Solutions in Hölder spaces of boundary-value problems for parabolic equations with nonconjugate initial and boundary data

The first and second one-dimensional boundary-value problems for parabolic equations are investigated in the case where the conjugation conditions for all required orders are not satisfied. The existence and uniqueness are proved. Estimates of solutions in classical and weighted Hölder spaces are obtained. We prove that the violation of conjugation for the given functions on the boundary of the domain at the initial-time moment causes the appearance of singular solutions. The order of singularity (as a power of t) is found for the singular solutions for t = 0.     

Conformational Mobility and Phase Transitions in Alkyloxybenzoate of Cholesterol

Abstract

The structural particularities of polymorphic modifications and cholesterol liquid crystal phase have been investigated by theoretical and experimental IR spectroscopy methods. The spectra were recorded in the interval of temperatures 293–523 K within the range of 600–3600 cm^?1. The frequencies of normal modes and intensities in the IR spectra have been calculated for the alkyloxybenzoate of cholesterol conformers, which may be realized under certain temperatures. Comparison of results of theoretical modelling and recorded spectra confirmed suggestion about conformational mobility basically defined with changing of steroid kennel orientation comparatively stayed part of molecule in the different phase state.     

Long-range chemical interactions in solid-state reactions: effect of an inert Ag interlayer on the formation of L10-FePd in epitaxial Pd(0 0 1)/Ag(0 0 1)/Fe(0 0 1) and Fe(0 0 1)/Ag(0 0 1)/Pd(0 0 1) trilayers

The effect of 0, 0.5, and 1?μm-thick Ag interlayers on the chemical interaction between Pd and Fe in epitaxial Pd(0?0?1)/Ag(0?0?1)/Fe(0?0?1)/MgO(0?0?1) and Fe(0?0?1)/Ag(0?0?1)/Pd(0?0?1)/MgO(0?0?1) trilayers has been studied using X-ray diffraction, ⁵⁷Fe Mössbauer spectroscopy, X-ray photoelectron spectroscopy, and magnetic structural measurements. No mixing of Pd and Fe occurs via the chemically inert Ag layer at annealing temperatures up to 400?°C. As the annealing temperature is increased above 400?°C, a solid-state synthesis of an ordered L1₀-FePd phase begins in the Pd(0?0?1)/Ag(0?0?1)/Fe(0?0?1) and Fe(0?0?1)/Ag(0?0?1)/Pd(0?0?1) film trilayers regardless of the thickness of the buffer Ag layer. In all samples, annealing above 500?°C leads to the formation of a disordered Fe_xPd_1?x(0?0?1) phase; however, in samples lacking the Ag layer, the synthesis of Fe_xPd_1?x is preceded by the formation of an ordered L1₂-FePd₃ phase. An analysis of the X-ray photoelectron spectroscopy results shows that Pd is the dominant moving species in the reaction between Pd and Fe. According to the preliminary results, the 2.2?μm-thick Ag film does not prevent the synthesis of the L1₀-FePd phase and only slightly increases the phase’s initiation temperature. Data showing the ultra-fast transport of Pd atoms via thick inert Ag layers are interpreted as direct evidence of the long-range character of the chemical interaction between Pd and Fe. Thus, in the reaction state, Pd and Fe interact chemically even though the distance between them is about 10⁴ times greater than an ordinary chemical bond length.     

High‐power HgGa2S4 optical parametric oscillator pumped at 1064 nm and operating at 100 Hz

The defect chalcopyrite crystal HgGa₂S₄ has been employed in a 1064‐nm pumped optical parametric oscillator operating at 100 Hz, to generate ∼5 ns long idler pulses near 4 µm with energies as high as 6.1 mJ and average power of 610 mW. At crystal dimensions comparable to those available for the commercial AgGaS₂ crystal, operation of the 1064‐nm pumped HgGa₂S₄ OPO is characterized by much lower pump threshold and higher conversion efficiency, with the most important consequence that such a device might become practical at pump levels sufficiently lower than the optical damage threshold.     

Updating the Chemiluminescence Oxygen‐Aftereffect Method for Determining the Rate Constant of the Peroxy‐Radical Self‐Reaction: Oxidation of Cyclohexene

Updating the facile chemiluminescence oxygen‐aftereffect method, most suitable for determining the rate constant (k_t) of the peroxy‐radical self‐reaction (main chemiluminescence channel), pertained to considering the sensitivity of such a method toward a disturbing influence of the peroxy radicals of the initiator of the chain oxidation process. Such a disturbance may derive from the side chemiluminescent reaction, which involves peroxy radicals of both hydrocarbon and initiator. To examine the applicability and limitations of the chemiluminescence method under present scrutiny, cyclohexene was used as the model oxidizable hydrocarbon substrate. Computer simulations of the reaction and chemiluminescence kinetics have demonstrated the validity of the considered methodology at the value of the rate constant of the propagation of the overall chain process by peroxy radicals of the initiator higher than 1 m ^?1 s^?1. Despite that the chemiluminescence time profile and the stationary level of the total chemiluminescence intensity depend on the kinetics of the side chemiluminescence channel and on the ratio of the excited‐state generation yields in the mentioned reaction channel and in the main chemiluminescence process, the value of k_t assessed by the oxygen‐aftereffect method has been found independent of variation of these characteristics.     

