Du Bois–Reymond Type Lemma and Its Application to Dirichlet Problem with the p(t)–Laplacian on a Bounded Time Scale

This paper is devoted to study the existence of solutions and their regularity in the p(t)–Laplacian Dirichlet problem on a bounded time scale. First, we prove a lemma of du Bois–Reymond type in time-scale settings. Then, using direct variational methods and the mountain pass methodology, we present several sufficient conditions for the existence of solutions to the Dirichlet problem.     

Self-organisation of di(perfluorohexyl)hexane in Langmuir and LB films

Symmetrical triblock semifluorinated n-alkane, di(perfluorohexyl)hexane of the formula F(CF₂)₆(CH₂)₆(CF₂)₆F (abbreviated F₆H₆F₆), has been synthesised and investigated at the air/water interface. Our results show for the first time that this unusual film-forming material, completely hydrophobic in nature and possessing no polar group, is capable of stable film formation at the free water surface. The surface pressure–area isotherm of the studied compound exhibited two regions: corresponding to monotonous pressure rise, followed by a pseudo-plateau region. Visualisation of film structure with Brewster angle microscope (BAM) proved the formation of domains within the pseudo-plateau region. A closer insight into the structure of these domains with atomic force microscope (AFM) proved their ordered, circular shape. The average area of F₆H₆F₆ domain was found to depend on surface pressure value, as it is 4.98 ± 1.75 μm² at π = 1.2 mN/m to 16.54 ± 0.31 μm² at π = 1.7 mN/m. Following performed quantum-chemical calculations, it can be concluded that the observed surface aggregates from F₆H₆F₆ are formed by linear conformers with shifted CF and CH parts. The calculated domain thickness is between 20 and 21 Å, which perfectly agrees with the experimental value estimated from AFM measurements (20.3 ± 1.4 Å).     

Critical behaviour of the smectic A*–C* phase transition and electroclinic effect of ferroelectric liquid crystals with terphenyl rigid core

The SmA*–SmC* phase transition was studied by measuring the temperature and electric field dependences of the optical tilt angle, the electric polarisation and the dielectric spectra collected in a wide frequency range. Critical behaviour of the phase transition was analysed by varying the length of the fluorinated part of the alkyl terminal chain and by differing fluorine substitution in the terphenyl core. Both tilt and polarisation show tricritical mean-field behaviour for all homologues with n?>?2. Almost all coefficients that describe the SmA*–SmC* transition in the frame of the Landau theory were derived for homologue series. Double fluorine substitution in the central ring of the core seems to promote the ‘de Vries'-type smectic A*–C* phase transition with a little layer shrinkage. These well correspond with the lower tilt angle and smaller changes of the birefringence at the phase transition compared to the other homologues.     

Helical twisting power of antiferroelectric chiral terphenyls in different matrices

To determine the influence of chemical structure on the Helical Twisting Power (HTP), we tested four optically active dopants having a terphenyl rigid core and the same chiral centre but differing in the length of nonchiral terminal chain and the substitution of benzene rings with fluorine atoms. The compounds were added to different achiral liquid crystalline matrices: nematic and smectic C. It was found that HTP as well as its temperature variation depends on the kind of used matrices. It gives a conclusion that information about HTP obtained in one matrix cannot be uncritically transferred to another one.     

Pure phase correlation with improved discrimination capability

Pure phase correlation with improved discrimination capability is proposed. The improvement is achieved by designing a region of support based on the discrimination capability (DC). We propose four approaches for designing this region; some of them consider the input scene in the design, while others are input scene invariant. The performances of these approaches are compared by numerical simulation. The DC is improved significantly for the multi-object scenes even when using an input scene invariant region of support design.     

Can 2‐acylpyrroles form an intramolecular hydrogen bond?

The formation of intramolecular hydrogen bonding by certain N‐substituted 2‐acylpyrroles has been demonstrated by B3LYP/aug‐cc‐pVDZ calculations, the quantum theory of atoms in molecules, and the natural bond orbital method. Total electron energy densities H_BCP at the bond critical point of the H?O bond were applied to analyze the strength of these interactions. The relations between quantum theory of atoms in molecules, carbonyl stretching vibrational modes ν_{C = O}, and natural bond orbital parameters associated with the formation of the C–H?O interaction have been established. The short contacts were found experimentally in the crystal structure of a new 2‐acylpyrrole derivative 5‐chloro‐2‐oxopentyl‐1‐(5‐chloro‐2‐oxopentyl)pyrrolo‐2‐carboxylate. The influence of 2‐ and N‐substitution of 2‐acylpyrroles on C‐H?O interaction energy is discussed. It was found that the methylene group may act as a proton donor leading to a red‐shift or blue‐shift phenomenon of the ν_C–H stretching mode. Copyright © 2015 John Wiley & Sons, Ltd.     

Interaction between rhodanine and silver species on a nanocolloidal surface and in the solid state

This paper discusses and compares molecular interactions of rhodanine (Rd), the heterocyclic compound containing N, S, and O atoms, with two forms of silver species, i.e. Ag(I) ions and silver nanocolloidal particles. Vibrational spectroscopic and powder crystallography studies on coordination of Ag(I) ions in the solid state, supported by density functional theory, clearly indicate complexation through the nitrogen (the deprotonated imino group) and exocyclic sulfur atoms. Molecules of the complex are arranged in a one‐dimensional infinite polymeric chain structure that intertwines to give a helix motif. On the other hand, adsorption geometry of Rd on the silver surface was determined by using surface‐enhancement Raman scattering (SERS) spectroscopy. Observed differences between the SERS and the normal Raman spectra of Rd suggest that Rd adsorbs on the silver species after the rearrangement of the keto‐thione form into the enol‐thiol tautomer in acidic and neutral solutions. This leads to adsorption on this silver species through the thiolate ion. On the other hand, the alkaline pH forces first N‐deprotonation of Rd, and, in consequence, the obtained anion of the keto‐thione form interacts with the silver surface as a result of the presence of lone pairs of nitrogen and sulfur atoms, similar to the case discussed for the solid state. Copyright © 2009 John Wiley & Sons, Ltd.