On Vekua Systems and Their Connections to Hyperbolic Function Theory in the Plane

In this paper we study the solutions of the equation $$\Delta w- \frac{\alpha}{y}\partial_{y}w = 0,$$ where w is a complex valued function. This equation is related to the generalized axially symmetric potential theory which has been studied notably by Weinstein, see [12]. We have researched this equation earlier in higher dimensions in connection with the hyperbolic function theory. In this paper will see how this equation is related to the generalized analytic functions in the hyperbolic upper half-plane. We also study harmonic differential forms in the hyperbolic plane and using these we obtain special type of solutions for the preceding equation.     

New upper bounds on the minimum size of covering designs

Let D = {B₁, B₂,…, B_b} be a finite family of k-subsets (called blocks ) of a v-set X(v) = {1, 2,…, v} (with elements called points ). Then D is a (v, k, t) covering design or covering if every t-subset of X(v) is contained in at least one block of D. The number of blocks, b, is the size of the covering, and the minimum size of the covering is called the covering number , denoted C(v, k, t). This article is concerned with new constructions of coverings. The constructions improve many upper bounds on the covering number C(v, k, t) © 1998 John Wiley & Sons, Inc. J Combin Designs 6:21–41, 1998     

Theoretical nuclear spin–spin coupling constants using atom–atom polarizabilities. 13C?H and H?H′ coupling constants of some [2.2.1] bicyclic compounds using the INDO approximation

Theoretical nuclear spin–spin coupling constants are calculated using mutual and self atom–atom polarizabilities according to a theory where no semi-empirical parameters are used, except Slater exponents which can be obtained from other sources. As an application, the ¹³C? H and H? H′ couplings of some [2.2.1] bicyclic compounds are calculated with the aid of INDO molecular orbitals and compared with the experimentally obtained coupling constants.     

Separation of eight selected flavan-3-ols on cellulose thin-layer chromatographic plates

The potential of microcristaline cellulose as sorbent in the separation of eight compounds: (+)-catechin (C), (-)-epicatechin (EC), (-)-gallocatechin (GC), (-)-epigallocatechin (EGC), (-)-epicatechin gallate (ECg), (-)-epigallocatechin gallate (EGCg), procyanidin B1 and procyanidin B2 was studied. Cellulose HPTLC plates prewashed in water (not necessary, when water was used as developing solvent) and dried with a hair dryer, bandwise application and development in horizontal developing chamber (sandwich configuration) gave the best results. Detection was performed using vanillin-H3PO4 reagent. Four new developing solvent systems were proposed: water, 1-propanol-water (20:80, v/v), 1-propanol-water-acetic acid (4:2:1, v/v) and 1-propanol-water-acetic acid (20:80:1, v/v), and at least two of them were needed for the differentiation between all eight compounds. Surprisingly, water enabled the separation of epimers C from EC and GC from EGC, as well as the dimers procianidin B1 and B2. Additionally, C, EGC, B1 and B2 were separated from all the other compounds. The best choice for developing solvent is given for each of the studied compounds. The best separation of the five main catechins (EC, GC, EGC, ECg, EGCg) present in green tea extract was achieved using 1-propanol-water-acetic acid (20:80:1, v/v). The chromatograms of oak bark extract developed in solvents with higher water content (1-propanol-water (1:4, v/v) and 1-propanol-water-acetic acid (20:80:1, v/v)) showed less bands than chromatograms developed in solvents with higher organic modifier content (e.g. 1-propanol-water-acetic acid (4:2:1, v/v)). It was proved that such behavior was due to the presence of procyanidins beside the main component catechin.     

Bond stretching and redox behavior in coinage metal complexes of the dichalcogenide dianions [(SPh2P)2CEEC(PPh2S)2]2- (E=S, Se): diradical character of the dinuclear copper(I) complex (E=S)

The metathetical reactions of a) [Li(tmeda)]₂[(S)C(PPh₂S)₂] (Li₂? 3 c ) with CuCl₂ and b) [Li(tmeda)]₂[(SPh₂P)₂CSSC(PPh₂S)₂] (Li₂? 4 c ) with two equivalents of CuCl both afford the binuclear Cu^I complex {Cu₂[(SPh₂P)₂CSSC(PPh₂S)₂]} ( 5 c ). The elongated (C)S? S(C) bond (ca. 2.54 and 2.72 Å) of the dianionic ligand observed in the solid‐state structure of 5 c indicate the presence of diradical character as supported by theoretical analyses. The treatment of [Li(tmeda)]₂[(SPh₂P)₂CSeSeC(PPh₂S)₂] (Li₂? 4 b ) and Li₂? 4 c with AgOSO₂CF₃ produce the analogous Ag^I derivatives, {Ag₂[(SPh₂P)₂CEEC(PPh₂S)₂]} ( 6 b , E=Se; 6 c , E=S), respectively. The diselenide complex 6 b exhibits notably weaker Ag? Se(C) bonds than the corresponding contacts in the Cu^I congeners, and the ³¹P NMR data suggest a possible isomerization in solution. In contrast to the metathesis observed for Cu^I and Ag^I reagents, the reactions of Li₂? 4 b and Li₂? 4 c with Au(CO)Cl involve a redox process in which the dimeric dichalcogenide ligands are reduced to the corresponding monomeric dianions, [(E)C(PPh₂S)₂]^2? ( 3 b , E=Se; 3 c , E=S), and one of the gold centers is oxidized to generate the mixed‐valent Au^I/Au^III complexes, {Au[(E)C(PPh₂S)₂]}₂ ( 7 b , E=Se; 7 c , E=S), with relatively strong aurophilic Au^I???Au^III interactions. The new compounds 5 c , 6 b , c and 7 b , c are characterized in solution by NMR spectroscopy and in the solid state by X‐ray crystallography ( 5 c , 6 b , 7 b and 7 c ) and by Raman spectroscopy ( 5 c and 6 c ). The UV‐visible spectra of coinage metal complexes of the type 5 , 6 and 7 are discussed in the light of results from theoretical analyses using time‐dependent density functional theory.     

