Some unique group-measure space decomposition results

Some Observations on Dirac Measure-Preserving Transformations and their Results

Dirac measure is an important measure in many related branches to mathematics. The current paper characterizes measure-preserving transformations between two Dirac measure spaces or a Dirac measure space and a probability measure space. Also, it studies isomorphic Dirac measure spaces, equivalence Dirac measure algebras, and conjugate of Dirac measure spaces. The equivalence classes of a Dirac ...

Some more space-group corrections.

A survey of approximately 100,000 entries in recent releases of the Cambridge Structural Database (CSD) has uncovered 156 crystal structures that were apparently described in inappropriate space groups. We have revised these space groups and prepared CIFs containing the new coordinates and brief comments describing the revisions.

Some Special Results of Measure Theory

Some Transformations Having a Unique Measure with Maximal Entropy

1. Introduction Let X be a compact metric space and T: X-> X a homeomorphism of X onto X. Let M(T) denote the collection of all T-invariant Borel probability measures on X. By Krylov and Bogolioubov's work we know M(T) is non-empty (see [10]). M{T) is a convex set and closed in the weak topology. For /x e M(T), h(T, p) will denote the measure-theoretic entropy of T with respect to p. Ifh top (T...

Some Results for the Hodge Decomposition Theorem in Euclidean Three-Space

The Hodge Decomposition Theorem plays a significant role in the study of partial differential equations. Several interrelated propositions which are required for the proof of the Hodge theorem in Euclidean three-space are introduced and proved in a novel way. Mathematics Subject Classification: 58A05, 58A10, 47J05