An Alternative Way to Generalize the Pentagon

We introduce the concept of a pentagonal geometry as a generalization of the pentagon and the Desargues configuration, in the same vein that the generalized polygons share the fundamental properties of ordinary polygons. In short, a pentagonal geometry is a regular partial linear space in which for all points x, the points not collinear with the point x, form a line. We compute bounds on their parameters, give some constructions, obtain some nonexistence results for seemingly feasible parameters and suggest a cryptographic application related to identifying codes of partial linear spaces.     

Mass separator for radioactive isotopes

A new isotope separator has been designed, constructed, and put into routine operation for separation of ¹³³Xe providing a major advancement and significant cost reduction in preparation of this radioactive isotope. The design features and advantages are discussed that expedite high purity separation of relatively small quantities of this isotope. These advantages could be easily used to expedite separation of other shorter-lived radioactive isotopes.     

Optical rectification coefficient in an oxide quantum dot with different confinement potentials

Exciton binding energies, oscillator strength, optical rectification coefficients and second harmonic generation are investigated using three different confinement potentials in a CdO/ZnO core/shell quantum dot. The bare potential, Smorodinsky–Winternitz potential and Woods–Saxon potential are employed in the Hamiltonian. The position dependent dielectric function is used. The electronic properties are found using variational formulism within a single band effective mass approximation whereas the optic properties are investigated using compact density matrix approach. The results show that different confinement potentials lead to significant changes in the coefficients of optical rectification and the second harmonic generations and the effects of confined potentials are more pronounced in the strong confinement region. The resonant peaks in the nonlinear optical rectification coefficients and second harmonic generation are blue shifted to larger photon energies with the various confined potentials and the results are enhanced using Smorodinsky–Winternitz potential. The obtained results can be applied for the potential applications for fabricating opto-electronic devices.     

Right-angled Coxeter polytopes, hyperbolic six-manifolds, and a problem of Siegel

By gluing together the sides of eight copies of an all-right angled hyperbolic six-dimensional polytope, two orientable hyperbolic six-manifolds with Euler characteristic ?1 are constructed. They are the first known examples of orientable hyperbolic six-manifolds having the smallest possible volume.