The number of ideals in a quadratic field

LetK be a quadratic Geld, and letR(N) be the number of integer ideals inK with norm at most AT. Letx with conductork be the quadratic character associated withK. Then |R(N)−NL(1,x)|⩽Bk ^50/73 N ^23/73(logN)^461/146 forN ≥Ak, whereA andB are constants. ForN ≥Ak ^c,C sufficiently large, the factork ^50/73 may be replaced by (d(k))^4/73 k ^46/73. Dedicated to the memory of Professor K G Ramanathan     

Reactions of amidoximes with orthoacetates

The reaction of two amidoximes 4 with ethyl orthoacetate in the presence of an acid catalyst gave triazine N-oxides 7 . A mechanism via a Beckmann rearrangement to a carbodiimide, followed by reaction with amidoxime and the ortho ester, is proposed.     

Kinetic and thermodynamic characterization of the cobalt and manganese oxyhydroxide cores formed in horse spleen ferritin

Horse spleen ferritin (HoSF) containing 800-1500 cobalt or 250-1200 manganese atoms as Co(O)OH and Mn(O)OH mineral cores within the HoSF interior (Co-HoSF and Mn-HoSF) was synthesized, and the chemical reactivity, kinetics of reduction, and the reduction potentials were measured. Microcoulometric and chemical reduction of HoSF containing the M(O)OH mineral core (M = Co or Mn) was rapid and quantitative with a reduction stoichiometry of 1.05 +/- 0.10 e/M forming a stable M(OH)(2) mineral core. At pH 9.0, ascorbic acid (AH(2)), a two-electron reductant, effectively reduced the mineral cores; however, the reaction was incomplete and rapidly reached equilibrium. The addition of excess AH(2) shifted the reaction to completion with a M(3+)/AH(2) stoichiometry of 1.9-2.1, consistent with a single electron per metal atom reduction. The rate of reaction between M(O)OH and excess AH(2) was measured by monitoring the decrease in mineral core absorbance with time. The reaction was first order in each reactant with second-order rate constants of 0.53 and 4.74 M(-1) min(-1), respectively, for Co- and Mn-HoSF at pH 9.0. From the variation of absorbance with increasing AH(2) concentration, equilibrium constants at pH 9.0 of 5.0 +/- 1.9 for Co-HoSF and 2.9 +/- 0.9 for Mn-HoSF were calculated for 2M(O)OH + AH(2) = 2M(OH)(2) + D, where AH(2) and D are ascorbic acid and dehydroascorbic acid, respectively. Consistent with these equilibrium constants, the standard potential for the reduction of Co(III)-HoSF is 42 mV more positive than that of the ascorbic acid reaction, while the standard potential of Mn(III)-HoSF is 27 mV positive relative to AH(2). Fe(2+) in solution with Co- and Mn-HoSF under anaerobic conditions was oxidized to form Fe(O)OH within the HoSF interior, resulting in partial displacement of the Co or Mn by iron.     

A new approach to the synthesis of conjugated polymer-nanocrystal composites for heterojunction optoelectronics

We report a simple one pot process for the preparation of lead sulfide (PbS) nanocrystals in the conjugated polymer poly (2-methoxy-5-(2'ethyl-hexyloxy)-p-phenylene vinylene)(MEH-PPV), and we demonstrate electronic coupling between the two components.     

Vibrational spectra of nitromethanes and the effects of internal rotation

Infrared spectra have been obtained in gas and crystalline phases for CH₃NO₂, CD₃NO₂, and CHD₂NO₂. A few Raman liquid measurements have also been made. The crystal spectra show the methyl group to be locked in conformation I,

with isolated CH stretching frequencies 3065 (ν_∥CH) and 3000 (ν_⊥CH), respectively. In the gas phase, the bands due to ν_aCH₃ and ν_aCD₃ are split, the splitting being compatible with isolated frequencies of 3065 (ν_∥CH) and 3006 (ν_⊥CH) cm^?1, respectively. These indicate a variation of 0.006 Å in bond length during internal rotation. The gas phase infrared band at 3028.7 cm^?1 and the Raman liquid band at 3024 cm^?1 in the spectra of CHD₂NO₂ represent averages of the frequencies during internal rotation. All calculations are performed with a potential function involving variations both in diagonal bond stretching, and in off-diagonal stretching interaction constants, proportional to cos2π, where π is the internal rotation angle.In the Appendix, vibrational assignments below 1600 cm^?1 are examined. Product rule considerations and intensity changes upon deuteration lead to a conflict with the infrared gas phase band contour over the assignment of the rCD₃ mode at 884 cm^?1. This and other features in the gas phase spectra may arise from the internal rotation.     

Visual Speech Recognition with Lightweight Psychologically Motivated Gabor Features

Extraction of relevant lip features is of continuing interest in the visual speech domain. Using end-to-end feature extraction can produce good results, but at the cost of the results being difficult for humans to comprehend and relate to. We present a new, lightweight feature extraction approach, motivated by human-centric glimpse-based psychological research into facial barcodes, and demonstrate that these simple, easy to extract 3D geometric features (produced using Gabor-based image patches), can successfully be used for speech recognition with LSTM-based machine learning. This approach can successfully extract low dimensionality lip parameters with a minimum of processing. One key difference between using these Gabor-based features and using other features such as traditional DCT, or the current fashion for CNN features is that these are human-centric features that can be visualised and analysed by humans. This means that it is easier to explain and visualise the results. They can also be used for reliable speech recognition, as demonstrated using the Grid corpus. Results for overlapping speakers using our lightweight system gave a recognition rate of over 82%, which compares well to less explainable features in the literature.     

Synthesis of Substituted Trans-1,6-Dimethylbicyclo[4.3.0]-non-2-enes Using A Claisen Rearrangement of α-(Thioalkoxy) Esters

The Claisen rearrangement of α-(thioalkoxy)-esters provided access to substituted trans-1, 6-dimethylbicyclo[4.3.0]non-2-enes characteristic of the CD rings of the cucurbitanes.     

Synthetic Approaches to Taxodione. Synthesis of Methyl 12-Oxopodocarpa-5,9(11)-diene-8β-Carboxylate

In connection with studies leading to the total synthesis of taxodione¹ (1), we required the tricyclic enone 3. We have previously described² an AB→ABC approach to this intermediate which was flawed by a low yield in the penultimate closure of the C ring (2→3). We now wish to report an alternate synthesis of 3 which involves a BC→ABC approach for the construction of this tricyclic system.