= Solution
All three processes are <weak charged current> transformations between neighboring <nuclear isobars>. Neglecting <neutrino masses>, and writing $M_a(A,Z)$ for a neutral atomic <mass>, their <Q values> are:
* <Beta-minus decay>: a <neutron> converts to a <proton>, emitting an <Electron> and an <electron antineutrino>,
$$
(A,Z)\longrightarrow(A,Z+1)+e^-+\bar\nu_e,\qquad
Q_{\beta^-}=M_a(A,Z)-M_a(A,Z+1)>0.
$$
* <Beta-plus decay>: a <proton> converts to a <neutron>, emitting a <Positron> and an <electron neutrino>,
$$
(A,Z)\longrightarrow(A,Z-1)+e^++\nu_e,\qquad
Q_{\beta^+}=M_a(A,Z)-M_a(A,Z-1)-2m_e>0.
$$
* <Electron capture>: a bound atomic <Electron> is absorbed in the conversion of a <proton> to a <neutron>,
$$
e^-+(A,Z)\longrightarrow(A,Z-1)+\nu_e,\qquad
Q_{\mathrm{EC}}=M_a(A,Z)-M_a(A,Z-1)>0.
$$
These formulae use the paper's <natural units>. With energies in MeV, <beta-plus decay> requires an atomic mass-energy difference exceeding $2m_ec^2=1.022\,\mathrm{MeV}$. The extra electron-mass subtraction arises from using neutral atomic rather than bare nuclear <masses>. <Electron capture> can occur when the atomic mass-energy difference is positive but below this threshold. For a particular capture shell or excited daughter, the available <energy> must also cover the electron-hole and nuclear <excitation energies>, and the small <nuclear recoil>. Small atomic binding corrections are suppressed in the displayed threshold formulae.
The question's fixed-$A$ family consists of <nuclear isobars>, rather than <isotopes>: <isotopes> have fixed $Z$. The <semi-empirical mass formula> gives a convex <nuclear mass parabola> as a function of $Z$ at fixed $A$. For odd $A$, <nuclear pairing> does not split the family into two branches, so there is \b[typically one beta-stable isobar], at the discrete minimum. Neighboring members can lower their <mass> by changing $Z$ toward it.
For even $A$, <nuclear pairing> lowers even-even <nuclei> and raises odd-odd <nuclei>, producing two offset <nuclear mass parabolas>. There are \b[often two beta-stable even-even isobars], separated by an odd-odd member to which neither can energetically decay. The number is not an exact universal rule: some even-$A$ chains have one or more than two such minima against single <beta decay>, and a few light odd-odd <nuclei> are stable. Stability against single <beta decay> also does not guarantee stability against <double beta decay>.
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