Free Analogue Research Articles

A one-parameter family of transforms, linearizing convolution laws for probability distributions

We study a family of transforms, depending on a parameterq∈[0,1], which interpolate (in an algebraic framework) between a relative (namely: -iz(log ℱ(·)) ′(-iz)) of the logarithm of the Fourier transform for probability distributions, and its free analogue constructed by D. Voiculescu ([16, 17]). The classical case corresponds toq=1, and the free one toq=0.We describe these interpolated transforms: (a) in terms of partitions of finite sets, and their crossings; (b) in terms of weighted shifts; (c) by a matrix equation related to the method of Stieltjes for expanding continuedJ-fractions as power series. The main result of the paper is that all these descriptions, which extend basic approaches used forq=0 and/orq=1, remain equivalent for arbitraryq∈[0, 1].We discuss a couple of basic properties of the convolution laws (for probability distributions) which are linearized by the considered family of transforms (these convolution laws interpolate between the usual convolution — atq=1, and the free convolution introduced by Voiculescu — atq=0). In particular, we note that description (c) mentioned in the preceding paragraph gives an insight of why the central limit law for the interpolated convolution has to do with theq-continuous Hermite orthogonal polynomials.

Interaction of Ant-ATP with Tubulin: Evidence for ATP Competition for the GTP E-Site on Tubulin

The interaction of the ribose-moditied ATP analogue 3′- O-anthraniloyl adenosine 5′-triphosphate (Ant-ATP) with tubulin has been studied using steady-state fluorescence techniques. This analogue inhibits the polymerization of tubulin induced by ATP or GTP. When this analogue binds to tubulin, an increase in the fluorescence intensity of the analogue and a blue shift of about 10 nm in the emission maximum have been observed. It has been found that Ant-ATP binds to tubulin at a single binding site in the hydrophobic region with a dissociation constant of 0.5-1.0 μM. It has been possible to restore the fluorescence emission intensity of the tubulin-bound analogue to that of the free ligand with a concomitant shift in the wavelength of emission maximum to that of the free analogue by displacing the analogue with ATP or GTP. These results can be interpreted to suggest that ATP and GTP compete for the Ant-ATP binding site and that ATP binds at the GTP exchangeable site (E-site).

Micellized sequestered silver atoms and small silver clusters

Pulse radiolysis was used to examine the nature of the silver species obtained when an aqueous solution containing sequestered Ag{sup +} ions was reduced by hydrated electrons in the presence of a surfactant macrocyclic crown ether, labeled L, and/or a maltoside surfactant. The initially formed product is the Ag{sup 0}(L) species which rapidly loses its ligand (half-life {le}5 {mu}s) and reacts with another Ag{sup +}(L) ion to form Ag{sub 2}{sup +}(L). The latter species decays by a bimolecular process to form the Ag{sub 4}{sup 2+}(L){sub n} species at a faster rate than its ligand free analogue. Ultimately, colloidal metallic silver, (Ag){sub n}, forms which is stabilized by the surfactant moieties. No long-term stability to the reduced monomolecular species could be obtained.

Facilitated diffusion of 6-deoxy-d-glucose by the oxidative yeast, Kluyveromyces lactis

The inducible glucose transport system of the yeast, Kluyveromyces lactis, was studied using the nonmetabolizeable glucose analogue, 6-deoxyglucose. The free sugar analogue is transported into glucose-grown cells via a facilitated diffusion system as determined by the nonconcentrative uptake of the sugar analogue, by the failure of energy inhibitors to reduce the rate of transport and by exchange diffusion across the membrane. Free 6-deoxyglucose is also transported into succinate-grown cells passively. Induction experiments revealed that 6-deoxyglucose serves as a gratuitous inducer for the glucose transport system in this yeast.

An Evaluation of the l-Methionine Activity of the Hydroxy Analogue of Methionine

Three product forms of methionine hydroxy analogue were prepared for biological evaluation of their l-methionine activity for broiler strain chickens (Vantress × Arbor Acres).Two samples of the acid of the analogue HA-50, LMA-70 and one sample of a commercial grade (90%) MHA® were standarized by gas liquid chromatography to contain a known amount of l-methionine activity as the free analogue acid.Each product form was tested in a separate experiment. The experimental chickens were fed a practical corn-soybean meal basal diet for the first seven days of the test. A semi-purified diet composed primarily of cerelose, isolated soybean protein and soybean meal was used for the remainder of the experimental period.HA-50 and the commercial form of the hydroxy analogue were formulated to contain 50% l-methionine activity. Hence, they were added to the diets at 0.1 and 0.2% and compared to the l-methionine standard which was added at levels of 0.05, 0.1 and 0.15%. LMA-70 was formulated to contain 70% l-methionine activity and was added to the experimental diets at 0.07 and 0.14% and compared to the l-methionine standard at the same levels used in the other experiments.Statistical analysis of four-week data revealed no difference between the biological response of l-methionine and the three forms of the analogue when tested at comparable l-methionine activity levels. The biological response of the analogue products was in good agreement with the l-methionine activity determined by gas liquid chromatography.

The Fabry-Perot Interferometer at Millimetre Wavelengths

The design and operation of an interferometer of the Fabry-Perot type at wavelengths around 8 mm is discussed. The reflectors have been made using multiple quarter wavelength sheets of dielectric, and extremely sharp fringes have been obtained giving selectivity or Q factors exceeding 60 000. The effects of diffraction on the interferometer are discussed and wavelength measurements made at various positions. The frequency of the millimetre wave source has been stabilized to a high degree and the wavelength measurements at wider reflector spacings shown to agree with a substandard cavity wavemeter within the accuracy attempted of a few parts in 105. Errors in the measured wavelengths at other positions of the interferometer do not exceed a few parts in 104, the measured values being greater than the true value. Measurements of dielectric constants and dielectric loss have been made using the interferometer, and results are in agreement with values obtained by other methods. Since the interferometer is the free space analogue of the cavity wavemeter it is particularly suitable for measurements on materials of low loss tangent at millimetre wavelengths. Finally, the use of the interferometer for length measurements is mentioned, and also its possible use for the accurate determination of the velocity of electromagnetic waves.