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A bstract We report the first measurement of the inclusive
e +e − → $$ b\overline{b} $$ → $$ {D}_s^{\pm } $$ X ande +e − → $$ b\overline{b} $$ → D 0/ $$ {\overline{D}}^0 $$ X cross sections in the energy range from 10. 63 to 11. 02 GeV. Based on these results, we determineσ (e +e − → $$ {B}_s^0{\overline{B}}_s^0 $$ X ) andσ (e +e − → $$ B\overline{B} $$ X ) in the same energy range. We measure the fraction of events at Υ(10860) to be$$ {B}_s^0 $$ f s= ( )%. We determine also the ratio of the$$ {22.0}_{-2.1}^{+2.0} $$ inclusive branching fractions$$ {B}_s^0 $$ ($$ \mathcal{B} $$ $$ {B}_s^0 $$ → D 0/ $$ {\overline{D}}^0 $$ X )/ ($$ \mathcal{B} $$ $$ {B}_s^0 $$ → $$ {D}_s^{\pm } $$ X ) = 0. 416 ± 0. 018 ± 0. 092. The results are obtained using the data collected with the Belle detector at the KEKB asymmetric-energye +e − collider.