A Method for Establishing Optimality Conditions for a Nonsmooth Vector-Valued Minimax Problem

Using a method of uniform approximations, necessary and sufficient conditions for a nonsmooth constrained vector-valued minimax problem are established in terms of Mordukhovich subdifferentials.     

Extent of complex participation in the rate of copolymerization of styrene with maleic anhydride in methyl ethyl ketone

Georgiev and Shirota's simplified terminal complex model was applied to the dilatometrically measured initial rate of copolymerization of sytrene (ST) with maleic anhydride (MA) in methyl ethyl ketone (MEK) at 50°C. The rate was maximum at the feed MA mole fractions of 0.752, 0.769, and 0.806 at the total monomer concentrations of 2M, 1.5M, and 0.5M, respectively. Shirota's method gave the following ratios of propagation rate constants: β_A=k_AC/k_AD = 8.25 and β_D = k_DC/k_DA = 2.70. Georgiev's method gave β_A = 14, β_D = 2.7, and α = k_AD/k_DA = 22. The equilibrium constant of the donor-acceptor complexation between ST and MA in MEK was measured to be 0.045 dm³/mol at room temperature.     

Correlation between Solution and the Solid State: The pH Dependent Composition in the Ternary System [Co(H2O)6]2+ or [Ni(H2O)6]2+/Piperazine/Phosphate

The protolytic equilibria of piperazine (C₄H₁₀N₂) and phosphate have been investigated in the presence of cobalt or nickel chloride or nitrate by potentiometric titrations between pH 2 and 8. Potentiometric titrations suggest the presence of [M²⁺(H₂O)₅(C₄H₁₁N₂⁺)]³⁺ and [M²⁺(H₂O)₅(C₄H₁₀N₂)]²⁺ in solution with stability constants logK of 3.1 and 3.8 for M = Co and 3.1 and 3.6 for M = Ni, respectively. Crystallization experiments were then conducted at selected pH values to isolate desired species from the known solution composition. Crystallization afforded [M(H₂O)₆]²⁺(C₄H₁₂N₂²⁺)(HPO₄^2—)₂ at pH 3.5 and 6.2 (M = Co, Ni), and Co₃(PO₄)₂·8H₂O at pH 10.5. No crystals with the dihydrogenphosphate anion or a metal‐bound piperazine ligand could be isolated under the reaction conditions. The solid‐state assembly in the isomorphous structures of [M(H₂O)₆](C₄H₁₂N₂)(HPO₄)₂ with M = Co and Ni is based on an extended hydrogen bonded network between the three ionic building blocks.     

Nonsmooth multiobjective programming

Necessary Lagrangian conditions are obtained for a weak minimum of a nonsmooth constrained multiobjective programming problem, assuming Lipschitzfunctions and general cone constraints. This generalizes a result of F. Clarke. A vector dual problem is deduced.     

Hemostatic efficacy and tissue reaction of oxidized regenerated cellulose hemostats

Oxidized regenerated cellulose (ORC) has been used as an absorbable hemostat since World War II. In the present study, hemostasis time was determined in a spleen incision model in swine. The effect of mass on absorbable hemostat efficacy and hemostasis time was evaluated by standardizing the ORC materials on a mass basis. The median hemostasis time for a single layer of the new nonwoven ORC was as much as 51 % shorter than woven ORC (P < 0.001). The mean hemostasis time for nonwoven ORC was not affected by the mass of hemostat applied to the wound. The hemostatic efficacy of woven ORC increased with the mass (layers) of hemostat applied to the wound. Nonwoven ORC is significantly faster in achieving hemostasis than woven ORC, and its hemostatic efficacy is not influenced by the mass of material applied. Tissue reaction was minimal and the material was fully absorbed by 14 days.     

Hydrogen bonding effects on molecular structure: crystallographic studies of barbiturates

X-ray crystal structure determinations show systematic perturbations of the order of 0.01 Å in the oxopyrimidine rings of twelve barbiturate molecules. They appear to be related to the mode of intermolecular NHβO hydrogen bonding.