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Using a 3.19 fb−1 data sample collected at an 𝑒+𝑒− center-of-mass energy of 𝐸cm=4.178 GeV with the BESIII detector, we measure the branching fraction of the leptonic decay 𝐷+𝑠→𝜇+𝜈𝜇 to be ℬ𝐷+𝑠→𝜇+𝜈𝜇=(5.49±0.16stat±0.15syst)×10−3. Combining our branching fraction with the masses of the 𝐷+𝑠 and 𝜇+ and the lifetime of the 𝐷+𝑠, we determine 𝑓𝐷+𝑠|𝑉𝑐𝑠|=246.2±3.6stat±3.5syst MeV. Using the 𝑐→𝑠 quark mixing matrix element |𝑉𝑐𝑠| determined from a global standard model fit, we evaluate the 𝐷+𝑠 decay constant 𝑓𝐷+𝑠=252.9±3.7stat±3.6syst MeV. Alternatively, using the value of 𝑓𝐷+𝑠 calculated by lattice quantum chromodynamics, we find |𝑉𝑐𝑠|=0.985±0.014stat±0.014syst. These values of ℬ𝐷+𝑠→𝜇+𝜈𝜇, 𝑓𝐷+𝑠|𝑉𝑐𝑠|, 𝑓𝐷+𝑠 and |𝑉𝑐𝑠| are each the most precise results to date.
Using 16 energy points of e+e− annihilation data collected in the vicinity of the J/ψ resonance with the BESIII detector and with a total integrated luminosity of around 100 pb−1, we study the relative phase between the strong and electromagnetic amplitudes of J/ψ decays. The relative phase between J/ψ electromagnetic decay and the continuum process (e+e− annihilation without the J/ψ resonance) is confirmed to be zero by studying the cross section lineshape of μ+μ− production. The relative phase between J/ψ strong and electromagnetic decays is then measured to be (84.9 ± 3.6)◦ or (−84.7 ± 3.1)◦ for the 2(π+π−)π0 final state by investigating the interference pattern between the J/ψ decay and the continuum process. This is the first measurement of the relative phase between J/ψ strong and electromagnetic decays into a multihadron final state using the lineshape of the production cross section. We also study the production lineshape of the multihadron final state ηπ+π− with η → π+π−π0, which provides additional information about the phase between the J/ψ electromagnetic decay amplitude and the continuum process. Additionally, the branching fraction of J/ψ → 2(π+π−)π0 is measured to be (4.73 ± 0.44)% or (4.85 ± 0.45)%, and the branching fraction of J/ψ → ηπ+π− is measured to be (3.78 ± 0.68) × 10−4. Both of them are consistent with the world average values. The quoted uncertainties include both statistical and systematic uncertainties, which are mainly caused by the low statistics.