We present an X-ray spectroscopic analysis of two active dwarf stars with e
xtremely short rotation periods, HD 197890 (Speedy Mic) and Gliese 890, usi
ng X-ray data acquired with the ASCA observatory. We analyze the X-ray spec
trum of Speedy Mic in two separate time intervals, one corresponding to an
apparent stellar flare, the other to "quiescence" or the nonflaring state.
We also present a reanalysis of the ASCA spectrum of the M dwarf stellar bi
nary YY Gem, during both quiescent and flaring states. We use the recently
updated MEKAL plasma code to model these spectra and find that a minimum of
two temperature components are required to obtain good fits for all three
stars. The inferred emission measures of the hot components in YY Gem and S
peedy Mic, and the temperature of the hot component in the case of YY Gem,
increase significantly during the observed X-ray flares, in agreement with
previous studies of similar stellar X-ray flares. In addition, metal abunda
nces that are low compared to the solar photospheric values are preferred (
but not required) for the quiescent coronae of Gliese 890 and Speedy Mic, w
hile for the quiescent corona of YY Gem, subsolar metal abundances are requ
ired and solar abundance models can be ruled out with high confidence. We c
ombine the results of this study with those of previous ASCA and ROSAT anal
yses of late-type dwarf stars with known rotation rates to obtain a sample
of 17 G, K, and M dwarfs. We find a strong correlation of the X-ray to bolo
metric luminosity ratio, L-X/L-bol, both with the rotation period and the R
ossby number (R-o), in agreement with previous studies. Using a homogeneous
subset of 10 dwarfs for which we have purely ASCA-derived temperatures and
elemental abundances, we find that the temperature of the hottest componen
t present in their coronae is correlated with this luminosity ratio, as exp
ected. Finally, we note that the Fe abundances for all active dwarf stars h
aving normalized X-ray luminosities log (L-X/L-bol) -3.7 are significantly
subsolar, whereas the Fe abundances in the less active stars are within a f
actor of 2 of the solar value.