Search results for nucleon decays $p rightarrow e^+X$, $p rightarrow mu^+X$, $n rightarrow ugamma$ (where $X$ is an invisible, massless particle) as well as dinucleon decays $np rightarrow e^+ u$, $np rightarrow mu^+ u$ and $np rightarrow tau^+ u$ in the Super-Kamiokande experiment are presented. Using single-ring data from an exposure of 273.4 kton $cdot$ years, a search for these decays yields a result consistent with no signal. Accordingly, lower limits on the partial lifetimes of $tau_{p rightarrow e^+X} > 7.9 times 10^{32}$ years, $tau_{p rightarrow mu^+X} > 4.1 times 10^{32}$ years, $tau_{n rightarrow ugamma} > 5.5 times 10^{32}$ years, $tau_{np rightarrow e^+ u} > 2.6 times 10^{32}$ years, $tau_{np rightarrow mu^+ u} > 2.2 times 10^{32}$ years and $tau_{np rightarrow tau^+ u} > 2.9 times 10^{31}$ years at a $90 % $ confidence level are obtained. Some of these searches are novel.
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