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We report the first measurement of the inclusivee⁺e⁻→$$ b\overline{b} $$$b\overline{b}$→$$ {D}_s^{\pm } $$$D_s^{\pm }$Xande⁺e⁻→$$ b\overline{b} $$$b\overline{b}$→ D⁰/$$ {\overline{D}}^0 $$${\overline{D}}^0$Xcross sections in the energy range from 10.63 to 11.02 GeV. Based on these results, we determineσ(e⁺e⁻→$$ {B}_s^0{\overline{B}}_s^0 $$$B_s^0{\overline{B}}_s^0$X) andσ(e⁺e⁻→$$ B\overline{B} $$$B\overline{B}$X) in the same energy range. We measure the fraction of$$ {B}_s^0 $$$B_s^0$events at Υ(10860) to bef_s= ($$ {22.0}_{-2.1}^{+2.0} $$${22.0}_{-2.1}^{+2.0}$)%. We determine also the ratio of the$$ {B}_s^0 $$$B_s^0$inclusive branching fractions$$ \mathcal{B} $$$B$($$ {B}_s^0 $$$B_s^0$→ D⁰/$$ {\overline{D}}^0 $$${\overline{D}}^0$X)/$$ \mathcal{B} $$$B$($$ {B}_s^0 $$$B_s^0$→$$ {D}_s^{\pm } $$$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.

We present a search for the lepton-flavor-violating decays$$ {B}_s^0 $$$B_s^0$→ℓ^∓τ^±, whereℓ=e, μ, using the full data sample of 121 fb⁻¹collected at the Υ(5S) resonance with the Belle detector at the KEKB asymmetric-energye⁺e⁻collider. We use$$ {B}_s^0{\overline{B}}_s^0 $$$B_s^0{\overline{B}}_s^0$events in which one$$ {B}_s^0 $$$B_s^0$meson is reconstructed in a semileptonic decay mode and the other in the signal mode. We find no evidence for$$ {B}_s^0 $$$B_s^0$→ ℓ^∓τ^±decays and set upper limits on their branching fractions at 90% confidence level as$$ \mathcal{B} $$$B$($$ {B}_s^0 $$$B_s^0$→ e^∓τ^±)<14×10⁻⁴and$$ \mathcal{B} $$$B$($$ {B}_s^0 $$$B_s^0$→ μ^∓τ^±)<7.3×10⁻⁴. Our result represents the first upper limit on the$$ {B}_s^0 $$$B_s^0$→ e^∓τ^±decay rate.