On the support of general local cohomology modules and filter regular sequences

Let R be a commutative Noetherian ring with non-zero identity and a an ideal of R. In the present paper, we examine the question whether the support of Hn a (N;M) must be closed in Zariski topology, where Hn a (N;M) is the nth general local cohomology module of nitely generated R-modules M and N with respect to the ideal a

Different mechanism of two-proton emission from proton-rich nuclei 23^{23}Al and 22^{22}Mg

Two-proton relative momentum ($q_{pp}$) and opening angle ($\theta_{pp}$) distributions from the three-body decay of two excited proton-rich nuclei, namely $^{23}$Al $\rightarrow$ p + p + $^{21}$Na and $^{22}$Mg $\rightarrow$ p + p + $^{20}$Ne, have been measured with the projectile fragment separator (RIPS) at the RIKEN RI Beam Factory. An evident peak at $q_{pp}\sim20$ MeV/c as well as a peak in $\theta_{pp}$ around 30$^\circ$ are seen in the two-proton break-up channel from a highly-excited $^{22}$Mg. In contrast, such peaks are absent for the $^{23}$Al case. It is concluded that the two-proton emission mechanism of excited $^{22}$Mg is quite different from the $^{23}$Al case, with the former having a favorable diproton emission component at a highly excited state and the latter dominated by the sequential decay process