Prototype structure of Pb5Ge3O11

The prototypic structure of the optically active ferroelectric Pb₅Ge₃O₁₁ has been deduced from packing considerations and refined from single-crystal diffractometer data. Interleaving segments of the apatite and nasonite structures in layers perpendicular to c gives the lead germanate structure. The space group of the prototype is $\text{P}\text{6}$, with a = 10.190, c = 10.624 Å, and Z = 3. Atomic coordinates were refined to give an R-factor of 0.093 using 463 X-ray reflections. The structure contains tetrahedral GeO₄ groups and double tetrahedral Ge₂O₇ groups in equal numbers. Lead is found in both trigonal pyramid and trigonal prism configurations.     

Estimating need and demand for prehospital care

Models estimating demand and need for emergency transportation services are developed. These models can provide reliable estimates which can be used for planning purposes, by complementing and/or substituting for historical data. The model estimating demand requires only four independent variables: population in the area, employment in the area, and two indicators of socioeconomic status which can be obtained from census data. The model can be used to estimate demand according to 4 operational categories and 11 clinical categories. The parameters of the model are calibrated with 1979 data from 82 ambulance services covering over 200 minor civil divisions in Southwestern Pennsylvania. This model was tested with data from another 55 minor civil divisions, also in Southwestern Pennsylvania, and it provided good estimates to total demand. The model to estimate need evolves from the demand model. It enables planners to estimate unmet need occurring in the region. The effect of emergency transportation service (ETS) provider characteristics on demand was also investigated. Statistical tests show that, for purposes of forecasting demand, when the sociodemographic factors are taken into account, provider characteristics are not significant.     

An existence-convergence theorem for a class of iterative methods

LetM ₀, characterized byx _k+1=G ₀(x _k),k?0,x ₀ prescribed, be an iterative method for the solution of the operator equationF(x)=0, whereF:X → X is a given operator andX is a Banach space. Let ω:X → X be a given operator, and let the methodM _mbe characterized byx _x+1,m =G _m(x _k,m),k?0,x _0,m prescribed, where $$G_i (x) = G_0 (x) - \sum\limits_{j = 0}^{i - 1} { F'(\omega (x))^{ - 1} F(G_j (x)), i = 1, . . . ,m,} $$ in whichG ₀:X → X is a given operator andF′:X → L(X) is the Fréchet derivative ofF. Sufficient conditions for the existence of a solutionx* _m ofF(x)=0 to which the sequence (x _k,m) generated from methodM _mconverges are given, together with a rate-of-convergence estimate.