  The observations of the total electronic component and the positron fraction
in cosmic rays by the FERMI, HESS, ATIC, and PAMELA instruments are studied
with analytical propagation models, both for a set of discrete sources and for
a spatially smooth source distribution. The positron fraction over the entire
energy range of ~1-100 GeV is shown to fit with the nested leaky box model. We
derive the spectrum of electrons in cosmic rays arising from direct
acceleration by the sources and discuss the narrow spectral feature in the
spectrum.
