Unsteady motion in single-line flow-injection systems

Unsteady motion in single-line flow-injection systems consisting of n tubular elements with valve or hydrodynamic injection is studied theoretically. A formula for the duration of the initial period of unsteady flow is derived. This initial period is much shorter than the mean residence time of the analyte in practical systems. It can therefore be neglected in mathematical modelling of such systems. Experimental data obtained with single-line systems with valve and hydrodynamic injection confirmed the validity of the theoretical equations.     

Cyclic Hypomonotonicity,Cyclic Submonotonicity,and Integration

Rockafellar has shown that the subdifferentials of convex functions are always cyclically monotone operators. Moreover, maximal cyclically monotone operators are necessarily operators of this type, since one can construct explicitly a convex function, which turns out to be unique up to a constant, whose subdifferential gives back the operator. This result is a cornerstone in convex analysis and relates tightly convexity and monotonicity. In this paper, we establish analogous robust results that relate weak convexity notions to corresponding notions of weak monotonicity, provided one deals with locally Lipschitz functions and locally bounded operators. In particular, the subdifferentials of locally Lipschitz functions that are directionally hypomonotone [respectively, directionally submonotone] enjoy also an additional cyclic strengthening of this notion and in fact are maximal under this new property. Moreover, every maximal cyclically hypomonotone [respectively, maximal cyclically submonotone] operator is always the Clarke subdifferential of some directionally weakly convex [respectively, directionally approximately convex] locally Lipschitz function, unique up to a constant, which in finite dimentions is a lower C² function [respectively, a lower C¹ function].     

Residence times in kink sites and Markov chain model of alloy and intermetallic compound deposition

The concept of the residence time τ_ksp of an atom in a kink site has recently been suggested to understand the processes in electrochemical deposition of alloys and intermetallic compounds. Different kink sites with different residence times must be defined for alloys and intermetallic compounds. Based on this model, the finite Markov chain theory is applied to describe the selectivity of the growth process. An analytical relationship between the alloy composition and the metal ion concentrations in the electrolyte is derived. General model parameters are ratios g _i = K _ii/K _ij of equilibrium constants of the reaction of electrolyte ions with different kink sites on the surface (i, j representing different alloy components). These ratios are called selectivity constants. For simple conditions, the equation g _i ≈ τ_ii/τ_ij connects the g _i values with the residence times. The theory is tested in the deposition of alloys Co-Ni (anomalous co-deposition) and Ni-Mo (induced co-deposition). Additionally, Bi₂Te₃, an example of stoichiometric semiconductor deposition, is treated. Published in Russian in Elektrokhimiya, 2006, Vol. 42, No. 10, pp. 1216–1223. The text was submitted by the authors in English.     

Second-order subdifferentials of C1,1 functions and optimality conditions

We present second-order subdifferentials of Clarke's type of C ^1,1 functions, defined in Banach spaces with separable duals. One of them is an extension of the generalized Hessian matrix of such functions in ⁿ , considered by J. B. H.-Urruty, J. J. Strodiot and V. H. Nguyen. Various properties of these subdifferentials are proved. Second-order optimality conditions (necessary, sufficient) for constrained minimization problems with C ^1,1 data are obtained.This work was partially supported by the National Foundation for Scientific Investigations in Bulgaria under contract No. MM-406/1994.     

Numerical solution of hydraulic models based on the axially-dispersed plug flow model by Laplace transforms

The problem of solving hydraulic models based on the axially-dispersed plug flow model which are applicable for the mathematical modelling of different flow-through systems both in chemical analysis (e.g., chromatography, flow injection analysis) and chemical industry (e.g., different tubular reactors) is discussed. Methods for numerical inversion of the model solution in the Laplace domain by expanding it into series of orthogonal functions are compared. Best results with respect to precision and consumption of computation time are given by the methods employing Chebyshov polynomials of the first kind and Fourier sine series. These methods were found to be better in these respects than some other frequently used numerical inversion methods.     

