Comparison of interpolation polynomials with divided differences,interpolation polynomials with finite differences,and quadratic functions obtained by the least squares method in modeling of chromatographic responses

A novel approach to mathematical modeling of chromatographic responses based on interpolation polynomials with divided differences and with finite differences is discussed. These interpolational techniques as well as traditionally applied second‐order polynomial models obtained by least squares are compared. Interpolation techniques can be useful in situations where commonly used linear or quadratic models are not applicable: when the nature of dependence is complex or the investigated factor intervals are broad. The three analyzed modeling techniques are incorporated in a design of experiments methodology for systematic development and optimization of liquid chromatographic methods. The direct modeling of retention factors is carried out first, while the objective function for final quality measurement is calculated last. An interpolation polynomial with divided differences resulted in a high quality fit compared with the results obtained by the other two modeling approaches and succeeded in locating the desired optimum. It is shown that this modeling technique can be a useful alternative for modeling of chromatographic responses. Copyright © 2013 John Wiley & Sons, Ltd.     

Reaction of Some Alkenols with Tetrachloromethane

 The reaction of some alkenols with tetrachloromethane in the presence of a radical initiator was investigated. Regarding the effects of structural features of the starting alkenol (number and position of methyl substituents at the double bond and at the carbinol carbon atom, constitutional relationship between the double bond and the hydroxyl group) there are two possible competing reactions: addition and cyclization. In the case of the simplest alkenols (without substituents and with a more remote double bond) addition occurs; mono- and disubstituted secondary and tertiary Δ⁴- and Δ⁵-alkenols cyclize in high yields to give the corresponding cyclic ethers.     

Study of the structure,prooxidative, and cytotoxic activity of some chelate copper(II) complexes

The six chelate N,O-copper(II) complexes were synthesised starting from salicylaldehyde anil Schiff bases, as ligands. Their structure is elucidated using experimental and theoretical tools. In vitro biological activities, i.e. cytotoxic and prooxidative effects against human epithelial mammary gland/breast metastatic carcinoma MDA-MB-231, epithelial colorectal carcinoma HCT-116, and foetal lung fibroblast healthy MRC-5 cell lines of investigated compounds are also determined. Complexes Cu-1, Cu-6, and especially Cu-7 showed significant cytotoxic effects, with IC₅₀ values comparable with effects of positive control CisPt. In addition, investigated complexes induced extreme oxidative and nitrosative stress in all treated cell lines. The most prominent effect is observed on HCT-116 cells, and on MRC-5 cells, while MDA-MB-231 cells showed higher resistance to the investigated cell lines, giving us direction towards the substances with more specific selectivity.     

Euler–Lagrange Equations for Lagrangians Containing Complex-order Fractional Derivatives

Two variational problems of finding the Euler–Lagrange equations corresponding to Lagrangians containing fractional derivatives of real- and complex-order are considered. The first one is the unconstrained variational problem, while the second one is the fractional optimal control problem. The expansion formula for fractional derivatives of complex-order is derived in order to approximate the fractional derivative appearing in the Lagrangian. As a consequence, a sequence of approximated Euler–Lagrange equations is obtained. It is shown that the sequence of approximated Euler–Lagrange equations converges to the original one in the weak sense as well as that the sequence of the minimal values of approximated action integrals tends to the minimal value of the original one.     

Direct Separation of the Enantiomers of (±)-Metoprolol Tartrate on Impregnated TLC Plates with d-(−)-Tartaric Acid as a Chiral Selector

JPC – Journal of Planar Chromatography – Modern TLC - A method for chromatographic separation of the enantiomers of (±)-metoprolol tartrate (±MeT) employing a chiral mobile...     

An Improved Phenylselenoetherification of Pent-4-en-1-ol

Summary. The procedure employs phenylselenyl chloride or bromide, pent-4-en-1-ol, and additives, like pyridine and silver(I) salts, to generate the cyclic ether of tetrahydrofuran type in high yields. A catalytic amount of additive leads to higher yields, but equimolar amounts achieved almost quantitative yields under extremely mild experimental conditions. The effect of the halide ion of the selenylating reagent is not significant.     

The electrical conductance growth of a metallic granular packing

We report on measurements of the electrical conductivity on a two-dimensional packing of metallic disks when a stable current of ~1 mA flows through the system. At low applied currents, the conductance σ is found to increase by a pattern σ(t) = σ _∞ ? Δσ E _α [ ? (t/τ) ^α ], where E _α denotes the Mittag-Leffler function of order α ∈ (0,1). By changing the inclination angle θ of the granular bed from horizontal, we have studied the impact of the effective gravitational acceleration g _eff = gsinθ on the relaxation features of the conductance σ(t). The characteristic timescale τ is found to grow when effective gravity g _eff decreases. By changing both the distance between the electrodes and the number of grains in the packing, we have shown that the long term resistance decay observed in the experiment is related to local micro-contacts rearrangements at each disk. By focusing on the electro-mechanical processes that allow both creation and breakdown of micro-contacts between two disks, we present an approach to granular conduction based on subordination of stochastic processes. In order to imitate, in a very simplified way, the conduction dynamics of granular material at low currents, we impose that the micro-contacts at the interface switch stochastically between two possible states, “on” and “off”, characterizing the conductivity of the micro-contact. We assume that the time intervals between the consecutive changes of state are governed by a certain waiting-time distribution. It is demonstrated how the microscopic random dynamics regarding the micro-contacts leads to the macroscopic observation of slow conductance growth, described by an exact fractional kinetic equations.