Hyperbolic Laplace Operator and the Weinstein Equation in {\mathbb{R}^3}

We study the Weinstein equation $$\Delta u - \frac{k}{{x}_{2}} \frac{\partial}{\partial{x}_{2}} + \frac{l}{x^{2}_{2}}u = 0$$ , on the upper half space ${\mathbb{R}^3_{+} = \{ (x_{0}, x_{1}, x_{2}) \in \mathbb{R}^{3} | x_2 > 0\}}$ in case ${4l \leq (k + 1)^{2}}$ . If l =  0 then the operator ${x^{2k}_{2} (\Delta - \frac{k}{x_{2}} \frac{\partial}{\partial{x}_{2}})}$ is the Laplace- Beltrami operator of the Riemannian metric ${ds^2 = x^{-2k}_{2} (\sum^{2}_{i = 0} dx^{2}_{i})}$ . The general case ${\mathbb{R}^{n}_{+}}$ has been studied earlier by the authors, but the results are improved in case ${\mathbb{R}^3_{+}}$ . If k =  1 then the Riemannian metric is the hyperbolic distance of Poincaré upper half-space. The Weinstein equation is connected to the axially symmetric potentials. We compute solutions of the Weinstein equation depending only on the hyperbolic distance and x ₂. The solutions of the Weinstein equation form a socalled Brelot harmonic space and therefore it is known that they satisfy the mean value properties with respect to the harmonic measure. However, without using the theory of Brelot harmonic spaces, we present the explicit mean value properties which give a formula for a harmonic measure evaluated in the center point of the hyperbolic ball. Earlier these results were proved only for k =  1 and l =  0 or k =  1 and l =  1. We also compute the fundamental solutions. The main tools are the hyperbolic metric and its invariance properties. In the consecutive papers, these results are applied to find explicit kernels for k-hypermonogenic functions that are higher dimensional generalizations of complex holomorphic functions.     

Determination of soman and VX degradation products by an aspiration ion mobility spectrometry

An aspiration type ion mobility spectrometry (IMS) has been used to determine chemical warfare agent (CWA) degradation products from liquid samples. This technique is based on ion mobility which depends on the molecular weight, charge and shape. With this method, it is possible to measure the mobility distribution of positive and negative ion clusters simultaneously in six different electrodes. Each measuring electrode determines a different portion of the ion mobility distribution formed within the cell’s radioactive source. The strongest responses for all CWA degradation products and 2-propanol were seen in the order of sixth, fifth and second channels. On the basis of projection calculation, the fingerprints for 2-propanol and soman (GD; pinacolyl methylphosphonofluoridate) and VX o-ethyl-S-[2(diisopropylamino)ethyl] methylphosphonothioate) degradation products can be separated from each other. The detection levels for ethyl methylphosphonate (EMPA), pinacolyl methylphosphonate (PMPA), and ethylphosphonic acid (EPA) were 37.2 (37.2 μg/ml), 54.1 (54.1 μg/ml) and 55.1 ppm (55.1 μg/ml), respectively. However, the separation efficiency between different CWA degradation products was quite poor. The projections of these compounds were between 0.9976 and 0.9989, and this means that these fingerprints were identical. Thus, it is only possible to get one profile for all these degradation products of soman and VX. The data provided show that IMS is suitable as a simple technique for screening of CWA degradation products.     

Polystyrene latex particles coated with crosslinked poly(N-isopropylacrylamide)

Thermoresponsive colloidal particles were prepared by seeded precipitation polymerization of N-isopropylacrylamide (NIPAM) in the presence of a crosslinking monomer, N,N-methylenebisacrylamide (MBA), using polystyrene latex particles (ca. 50 nm in diameter) as seeds in aqueous dispersion. Phase transitions of the prepared poly(N-isopropylacrylamide), PNIPAM, shells on polystyrene cores were studied in comparison to colloidal PNIPAM microgel particles, in H₂O and/or in D₂O by dynamic light scattering, microcalorimetry and by ¹H NMR spectroscopy including the measurements of spin–lattice (T1) and spin–spin (T2) relaxation times for the protons of PNIPAM. As expected, the seed particles grew in hydrodynamic size during the crosslinking polymerization of NIPAM, and a larger NIPAM to seed mass ratio in the polymerization batch led to a larger increase of particle size indicating a product coated with a thicker PNIPAM shell. Broader microcalorimetric endotherms of dehydration were observed for crosslinked PNIPAM on the solid cores compared to the PNIPAM microgels and also an increase of the transition temperature was observed. The calorimetric results were complemented by the NMR spectroscopy data of the ¹H-signal intensities upon heating in D₂O, showing that the phase transition of crosslinked PNIPAM on polystyrene core shifts towards higher temperatures when compared to the microgels, and also that the temperature range of the transition is broader.