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The four lowest Ω substates (X2Π3/2,g, X2Π1/2,g, A2Π3/2,u and A2Π1/2,u) of the cation have been studied by high-precision ab initio calculations in comparison with experimental high-resolution absorption spectra. The potential energy curves were calculated using the multi-reference configuration interaction (MRCI) method and Dirac method, respectively. Rovibrational levels of these electronic states were derived by solving the radial Schrödinger rovibrational equation. Molecular constants were obtained in fitting energy levels to a spectroscopic model. Using the fit spectroscopic constants and newly calculated transition dipole moment matrix elements, line strengths of vibronic bands in the A2Π3/2,u- X2Π3/2,g system, as well as Einstein A coefficients for 45 of these bands with ν′ = 11–19 and ν′′ = 1–5, have been derived. The Einstein A coefficients were used to compute radiative lifetimes of the ν′ = 11–19 vibrational levels of the A2Π3/2,u state. Enhancement factors for detecting the variation of the fine-structure constant (α) and the proton-to-electron mass ratio(µ) using transitions between nearly degenerate rovibronic levels of these low-lying states have been calculated. 

The fusion of living bacteria and man-made materials represents a new frontier in medical and biosynthetic technology. However, the principles of bacterial signal processing inside synthetic materials with three-dimensional and fluctuating environments remain elusive. Here, we study bacterial growth in a three-dimensional hydrogel. We find that bacteria expressing an antibiotic resistance module can take advantage of ambient kinetic disturbances to improve growth while encapsulated. We show that these changes in bacterial growth are specific to disturbance frequency and hydrogel density. This remarkable specificity demonstrates that periodic disturbance frequency is a new input that engineers may leverage to control bacterial growth in synthetic materials. This research provides a systematic framework for understanding and controlling bacterial information processing in three-dimensional living materials. 

Abstract In this paper, we study the product of orders of composition factors of odd order in a composition series of a finite linear group.First we generalize a result by Manz and Wolf about the order of solvable linear groups of odd order.Then we use this result to find bounds for the product of orders of composition factors of odd order in a composition series of a finite linear group.