27 research outputs found
A Compact Minimal Space Whose Cartesian Square Is Not Minimal
A compact metric space X is called minimal if it admits a minimal homeomorphism; i.e. a homeomorphism h:X→ X such that the forward orbit {hn(x):n=1, 2, ...} is dense in X, for every x ∈ X. In my talk I shall outline a construction of a family of 1-dimensional minimal spaces from A compact minimal space Y such that its square YxY is not minimal whose existence answer the following long standing problem in the negative.
Problem. Is minimality preserved under Cartesian product in the class of compact spaces?
Note that for the fixed point property this question had been resolved in the negative already 50 years ago by Lopez, and a similar counterexample does not exist for flows, as shown by Dirbák
Correlation-Polarization Effects in Electron/Positron Scattering from Acetylene: A Comparison of Computational Models
Different computational methods are employed to evaluate elastic
(rotationally summed) integral and differential cross sections for low energy
(below about 10 eV) positron scattering off gas-phase CH molecules. The
computations are carried out at the static and static-plus-polarization levels
for describing the interaction forces and the correlation-polarization
contributions are found to be an essential component for the correct
description of low-energy cross section behavior. The local model potentials
derived from density functional theory (DFT) and from the distributed positron
model (DPM) are found to produce very high-quality agreement with existing
measurements. On the other hand, the less satisfactory agreement between the
R-matrix (RM) results and measured data shows the effects of the slow
convergence rate of configuration-interaction (CI) expansion methods with
respect to the size of the CI-expansion. To contrast the positron scattering
findings, results for electron-CH integral and differential cross
sections, calculated with both a DFT model potential and the R-matrix method,
are compared and analysed around the shape resonance energy region and found to
produce better internal agreement