), where the critical Hölder smoothness exponent of a function f : R2 7→ R is defined to be ν∞(f) := sup{ν : f ∈ Lip ν}. On the other hand, for both regular ...

A von Neumann regular extension of a semiprime ring naturally deenes a epimorphic extension in the category of rings. These are studied, and four natural examples are considered, two in commutative ring theory, and two in rings of continuous functions.

The concept of convex ordered hyperrings associated with a strongly regular relation was investigated in this study. In paper, we first studied hyperatom elements and then characterizations quotient rings. Is there θ on hyperring R for which R/θ is ring? This leads to an ring obtained from hyperring.