Bifurcations with nonuniversal exponents in a lattice model

The bifurcations of a two-dimensional area preserving mapping with a cubic term are studied. This mapping shows a large number of bifurcations where the period becomes a multiple. For a given order of bifurcation exponents are found which depend on the series considered. The exponents calculated numerically are compared with renormalisation calculations for a number of cases.     

Kalman filter applied to setpoint control in continuous titrations

A state-space model is described for continuous titrations based on first-order dynamics. The Kalman filter allows on-line monitoring of an empirically established setpoint in the titration curve. The algorithm advocated is examined for potentiometric titrations of ca. 10^?3 M solutins of acids, silver(I) and copper(II). Only gross indications of the essential parameters such as the time constant and noise covariances are required. The computer-controlled titration system is compared with a conventional setpoint titrator. Especially in cases of slow response times and steep inflections, there are advantages in both accuracy and speed when the Kalman filter is applied.     

Skew-symmetric vanishing lattices and their monodromy groups

Mathematische Annalen -     

Hybrid measurement of auditory steady-state responses and distortion product otoacoustic emissions using an amplitude-modulated primary tone

A maximum auditory steady-state response (ASSR) amplitude is yielded when the ASSR is elicited by an amplitude-modulated tone (f(c)) with a fixed modulation frequency (f(m) = 40 Hz), whereas the maximum distortion product otoacoustic emission (DPOAE) level is yielded when the DPOAE is elicited using a fixed frequency ratio of the primary tones (f2/f1 = 1.2). When eliciting the DPOAE and ASSR by the same tone pair, optimal stimulation is present for either DPOAE or ASSR and thus adequate simultaneous DPOAE/ASSR measurement is not possible across test frequency f2 or f(c), respectively. The purpose of the present study was to determine whether the ASSR and DPOAE can be measured simultaneously without notable restrictions using a DPOAE stimulus setting in which one primary tone is amplitude modulated. A DPOAE of frequency 2f1-f2 and ASSR of modulation frequency 41 Hz were measured in ten normal hearing subjects at a test frequency between 0.5 and 8 kHz (f2 = f(c)). The decrease in the DPOAE level and the loss in ASSR amplitude during hybrid mode stimulation amounted, on average, to only 2.60 dB [standard deviation (SD) = 1.38 dB] and 1.83 dB (SD = 2.38 dB), respectively. These findings suggest simultaneous DPOAE and ASSR measurements to be feasible across all test frequencies when using a DPOAE stimulus setting where the primary tone f2 is amplitude modulated.     

Isotopic composition and concentration measurements of atmospheric CO2 with a diode laser making use of correlations between non-equivalent absorption cells

Correlations between a sample and a sealed reference cell of a tunable diode laser spectrometer for the measurement of the isotopic composition (δ ¹³C) and the concentration of atmospheric carbon dioxide in air have been investigated. Likely due to fluctuations of the laser emission profile, these correlations have been used to improve the performance of the instrument. In a comparison with isotope ratio mass spectrometer and gas chromatographic measurements, an accuracy of 0.15‰ for δ ¹³C and 0.05 ppmv for the CO₂ concentration is demonstrated for 40 s integration time. Long-term stability and field deployment of the instrument have been investigated during a few days measurement campaign in Paris.     

Synthesis and characterization of long perylenediimide polymer fibers: from bulk to the single-molecule level

The synthesis and characterization of perylenediimide polyisocyanides is reported. In addition to short oligomers, our synthetic approach results in the formation of extremely long, well-defined, and rigid perylenediimide polymers. Ordering and close-packing of the chromophores in these long polymers is guaranteed by attachment to a polyisocyanide backbone with amino acid side chains. Hydrogen bonding interactions between those groups stabilize and rigidify the helical polymer structure. The rodlike nature of the synthesized long perylenediimide pendant polyisocyanides as well as the helical arrangement of the chromophores is demonstrated by means of atomic force microscopy. Remarkably, polymer fibers up to 1 mum in length have been visualized, containing several thousands of perylenediimide molecules. Circular dichroism spectroscopy reveals the chiral organization of the chromophore units in the polymer, whereas absorption and emission measurements prove the occurrence of excited-state interactions between those moieties due to the close packing of the chromophore groups. However, an intricate optical behavior is encountered in bulk as a result of the coexistence of short oligomers and long polymers of perylenediimide, a situation subsequently uncovered by means of single-molecule experiments. Individual long helical perylenediimide polyisocyanides exhibit a typical red-shifted fluorescence spectrum, which, together with depolarized emission continuously decreasing in time, demonstrate that fluorescence arises from multiple excimer-like species in the polymer. Upon continuous irradiation of these long polymers, a fast decay in fluorescence lifetime is observed, a situation explained by photoinduced creation of quenching sites. Radical/ion formation by intramolecular electron transfer between close-by perylenediimide moieties is the most probable mechanism for this process. Appropriate control of the electron-transfer process might open the possibility of applying these polymers as perylenediimide-based supramolecular nanowires.     

Determination of low degrees of hardness in water using a soap solution according to clark. I

1. The determination of low degrees of hardness in water according to the usual methods does not yield satisfactory results. Therefore an investigation was carried out with a soap solution of sodium, oleate according to clarke, and also nephelometric measurements were made. 2. Measurements were cairied out at degrees of hardness from 0.5 to 39.0 p.p.m. (i.e. 0°.005–3°.09 FH; or 0°.003–2°.18 DH), made out of pure calcium chloride solutions, at different pH values; also with calcium chloride solations, containing NaCI and alcohol. Magnesium, chloride solutions were investigated in the same way. 3. The calcium oleate, that precipitates when the hardness is determined, has a composition of 5 CaOl₂-2NaOl. The magnesium oleate has a corresponding composition. Dependent on the circumstances also 5 CaOl₂-3NaOl and calcium oleates. containing yet more sodium oleate may be formed. This phenomenon occurs especially at very low degrees of hardness. 4. No turbidity of calcium oleate arises when precipitation takes place at degrees of liardness lower tlian 1.2 p.p.m. CaCO₃(0°.07 DH), Magnesium olcate does not precipitate at degrees of hardness lower than 3.2 p.p.m. (0°.18 DH). 5. As a result of the phenomenon referred to in. point 3 the determination according to clarke for degrees of hardness below 5 p.p.m. CaCO₃(0°.3 DH) are only reliable if very important errors (up to 30%) are tolerated. In order to determine these degrees of hardness it is therefore advisable to add so much concentrated CaCl₂ solution as to reach a handy hardness of the water sample.