Facile Synthesis and Properties of 2‐λ5‐Phosphaquinolines and 2‐λ5‐Phosphaquinolin‐2‐ones

Treatment of 2‐ethynylanilines with P(OPh)₃ gives either 2,2‐diphenoxy‐2‐λ⁵‐phosphaquinolines or 2‐phenoxy‐2‐λ⁵‐phosphaquinolin‐2‐ones under transition‐metal‐free conditions. This reaction offers access to an underexplored heterocycle, which opens up the study of the fundamental nature of the N?P^V double bond and its potential for delocalization within a cyclic π‐electron system. This heterocycle can serve as a carbostyril mimic, with application as a bioisostere for pharmaceuticals based on the 2‐quinolinone scaffold. It also holds promise as a new fluorophore, since initial screening reveals quantum yields upwards of 40 %, Stokes shifts of 50–150 nm, and emission wavelengths of 380–540 nm. The phosphaquinolin‐2‐ones possess one of the strongest solution‐state dimerization constants for a D–A system (130 M ^?1) owing to the close proximity of a strong acceptor (P?O) and a strong donor (phosphonamidate N? H), which suggests that they might hold promise as new hydrogen‐bonding hosts for optoelectronic sensing.     

Dynamics of social group competition: modeling the decline of religious affiliation

When social groups compete for members, the resulting dynamics may be understandable with mathematical models. We demonstrate that a simple ordinary differential equation (ODE) model is a good fit for religious shift by comparing it to a new international data set tracking religious nonaffiliation. We then generalize the model to include the possibility of nontrivial social interaction networks and examine the limiting case of a continuous system. Analytical and numerical predictions of this generalized system, which is robust to polarizing perturbations, match those of the original ODE model and justify its agreement with real-world data. The resulting predictions highlight possible causes of social shift and suggest future lines of research in both physics and sociology.     

Incorporating BODIPY fluorophores into tetrakis(arylethynyl)benzenes

Six structural isomers of a tetrakis(arylethynyl)benzene (TAEB) chromophore functionalized with dibutylamine and BODIPY moieties as the corresponding donor and acceptor units were prepared. To evaluate the effectiveness of the donor group, two TAEB molecules and three structurally related bis(arylethynyl)benzene (BAEB) isomers containing only acceptors were also synthesized. The electronic absorption and emission spectra of each series were examined. Additionally, computational studies were employed to corroborate the relative energy levels and gaps present in each series.     

A Practical Application of Linear Programming in the Mining Industry

The paper describes the application of linear programming to the allocation of coking coals from twenty-eight collieries to seven central washeries and blending plants in one N.C.B. area. The problem, which is of the simplex type, is reduced to the transportation form. Some details are given of the production method, implementation of the linear programming model and the follow-up.