Partial regularity for minimisers of certain functionals having nonquadratic growth

We prove partial regularity results for local minimisers of

Anticancer agent development: X-ray crystal structure and keto-enol tautomerism of dimethyl 1-hydroxy-6,7-methylenedioxy-4-(3′,4′,5′-trimethoxyphenyl-trans-3,4-dihydronaphthalene-2,3-dicarboxylate

Structural and conformational information obtained from the crystal structure and solution¹H nmr investigations of the title compound are compared. The 4-aryltetralone, C₂₄H₂₄O₁₀, crystallizes as a chloroform solvate in the monoclinic space group, P2₁/n, witha=12.519(4),b=17.938(6),c=12.534(9)Å,=111.90(5)°, and D_calc=1.51 g cm^–3 forZ=4. The data for this compound were collected at –150°C. Least-squares refinement of 2796 observed [F _o5(F _o)] reflections led to the final agreement index ofR=0.062. A threefold static disorder was observed for one of the carboxyl groups. The second carboxyl group participates in an intramolecular hydrogen bond and is thus ordered. The¹H nmr spectrum revealed the title compound to exist as a keto-enol tautomeric mixture in solution. Vicinal hydrogen coupling constant analysis proved reliable in ascertaining B-ring stereochemistry of 2,3-disubstituted-4-aryltetralones.     

Optimal Discrete Approximations for Continuous Outcomes with Applications in Decision and Risk Analysis

In decision and risk analysis, it is common to use discrete probability distributions to approximate uncertain events with continuous outcomes. This paper discusses how these approximations may be selected. A class of approximations based on a modification to Taguchi's work on tolerance analysis is shown to be optimal under assumptions of independent uncertainties with normally distributed outcomes. The approximation procedure is shown to be robust in many other situations and is extremely easy to use in practice. We also show how the approximation may be integrated into the process of subjective probability estimation by a ‘subject-matter expert’.     

The many limits of mixed means

The sequences introduced by Carlson (1971) are variants of the Gauss arithmetic geometric sequences (which have been elegantly discussed by D. A. Cox (1984, 1985)). Given (complex)a ₀,b ₀ we define

High-performance liquid chromatography and thin-layer chromatography assays for Devil's Club (Oplopanax horridus)

Devil's root, Oplopanax horridus, is a widely used folk medicine in Alaska and British Columbia. The inner bark of the root and stem has been used to treat colds, cough, fever, and diabetes. The present study involves the development of high-pressure liquid chromatography (HPLC) and thin-layer chromatography (TLC) methods to detect the presence of trans-nerolidol and sterols in the root bark. The HPLC and TLC analytical methods presented are suitable for the characterization and identification of Oplopanax horridus.     

Self-assembly of a hydrophobic groove

Heptakis(2,6-di-O-methyl)-β-cyclodextrin interacts with 5,15-diphenylporphine to produce a 2:1 complex in dimethyl sulfoxide. This complex possesses a hydrophobic groove that circumscribes the metal binding site of the porphyrin moiety.     

Solvent dependence of the 2-naphthyl(carbomethoxy)carbene singlet-triplet energy gap

The solvent dependence of the 2-naphthyl(carbomethoxy)carbene (2) singlet-triplet energy gap has been examined by time-resolved infrared (TRIR) and computational methods. The ground state of 2 changes from the triplet state in hexane to the singlet state in acetonitrile. Preferential stabilization of the singlet carbene is the result of its increased dipole moment in polar solvents. Variable-temperature TRIR experiments provide measurements of the enthalpic and entropic differences between (1)2 and (3)2 and suggest that solvent and geometry effects on the entropy of singlet and triplet carbenes can offset differences arising from spin multiplicity. B3LYP calculations using the polarizable continuum solvation model (PCM) reproduce the general trends in enthalpic differences seen experimentally.