Gitterschwingungsspektren. LXIII. Be(lO3)2 · 4 H2O,ein Hydrat mit ungewöhnlicher Bindungsstruktur und Gitterdynamik

Lattice Vibration Spectra. LXIII. Be(IO₃)₂ · 4 H₂O, a Hydrate with Unusual Bonding and Lattice Dynamics The IR and Raman spectra (4000–50 cm^?1) of Be(IO₃)₂ · 4 H₂O and of deuterated specimens are recorded at 90 and 300 K and discussed in terms of the unusual relations of the masses of the atoms involved and the large polarization power of the beryllium ions. Thus, the translatory modes of the Be²⁺ ions (BeO₄ skeleton vibrations), the librations of the H₂O molecules, and the internal vibrations of the IO₃^? ions in the spectral regions of 300–400 and 600–1000 cm^?1 couple and coincide producing unusual v_H/v_D isotopic ratios of partly < 1. The H-bond donor strengths of the water molecules is so much increased (due to the very large ionic potential of Be²⁺ ions, viz. 49 e nm^?1) (synergetic effect) that the H-bonds formed are similar in strength as those in hydrates of hydroxides with the very strong H-bond acceptor group OH^? (v_OD of matrix isolated HDO molecules 2 074 and 2 244 (H₂O I) and 2 206 and 2 349 cm^?1 (H₂O II))     

Flow-injection approach for the determination of the dynamic response characteristics of ion-selective electrodes. Part 1. Theoretical considerations

A single-line flow-injection system with a straight tube reactor is proposed for investigating the dynamic response behaviour of ion-selective electrodes. The principle of the method is based on the fact that the concentration—time curve at the electrode surface can be described theoretically in the flow-injection system under certain practically realizable conditions. The response of the ion-selective electrode to that input signal can be measured experimentally. Thus, knowing the input and the output signal of an ion-selective electrode, an appropriate model describing its dynamic behaviour can be selected among the relevant models existing in the literature. Theoretical expressions for predicting the transient response of ion-selective electrodes in the flow system when the rate-determining step is an ion-transport process through a diffusion layer or a kinetic process were elaborated.     

Raman spectroscopic study of the hydration of short-chain poly(oxyethylene)s C <Subscript>1</Subscript>E<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript>C <Subscript>1</Subscript> (<Emphasis Type="Italic">n</Emphasis>=1−4)

The hypothesis that the degree of hydration of poly(oxyethylene) (POE) in aqueous solution depends on the mole ratio of water molecules to ether oxygen atoms in the molecule has been verified by studying the isotropic Raman spectra in the O−H stretching region for four short-chain POEs (C ₁E _n C ₁ withn=1−4). Excellent coincidence of the O−H stretching Raman band for all four POEs studied in the range of mole ratio H₂O/O _ether from 25 to 0.6 was observed, thus confirming the assumption stated above. A conclusion that all ether oxygen atoms in the POE molecule participate in hydrogen bonding with water molecules has been made.     

Virtual Screening and Hit Selection of Natural Compounds as Acetylcholinesterase Inhibitors

Acetylcholinesterase (AChE) is one of the classical targets in the treatment of Alzheimer’s disease (AD). Inhibition of AChE slows down the hydrolysis of acetycholine and increases choline levels, improving the cognitive function. The achieved success of plant-based natural drugs acting as AChE inhibitors, such as galantamine (GAL) from Galanthus genus and huperzine A from Huperzia serrate (approved drug in China), in the treatment of AD, and the fact that natural compounds (NCs) are considered as safer and less toxic compared to synthetic drugs, led us to screen the available NCs (almost 150,000) in the ZINC12 database for AChE inhibitory activity. The compounds were screened virtually by molecular docking, filtered for suitable ADME properties, and 32 ligands from 23 structural groups were selected. The stability of the complexes was estimated via 1 μs molecular dynamics simulation. Ten compounds formed stable complexes with the enzyme and had a vendor and a reasonable price per mg. They were tested for AChE inhibitory and antioxidant activity. Five compounds showed weak AChE inhibition and three of them exhibited high antioxidant activity.