Comparison of Green Functions and Harmonic Measures for Parabolic Operators

In this paper, we prove two-sided pointwise estimates for the Green function of a parabolic operator with singular first order term on a C^1,1-cylindrical domain . Basing on these estimates, we establish the equivalence of the parabolic measure, the adjoint parabolic measure and the surface measure on the lateral boundary of . These results are first studied by some authors for certain elliptic and less general parabolic operators. Mathematics Subject Classifications (2000) 31B25, 35B05, 35K10, 58J35.     

On a numerical technique for finding multiple zeros and its dynamic

An optimal method is developed for approximating the multiple zeros of a nonlinear function, when the multiplicity is known. Analysis of convergence for the proposed technique is studied to reveal the fourth-order convergence. We further investigate the dynamics of such multiple zero finders by using basins of attraction and their corresponding fractals in the complex plane. A fourth-order method will also be presented, when the multiplicity m is not known. Numerical comparisons will be made to support the underlying theory of this paper.     

Characterization methods for liquid interfacial layers

Liquid interfaces are met everywhere in our daily life. The corresponding interfacial properties and their modification play an important role in many modern technologies. Most prominent examples are all processes involved in the formation of foams and emulsions, as they are based on a fast creation of new surfaces, often of an immense extension. During the formation of an emulsion, for example, all freshly created and already existing interfaces are permanently subject to all types of deformation. This clearly entails the need of a quantitative knowledge on relevant dynamic interfacial properties and their changes under conditions pertinent to the technological processes. We report on the state of the art of interfacial layer characterization, including the determination of thermodynamic quantities as base line for a further quantitative analysis of the more important dynamic interfacial characteristics. Main focus of the presented work is on the experimental possibilities available at present to gain dynamic interfacial parameters, such as interfacial tensions, adsorbed amounts, interfacial composition, visco-elastic parameters, at shortest available surface ages and fastest possible interfacial perturbations. The experimental opportunities are presented along with examples for selected systems and theoretical models for a best data analysis. We also report on simulation results and concepts of necessary refinements and developments in this important field of interfacial dynamics.     

Alkynyl ruthenium colorimetric sensors: optimizing the selectivity toward fluoride anion

We report on the synthesis of alkynyl ruthenium colorimetric sensors whose receptors are constituted by thiazolidinedione, rhodanine, or barbituric heads as recognition centers for anions. As modifications in the charge density at these recognition centers affect the whole molecule, through the alkynyl ligand acting as a communicating wire, the effects of hydrogen-bonding interactions with the anions were observed with the naked eye and monitored by UV-vis absorption spectrometry. The selectivity of the sensors was improved through electronic modifications of the alkynyl ruthenium subunit: the higher the electron density at the receptor head, the higher the selectivity is. TD-DFT calculations rationalize the long-range electronic communication as a main characteristic of the alkynyl ruthenium species and as a key to improve the selectivity of alkynyl ruthenium-based sensors toward anions.     

Time-Domain Quantification of Multiple-Quantum-Filtered Na Signal Using Continuous Wavelet Transform Analysis

The application of continuous wavelet transform (CWT) analysis technique is presented to analyze multiple-quantum-filtered (MQF) ²³Na magnetic resonance spectroscopy (MRS) data. CWT acts on the free-induction-decay (FID) signal as a time-frequency variable filter. The signal-to-noise ratio (SNR) and frequency resolution of the output filter are locally increased. As a result, MQF equilibrium longitudinal magnetization and the apparent fast and slow transverse relaxation times are accurately estimated. A developed iterative algorithm based on frequency signal detection and components extraction, already proposed, was used to estimate the values of the signal parameters by analyzing simulated time-domain MQF signals and data from an agarose gel. The results obtained were compared to those obtained by measurement of signal height in frequency domain as a function of MQF preparation time and those obtained by a simple time-domain curve fitting. The comparison indicates that the CWT approach provides better results than the other tested methods that are generally used for MQF ²³Na MRS data analysis, especially when the SNR is low. The mean error on the estimated values of the amplitude signal and the apparent fast and slow transverse relaxation times for the simulated data were 2.19, 6.63, and 16.17% for CWT, signal height in frequency domain, and time-domain curve fitting methods, respectively. Another major advantage of the proposed technique is that it allows quantification of MQF ²³Na signal from a single FID and, thus, reduces the experiment time dramatically.     

