Letters to the Editor

The Mathematical Intelligencer encourages comments about the material in this issue. Letters to the editor should be sent to the editor-in-chieX Chandler Davis.     

On the reflexivity of subspaces of Toeplitz operators on the hardy space on the upper half-plane

The reflexivity and transitivity of subspaces of Toeplitz operators on the Hardy space on the upper half-plane are investigated. The dichotomic behavior (transitive or reflexive) of these subspaces is shown. It refers to the similar dichotomic behavior for subspaces of Toeplitz operators on the Hardy space on the unit disc. The isomorphism between the Hardy spaces on the unit disc and the upper half-plane is used. To keep weak* homeomorphism between L ^∞ spaces on the unit circle and the real line we redefine the classical isomorphism between L ¹ spaces.     

Characterization of oxidation progress by chemiluminescence: A study of polyethylene with pro-oxidant additives

Non-isothermal chemiluminescence measurements in nitrogen and isothermal measurements in oxygen were used for the evaluation of degradation in pre-oxidized polyethylene either pure or containing Mn-based pro-oxidant additives. The results were compared with infrared spectroscopy data. Chemiluminescence measurements of pure polyethylene and polyethylene with additive made it possible to calculate the set of rate constants, based on the Bolland-Gee oxidation scheme. The oxidation rate constants of polyethylene with additive were significantly higher, while the activation energy of the process appeared lower (65 kJ mol⁻¹), than those of pure polyethylene. The method provides an access to study oxidation processes during the induction period of oxidation when infrared spectroscopy cannot provide sufficient information.     

Separation and determination of terbinafine and its four impurities of similar structure using simple RP-HPLC method

A novel reversed-phase HPLC method for the simultaneous determination of active component terbinafine, its one impurity 1-methylaminomethylnaphtalene and three degradation products, β-terbinafine, Z-terbinafine and 4-methyl-terbinafine occurring in pharmaceutical formulations after long-term stability tests, was developed and validated using propylparaben as an internal standard.The chromatographic separation was performed on a NUCLEOSIL 100-5-CN column, mobile phase for separation of all compounds consisted of a mixture of tetrahydrofurane, acetonitrile and citrate buffer pH 4.50 (10:20:70, v/v/v). The analysis time was less than 32 min at flow-rate of 0.8 ml min⁻¹. UV detection was performed at 226 nm. The method was validated and system suitability parameters were investigated. Method robustness and short-term standard solution stability were verified. Limits of detection for terbinafine degradation products/impurity were from 0.023 to 0.098 μg ml⁻¹, limits of quantitation were from 0.078 to 0.327 μg ml⁻¹. The method was applicable for routine determination of terbinafine and all its found impurities of similar structure with sufficient selectivity, precision and accuracy.     

VUV photon induced fluorescence study of SF5CF3

The interaction of SF(5)CF(3) with vacuum-UV radiation has been investigated by photon induced fluorescence spectroscopy. Total fluorescence yield and dispersed fluorescence spectra of SF(5)CF(3) were recorded in the 200-1000 nm fluorescence window. In all cases, the fluorescence spectra resemble those of CF(3)X (X = H, F, Cl, and Br) molecules. At photon energies below 20 eV, the emission is attributed to the excited CF(3) and CF(2) fragments. The threshold for the CF(3) emission is 10.2 +/- 0.2 eV, giving an upper limit estimate for the SF(5)-CF(3) bond dissociation energy of 3.9 +/- 0.3 eV. The excitation functions of the CF(3) and CF(2) emissions were measured in the photon energy range 13.6-27.0 eV. The resonant structures observed in SF(5)CF(3) are attributed to electronic transitions from valence to Rydberg orbitals, following similar assignments in CF(3)X molecules. The photoabsorption spectrum of SF(5)CF(3) shows features at the same energies, indicating a strong contribution from Rydberg excitations.     

Synthesis and cytostatic activity of 4,7-dihydroxythioaurone derivatives. Effect of B ring substitution on the activity

Biological activity of thioaurones was not tested so far and the group constitute completely unexplored source of new molecules of pharmacological interest. We report synthesis and evaluation of cytotoxic activity of thioaurone derivatives bearing p-hydroquinone system in ring A. Their activity was found to depend strongly on substitution pattern, so eventually both the activity and pharmacokinetic parameters of the molecules could be tailored by further structural modifications.     

Ethanol production in a bioreactor with an integrated membrane distillation module

Ethanol production in a bioreactor with integrated membrane distillation (MD) module has been investigated. A hydrophobic capillary polypropylene membrane (Accurel PP V8/2 HF), with an external/internal diameter ratio, d _out/d _in = 8.6 mm/5.5 mm and pore size 0.2 μm, was used in these studies. The products (mainly ethanol and acetic acid) formed during the fermentation of sugar with Saccharomyces cerevisiae inhibited the process. These products were selectively removed from the fermentation broth by the MD process, which increased the efficiency of the conversion of sugar to alcohol from 0.45 g to 0.5 g EtOH per g of fermented sucrose. The bioreactor efficiency also increased by almost 30 %. Separation of alcohol by the MD generates a higher yield of ethanol in the permeate than in the broth. The enrichment coefficient amounted to 4-8, and depended on the ethanol concentration in the broth. The separated solutions did not wet the membrane in use for 2500 h of the MD experiments and the retention of inorganic solutes was close to 100 %.     

Synthesis of β-ketophosphonates with electron rich β-aryl groups as useful organophosphorus reagents in lignans synthesis

Investigation of the oxidation reaction of electron rich alkoxy substituted β-aryl β-hydroxyphosphonates to corresponding β-ketophosphonates, which may be utilized in syntheses of lignans with various oxidizing agents (PCC, PDC, SIBX, CAN, Oxone^®, KMNO₄/SiO₂, KMnO₄/MS 4 Å, KMnO₄/CuSO₄, KMnO₄/CuSO₄/Al₂O₃, MnO₂, CrO₃/SiO₂, H₂O₂/salen) is described. The effect of oxidants and reaction conditions on the reaction efficiency and yield was also investigated.     

Nuclear resonance vibrational spectra of five-coordinate imidazole-ligated iron(II) porphyrinates

Nuclear resonance vibrational spectra have been obtained for six five-coordinate imidazole-ligated iron(II) porphyrinates, [Fe(Por)(L)] (Por = tetraphenylporphyrinate, octaethylporphyrinate, tetratolylporphyrinate, or protoporphyrinate IX and L = 2-methylimidazole or 1,2-dimethylimidazole). Measurements have been made on both powder and oriented crystal samples. The spectra are dominated by strong signals around 200-300 cm(-1). Although the in-plane and out-of-plane vibrations are seriously overlapped, oriented crystal spectra allow their deconvolution. Thus, oriented crystal experimental data, along with density functional theory (DFT) calculations, enable the assignment of key vibrations in the spectra. Molecular dynamics are also discussed. The nature of the Fe-N(Im) vibrations has been elaborated further than was possible from resonance Raman studies. Our study suggests that the Fe motions are coupled with the porphyrin core and peripheral groups motions. Both peripheral groups and their conformations have significant influence on the vibrational spectra (position and shape).