A Lower Bound for the Differences of Powers of Linear Operators

Let T be a bounded linear operator in a Banach space, with σ（T）={1}. In 1983, Esterle-Berkani＇ s conjecture was proposed for the decay of differences （I - T） T^n as follows： Eitheror lim inf （n→∞（n＋1）｜｜（I-T）T^n｜｜≥1/e or T = I. We prove this claim and discuss some of its consequences.     

Spectral pattern recognition of improved voice quality

The self-organizing map (a neural network) was applied to the spectral pattern recognition of voice quality in 34 subjects: 15 patients operated on because of insufficient glottal closure and 19 subjects not treated for voice disorders. The voice samples, segments of sustained /a/, were perceptually rated by six experts. A self-organized acoustic feature map was first computed from tokens of /a/ and then used for the analysis of the samples. The locations of the samples on the map were determined and the distances from a normal reference were compared with the perceptual ratings. The map locations corresponded to the degree of audible disorder: the samples judged as normal were overlapping or close to the normal reference, whereas the samples judged as dysphonie were located further away from it. The comparison of pre- and postoperative samples of the patients showed that the perceived improvement of voice quality was also detected by the map.     

Co-eluent effect in partition chromatography. Rhamnose-xylose separation with strong and weak cation-exchangers in aqueous ethanol

The effect of ethanol in aqueous eluent on the chromatographic separation was studied at 298 K. Two sugars, L-rhamnose and D-xylose, were separated by using strong and weak cation-exchangers as a stationary phase. The ionic form of the resins was Na+ or Ca2+. The separations were carried out with sugar feed concentrations up to 35 wt% and with both low (about 1%) and high (about 10%) feed volume to bed volume ratios. The separation of the sugars was improved by adding ethanol into the eluent. The separation was also significantly enhanced when the weak cation-exchangers with the greatest affinity for water were used instead of strong cation-exchangers as a separation medium for the sugars having different hydrophilicities. The experimental data were successfully explained with a rate-based column model, which accounted for the volume changes of the stationary phase. A thermodynamic sorption model was utilized in column calculations.     

Electronic structure of the enolate anion of chlorophyll b

The enolate anion of chlorophyll b (Chl b) has been synthesized under deoxygenated conditions and its electronic structure characterized for the first time by ¹H NMR and electronic absorption spectroscopy. The formation of the enolate anion caused a marked perturbation to the 18 π-electron [18]diazaannulene aromatic pathway of Chl b. This perturbation appeared as noticeable upfield shifts, exceeding 1 ppm, for the meso-CH protons of the Chl b enolate anion. Nevertheless, the enolate anion remained diatropic, maintaining aromaticity in its delocalized macrocycle.     

Influence of pH on formation and stability of phosphatidylcholine/phosphatidylserine coatings in fused-silica capillaries

The effect of pH on the formation and stability of phospholipid coatings in fused-silica capillaries in electrophoresis was investigated. A liposome solution consisting of 3 mM of 80:20 mol% phosphatidylcholine/phosphatidylserine (PC/PS) in N-(2-hydroxyethyl)piperazine-N'-(2-ethanesulfonic acid) (HEPES) buffer was used as coating material. The coating was prepared by a method described earlier and five steroids were used as neutral model analytes. First, the effect of pH of the coating solution on the formation and stability of phospholipid coatings was studied at pH 6.5-8.5. The pH of the background electrolyte (BGE) solution (HEPES) was either kept constant at pH 7.4 or made similar to the pH of the liposome coating solution. Results showed that attachment of the coating on the fused-silica wall mostly depends on the protonation of amines of the phospholipids and HEPES. The ability of the phospholipid coating to withstand changes in pH was then investigated by coating at pH 7.5 and separating steroids with acetic acid, 3-(cyclohexylamino)-1-propanesulfonic acid (CAPS), HEPES, or glycine BGE, adjusted to pH between 4.5 and 10.8. The results showed that with use of BGE solution at pH 10.8, the separation of steroids was not successful and the electroosmotic flow was high because of leakage of the phospholipid coating during preconditioning of the capillary with BGE solution. There was no phospholipid leakage with a BGE solution of pH 4.5, indicating that the protonated form of the functional groups of PS and HEPES participating in the attachment of the phospholipid coating to the capillary play an essential role in the success of the coating.     