Stability indicating method for famotidine in pharmaceuticals using porous graphitic carbon column

A simple, sensitive and rapid HPLC method was developed and validated for the simultaneous determination of famotidine (FMT) and related impurities in pharmaceuticals. Chromatographic separation was accomplished within 10 min on a porous graphitic carbon (PGC) column using 50:50 v/v ACN-water containing 0.5% pentane sulphonic acid (PSA) as the mobile phase. Separation was achieved with a flow rate of 1 mL/min and a detection wavelength of 265 nm. The calibration curves were linear over a concentration range of 1.5-100 microg/mL. The intra- and interday RSDs (n = 5) for the retention times and peak area were all less than 2%. The method was sensitive with an LOD (S/N = 3) of 0.1 microg/mL for FMT, imp. C and 0.05 microg/mL for imp. 2, A and D. All recoveries were greater than 98%. The method was demonstrated to be precise, accurate and specific with no interference from the tablet ingredients and separation of the drug peak from the peaks of the degradation products (oxidative degradation and acid and base degradation). The results indicated that the proposed method could be used for the determination of FMT in commercial dosage forms and as a stability-indicating assay.     

Effect of Host Medium on the Fluorescence Emission Intensity of Rhodamine B in Liquid and Solid Phase

In this work, we study the effect of concentration, host medium, PH and phase states on the fluorescence emission from the laser dye Rhodamine B pumped by UV laser as exited source. The polymethylmethacrylate PMMA is used as a host medium in case of solid phase samples while, ethanol and Tetrahydrofuran (THF) are used in case of a liquid one. Laser Induced Fluorescence (LIF) technique was used to study the fluorescence properties of both cases of liquid and thin film solid-state samples. In addition, the Dual Thermal Lens (DTL) technique was used to study the quantum yield of these samples. The concentrations of Rhodamine B in ethanol as solvent between 2 × 10⁻² M and 5 × 10⁻⁶ M were studied. The maximum fluorescence emission is observed at concentration of Rhodamine B C = 3 × 10⁻⁴ M. Comparison studies were investigated for different host medium such as ethanol, THF, PMMA in liquid phase state and PMMA in solid phase state. The measurements revealed that, the behavior of both phases state was analogous. Rhodamine B/PMMA thin film sample by ratio of 4:1 and thickness 0.12 mm was found to have the best photostability sample with a quantum yield about ≈0.82.     

On the Symmetric H q -Semiclassical Polynomial Sequences of Even Class. Some Examples from the Class Two

In the present work, we deal with the quadratic decomposition of symmetric H _q -semiclassical polynomial sequences of even class. Some examples from class two are settled. We give an integral and discrete measure representations for each of considered symmetric forms.     

Purification and structure elucidation of three naturally bioactive molecules from the new terrestrial Streptomyces sp. TN17 strain

Thirty litres of fermentation broth was extracted from the newly isolated Streptomyces sp. strain TN17 and various separation and purification steps led to the isolation of three pure bioactive compounds (1-3). Compound 1: cyclo (L-Leu-L-Arg), a diketopiperazine 'DKP' derivative; 2: di-(2-ethylhexyl) phthalate, a phthalate derivative; and 3: cyclo 1-[2-(cyclopentanecarbonyl-3-phenyl-propionyl]-pyrrolidine-2-carboxylic acid (1-carbamoyl-propyl)-amide, a cyclic tetrapeptide derivative. The chemical structure of these three active compounds was established on the basis of spectroscopic studies (MS and NMR) and by comparison with data from the literature. According to our biological studies, the pure compounds (1-3) possess antibacterial and antifungal activities.