Optimization of the dimensions of an Yb(3+):ZBLANP optical fiber sample for laser cooling of solids

We propose a theoretical model for an optimized fiber structure for use in anti-Stokes laser cooling of solids. The sample is an optical fiber fabricated from a fluorozirconate glass ZBLANP with a core doped with Yb(3+) ions. The diameter of the fiber core is optimized to achieve the largest temperature change in the sample. It is shown that for each value of the pump power there is an optimized diameter of the fiber core, which permits the largest drop in the temperature of the sample.     

Detection of tobacco smoke deposition by hyperpolarized krypton-83 MRI

Despite the importance of the tobacco smoke particulate matter in the lungs to the etiology of pulmonary disease in cigarette smokers, little is currently known about the spatial distribution of particle deposition or the persistence of the resulting deposits in humans, and no satisfactory technique currently exists to directly observe tobacco smoke condensate in airways. In this proof-of-principle work, hyperpolarized (hp) 83Kr MRI and NMR spectroscopy are introduced as probes for tobacco smoke deposition in porous media. A reduction in the hp-83Kr longitudinal (T1) relaxation of up to 95% under near-ambient humidity, pressure and temperature conditions was observed when the krypton gas was brought into contact with surfaces that had been exposed to cigarette smoke. This smoke-induced acceleration of the 83Kr self-relaxation was observed for model glass surfaces that, in some experiments, were coated with bovine lung surfactant extract. However, a similar effect was not observed with hp-(129)Xe indicating that the 83Kr sensitivity to smoke deposition was not caused by paramagnetic species but rather by quadrupolar relaxation due to high adsorption affinity for the smoke deposits. The 83Kr T1 differences between smoke-treated and untreated surfaces were sufficient to produce a strong contrast in variable flip angle FLASH hp-83Kr MRI, suggesting that hp-83Kr may be a promising contrast agent for in vivo pulmonary MRI.     

Synthesis and structural consideration of 1‐chloro‐N,N′,N″‐tris(pentafluorophenyl)azagermatrane: Azagermatrane with the shortest intramolecular N → Ge bond

Two compounds of a novel‐type azagermatrane, N(CH₂CH₂NC₆F₅)₃Ge‐Hal: HalCl ( 1 ), Br ( 2 ), were prepared via a metathetical reaction of trilithium salt of tetramine, N[CH₂CH₂N(Li)C₆F₅]₃, with corresponding GeHal₄. A single crystal structure of 1 was determined by the X‐ray diffraction study: The compound shows the strongest transannular N_ax → Ge interaction (2.148(7) Å) among other studied azagermatranes. © 2008 Wiley Periodicals, Inc. Heteroatom Chem 19:738–741, 2008; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/hc.20476     

Edge-defined film-fed growth of Yb:YVO4 single crystal plates

The applicability of the edge-defined film-fed growth (EFG) technique for Yb_xY_(1−x)VO₄ (x=0.05, 0.1 and 1) was approved by successful growth of crystals up to 80 mm in length as the thin plates. Low-angle grain boundaries and the crystal coloration as main defects were found. Optimal seed orientation was suggested on the strength of vanadate crystal plate morphology. Optical properties, chemical composition and the crystalline quality were investigated.     

Fluorescent core-shell polymer particles containing luminophore dyes: synthesis and optical response to acetone

Monodisperse dye-containing crosslinked particles are promising for application in novel optical chemical sensors due to their intrinsic sensitivity. However, preparation of these particles in aqueous media still remains a challenge, since luminophores inhibit radical processes or else cannot embed into polymer chains because of difference in monomer reactivity ratios. In this work, novel dye-containing monodisperse crosslinked particles were prepared and characterized. In order to obtain dye-containing monodisperse crosslinked particles, we studied seed copolymerization of styrene in the presence of divinylbenzene. The influence of nature and concentration of the used comonomers and co-solvents on shape, size distributions and surface characteristics of the particles formed was investigated. Shapes and diameters of the particles were analyzed by DLS, TEM and SEM. The data of SEM and optical spectroscopy studies demonstrated that the synthesized particles were able to self-assemble into thin-film three-dimensional ordered structures. Finally, the structures under study are promising for development of sensor devices with optical response to acetone.