Boundary Value Problems with a Parameter of Differential Equations with Deviated Arguments

The aim of the present paper is to study boundary value problems with a parameter of differential equations with deviated arguments. The existence, uniqueness and continuous dependence of the solution on the right-hand side of our problem are considered.     

Hydroxylation of the silica in microfabricated thin layer chromatography plates as probed by time‐of‐flight secondary ion mass spectrometry and diffuse reflectance infrared Fourier transform spectroscopy

Microfabricated silica thin layer chromatography (TLC) plates have previously been prepared on patterned carbon nanotube forests. The high temperatures used in their fabrication reduce the number of hydroxyl groups on their surfaces. Fortunately, silica can be rehydroxylated. In diffuse reflectance infrared Fourier transform spectroscopy (DRIFT), a silanol peak below 3740 cm^?1 indicates a well‐hydroxylated silica surface that is fit for chromatography. Hydroxylations of our materials with HF are so effective that it is not possible to discern the position of this peak. In contrast, this signal is discernable when the plates are treated with NH₄OH. To find a more convenient method for studying the surfaces of TLC plates, time‐of‐flight secondary ion mass spectroscopy (ToF‐SIMS) was considered. ToF‐SIMS is advantageous because multiple microfabricated TLC plates must be scraped to obtain enough silica for one DRIFT analysis, while static SIMS can be performed on very small regions (500 × 500 µm² or less) of individual plates. Ratios of the SiOH⁺ and Si⁺ ToF‐SIMS signals for microfabricated TLC plates correlated well with ~3740 cm^?1 silanol peaks from DRIFT. Thus, SIMS allows direct analysis of all of our treated and untreated plates, including those hydroxylated with HF. The best hydroxylation condition for HF, which was better than any studied for NH₄OH, was around 150 ppm at room temperature. The best hydroxylation condition for NH₄OH was 50 °C for 72 h. ToF‐SIMS versus DRIFT results of commercial TLC plates were also obtained and evaluated. Copyright © 2014 John Wiley & Sons, Ltd.     

Thermal response of a periodic boundary layer near an axisymmetric stagnation point on a circular cylinder

Boundary layer solutions are provided to study the time-mean heat transfer characteristics in a laminar flow in the vicinity of an axisymmetric stagnation point. The velocity of the oncoming flow is assumed to oscillate relative to the body. Different solutions are constructed for the small and high values of the reduced frequency parameter. Numerical solutions for the temperature functions are presented, and the wall values of the thermal gradients are tabulated.     

Surface‐Plasmon‐Coupled Emission of Rhodamine 110 in a Silica Nanolayer

The first observation of strong directional surface‐plasmon‐coupled emission (SPCE) of Rhodamine 110 in silica nanofilms deposited on silver nanolayers is reported. The preparation of the material is described in detail. The intensity of SPCE exceeds 10 times that of free space fluorescence and total linear light polarization in the SPCE ring is observed. A new experimental setup and an original data collection method is presented. Our material completely preserves its fluorescence properties for at least eight months.     

From Y- to Siamese-twin shaped glycolipids

Summary A set of Y-shaped and Siamese-twin shaped carbohydrate based glycolipids was investigated using polarising microscopy. The structure was changed from the normal type (1 head, two chains) to complex inverted structures (2 heads outside 1 to 3 chains in the middle part). The carbohydrate headgroup was changed from mono- to disaccharide; also the alkyl chain length was varied systematically. The compounds displayed different thermotropic mesophases (Smectic A phases, columnar phases and cubic phases) depending on the type of carbohydrate headgroup and the alkyl chain length.     

The 2:1 cocrystal of benzamide and penta­fluoro­benzoic acid

The crystal structure of the title compound, benzamide–2,3,4,5,6‐penta­fluoro­benzoic acid (2/1), 2C₇H₇NO·C₇HF₅O₂, consists of centrosymmetric hexa­meric supermolecules composed of four amide and two carboxylic acid mol­ecules connected via O—H⋯O and N—H⋯O hydrogen bonds. No phen­yl–perfluoro­phenyl π–π stacking inter­actions are observed in this cocrystal.     

Davidson-type corrections for quasidegenerate states

Two new extensions of Davidson-type size-consistency collections to the case of quasidegenerate states are presented and applied to a simple model system in which the degree of quasidegeneracy can be continuously varied. The eight-electron model studied is a minimum basis set model involving eight hydrogen atoms in various spatial arrangements. The results are compared with the full CI energies as well as with those obtained with the CI-D, MRCI-D, coupled-pair, and linear coupled-pair methods. Two extensions of the Davidson correction recently devised by Paldus are also employed. The results indicate that all the Davidson-type corrections yield reliable correlation energies in the case of strong quasidegeneracies.     

Accuracy of first-order wavefunctions for ten-electron atomic systems

It is demonstrated that for Ne-like systems, the zeroth-plus-first-order wavefunctions, obtained within Rayleigh—Schrödinger perturbation theory based on H₀ = H_HF, are of the same accuracy as variational wavefunctions obtained in CI calculations using very extensive sets of singly and doubly excited configurations. Variational correlation energies for Na⁺, Mg²⁺ and Ar⁸⁺ are reported for the first time.