Hadronic transitions of χ cJ → η c π + π − (J = 0, 1, 2) are searched for using a sample of 1.06 × 10 8 ψ(3686) events collected with the BESIII detector at the BEPCII storage ring. The η c is reconstructed with K 0 S K ± π ∓ and K + K − π 0 final states. No signals are observed in any of the three χ cJ states in either η c decay mode. At the 90% confidence level, the upper limits are determined to be B(χ c0 → η c π + π − ) < 0.07%, B(χ c1 → η c π + π − ) < 0.32%, and B(χ c2 → η c π + π − ) < 0.54%. The upper limit of B(χ c1 → η c π + π − ) is lower than the existing theoretical prediction by almost an order of magnitude. The branching fractions of χ cJ → K 0 S K ± π ∓ π + π − , K + K − π + π − π 0 , ωK + K − and φπ + π − π 0 (J = 0, 1, 2) are measured for the first time.
Aiming at the multiband pattern synthesis problem of time-modulated conformal array antenna, a quadratic convex optimization algorithm is proposed for sum and difference beamforming with low sidelobe levels. This articles method synthesizes a difference beam with a low sidelobe level by generating nulls at the center frequency band and optimizing the switch-on duration time of array elements. And the sum beamforming and sidelobe suppression of the first-order sideband are realized by optimizing the switch-on instant time of the array elements. The proposed algorithm has excellent properties of sidelobe suppression and angular sweep. The simulation results of circular and satellite array antenna verify the effectiveness of the algorithm.
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