Orthonormal bases generated by Cuntz algebras

We show how some orthonormal bases can be generated by representations of the Cuntz algebra; these include Fourier bases on fractal measures, generalized Walsh bases on the unit interval and piecewise exponential bases on the middle third Cantor set.     

Kinetic Studies of the Thermal cis-to-trans Isomerization of Dioxaphospholanes

By following a previously reported method,¹ the synthesis of r-2-alkoxy-cis-4-cis-5-dimethyl-1,3,2-λ³-dioxaphospholanes ligands (1 and 3) was carried out. The purpose of this work is the kinetic study of the inversion barrier at phosphorus for 1 and 3 and the comparison with the already informed dioxaphospholane 2. The kinetic measurements of the thermal isomerization cis-to-trans were performed by ³¹P NMR spectroscopy, observing a first order kinetics for both compounds. The energy of activation (E_a) for the epimerization of compounds cis-1 and cis-3 was calculated to be 16.0 ± 0.6 and 11.8 ± 0.8 kcal/mol, respectively. The values of the thermodynamic parameters of the transition state (Δ H^≠, Δ S^≠, Δ G^≠) suggest that the inversion at phosphorus not only depends on the spatial requirements of the alkoxy substituent but also on entropic effects. The thermodynamic parameters Δ H°, Δ S°, and Δ G° were also evaluated and they show that the cis isomers are preferred from enthalpic point of view, but entropic effects dominate the equilibrium trans ? cis leading to the entropically favored trans isomers. Furthermore, the results are supported by density functional theory calculations of 1–4 at the B3LYP/6-31G** level.     

Substituent Effects on 31P NMR Chemical Shifts and 1JP–Se of triarylselenophosphates

The effect of electron-withdrawing (EW) and electron-releasing (ER) substituents on the ³¹P NMR chemical shifts and the structural parameters of a series of tris-(p-X-aryl)selenophosphates is reported in this article. Similarly to O-aryl phosphates and O-aryl thiophosphates, EW groups attached to aromatic rings induce a shielding effect on the ³¹P NMR signal. After a detailed experimental and theoretical analysis, we confirmed that the selenium atom is the main part responsible for the charge density transfer toward phosphorus through a back-bonding effect. The obtained ¹J_P-Se values for the complete series agree with this observation.

Supplemental materials are available for this article. Go to the publisher's online edition of Phosphorus, Sulfur, and Silicon and the Related Elements to view the free supplemental file.     

Distribution of Methoxyl Groups in the Methylation of Starch Alkoxides Obtained by Metallation with Alkali Metal Naphthalene

Abstract

The distribution of the alkoxide groups obtained in the metallation of starch in dimethyl sulfoxide solution by alkali metal naphthalenes was studied. The starch alkoxide was reacted with methyl iodide, and the methylated starch was hydrolyzed and analyzed for glucose and O-methyl glucose derivatives. The metallation reaction was found to be random, as seen from the fact that at low alkoxide concentration (D.S = 0.6), 2,3,6-tri-O-methyl glucose was formed, while at relatively high alkoxide concentration (D.S. = 1.5) unreacted glucose was still present. At low alkoxide concentration (D.S. ? 0.6) there was, to a certain extent, preferential metallation at the C₂ hydroxyl groups, and to a lesser extent at the C₆ hydroxyl groups, as seen from the relative molar ratios of about 10:4:1 of the 2-, 6-, and 3-O-methyl glucose derivatives obtained, respectively. An increase in the metallation at the C₃ hydroxyl occurred with increasing alkoxide concentration. The distribution of the methoxyl groups with the three alkali metals potassium, sodium, and lithium was similar; there were differences only in the ease of metallation of the starch by the various alkali metal naphthalenes and in the efficiency of the coupling reaction with methyl iodide.     

