225Ac/213Bi generator based on inorganic sorbents

A scheme of an “inverse” generator based on an inorganic sorbent (annealed zirconium and yttrium mixture oxides) has been proposed and tested. The generator demonstrated high yield of the 213Bi product (up to 97 % in 0.5 mL of eluate), high degree of purification from the actinium isotopes (up to 10−2 % of initial 225Ac in 3 M NaNO3 solution), as well as the products of 227Ac decay, and low radiation impact on the sorbent. Application of circulating approach to the sorption of 213Bi provides decreasing processing time to 5 min at higher yield of the product.

Inverses of generators of integrated fractional resolvent operator functions

This paper is devoted to the inverse generator problem in the setting of generators of integrated resolvent operator functions. It is shown that if the operator A is the generator of a tempered β-times integrated α-resolvent operator function ((α, β)-ROF) and it is injective, then the inverse operator A−1 is the generator of a tempered (α, γ)-ROF for all γ > β + 1/2, by means of an explicit representation of the integrated resolvent operator function based in Bessel functions of first kind. Analytic resolvent operator functions are also considered, showing that A−1 is in addition the generator of a tempered (δ, 0)-ROF for all δ < α. Moreover, the optimal decay rate of (α, β)-ROFs as t → ∞ is given. These result are applied to fractional Cauchy problem unsolved in the fractional derivative.