Löwner expansions

A fundamental problem is to estimate the logarithmic coefficients of a power series with constant coefficient zero which represents a function which has distinct values at distinct points of the unit disk. A source of estimates is an expansion theorem for the Löwner equations which is obtained from a study of contractive substitutions in Hilbert spaces of analytic functions. The methods are an outgrowth of the theory of square summable power series [1]. Assume that σ_n is a given function of nonnegative integers n, with nonnegative values, such that σ₀ = 0 and such that σ_{n ? 1} ? σ_n when n is positive. Infinite values are allowed. The underlying Hilbert space is the set $\text{G}$_σ(0) of equivalence classes of power series f(z) = ∑ a_nzⁿ with constant coefficient zero such that f(z)²_{$\text{G}$σ⁽⁰⁾} = ∑(n/σ_n)|a_n|² is finite. Equivalence of power series f(z) and g(z) means that the coefficient of zⁿ in f(z) is equal to the coefficient of zⁿ in g(z) when σ_n is finite.     

Integration of auditory and vibrotactile stimuli: effects of frequency

Perceptual integration of vibrotactile and auditory sinusoidal tone pulses was studied in detection experiments as a function of stimulation frequency. Vibrotactile stimuli were delivered through a single channel vibrator to the left middle fingertip. Auditory stimuli were presented diotically through headphones in a background of 50 dB sound pressure level broadband noise. Detection performance for combined auditory-tactile presentations was measured using stimulus levels that yielded 63% to 77% correct unimodal performance. In Experiment 1, the vibrotactile stimulus was 250 Hz and the auditory stimulus varied between 125 and 2000 Hz. In Experiment 2, the auditory stimulus was 250 Hz and the tactile stimulus varied between 50 and 400 Hz. In Experiment 3, the auditory and tactile stimuli were always equal in frequency and ranged from 50 to 400 Hz. The highest rates of detection for the combined-modality stimulus were obtained when stimulating frequencies in the two modalities were equal or closely spaced (and within the Pacinian range). Combined-modality detection for closely spaced frequencies was generally consistent with an algebraic sum model of perceptual integration; wider-frequency spacings were generally better fit by a Pythagorean sum model. Thus, perceptual integration of auditory and tactile stimuli at near-threshold levels appears to depend both on absolute frequency and relative frequency of stimulation within each modality.     

Electrochemical rectification by redox-labeled bioconjugates: molecular building blocks for the construction of biodiodes

In the present work, we describe the properties of a bifunctional redox-labeled bioconjugate at electrode surfaces mediating the electron transfer across the electrode-electrolyte interface. We show that the assembly of ferrocene-labeled streptavidin on biotinylated electrodes results in a reproducible unidirectional current flow in the presence of electron donors in solution. Such rectifying films were built up by spontaneous binding of tetrameric streptavidin molecules to biotin centers immobilized on the electrode surface. Due to the high affinity of biotin to streptavidin, such bifunctional films completely bind any biotinylated compounds. The charge transport between donors in solution and the Au electrode is mediated by the ferrocene moieties, allowing us to develop a molecular rectifier. Our experimental results suggest that such redox-labeled proteins with a high binding capacity constitute a promising alternative to organic compounds used in molecular electronics.     

Dititanium-containing 19-tungstodiarsenate(III) [Ti2(OH)2As2W19O67(H2O)]8-: synthesis, structure, electrochemistry, and oxidation catalysis

The dititanium-containing 19-tungstodiarsenate(III) [Ti(2)(OH)(2)As(2)W(19)O(67)(H(2)O)](8-) (1) has been synthesized and characterized by IR, TGA, elemental analysis, electrochemistry, and catalytic studies. Single-crystal X-ray analysis was carried out on Cs(8)[Ti(2)(OH)(2)As(2)W(19)O(67)(H(2)O)].2CsCl.12H(2)O (Cs-1), which crystallizes in the monoclinic system, space group P2(1)/m, with a=12.7764(19), b=19.425(3), c=18.149(3) A, beta=110.234(3) degrees, and Z=2. Polyanion 1 comprises two (B-alpha-As(III)W(9)O(33)) Keggin moieties linked through an octahedral {WO(5)(H(2)O)} fragment and two unprecedented square-pyramidal {TiO(4)(OH)} groups, leading to a sandwich-type structure with nominal C(2v) symmetry. Synthesis of 1 was accomplished by reaction of TiOSO(4) and K(14)[As(2)W(19)O(67)(H(2)O)] in a 2:1 molar ratio in aqueous, acidic medium (pH 2). Polyanion 1 could also be isolated as a tetra-n-butyl ammonium (TBA) salt, {(n-C(4)H(9))(4)N}(5)H(3)[Ti(2)(OH)(2)As(2)W(19)O(67)(H(2)O)] (TBA-1). TBA-1 was studied by cyclic voltammetry in acetonitrile (MeCN) solutions containing 0.1 M LiClO(4) and compared with the results obtained with Cs-1 in aqueous media. In MeCN, the Ti(IV) and W(VI) waves could not be separated distinctly. An important adsorption phenomenon on the glassy carbon working electrode was encountered both in cyclic voltammetry and in controlled potential electrolysis and was confirmed by Electrochemical Quartz Crystal Microbalance (EQCM) studies on a carbon film. TBA-1, dissolved in MeCN, reacts with H(2)O(2) to give peroxo complexes stable enough for characterization by UV-visible spectroscopy, cyclic voltammetry, and EQCM. TBA-1 shows high catalytic activity (TOF=11.3 h(-1)) in cyclohexene oxidation with aqueous H(2)O(2) producing products typical of a heterolytic oxidation mechanism. The stability of TBA-1 under turnover conditions was confirmed by using IR, UV-visible spectroscopy as well as cyclic voltammetry.     

