On the stability of Cartan embeddings of compact symmetric spaces

Dedicated to Professor Tadashi Nagano on his sixtieth birthday     

Proton-neutron quasiparticle RPA with separable Gamow-Teller forces

A comprehensive representation is presented of a generalized form of the proton-neutron quasiparticle RPA model, originally introduced by Halbleib and Sorensen almost thirty years ago. The model uses separable Gamow-Teller forces, including, in addition to the particle-hole force of the former model, the particle-particle force, which is of decisive importance for β⁺ decay andββ decay. The above model has further been extended to the treatment of odd-odd nuclei. An extension is also made to transitions from nuclear excited states. This is essential for calculations of nuclear weak transition rates in the high-temperature interior of massive stars. Complementing the discussion of Halbleib and Sorensen on the particle-hole force, the structure of the RPA dispersion relation is discussed with emphasis on effects of the particle-particle force.     

A characterization of ℵ1-free abelian groups and its application to the chase radical

A groupA is an ℵ₁-free abelian group iffA is a subgroup of the Boolean power Z^(B) for some complete Boolean algebraB. The Chase radicalvA=Σ{C≦A: Hom(C, Z)=0 &C is countable). The torsion class {A:vA=A} is not closed under uncountable direct products.     

Shape Measurement from Endoscopic Images: Determination of Dimensional Scale Factor by a Photometric Method

We propose a new method to measure surface topography using a monocular endoscope. The surface structure is obtained up to a scale factor from an image sequence taken through a conventional CCD endoscope. The scale factor is determined by a photometric method, and the actual size of the object can be determined. The principle and experimental results are presented.