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.     

On classifying unitary modules by their Dirac cohomology

Let G be a connected real reductive group with maximal compact subgroup K of the same rank as G. Dirac cohomology of an A_q(λ) module can be identified with a geometric object—the k-dominant part of a face of the convex hull of the Weyl group orbit of the parameter λ + ρ. We show how Dirac cohomology can be used as a parameter to classify the A_q(λ) modules.     

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.     

J-means and I-means for minimum sum-of-squares clustering on networks

Given a graph, the Edge minimum sum-of-squares clustering problem requires finding p prototypes (cluster centres) by minimizing the sum of their squared distances from a set of vertices to their nearest prototype, where a prototype can be either a vertex or an inner point of an edge. In this paper we have implemented Variable neighborhood search based heuristic for solving it. We consider three different local search procedures, K-means, J-means, and a new I-means heuristic. Experimental results indicate that the implemented VNS-based heuristic produces the best known results in the literature.     

Symbolic–numeric computation of orthogonal polynomials and Gaussian quadratures with respect to the cardinal <Emphasis Type="Italic">B</Emphasis>-spline

The first 60 coefficients in the three-term recurrence relation for monic polynomials orthogonal with respect to cardinal B-splines φ _m as the weight functions on [0, m] (m ∈ ?) are obtained in a symbolic form. They enable calculation of parameters, nodes, and weights, in the corresponding Gaussian quadrature up to 60 nodes. The efficiency of these Gaussian quadratures is shown in some numerical examples. Finally, two interesting conjectures are stated.     

Stochastic upscaling of random microstructures

In this work we present an upscaling technique for multi-scale computations based on random microstructures modelled as realisations of lognormally distributed random fields, or described by randomly distributed inclusions in a homogeneous matrix. Their corresponding coarse-scale model parameters are considered as uncertain, and are approximated by random variables, the distributions of which are obtained via polynomial chaos based Bayesian procedures in which the fine-scale energy is used as an observation. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Bounds for Shannon and Zipf‐Mandelbrot entropies

Shannon and Zipf‐Mandelbrot entropies have many applications in many applied sciences, for example, in information theory, biology and economics, etc. In this paper, we consider two refinements of the well‐know Jensen inequality and obtain different bounds for Shannon and Zipf‐Mandelbrot entropies. First of all, we use some convex functions and manipulate the weights and domain of the functions and deduce results for Shannon entropy. We also discuss their particular cases. By using Zipf‐Mandelbrot laws for different parameters in Shannon entropies results, we obtain bounds for Zipf‐Mandelbrot entropy. The idea used in this paper for obtaining the results may stimulate further research in this area, particularly for Zipf‐Mandelbrot entropy.     

The intermediate disorder regime for a directed polymer model on a hierarchical lattice

We study a directed polymer model defined on a hierarchical diamond lattice, where the lattice is constructed recursively through a recipe depending on a branching number $b\in \mathbb{N}$ and a segment number $s\in \mathbb{N}$. When $b\le s$ it is known that the model exhibits strong disorder for all positive values of the inverse temperature $\beta$, and thus weak disorder reigns only for $\beta =0$ (infinite temperature). Our focus is on the so-called intermediate disorder regime in which the inverse temperature $\beta \equiv {\beta }_n$ vanishes at an appropriate rate as the size $n$ of the system grows. Our analysis requires separate treatment for the cases $b<s$ and $b=s$. In the case $b<s$ we prove that when the inverse temperature is taken to be of the form ${\beta }_n=\stackrel{?}{\beta }{(b/s)}^{n/2}$ for $\stackrel{?}{\beta }>0$, the normalized partition function of the system converges weakly as $n\to \infty$ to a distribution $L\left(\stackrel{?}{\beta }\right)$ and does so universally with respect to the initial weight distribution. We prove the convergence using renormalization group type ideas rather than the standard Wiener chaos analysis. In the case $b=s$ we find a critical point in the behavior of the model when the inverse temperature is scaled as ${\beta }_n=\stackrel{?}{\beta }/n$; for an explicitly computable critical value ${\kappa }_b>0$ the variance of the normalized partition function converges to zero with large $n$ when $\stackrel{?}{\beta }\le {\kappa }_b$ and grows without bound when $\stackrel{?}{\beta }>{\kappa }_b$. Finally, we prove a central limit theorem for the normalized partition function when $\stackrel{?}{\beta }\le {\kappa }_b$.