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Abstract We obtain generalizations of the classical Menchov–Rademacher theorem to the case of continuous orthogonal systems. These results are applied to show the existence of Moller wave operators in Schrödinger evolution. 

How can an electron induce oxidative damage in DNA DNA damage caused by the dissociative electron attachment (DEA) has been well-studied in the gas and solid phases. However, understanding of this process at the fundamental level in solution is still a challenge. The electrons, after losing their kinetic energy via ionization and excitation events, are thermalized and undergo a multistep hydration process with a time constant of ca. ≤ 1 ps, to becoming fully trapped as a hydrated or solvated electron (esol- or eaq-). Prior to the formation of esol-, the electron exists in its presolvated (or prehydrated) state (epre-) with no kinetic energy. We used picosecond pulse radiolysis to generate electrons in water or in liquid diethylene glycol (DEG) to observe the dynamics of capture of these electrons by DNA/RNA bases, nucleosides, and nucleotides. In diethylene glycol, we demonstrate that unlike esol- and epre-, eqf- effectively attaches itself to the RNA-nucleoside, ribothymidine, forming the excited state of the anion that undergoes the N1-C1 ́ glycosidic bond dissociation. Thanks to DEA, this process induced in fact by eqf- leads to an oxidation of the parent molecule similar to the hydroxyl radical (•OH), leading to the same glycosidic bond (N1-C1 ́) cleavage.