Off-day scheduling with hierarchical worker categories

A work force includes workers of m types. The worker categories are ordered, with type-1 workers the most highly qualified, type-2 the next, and so on. If the need arises, a type-k worker is able to substitute for a worker of any type j greater than k (k = 1, ..., m - 1). For 7-day-a-week operation, daily requirements are for at least Dk workers of type-k or better, of which at least dk must be precisely type-k. Formulas are given to find the smallest number and most economical mix of workers, assuming that each worker must have 2 off-days per week and a given fraction of weekends off. Algorithms are presented which generate a feasible schedule, and provide work stretches between 2 and 5 days, and consecutive weekdays off when on duty for 2 weekends in a row, without additional staff.     

Spectrophotometric determination of phosphorus as phosphate in organic compounds and materials of biological origin using a flow-injection manifold with a mixing chamber

Summary A flow-injection manifold with mixing chamber has been developed for the determination of phosphate by reaction with molybdate and crystal violet. The insoluble blue dye salt is kept in colloidal solution with poly(vinyl alcohol) and measured at 560 nm. The injection rate is 100 h^–1. The detection limit is 0.01 g PO ₄ ^3– /ml based on 250 l injection volumes. The system has been applied to the determination of phosphate in serum samples and after appropriate mineralisation to organic compounds and to plant materials.     

Uranium (III) scorpionates: synthesis and structure of [(TpMe2)2U[N(C6H5)2]] and [(TpMe2)2U[N(SiMe3)2]

Reaction of [(Tp(Me)2)(2)UI] with KNR(2) (R = C(6)H(5), SiMe(3)) in tetrahydrofuran (THF) afforded the monomeric trivalent actinide amide complexes [(Tp(Me)2)(2)U[N(C(6)H(5))(2)]], 1, and [(Tp(Me)2)(2)U[N(SiMe(3))(2)]], 2. The complexes have been fully characterized by spectroscopic methods and their structures were confirmed by X-ray crystallographic studies. In the solid state 1 and 2 exhibit distorted pentagonal bipyramidal geometries. The U-NR(2) bond lengths in both complexes are the same but in complex 2 the greater steric demands of the N(SiMe(3))(2) ligand led to elongated U-N(pz) bonds, especially those opposite the amido ligand.     

An unprecedented uranyl phosphate framework in the structure of [(UO2)3(PO4)O(OH)(H2O)2](H2O)

The new uranyl phosphate [(UO2)3(PO4)O(OH)(H2O)2](H2O) (1) with an unprecedented framework structure has been synthesized at 150 and 185 degrees C. The structure (tetragonal, P4(2)/mbc, a = 14.015(1) A, c = 13.083(2) A, V = 2575.6(4) A(3), Z = 8) contains uranyl phosphate chains composed of uranyl pentagonal and hexagonal bipyramids and phosphate tetrahedra linked by sharing of polyhedral edges. The uranyl phosphate chains are aligned both along [100] and [010] and are linked into a novel framework structure involving channels along [001]. Topologically identical chains occur linked into sheets in more than a dozen uranyl phosphate minerals, but these chains have never been observed in opposing orientations and linked into a framework as in 1.     

Inhomogeneous Distribution of Cationic Surfactants around Anionic Molecular Clusters

An interesting phenomenon is reported when uranyl peroxide nanoclusters U₆₀ (Li_48+mK₁₂(OH)_m[UO₂(O₂)(OH)]₆₀ (H₂O)_n, m≈20 and n≈310) interact with a small number of cationic surfactant molecules. Cationic surfactant molecules do not distribute evenly around the U₆₀ clusters during the interaction as expected. Instead, a small fraction of U₆₀ clusters attract almost all the surfactant molecules, leading to the self-assembly into supramolecular structures by using surfactant–U₆₀ complexes as building locks, and later further aggregate and precipitate based on hydrophobic interaction, whereas the rest of the clusters remained unbounded soluble macroions in bulk dispersion. This phenomenon nicely demonstrates a unique feature of macroion solutions. Considering that Debye–Hückel approximation is no longer valid in such solutions, the competition between the local electrostatic interaction and hydrophobic interaction becomes important to regulate the solution behaviors of macroions.     

Experimental and Computational Study of the Thermal Decomposition of 3‐Methyl‐3‐buten‐1‐ol in m‐Xylene Solution

An experimental study of the thermal decomposition of a β‐hydroxy alkene, 3‐methyl‐3‐buten‐1‐ol, in m‐xylene solution, has been carried out at five different temperatures in the range of 513.15–563.15 K. The temperature dependence of the rate constants for the decomposition of this compound in the corresponding Arrhenius equation is given by ln k (s^?1) = (25.65 ± 1.52) ? (17,944 ± 814) (kJ·mol^?1)·T^?1. A computational study has been carried out at the M05–2X/6–31+G(d,p) level of theory to calculate the rate constants and the activation parameters by the classical transition state theory. There is a good agreement between the experimental and calculated rate constants and activation Gibbs energies. The bonding characteristics of reactant, transition state, and products have been investigated by the natural bond orbital analysis, which provides the natural atomic charges and the Wiberg bond indices. Based on the results obtained, the mechanism proposed is a one‐step process proceeding through a six‐membered cyclic transition state, being a concerted and slightly asynchronous process. The results have been compared with those obtained previously by us (Struct Chem 2013, 24, 1811–1816) for the thermal decomposition of 3‐buten‐1‐ol, in m‐xylene solution. We can conclude that in the compound studied in this work, 3‐methyl‐3‐buten‐1‐ol, the effect of substitution at position 3 by a weakly activating CH₃ group is the stabilization of the transition state formed in the reaction and therefore a small increase in the rate of thermal decomposition.