Field-flow fractionation in microfluidic channels of low aspect ratio

The shape of the steady-state three-dimensional flow velocity profile established in carrier liquid flowing inside the rectangular cross-sectional channel for field-flow fractionation should be taken into account to optimize the separation. The central parts of this profile in the planes parallel to the main channel walls are flat with almost identical flow velocities which drop down to zero at the side walls. The separated species transported by the flow in the close-to-side walls regions move with lower average velocities compared to the species transported in the central part of the channel and are undesirably broadened. The hydrodynamic splitting of the carrier liquid at the entry of the channel where the sample is injected only into the central part of the channel eliminates the excessive zone broadening. The aspect ratio of the breadth to the thickness of the channel ratio can thus be reduced. The effect of various aspect ratios on the shape of the flow velocity profile is calculated and the results are used to optimize the aspect ratio of microfluidic channels. The experiments carried out by microthermal field-flow fractionation confirmed that the aspect ratio cannot be reduced to a value of 1, proposed by other authors.     

Influence of selected mobile phase properties on the TLC retention behavior of ziprasidone and its impurities

ABSTRACT

Influence of nine different solvents, either alone or in a mixture, on the retention behavior of ziprasidone and its five impurities were examined by normal-phase thin-layer chromatography. Migration distances of the examined compounds obtained under the examined chromatographic conditions were correlated with calculated mobile phase properties, such as Snyder polarity and Hansen solubility. Linear or second-order polynomial relationships with high correlation coefficients were established between investigated variables. The obtained mathematical functions and statistical results indicated that selected mobile phase properties can be used for the prediction of the retention behavior of ziprasidone and its five impurities.     

Development and validation of high-performance thin-layer chromatographic method for determination of amygdalin

ABSTRACT

A new method for the extraction and quantitative determination of amygdalin has been proposed. Accelerated solvent extraction was applied for the extraction, and reversed-phase high-performance thin-layer chromatography method was developed, validated, and applied for the determination of amygdalin in the extracts of apricot, plum, almond, and peach kernels. The chromatographic system used was RP-18 silica, as stationary phase and acetonitrile/water (50:50, v/v), as mobile phase. Densitometric scanning was performed at 210 nm. The method was validated with respect to specificity, linearity, precision, and accuracy. The results showed that the peak area responses were linear within the concentration range of 2.5–50.0 µg/spot (R² = 0.9984). The limit of quantification was 4.28 µg/spot, and the detection limit 1.28 µg/spot. The intra-day and inter-day reproducibility, in terms of %RSD, were in the range of 0.81–1.15 and 1.32–1.89, respectively. The accuracy data were in the range from 99.98 to 100.56%. The method is linear, quantitative and reproducible, and could be used as an efficient and economical green chromatographic procedure for the determination of amygdalin in the fruit kernel.     

Solving the robust two-stage capacitated facility location problem with uncertain transportation costs

In this study, we start from a multi-source variant of the two-stage capacitated facility location problem (TSCFLP) and propose a robust optimization model of the problem that involves the uncertainty of transportation costs. Since large dimensions of the robust TSCFLP could not be solved to optimality, we design a memetic algorithm (MA), which represents a combination of an evolutionary algorithm (EA) and a modified simulated annealing heuristic (SA) that uses a short-term memory of undesirable moves from previous iterations. A set of computational experiments is conducted to examine the impact of different protection levels on the deviation of the objective function value. We also investigate the impact of variations of transportation costs that may occur on both transhipment stages on the total cost for a fixed protection level. The obtained results may help in identifying a sustainable and efficient strategy for designing a two stage capacitated transportation network with uncertain transportation costs, and may be applicable in the design and management of similar transportation networks.     

Local probabilities and total variation distance for random permutations

We are concerned with permutations taken uniformly at random from the symmetric group. Firstly, we study the probability of a permutation missing short cycles. Secondly, the result is employed to establish a formula for total variation distance between the process of multiplicities of cycle lengths in a random permutation and a process of independent Poisson random variables. We apply an analytic approach originated in number theory (K. Gyory et al. (Eds.) in Number Theory in Progress, 1999).     

