A motivated proof of the Göllnitz–Gordon–Andrews identities

We present what we call a “motivated proof” of the Göllnitz–Gordon–Andrews identities. A similar motivated proof of the Rogers–Ramanujan identities was previously given by G. E. Andrews and R. J. Baxter, and was subsequently generalized to Gordon’s identities by J. Lepowsky and M. Zhu. We anticipate that the present proof of the Göllnitz–Gordon–Andrews identities will illuminate certain twisted vertex-algebraic constructions.     

Covalent Functionalization of HiPco Single‐Walled Carbon Nanotubes: Differences in the Oxidizing Action of H2SO4 and HNO3 during a Soft Oxidation Process

The results of a study on the evolution of HiPco single‐walled carbon nanotubes during the oxidizing action of H₂SO₄ and HNO₃ are presented. The process conditions used have been chosen so as to avoid any significant damage to the nanotube structure. The type and level of functionalization, the location of the grafted functions on the surface of the nanotube and the changes in morphological characteristics of the samples were examined by using a wide and complementary range of analytical techniques. We propose an explanation for the differences in the oxidizing action of sulfuric and nitric acids. The combined results allow us to suggest possible reaction mechanisms that occur on the surface of the nanotube.     

LC-MS/MS quantitative analysis of reducing carbohydrates in soil solutions extracted from crop rhizospheres

A simple, sensitive, and specific analytical method has been developed for the quantitative determination of 15 reducing carbohydrates in the soil solution of crop rhizosphere. Reducing carbohydrates were derivatized with 1-phenyl-3-methyl-5-pyrazolone, separated by reversed-phase high-performance liquid chromatography and detected by electrospray ionization tandem mass spectrometry. Lower limits of quantitation of 2 ng/mL were achieved for all carbohydrates. Quantitation was performed using peak area ratios (analyte/internal standard) and a calibration curve spiked in water with glucose-d₂ as the internal standard. Calibration curves showed excellent linearity over the range 2–100 ng/mL (10–1,000 ng/mL for glucose). The method has been tested with quality control samples spiked in water and soil solution samples obtained from the rhizosphere of wheat and canola and has been found to provide accurate and precise results.     

IR-spektroskopische Untersuchungen am Poly?thylen. 3. Mitt. Die Bromierung unges?ttigter Gruppen

Ohne Zusammenfassung     

Total synthesis of the epidermal growth factor inhibitor (-)-reveromycin B

The total synthesis of the epidermal growth factor inhibitor reveromycin B (2) in 25 linear steps from chiral methylene pyran 13 is described. The key steps involved an inverse electron demand hetero-Diels-Alder reaction between dienophile 13 and diene 12 to construct the 6,6-spiroketal 11 which upon oxidation with dimethyldioxirane and acid catalyzed rearrangement gave the 5,6-spiroketal aldehyde 9. Lithium acetylide addition followed by oxidation/reduction and protective group manipulation provided the reveromycin B spiroketal core 8 which was converted into the reveromycin A (1) derivative 6 in order to confirm the stereochemistry of the spiroketal segment. Introduction of the C1-C10 side chain began with sequential Wittig reactions to form the C8-C9 and C7-C6 bonds, and a tin mediated asymmetric aldol reaction installed the C4 and C5 stereocenters. The final key steps to the target molecule 2 involved a Stille coupling to introduce the C21-C22 bond, succinoylation, selective deprotection, oxidation, and Wittig condensation to form the final C2-C3 bond. Deprotection was effected by TBAF in DMF to afford reveromycin B (2) in 72% yield.     

A novel one step synthesis of a dihydropentalene

1,4-Dipyrrolidinocyclohexa-1, 3-diene 4 reacts with dimethyl acetylenedicarboxylate i an unexpected manner to produce the substituted dihydropentalene 6.     

A practical preparation of aryl β-ketophosphonates

The condensation of alkyl phosphonates with aryl esters to give β-ketophosphonates may be carried out at elevated temperatures mediated by LiHMDS under Barbier type conditions. The reaction is scalable, does not require specialized cryogenic equipment, and is general for all aryl and heteroaryl esters examined.     

The Forbidden RotationalQ-Branch of CH3CF3: Torsional Properties and (A1−A2) Splittings

The pure rotational spectrum driven by the small distortion dipole moment perpendicular to the symmetry axis has been investigated between 8 and 18 GHz for CH₃CF₃in the ground vibrational state using a pulsed Fourier transform waveguide spectrometer. This molecule has been selected as a prototype for the case of a symmetric top with small (∼500 kHz) torsional energy splittings in the ground torsional state (ν₆= 0). In this state, six (k± 3 ←k)Q-branch series have been measured for lower stateK= |k| between 3 and 8 with 27 ≤J≤ 75. For (ν₆= 1), three series with lower stateKbetween 5 and 7 with 49 ≤J≤ 66 have been observed. In two of these series, the torsional fine structure extending over ∼6.8 MHz has been fully resolved. The (A₁−A₂) splitting has been measured in the (ν₆= 0) series (K= 6 ← 3) for 37 ≤J≤ 74. The global data set of 443 frequencies included avoided-crossing molecular-beam splittings of Meerts and Ozier (1991.Chem. Phys.152, 241–259) and mm-waveR-branch measurements of Bocquetet al.(1994.J. Mol. Spectrosc.165, 494–499). In a weighted least-squares analysis, a good fit was obtained by varying 18 parameters in a Hamiltonian that represented both the torsional effects and the sextic splittings. Effective values have been determined for both rotational constants, eight torsional parameters including the barrier height, six diagonal centrifugal distortion constants, and two centrifugal distortion constants (? and ?_J) that characterize the (Δk= ±3) matrix elements. The difficulties are discussed that arise in defining a unique model for the torsional terms in the Hamiltonian when a high barrier symmetric top is investigated by distortion moment spectroscopy. The redundancies are investigated that exist in the quartic and sextic Hamiltonian for a near-spherical top such as CH₃CF₃.