Topologically Irreducible Representations and Radicals in Banach Algebras

It is shown that the topologically irreducible representationsof a normed algebra define a certain topological radical inthe same way that the strictly irreducible representations definethe Jacobson radical and that this radical can be strictly smallerthan the Jacobson radical. An abstract theory of ‘topologicalradicals’ in topological algebras is developed and usedto relate this radical to the Baer radical (prime radical).The relations with topologically transitive representationsand standard representations in the sense of Meyer are alsoexplored. 1991 Mathematics Subject Classification: 46H15, 46H25,16Nxx.     

Crystallization of the charged Bose gas at 0 K

From variational upper bounds of the ground state energies of the fluid and solid phases, we estimate that charged bosons melt at r_s ≈ 135, while charged fermions melt around r_s ≈ 70.     

Iron oxyhydroxide colloid formation by gamma-radiolysis

Gamma-irradiation of deaerated aqueous solutions containing FeSO(4) leads to the formation of uniform-sized colloidal particles of γ-FeOOH. At short irradiation times, or in solutions with a low initial [Fe(2+)](0), spherical particles with a size less than 10 nm are formed. These primary particles grow to form a dendritic structure upon longer irradiation, and the final size of the large particles is ～60 nm with a very narrow size distribution. Further prolonged irradiation does not change the final particle size. The narrow size distribution is attributed to rapid homogeneous radiolytic oxidation of soluble Fe(2+) to relatively insoluble Fe(3+) hydroxides [Fe(H(2)O)(6-n)(OH)(n)](3-n) leading to particle nucleation by spontaneous condensation. These primary particles then grow into γ-FeOOH particles with a dendritic structure. The final size reached at long times is regulated by the steady-state redox conditions established during long-term irradiation at the aqueous-solid interface.