Thermal analysis of heat-treated silver fir wood and larval frass

Glasses having composition 5Li₂O–5ZnO– xBi₂O₃ –(90 ? x) P₂O₅ (x = 5, 10, 15, 20 and 25 mol%) were prepared by the normal melt quenching technique. Nanocomposite glass containing bismuth phosphate BiPO₄ nanocrystals was obtained, which can be attributed to homogeneous nucleation process. The formation of BiPO₄ nanocrystals was confirmed and characterized by X-ray diffraction patterns (XRD), transmission electron microscopy (TEM), differential scanning calorimetry, optical absorption (UV–Vis) and micro-hardness studies. The morphological analysis by XRD and TEM microscopy showed the formation of hexagonal BiPO₄ nanocrystals, and its estimated nanocrystalline sizes were found to be varying from 5.35 to 11.53 nm depending on the Bi₂O₃ concentrations. The density (ρ) and molar volume (V _m) were also determined and found to be in compositional dependence. Glass transition temperature (T _g) and glass crystallization temperature (T _c) were obtained and found to be increased (from 240.0 to 337.2 °C) with increasing Bi₂O₃ up to 20 mol% and then decreased (from 337.2 to 331.8 °C) due to the structural changes in the glass network. Effect of BiPO₄ content on the optical properties had been investigated. From the UV–Vis spectra, it was observed that the fundamental absorption edge shifts toward lower wavelengths, i.e., blueshifts with increasing Bi₂O₃ mol% up to 20 mol%, and then shifts toward higher wavelengths, i.e., redshifts beyond 20 mol%. It was also observed that the obtained E _opt (for indirect and direct transitions) increases with gradual increase in Bi₂O₃ content up to 20 mol% and then decreases beyond 20 mol%. This may be due to the introduction of Bi cations into the glass network as a network former up to 20 mol% causing a decrease in ΔE values, beyond 20 mol%, the introduction of Bi ions into the glass network interstitially leads to increase the values of ΔE. The optical properties of the present nanocrystallized glasses showed a quantum size dependence, in which the optical band gap energy (E _opt) was changed as a function of BiPO₄ nanocrystalline sizes.     

A fuzzy extension of Analytic Hierarchy Process based on the constrained fuzzy arithmetic

The aim of the paper is to highlight the necessity of applying the concept of constrained fuzzy arithmetic instead of the concept of standard fuzzy arithmetic in a fuzzy extension of Analytic Hierarchy Process (AHP). Emphasis is put on preserving the reciprocity of pairwise comparisons during the computations. For deriving fuzzy weights from a fuzzy pairwise comparison matrix, we consider a fuzzy extension of the geometric mean method and simplify the formulas proposed by Enea and Piazza (Fuzzy Optim Decis Mak 3:39–62, 2004). As for the computation of the overall fuzzy weights of alternatives, we reveal the inappropriateness of applying the concept of standard fuzzy arithmetic and propose the proper formulas where the interactions among the fuzzy weights are taken into account. The advantage of our approach is elimination of the false increase of uncertainty of the overall fuzzy weights. Finally, we advocate the validity of the proposed fuzzy extension of AHP; we show by an illustrative example that by neglecting the information about uncertainty of intensity of preferences we lose an important part of knowledge about the decision making problem which can cause the change in ordering of alternatives.     

Nonuniform exponential dichotomies and Lyapunov functions

For the nonautonomous dynamics defined by a sequence of bounded linear operators acting on an arbitrary Hilbert space, we obtain a characterization of the notion of a nonuniform exponential dichotomy in terms of quadratic Lyapunov sequences. We emphasize that, in sharp contrast with previous results, we consider the general case of possibly noninvertible linear operators, thus requiring only the invertibility along the unstable direction. As an application, we give a simple proof of the robustness of a nonuniform exponential dichotomy under sufficiently small linear perturbations.