Effects of various washing procedures on the chromium content of human scalp hair

The effects of four wash procedures on the concentration of chromium in a pooled sample of human scalp hair are compared. The wash solutions examined are Triton X-100, sodium lauryl sulphate, acetone, and a mixture (1 + 1) of hexane and ethanol. The plateaux reached for hair chromium concentration are functions of the number of washings, and are characteristic for each wash solution. The wash procedure recommended involves two 20-min washes with aqueous 1% sodium lauryl sulphate solution after a hexane rinse.     

Elementary-field modeling of surface-plasmon excitation with partially coherent light

We present a mathematical model and its numerical implementation for the analysis of the interaction of spatially partially coherent electromagnetic fields with micro- and nanostructured objects. The model is based on the decomposition of the incident field into a set of fully coherent but mutually uncorrelated elementary field modes, and the use of the Fourier Modal Method (FMM) with the S-matrix propagation algorithm. We apply the model to studies of the excitation of surface plasmons in thin metallic slabs, nanowires, and resonant structures. We demonstrate, e.g., that the plasmon excitation efficiency is not essentially affected by the degree of spatial coherence. However, certain plasmon interference effects can be efficiently smoothed out by using illumination with reduced coherence.     

A note about Volterra operators on weighted Banach spaces of entire functions

We characterize boundedness, compactness and weak compactness of Volterra operators acting between different weighted Banach spaces of entire functions with sup‐norms in terms of the symbol g; thus we complement recent work by Bassallote, Contreras, Hernández‐Mancera, Martín and Paul 3 for spaces of holomorphic functions on the disc and by Constantin and Peláez 16 for reflexive weighted Fock spaces.     

New isomers of 4,1-benzothiazepines. The first evidence for the desmotropy of seven-membered heterocycles

A novel procedure was developed for the preparation of 2,3-disubstituted 4,1-benzothiazepines, via the ring transformation of (2R^∗,2aS^∗)-2-chloro-2a-phenyl-2,2a-dihydro-2H,4H-azeto[1,2-a][3,1]benzothiazin-1-one (1) with sodium ethoxide in ethanol. The tautomeric products (R^∗)-3-ethoxycarbonyl-2-phenyl-3,5-dihydro-4,1-benzothiazepine (4) and 3-ethoxycarbonyl-2-phenyl-1,5-dihydro-4,1-benzothiazepine (5) exhibit the rare phenomenon of desmotropy of the condensed seven-membered heterocycles. Surprisingly, these desmotropes could be separated by column chromatography. The products are unexpectedly stable in solution and their structures were proved by means of NMR and mass spectrometry.     

Cobalt complexes of a selenium diimide and a tellurium diimide dimer

[CoCl₂{N,N′-Te₂(N^tBu)₄}] (1) was obtained in good yields by the reaction of equimolar amounts of (^tBu)NTe(μ-N^tBu)₂TeN(^tBu) and CoCl₂ in toluene under an argon atmosphere. The crystal structure of 1·CH₂Cl₂ showed that the dimeric tellurium diimide ligand is N,N′-chelated to cobalt. The related reaction of Se(N^tBu)₂ and CoCl₂ affords a green product tentatively identified as a 1:1 adduct [CoCl₂{N,N′-Se(N^tBu)₂}] (CHN analysis). However, recrystallization from thf produces the ion-separated complex [Co₂(μ-Cl)₃{N,N′-Se(N^tBu)₂}₂(thf)₂][CoCl₃{NH₂(^tBu)}]·1½thf (2·1½thf), in which the monomeric selenium diimide ligand is N,N′-chelated to cobalt in the cation. A pathway for the formation of 2 from [CoCl₂{N,N′-Se(N^tBu)₂}] in thf is proposed.