Quasi-two-body decays B→DK∗(892)→DKπB \to D K^*(892) \to D K \pi in the perturbative QCD approach

We study the quasi-two-body decays $B\to D K^*(892) \to D K\pi$ by employing the perturbative QCD approach. The two-meson distribution amplitudes \Phi_{K\pi}^{\text{P-wave}} are adopted to describe the final state interactions of the kaon-pion pair in the resonance region. The resonance line shape for the $P$-wave $K\pi$ component $K^*(892)$ in the time-like form factor $F_{K\pi}(s)$ is parameterized by the relativistic Breit-Wigner function. For most considered decay modes, the theoretical predictions for their branching ratios are consistent with currently available experimental measurements within errors. We also disscuss some ratios of the branching fractions of the concerned decay processes. More precise data from LHCb and Belle-II are expected to test our predictions.Comment: 10 pages, 3 figures and 2 tables.To be published in EPJ

On the distributivity equation for uni-nullnorms

summary:A uni-nullnorm is a special case of 2-uninorms obtained by letting a uninorm and a nullnorm share the same underlying t-conorm. This paper is mainly devoted to solving the distributivity equation between uni-nullnorms with continuous Archimedean underlying t-norms and t-conorms and some binary operators, such as, continuous t-norms, continuous t-conorms, uninorms, and nullnorms. The new results differ from the previous ones about the distributivity in the class of 2-uninorms, which have not yet been fully characterized

A second ortho­rhom­bic polymorph of 3,5-diphenyl-4H-1,2,4-triazol-4-amine

The present crystal structure is the second ortho­rhom­bic polymorph of the title compound, C14H12N4. Whereas the structure in Pnma with Z′ = 0.5 is already known [Ikemi et al. (2002 ▶). Heterocycl. Commun. 8, 439–442], the present structure crystallizes in the space group Pbca with Z′ = 1. The dihedral angle between the two phenyl rings is 23.5 (4)° and the dihedral angles between central ring and the phenyl rings are 41.0 (3) and 26.3 (5)°. In the 4-amino-1,2,4-trizole fragment, the C=N distances are 1.321 (3) and 1.315 (3) Å, which are much shorter than the C—N distances of 1.367 (3) and 1.357 (3) Å. In the crystal, adjacent mol­ecules are linked by N—H⋯N hydrogen bonds