Incorporation of a Phenanthrene Subunit into a Sapphyrin Framework: Synthesis of Expanded Aceneporphyrinoids

32‐Hetero‐5,6‐dimethoxyphenanthrisapphyrins—macrocycles that link structural features of polycylic aromatic hydrocarbons and expanded porphyrins—were obtained in a straightforward [3+1] condensation reaction of dimethoxyphenanthritripyrrane and 2,5‐bis(arylhydroxymethyl)heterocyclopentadienes. The highly folded conformation of formally 4 n π‐electron macrocycles causes them to manifest only limited macrocyclic π conjugation as explored by means of NMR spectroscopic and X‐ray structural analyses, and supported by DFT calculations. Although protonation does not change their π‐conjugation characteristics, the cleavage of ether groups at the phenanthrenylene moiety yields nonaromatic 32‐hetero‐5,6‐dioxophenanthrisapphyrins.     

Variation of student numerical and figural reasoning approaches by pattern generalization type,strategy use and grade level

This paper explored variation of student numerical and figural reasoning approaches across different pattern generalization types and across grade level. An instrument was designed for this purpose. The instrument was given to a sample of 1232 students from grades 4 to 11 from five schools in Lebanon. Analysis of data showed that the numerical reasoning approach seems to be more dominant than the figural reasoning approach for the near and far pattern generalization types but not for the immediate generalization type. The findings showed that for the recursive strategy, the numerical reasoning approach seems to be more dominant than the figural reasoning approach for each of the three pattern generalization types. However, the figural reasoning approach seems to be more dominant than the numerical reasoning approach for the functional strategy, for each generalization type. The findings also showed that the numerical reasoning was more dominant than the figural reasoning in lower grade levels (grades 4 and 5) for each generalization type. In contrast, the figural reasoning became more dominant than the numerical reasoning in the upper grade levels (grades 10 and 11).     

On a nonoverlapping additive Schwarz method for h‐p discontinuous Galerkin discretization of elliptic problems

The condition number of a discontinuous Galerkin finite element discretization preconditioned with a nonoverlapping additive Schwarz method is analyzed. We improve the result of Antonietti and Houston (J Sci Comput 46 (2011), 124–149), where a bound has been proved for a two‐level nonoverlapping additive Schwarz method with coarse problem using polynomials of degree on a coarse mesh size . In a more general framework, where the concurrency of the algorithm is increased by applying solvers on subdomains smaller than the coarse grid cells, we prove that the condition number of the preconditioned system is where is the coarse space element degree polynomial and is the size of subdomain where local problems are solved in parallel. Our result also extends to the case of discontinuous coefficient, piecewise constant on the coarse grid, for a composite continuous–discontinuous Galerkin discretization. © 2016Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 1572–1590, 2016     

Use of microdevices to determine the diffusion coefficient of electrochemically generated species: application to binary solvent mixtures and micellar solutions

A new approach for the determination of diffusion coefficient, D, of redox species is presented. It is based on the use of a home-constructed twin electrode within a thin-layered cell (TETLC) filled with a solution of electroactive species. Values of D are readily calculated, provided that the time required for the electrochemically generated species (produced at the generator electrode) to reach the collector electrode and the distance between both electrodes are known. Other parameters typically required to calculate D, e.g., concentration of the redox species, area of the electrode, and number of electrons transferred, are not needed. Diffusion coefficients of Fe(CN)(6)(3-), Ru(NH3)(6)(2+), and quinone were determined in water and, for Fe(CN)(6)(4-), in binary mixtures with glycerol. The results obtained were in good agreement with literature values. Aqueous glycerol solutions are microheterogeneous, as shown by the dependence on medium composition of the empirical solvent polarity scale, ET(30), determined by the solvatochromic probe RB. The responses of RB and the electrochemically generated species (Fe(CN)(6)(4-)) to the composition of aqueous glycerol mixtures were found to be remarkably similar. Measurements of D of ferrocene in micellar solutions of the cationic surfactant CTABr were also performed. Values of D for ferrocene and the ferrocenium cation are very different, in agreement with the chemical affinity of both species for the cationic micelle.     

