On the aronszajn property for a differential equation of fractional order in Banach spaces

In this paper we investigate some topological properties of solution sets of a differential equation of fractional order in Banach spaces. Our assumptions and proofs are expressed in terms of measures of noncompactness.     

Retention behaviour of imidazolium ionic liquid cations on 1.7 μm ethylene bridged hybrid silica column using acetonitrile-rich and water-rich mobile phases

The potential of 1.7 μm ethylene bridged hybrid silica phase was investigated for the separation of twelve imidazolium-based ionic liquid cations. U-shaped retention profile was observed for all solutes with an increase in retention at both low and high acetonitrile content. Chromatographic behaviour of imidazolium cations in both hydrophilic interaction chromatography (HILIC) and per aqueous liquid chromatography (PALC) modes was studied by varying key parameters such as buffer concentration and pH, acid additive, organic modifier and column temperature. Experimental data provided some evidences that under PALC conditions cationic solutes are retained predominantly by mixed hydrophobic/ion-exchange interactions. In the HILIC mode, both partitioning and ion-exchange interactions are responsible for the retention of solutes. Compared to PALC, HILIC provided significantly higher efficiencies with less or even no peak tailing, better separation selectivity and greater resistance to overload. In PALC mode gradient elution was required to achieve adequate retentivity of all solutes but selectivity was not sufficient to distinguish between solutes with very similar hydrophobicity. In contrast, under HILIC conditions twelve solutes were almost completely resolved in less than 4 min by using isocratic elution. Summarizing, it could be concluded that ethylene bridged hybrid silica column providing a dual retention mechanism offers the possibility of selecting between the two retention modes with opposite separation selectivity, just by changing the composition of the mobile phase.     

Raman spectroelectrochemical study of Meldola blue, adsorbed and electropolymerized at a gold electrode

Surface-enhanced Raman spectroscopy (SERS) was used to probe the structure of adsorbed and electropolymerized Meldola blue (MB) films on roughened gold surfaces in solutions with pH 1.0 and 7.0 by using 785 nm excitation wavelength. Spectral bands were assigned based on density functional theory (DFT) calculations at B3LYP/6-311+G(2d, p) level. The most characteristic band of the oxidized MB form was found to be the breathing vibration of the central ring containing heteroatoms at 596 cm(-1). Based on a red shift of bands assigned to vibrations of double C=N(C(2)H(6)) bonds and adjacent ring C=C bonds in surface spectra as compared with solution 1 it was suggested that polymerization and interaction with an electrode surface proceed through these moieties. The presence of out-of-plane bands in SERS spectra was attributed to "flat" or slightly "tilted" orientation of aromatic rings at the interface. Potential-dependent spectral changes were followed by SERS spectroscopy. Raman spectra of the reduced MB form were obtained in both pH 1.0 and pH 7.0 solutions by analysis of the potential-difference SERS spectra. Reduced MB form can be recognized by characteristic bands near 1620, 1574, 1374, and 1234 cm(-1). By comparing the intensities of 1637 cm(-1) (oxidized MB form) and 1374 cm(-1) (reduced MB form) bands in experimental spectra of polymerized MB in pH 1.0 solution, a reduction-induced decrease by factor of 7 was estimated. A similar tendency in intensity changes showed calculations indicating that this effect is associated with reduction-induced changes in the molecular structure of the dye.     

Intermolecular interactions in mixtures of dichroic dyes with n-alkyl-4-(4-isothiocyanatophenyl)bicyclo[2,2,2]octanes

On the basis of the polarized absorption spectra, the guest order parameter as a function of temperature for five dichroic azo dyes dissolved in four members (pentyl to octyl) of the homologous series of n-alkyl-4-(4-isothiocyanatophenyl)bicyclo[2,2,2]octanes has been evaluated. Moreover, the influence of the dichroic dye addition on the nematic-isotropic phase transition temperature has been examined. The relation between the molecular geometry of the guest, its orientation efficiency in the nematic host and the clearing temperature of the azo dye-liquid crystal mixtures has been determined. The experimental results have been compared in some detail with calculations performed on the basis of the mean field theory for binary mixtures.     

Some decidable classes of formulas of pure hybrid logic

We consider the formulas of pure hybrid logic without occurrences of a satisfaction operator. We describe a couple of formula derivation tactics in sequent calculus and prove the decidability of two classes of formulas. Decidable classes are obtained by setting restrictions on nominal occurrences in the formulas. Published in Lietuvos Matematikos Rinkinys, Vol. 44, No. 4, pp. 563–572, October–December, 2007.     

Bidegree (2,1) parametrizable surfaces in projective 3-space

The main purpose of this paper is to study projective classes of bidegree (2,1) parametrizable surfaces in a real projective 3-space. It turns out that the implicit degree of such surfaces is two, three, or four, and singular curves have degree three. We describe all possibilities for singular curves and pinch points on such surfaces. The presentation has been made from the point of view of analytic geometry and does not presume a deep knowledge of algebraic geometry. Partially supported by the Lithuanian State Science and Studies Foundation. Vilnius University, Naugarduko 24, 2006 Vilnius, Lithuania. Published in Lietuvos Matematikos Rinkinys, Vol. 38, No. 3, pp. 379–402, July–September, 1998.