  To look for possible phenomenological connections between pulsar's timing
properties and emissions from pulsar wind nebulae and their pulsars, we studied
the power-law component of the X-ray emissions from 35 pulsar wind nebulae
which have a detected pulsar in X-rays. Our major results are in the following:
(1) The power-law component of the X-ray luminosities, in the energy range from
0.5 keV to 8 keV, of the nebulae and of the pulsar both show a strong
correlation with the pulsar spin-down power ($\dot{E}$), consistent with
earlier studies. However, equally significant correlations with the magnetic
field strength at the light cylinder ($B_{\rm lc}$) are also found. The similar
significance level of the correlations with $\dot{E}$ and with $B_{\rm lc}$
suggests that not only $\dot{E}$ but also $B_{\rm lc}$ plays an important role
in understanding these power-law emissions. (2) Thermal X-ray emissions are
detected in 12 pulsars among the 35 samples. With derived temperature as one
additional variable, we found that the photon indices of pulsar's non-thermal
X-ray power-law spectra can be well described by a linear function of $\log P$,
$\log\dot{P}$ and temperature logarithm $\log T$. It indicates that the surface
temperature of neutron stars plays an important role in determining the energy
distribution of the radiating pair plasma in pulsar's magnetospheres.