Synthesis and structure of novel copper(II) complexes with pyrazole derived ligands and metal–ligand interaction in solution

Two new ligands of the coumarin type have been synthesized and characterized by ¹H, ¹³C NMR, IR and MS. The crystal and molecular structures of ligand 2, determined by the X-ray diffraction method, are presented. With copper(II) these ligands create solid complexes of the type CuLCl₂, where L is 5-(2-hydroxybenzoyl)-3-methyl-1-(2-pyridinyl)pyrazol-4-carboxylic acid methyl ester (2) or 3-methyl-1-(2-pyridinyl)-1H-chromene[4,3-c]pyrazol-4-on (3). The new copper(II) complexes have been characterized by elemental analysis and solid state FT-IR. The protonation constants of ligands 2 and 3 have been determined in 5% v/v 1,4-dioxane–water solution (25 °C). The coordination modes in the complexes with copper(II) are discussed for 2 on the basis of potentiometric and UV–Vis data.     

Assignment of the 1H and 13C NMR signals of some hydroxyphenylcoumarins

The complete 1H and 13C NMR assignments of six hydroxyphenylcoumarins have been made using 1D and 2D NMR techniques, including COSY, HMQC and HMBC experiments.     

Characterization of the covalently bound anionic flavin radical in monoamine oxidase a by electron paramagnetic resonance

It was recently suggested that partially reduced monoamine oxidase (MAO) A contains an equilibrium mixture of an anionic flavin radical and a tyrosyl radical (Rigby, S. E.; et al. J. Biol. Chem. 2005, 280, 4627-4632). These observations formed the basis for a revised radical mechanism for MAO. In contrast, an earlier study of MAO B only found evidence for an anionic flavin radical (DeRose, V. J.; et al. Biochemistry 1996, 35, 11085-11091). To resolve the discrepancy, we have performed continuous-wave electron paramagnetic resonance at 94 GHz (W-band) on the radical form of MAO A. A comparison with d-amino acid oxidase (DAAO) demonstrates that both enzymes only contain anionic flavin radicals. Pulsed electron-nuclear double resonance spectra of the two enzymes recorded at 9 GHz (X-band) reveal distinct hyperfine coupling patterns for the two flavins. Density functional theory calculations show that these differences can be understood in terms of the difference at C8alpha of the isoalloxazine ring. DAAO contains a noncovalently bound flavin whereas MAO A contains a flavin covalently bound to a cysteinyl residue at C8alpha. The similar electronic structures and hydrophobic environments of MAO and DAAO, and the similar structural motifs of their substrates suggest that a direct hydride transfer catalytic mechanism established for DAAO (Umhau, S.; et al. Proc. Natl. Acad. Sci. U.S.A. 2000, 97, 12463-12468) should be considered for MAO.     

Nonradial large solutions of sublinear elliptic problems

Let p be a nonnegative locally bounded function on , N3, and 0<γ<1. Assuming that the oscillation sup_|x|=rp(x)−inf_|x|=rp(x) tends to zero as r→∞ at a specified rate, it is shown that the equation Δu=p(x)u^γ admits a positive solution in satisfying lim_|x|→∞u(x)=∞ if and only if

     

An electrochemiluminescence-based competitive displacement immunoassay for the type-2 brevetoxins in oyster extracts

A new competitive electrochemiluminescence-based immunoassay for the type-2 brevetoxins in oyster extracts was developed. The assay was verified by spiking known amounts of PbTx-3 into 80% methanol extracts of Gulf Coast oysters. We also provide preliminary data demonstrating that 100% acetone extracts, aqueous homogenates, and the clinical matrixes urine and serum can also be analyzed without significant matrix interferences. The assay offers the advantages of speed ( 2 h analysis time); simplicity (only 2 additions, one incubation period, and no wash steps before analysis); low limit of quantitation (conservatively, 50 pg/mL = 1 ng/g tissue equivalents); and a stable, nonradioactive label. Due to the variety of brevetoxin metabolites present and the lack of certified reference standards for liquid chromatography-mass spectrometry confirmation, a true validation of brevetoxins in shellfish extracts is not possible at this time. However, our assay correlated well with another brevetoxin immunoassay currently in use in the United States. We believe this assay could be useful as a regulatory screening tool and could support pharmacokinetic studies in animals and clinical evaluation of neurotoxic shellfish poisoning victims.