Detection of vanadium by means of spot tests

Zusammenfassung Zwei neue Tüpfelreaktionen für Vanadinum werden beschrieben.-Benzoinoxim gibt einen gelben Niederschlag in schwefelsauren Vanadatlösungen, der auf der Tüpfelplatte den Nachweis von 1 Vanadinum ermöglicht. Der Nachweis der durch Zusatz von Vanadylsalz zu Ferrichlorid gebildeten Ferroionen kann auf der Tüpfelplatte mit,-Dipyridyl oder mit o-Phenanthrolin durchgeführt werden. In beiden Fällen wird eine Erfassungsgrenze von 0,1 Vanadinum erreicht und nur wenige Ionen stören den Nachweis.Der Nachweis der Ferroionen mit Hilfe von Dimethylglyoxim (1 V) und auch der Vanadatnachweis durch die durch Wolframat erzeugte Gelbfärbung (0,3 V) wurden in bezug auf Störungen durch gleichzeitig anwesende Stoffe gründlich untersucht. Die Dimethylglyoximprobe wird durch Zusatz von Phosphat wesentlich verbessert.

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Résumé Deux nouvelles réactions à la touche sont décrites pour le vanadium. L'-benzoinoxime donne un précipité jaune en solution sulfurique de vanadate qui, sur la plaquette à touche, rend possible la recherche de 1 vanadium. La recherche des ions ferreux formés par addition d'un sel de vanadyle au chlorure ferrique peut être conduite sur plaquette avec l', -dipyridyle ou l'o-phénanthroline. Dans les deux cas, on atteint une limite de sensibilité de 0,1 de vanadium et quelques ions seulement gênent la recherche.Celle des ions ferreux au moyen de la diméthylglyoxime (1 de vanadium) et aussi la recherche des vanadates par la coloration jaune donnée avec un tungstate (0,3 de vanadium) furent expérimentées d'une manière approfondie en fonction des interférences par les substances simultanément présentes. L'essai à la diméthylglyoxime est essentiellement amélioré par addition de phosphate.

     

Coulometric determination of chromium

This paper describes an accurate and precise method for the determination of chromium by coulometry at controlled potential. A solution of the sample in 6M hydrochloric acid is electrolyzed at a large stirred mercury cathode whose potential is maintained constant at —1.10 V vs. S.C.E. ;this reduces the chromium quantitatively to the +2 state. Copper, lead, and a number of other elements are next eliminated by simply discarding the mercury and replacing it with fresh mercury ;then uranium is re-oxidized to non-interfering uranium(IV) by a second controlled-potential electrolysis at —0.80 V vs. S.C.E.; and finally the solution is electrolyzed at a working electrode potential of —0.40 V vs. S.C.E. This serves to re-oxidize the chromium quantitatively to the +3 state, and the analysis consists of measuring the quantity of electricity consumed in this oxidation.Of the elements commonly associated with chromium, only vanadium (and, when it is present in large amounts, molybdenum) interfere in this procedure.     

Multipole interactions and macroscopic differences in ortho and para hydrogen

Differences in the low temperature viscosity and virial coefficients of ortho and para hydrogen are attributed to centrifugal stretching, exchange symmetry, and, to a lesser extent, molecular anisotorpy. Of the latter, quadrupole interactions are the most important.     

Circularly Polarized Luminescence and Circular Dichroism of Bichromophoric Difluoroboron-β-diketonates: Inversion and Enhanced Chirality Based on Spatial Arrangements and Self-Assembly

We synthesized two bichromophoric difluoroboron-β-diketonates (DFB) connected in para and meta positions by using cyclohexane diamine as a chiral bridge ( para and meta (R/S)-CyDFB ). TD-DFT calculations revealed that the variation in connectivity of the DFB units leads to different spatial arrangements and a chirality inversion of the bichromophoric DFB. Higher g_abs values were obtained in (R/S)-CyDFB connected in para as compared to meta position. Aggregation of para (R/S)-CyDFB in mixture of solvents increase the g_lum values as compared to its monomeric form. Ultrasonication and heating induced the formation of highly ordered nano-helical wires of para (R/S)-CyDFB that increased the g_lum values to 0.015. On the other hand, meta (R/S)-CyDFB failed to form highly ordered self-assembled wires due to hindered H-binding sites. These observations indicate that the chiroptical properties of DFB bi-chromophore system can be modulated with self-assembly and spatial arrangement of the chromophores.