Spectrum of linearized operator at ground states of a system of Klein-Gordon equations

Previously, the existence of ground state solutions of a family of systems of Klein-Gordon equations has been widely studied. In this article, we will study the linearized operator at the ground state and give a complete description of the spectrum for this operator in the radial case: the existence of a unique negative eigenvalue, no resonance at '1'(the bottom of the essential spectrum), no embedded eigenvalue in the essential spectrum and the spectral gap property (i.e., there is no eigenvalue in the interval (0,1])

Contributions of K0∗(1430)K_0^*(1430) and K0∗(1950)K_0^*(1950) in the charmed three-body BB meson decays

In this work, we investigate the resonant contributions of $K_0^*(1430)$ and $K_0^*(1950)$ in the three-body $B_{(s)}\to D_{(s)}K\pi$ within the perturbative QCD approach. The form factor $F_{k\pi}(s)$ are adopted to describe the nonperturbative dynamics of the S-wave $K\pi$ system. The branching ratios of all concerned decays are calculated and predicted to be in the order of $10^{-10}$ to $10^{-5}$. The ratio $R$ of branching fractions between $B^0\to \bar{D}^0 K_0^{*0}(1430) \to \bar{D}^0K^+\pi^-$ and $B_s^0 \to \bar{D}^0 \bar{K}_0^{*0}(1430)\to \bar{D}^0K^-\pi^+$ are predicted to be 0.0552, which implies the discrepancy for the LHCb measurements. We expect that the predictions in this work can be tested by the future experiments, especially, to resolve $R$ ratio discrepancy

Tetra­aqua­bis(3-carboxyl­atopyridine N-oxide-κO 3)cadmium(II)

In the title complex, [Cd(C6H4NO3)2(H2O)4], the CdII atom is situated on a crystallographic centre of inversion. The CdII atom shows a slightly distorted octa­hedral geometry and is coordinated by four O atoms from water mol­ecules and two O atoms from deprotonated carboxyl groups of nicotinic acid N-oxide ligands. The mononuclear complex mol­ecules are linked by O—H⋯O hydrogen bonds, forming a three-dimensional network structure