Assigning patients to nurses in neonatal intensive care

An intensive care nursery provides health care for critically ill newborn infants. During a typical shift, infants range from those needing only occasional care to those requiring constant attention. At the beginning of each shift, the head nurse groups the patients for assignment to staff nurses. Typically each nurse cares for one group of infants throughout the shift. The large variation in infant conditions along with several complicating side constraints makes it difficult to develop balanced nurse work loads. We develop a mathematical programming approach for achieving better workload balance. We first develop a detailed neonatal acuity system that quantifies the nursing workload of each patient. We then develop an integer linear program that assigns patients to nurses while balancing nurse workloads. Because this model is computationally intractable, we develop a heuristic that exploits the fact that most nurseries are divided into a number of physical zones. We use ten case studies taken from a major university hospital to benchmark the performance of this heuristic. We also perform a designed experiment using randomly generated problems that examines the effect of nursery parameters on heuristic performance.     

An improved error bound for a finite element approximation of a model for phase separation of a multi-component alloy

Using the approach of Rulla (1996 SIAM J. Numer. Anal. 33, 68-87)for analysing the time discretization error and assuming moreregularity on the initial data, we improve on the error boundderived by Barrett and Blowey (1996 IMA J. Numer. Anal. 16,257-287) for a fully practical piecewise linear finite elementapproximation with a backward Euler time discretization of amodel for phase separation of a multi-component alloy.     

Finite element approximation of a model for phase separation of a multi-component alloy with a concentration-dependent mobility matrix

We consider a model for phase separation of a multi-componentalloy with a concentration-dependent mobility matrix and logarithmicfree energy. In particular we prove that there exists a uniquesolution for sufficiently smooth initial data. Further, we provean error bound for a fully practical piecewise linear finiteelement approximation in one and two space dimensions. Finallynumerical experiments with three components in one space dimensionare presented.     

Tetragermacyclobutadiene: Energetically Disfavored with Respect to Its Structural Isomers

Germanium has been a central feature in the renaissance of main‐group inorganic chemistry. Herein, we present the stationary‐point geometries of tetragermacyclobutadiene and its related isomers on the singlet potential energy surface at the CCSD(T)/cc‐pVTZ level of theory. Three of these 12 structures are reported for the first time and one of them is predicted to lie only 0.4 kcal mol^?1 above the previously reported global minimum. Focal‐point analyses has provided electronic energies at the CCSD(T) level of theory, which are extrapolated to the complete basis‐set limit and demonstrate the convergence behavior of the electronic energies with improving levels of theory and increasing basis‐set size. The lowest‐energy structure is the bicyclic structure, which lies 35 kcal mol^?1 below the “all‐Ge” cyclobutadiene structure. The reaction energies for the association of known Ge hydrides (e.g., digermene) to form Ge₄H₄ indicate that Ge₄H₄ could be observed experimentally. We investigate the bonding patterns by examining the frontier molecular orbitals. Our results demonstrate that: 1) the cyclic isomers of (GeH)₄ distort to maximize the mixing of the p orbitals that are involved in the π system of tetragermacyclobutadiene and 2) the lowest‐energy isomers exhibit unusual bonding arrangements (e.g., bridging H bonds) that maximize the nonbonding electron density at the Ge centers.