Computational Study of the One‐ and Two‐Dimensional Infrared Spectra of a Proton‐Transfer Mode in a Hydrogen‐Bonded Complex Dissolved in a Polar Nanocluster

The signatures of nanosolvation on the one‐ and two‐dimensional (1D and 2D) IR spectra of a proton‐transfer mode in a hydrogen‐bonded complex dissolved in polar solvent molecule nanoclusters of varying size are elucidated by using mixed quantum–classical molecular dynamics simulations. For this particular system, increasing the number of solvent molecules successively from N=7 to N=9 initiates the transition of the system from a cluster state to a bulk‐like state. Both the 1D and 2D IR spectra reflect this transition through pronounced changes in their peak intensities and numbers, but the time‐resolved 2D IR spectra also manifest spectral features that uniquely identify the onset of the cluster‐to‐bulk transition. In particular, it is observed that in the 1D IR spectra, the relative intensities of the peaks change such that the number of peaks decreases from three to two as the size of the cluster increases from N=7 to N=9. In the 2D IR spectra, off‐diagonal peaks are observed in the N=7 and N=8 cases at zero waiting time, but not in the N=9 case. It is known that there are no off‐diagonal peaks in the 2D IR spectrum of the bulk version of this system at zero waiting time, so the disappearance of these peaks is a unique signature of the onset of bulk‐like behavior. Through an examination of the trajectories of various properties of the complex and solvent, it is possible to relate the emergence of these off‐diagonal peaks to an interplay between the vibrations of the complex and the solvent polarization dynamics.     

Extracellular Enzymes of the White-Rot Fungus Fomes fomentarius and Purification of 1,4-β-Glucosidase

Production of the lignocellulose-degrading enzymes endo-1,4-β-glucanase, 1,4-β-glucosidase, cellobiohydrolase, endo-1,4-β-xylanase, 1,4-β-xylosidase, Mn peroxidase, and laccase was characterized in a common wood-rotting fungus Fomes fomentarius, a species able to efficiently decompose dead wood, and compared to the production in eight other fungal species. The main aim of this study was to characterize the 1,4-β-glucosidase produced by F. fomentarius that was produced in high quantities in liquid stationary culture (25.9 U?ml^?1), at least threefold compared to other saprotrophic basidiomycetes, such as Rhodocollybia butyracea, Hypholoma fasciculare, Irpex lacteus, Fomitopsis pinicola, Pleurotus ostreatus, Piptoporus betulinus, and Gymnopus sp. (between 0.7 and 7.9 U?ml^?1). The 1,4-β-glucosidase enzyme was purified to electrophoretic homogeneity by both anion-exchange and size-exclusion chromatography. A single 1,4-β-glucosidase was found to have an apparent molecular mass of 58 kDa and a pI of 6.7. The enzyme exhibited high thermotolerance with an optimum temperature of 60 °C. Maximal activity was found in the pH range of 4.5–5.0, and K _M and V _max values were 62 μM and 15.8 μmol?min^?1?l^?1, respectively, when p-nitrophenylglucoside was used as a substrate. The enzyme was competitively inhibited by glucose with a K _i of 3.37 mM. The enzyme also acted on p-nitrophenylxyloside, p-nitrophenylcellobioside, p-nitrophenylgalactoside, and p-nitrophenylmannoside with optimal pH values of 6.0, 3.5, 5.0, and 4.0–6.0, respectively. The combination of relatively low molecular mass and low K _M value make the 1,4-β-glucosidase a promising enzyme for biotechnological applications.     

Total and inorganic mercury determination in fish tissue by flow injection cold vapour atomic fluorescence spectrometry

A simple and reliable method for Hg determination in fish samples has been developed. Lyophilised fish tissue samples were extracted in a 25% (w/v) tetramethylammonium hydroxide (TMAH) solution; the extracts were then analysed by FI-CVAFS. This method can be used to determine total and inorganic Hg, using the same FI manifold. For total Hg determination, a 0.1% (w/v) KMnO₄ solution was added to the FI manifold at the sample zone, followed by the addition of a 0.5% (w/v) SnCl₂ solution, whereas inorganic Hg was determined by adding a 0.1% (w/v) L-cysteine solution followed by a 1.0% (w/v) SnCl₂ solution to the FI system. The organic fraction was determined as the difference between total and inorganic Hg. Sample preparation, reagent consumption and parameters that can influence the FI-CVAFS performance were also evaluated. The limit of detection for this method is 3.7 ng g^?1 for total Hg and 4.3 ng g^?1 for inorganic Hg. The relative standard deviation for a 1.0 µg L^?1 CH₃Hg standard solution (n = 20) was 1.1%, and 1.3% for a 1.0 µg L^–1 Hg²⁺ standard solution (n = 20). Accuracy was assessed by the analysis of Certified Reference Material (dogfish: DORM-2, NRCC). Recoveries of 99.1% for total Hg and 93.9% inorganic Hg were obtained. Mercury losses were not observed when sample solutions were re-analysed after a seven day period of storage at 4°C.