Thin sequences and the Gram matrix

We provide a new proof of Volberg’s Theorem characterizing thin interpolating sequences as those for which the Gram matrix associated to the normalized reproducing kernels is a compact perturbation of the identity. In the same paper, Volberg characterized sequences for which the Gram matrix is a compact perturbation of a unitary as well as those for which the Gram matrix is a Schatten-2 class perturbation of a unitary operator. We extend this characterization from 2 to p, where 2 ≤ p ≤ ∞.     

Elementary teachers’ mathematical beliefs and mathematics anxiety: How do they shape instructional practices?

This quantitative study investigated the relationships among practicing elementary teachers’ (N = 153) beliefs about mathematics and its teaching and learning, mathematics anxiety, and instructional practices in mathematics. When viewed singly, the findings reveal the teachers with higher levels of mathematics anxiety tend to use less standards‐based instruction and those with beliefs oriented toward a problem‐solving view of mathematics reported more standards‐based teaching. A combined analysis shows that after controlling for mathematical beliefs, teaching longevity, and educational degree attainment, there is no relationship between teachers’ mathematics anxiety and instructional practices. These findings suggest a spurious relationship between anxiety and practices, with beliefs having the strongest relationship with practices. Several suggestions for positively influencing the mathematical beliefs and affect in general of elementary teachers while learning mathematics are offered.     

Sodium pyridine‐3‐carboxyl­ate

The title compound, also known as sodium nicotinate, Na⁺·C₆H₄NO₂⁻, consists of two unique Na atoms coordinated to two unique pyridine‐3‐­carboxyl­ate ligands through the N atoms and carboxylate groups. One Na atom and one pyridine‐3‐­carboxyl­ate ligand lie on a twofold axis. Extensive Na coordination results in a three‐dimensional array comprising infinite NaO₂CR chains linked by intrachain Na—N bonds.     

Oxidative dissolution of copper and zinc metal in carbon dioxide with tert-butyl peracetate and a beta-diketone chelating agent

A series of beta-diketone ligands, R(1)COCH(2)COR(2) [tmhdH (R(1) = R(2) = C(CH(3))(3)); tfacH (R(1) = CF(3); R(2) = CH(3)); hfacH (R(1) = R(2) = CF(3))], in combination with tert-butyl peracetate (t-BuPA), have been investigated as etchant solutions for dissolution of copper metal into carbon dioxide solvent. Copper removal in CO(2) increases in the order tfacH < tmhdH < hfacH. A study of the reactions of the hfacH/t-BuPA etchant solution with metallic copper and zinc was conducted in three solvents: scCO(2) (supercrical CO(2)); hexanes; CD(2)Cl(2). The etchant solution/metallic zinc reaction produced a diamagnetic Zn(II) complex, which allowed NMR identification of the t-BuPA decomposition products as tert-butyl alcohol and acetic acid. Gravimetric analysis of the amount of zinc consumed, together with NMR studies, confirmed the 1:1:2 Zn:t-BuPA:hfacH reaction stoichiometry, showing t-BuPA to be an overall two-electron oxidant for Zn(0). The metal-containing products of the copper and zinc reactions were characterized by elemental analysis, IR spectroscopy, and, as appropriate, NMR spectroscopy and single-crystal X-ray diffraction [trans-M(hfac)(2)(H(2)O)(CH(3)CO(2)H) (1, M = Cu; 2, M = Zn)]. On the basis of the experimental results, a working model of the oxidative dissolution reaction is proposed, which delineates the key chemical variables in the etching reaction. These t-BuPA/hfacH etchant solutions may find application in a CO(2)-based chemical mechanical planarization (CMP) process.     

Cell-wall engineering of living bacteria

The cell walls of living bacteria were chemically modified by adding cell-wall precursors. As the precursors to be incorporated into the cell wall, UDP-MurNAc pentapeptide, lipid I, and lipid II derivatives were synthesized. The aimed compounds were attached to the amine residue of lysine at the pentapeptide moiety. Fluorescein-attached UDP-MurNAc pentapeptide was efficiently incorporated into both Gram-positive and Gram-negative bacteria. In the case of Gram-negative bacteria, such as Escherichia coli, the permeability of the outer membrane (lipopolysaccharide layer) was enhanced by EDTA treatment before the incorporation. For Gram-positive bacteria, UDP-MurNAc derivatives were incorporated in the cell wall without EDTA treatment due to the lack of the lipopolysaccharide layer. Furthermore, instead of dyes, a ketone group was attached to the UDP-MurNAc pentapeptide. The ketone group was also delivered to the bacterial cell wall of lactic acid bacteria, giving a platform to attach large molecules on the surface.     

Accuracy and robustness of clustering algorithms for small-size applications in bioinformatics

The performance (accuracy and robustness) of several clustering algorithms is studied for linearly dependent random variables in the presence of noise. It turns out that the error percentage quickly increases when the number of observations is less than the number of variables. This situation is common situation in experiments with DNA microarrays. Moreover, an a posteriori criterion to choose between two discordant clustering algorithm is presented.     

Syntheses of new conformationally constrained S‐[2‐[(1‐iminoethyl)amino] ethyl]homocysteine derivatives as potential nitric oxide synthase inhibitors

The efficient syntheses of two new types of conformationally constrained S‐[2‐[(1‐iminoethyl)amino]ethyl]homocysteine derivatives, 1‐amino‐3‐[2[(1‐iminoethyl)amino]ethylthio]cyclobutane carboxylic Acid ( 5 ) and (4S)‐4‐[[2‐[(1‐Iminoethyl)amino]ethyl]thio]‐L‐proline ( 6 ), are reported. These molecules represent the first attempts to probe conformational constraint near the α‐amino acid moiety of known homocysteine‐based inhibitors of nitric oxide synthase. Targets 5 and 6 were evaluated as potential inhibitors of the three human isoforms of nitric oxide synthase. © 2002 John Wiley & Sons, Inc. Heteroatom Chem 13:77–83, 2002; DOI 10.1002/hc.1109