Let $M_R$ be a non-zero‎ ‎module and ${mathcal F}‎: ‎sigma[M_R]times sigma[M_R]‎ ‎rightarrow$ Mod-$Bbb{Z}$ a bifunctor‎. ‎The‎ ‎$mathcal{F}$-reversibility of $M$ is defined by ${mathcal‎ ‎F}(X,Y)=0 Rightarrow {mathcal F}(Y,X)=0$ for all non-zero $X,Y$‎ ‎in $sigma[M_R]$‎. ‎Hom (resp‎. ‎Rej)-reversibility of $M$ is‎ ‎characterized in different ways‎. ‎Among other things‎, ‎it is shown‎ ‎th...

We propose to generate steady-state microbunching in a storage ring with a reversible seeding scheme. High gain harmonic generation (HGHG) and echo-enabled harmonic generation (EEHG) are two promising methods for microbunching linac electron beams. Because both schemes increase the energy spread of the seeded beam, they cannot drive a coherent radiator turn-by-turn in a storage ring. However, r...

To develop a π-conjugation circuit switched by redox reaction between 3-pyridone and 3-hydroxypyridine, ring-contracted analogue of oxypyriporphyrin, 2-oxypyritriphyrin(1.2.1) was prepared. When 2-oxypyritriphyrin treated with NaBH4, not only the 3-oxypyridine unit, but also meso-carbon reduced. The reduced analog could be oxidized again to afford in reversible manner.