A note on a property of a weak self-similar perfect set

Let S be a compact, weak self-similar perfect set based on a system of weak contractions f_j, j=1,…,m each of which is characterized by a variable contraction coefficient _j(l) as d(f_j(x),f_j(y)) _j(l)d(x,y), d(x,y)<l, l>0. If the relation ∑^m_j=1j(l₀)<1 holds at at least one point l₀, then every nonempty compact metric space is a continuous image of the set S.     

Determination of azide as the 3,5-dinitrobenzoyl derivative by capillary electrophoresis

A simple, rapid and reliable capillary electrophoresis method with a photodiode array detector was developed for determination of azide as the 3,5-dinitrobenzoyl derivative in drink samples fortified with sodium azide. Sample preparation was simple and rapid because no more than a simple dilution of samples is needed after quick derivatization. Separation was carried out using a buffer system comprising 25 mM phosphate buffer and 4 mM cetyltrimethylammonium hydroxide at pH 3.0. Methyl benzoate was selected as the internal standard (IS). This study investigated the influence of the concentration of phosphate buffer and electroosmotic flow (EOF) modifier, and the buffer pH on migration time and signal response. The optimized method made it possible to determine azide within 5 min. The limit of detection was determined to be 1.9 microg/ml with SIN > 3. The quantitation range was 6.5-323 microg/ml. By the method recoveries of azide in drink samples fortified with sodium azide were investigated. Mean recovery values ranged from 93.6 to 105.8% and results were satisfactory. In addition, no interference was observed in electropherograms of drink samples fortified with sodium azide. Thus, by this method, azide in drink samples can be determined rapidly with high recoveries and good selectivity despite extremely simple sample preparation.     

3-Aminobenzamide and 3-aminobenzoic acid, tags for capillary electrophoresis of complex carbohydrates with laser-induced fluorescent detection

The efficiencies in derivatization of reducing carbohydrates were compared by capillary electrophoresis using maltose as a model with nine monoaminobenzene derivatives by reductive amination in the presence of sodium cyanoborohydride. We found that aminobenzene derivatives substituted at the 3-position showed good reactivity with reducing carbohydrates as expected from the reaction mechanism, although the fluorescence intensities and molar absorptivities of these derivatives were not as high as those of 2- and 4-aminobenzene derivatives. The reagents, 3-aminobenzamide and 3-aminobenzoic acid, which showed the highest reactivity, were applied to the labeling of carbohydrate chains obtained from some sialic acid-containing glycoprotein samples, and also high-mannose and hybrid-type oligosaccharides. Capillary electrophoresis of these labeled carbohydrate chains in an inner surface-modified capillary with (50% phenyl)methylpolysiloxane allowed excellent separation of sialic acid-containing carbohydrate chains derived from fetuin and thyroglobulin as well as high mannose-type and hybrid-type carbohydrates derived from bovine pancreas ribonuclease B, soybean agglutinin and hen ovalbumin. The lower limit of calibration was as low as the 10(-16) mol (injected amount) with helium-cadmium laser induced detection.     

Rational design and real time, in-cell detection of the proapoptotic activity of a novel compound targeting Bcl-X(L)

Antiapoptotic Bcl-2-family proteins Bcl-2 and Bcl-X(L) have been recently validated as drug discovery targets for cancer. Here, by using a combination of molecular modeling, NMR-based structural analysis, fluorescence polarization assays, and cell-based assays, we have designed and characterized a novel proapoptotic compound targeting these proteins. Our compound, Apogossypol, is capable of binding and inhibiting Bcl-2 and Bcl-X(L) with high affinity and induces apoptosis of tumor cell lines. Mechanistic studies on the action of our compound were also performed via confocal microscopy that provided real-time detection of the interaction with Bcl-X(L) in intact cells. Finally, preliminary data on cells freshly isolated from patients affected by chronic lymphocytic leukemia strongly suggest potential applications of Bcl-2 antagonists as chemosensitizers in cancer therapy.     

A fully automated amino acid analyzer using NBD-F as a fluorescent derivatization reagent

A fully automated amino acid analyzer using NBD-F (4- fluoro-7-nitro-2,1,3-benzoxadiazole) as a fluorescent derivatization reagent was developed. The whole analytical process was fully automated from derivatization, injection to HPLC separation and quantitation. The derivatization reaction conditions were re-evaluated and optimized. Amino acids were derivatized by NBD-F for 40 min at room temperature in the borate buffer (pH 9.5). The derivatives were separated within 100 min and fluorometrically detected at 540 nm with excitation at 470 nm. The detection limits for amino acids were in the range of 2.8-20 fmol. The calibration curves were linear over the range of 20 fmol to 20 pmol on column with the correlation coefficients of 0.999. The coefficients of variation were less than 5% at 3 pmol injection for all amino acids. Amino acids in rat plasma were determined by the proposed HPLC method.     

Kinetics of the volume phase transition in poly(n‐isopropylacrylamide) gels prepared under high pressure

New poly(N‐isopropylacrylamide) gels were prepared under high pressure (ca. 200 MPa) during gelation. The preparation‐pressure dependence of the deswelling speed of the gels was measured with a conventional T‐jump method. The deswelling time of a gel rod 2.2 mm in diameter prepared at 193 MPa was about 200 s, 1000 times faster than that of a homogeneous poly(N‐isopropylacrylamide) gel. Moreover, the collective diffusion coefficient, the thermal fluctuation, and the ensemble‐average intensity of the swollen gel networks were obtained with dynamic light scattering measurements. Both the enthalpy and entropy of the gels were estimated from equilibrium swelling curves with the Flory–Huggins interaction parameter evaluated with mean field theory based on the Flory‐type of the Gibbs free‐energy formula. It was found that the networks of the gels had an inhomogeneous structure newly introduced by the preparation pressure. © 2001 John Wiley & Sons, Inc. J Polym Sci Part A: Polym Chem 39: 2315–2325, 2001     

Power-law distributions in random multiplicative processes with non-Gaussian colored multipliers

One class of universal mechanisms that generate power-law probability distributions is that of random multiplicative processes. In this paper, we consider a multiplicative Langevin equation driven by non-Gaussian colored multipliers. We analytically derive a formula that relates the power-law exponent to the statistics of the multipliers and numerically confirm its validity using multiplicative noise generated by chaotic dynamical systems and by a two-valued Markov process. We also investigate the relationship between our treatment and the large deviation analysis of time series, and demonstrate the appearance of log-periodic fluctuations superimposed on the power-law distribution due to the non-Gaussian nature of the multipliers.     

WeightedH p multipliers on locally compact Vilenkin groups

LetG be a locally compact Vilenkin group. We give a maximal function characterization of the weightedH ^p spaces overG, and give a Hörmander type multiplier theorem for these spaces.