  According to recent experimental data at GSI, the rates of the number of
daughter ions, produced by the nuclear K-shell electron capture (EC) decays of
the H-like ions 140Pr58+ and 142Pm60+, are modulated in time with periods
T_(EC) simeq 7 s and amplitudes a_(EC) simeq 0.20. We study a possible
time-dependence of the nuclear positron (beta^+) decay rate of the H-like
140Pr58+. We show that the time-dependence of the beta^+ decay rate of the
H-like 140Pr58+ ion as well as any H-like heavy ions cannot be observed. This
result can be used as a prediction for future analysis of the time-dependence
of the beta^+ decay rates of the H-like heavy ions 140Pr58+ and 142Pm60+ at GSI
for the test of the measuring method.
