Necessary and sufficient conditions for existence of exponential dichotomy of impulsive equations

Necessary and sufficient conditions for the existence of an exponential dichotomy of impulsive differential equations in a Hilbert space are found.     

Deuterium NMR studies of inositol liquid crystals [1]

Deuterium NMR investigations are presented on members of two new mesogenic series derived from the naturally occurring stereoisomers myo- and scW/o-inositol. Tetraethers of these two series exhibit thermotropic columnar phases in which the columns are apparently formed by stacked hydrogen bonded dimers of these molecules which chemically are vicinal diols. Deuterium NMR measurements were performed on the tetraoctyl homologues 2e (a cis diol) and 3e (a trans diol) of these series. We have investigated mixtures of these diols with small amounts of benzene-d₆ as probe molecules as well as samples of the neat diol compounds deuteriated at their hydroxyl groups. The results obtained show that the mesophases of both compounds are uniaxial and align partially in a magnetic field upon slow cooling from their isotropic liquids. The alignment is with the director parallel to the field direction indicating that the anisotropic magnetic susceptibility of this mesophase is positive. The deuterium quadrupole splitting of the benzene-d₆ probe in both systems is temperature dependent and in the trans diol 3e it even changes sign. This is interpreted in terms of a model in which the benzene-d₆ probe equilibrates rapidly between two (or more) solvation sites with quadrupole splittings of opposite signs The deuterium spectra of the neat deuterium labelled cis diol 2e exhibit two different signals due to the two deuterons which are located at the axial and equatorial hydroxyl groups. This indicates that there is no fast intra- or intermolecular exchange of the hydroxyl hydrogens. The overall quadrupole splittings of the hydroxyl deuterons in this compound are highly reduced compared to their static values and this is interpreted in terms of motional modes involving both reorientation of the hydroxyl deuterons about their C-O axis and overall reorientation of the molecules (or pairs of molecules) around the columnar axes. The corresponding spectra of the neat deuteriated trans diol 3e exhibit a single spectrum indicating that both hydroxyl deuterons in this compound are equivalent, or very nearly so. Within the mesophase region the spectrum undergoes gradual changes due to the increase in the molecular mobility, but the overall motional narrowing is less than in the cis isomer 2e. Apparently due to stronger hydrogen bonding in the trans isomer 3e the precession of the hydroxyl groups is hindered and a fast molecular reorientation is only possible at high temperatures.     

Oscillatory kinetics and mechanism of the chromate catalyzed decomposition of hydrogen peroxide

Oscillatory change of pH occurs during the chromate-catalyzed decomposition of hydrogen peroxide in a weakly acidic medium at elevated temperature and at high initial concentration of hydrogen peroxide. In a closed system, there are only two or three periods, but sustained oscillation occurs in a CSTR. In a CSTR bistability is also found. In closed systems the temperature exhibits a great maximum (up to 15°C increase), in a CSTR sustained oscillation occurs at a constant stationary temperature.     

Transport properties of a side-chain liquid-crystalline polymer. Poly(4-acryloyloxy biphenyl)

The transport properties of a side-chain liquid-crystalline polymer forming a smectic A phase have been investigated using dichloromethane as a permeant. Samples differing in the isotropization enthaoly were analyzed. A. Correlation between this thermal parameter and sorption has been found, while the diffusion coefficient is substantially the same in all samples. The results obtained can be explained in terms of a biphasis model in which a disordered permeable phase is present within the liquid-crystalline phase, which is impermeable to the diffusant molecules.     

The Interference Slow Wave in a Poroacoustic Biot Layer

It is shown that in a poroacoustic Biot layer placed inside an elastic medium, for any parameters of the model an interference slow wave exists. For low frequencies, the wave has very weak attenuation and the polarization of it coincides with the direction of the layer. This is evidence for the possibility of mapping subtle collectors inside an elastic medium in crosshole measurements. Bibliography: 7 titles.     

Effect of Finite Spectral Width on the Modulational Instability of Langmuir Waves described by a Nonlinear Schrödinger Equation

By using the two-point space correlation function an equation for the power spectral density for a random Langmuir field has been derived. The dispersion relation for a monochromatic wave is regained for a delta spectrum. For a Gaussian spectrum, the maximum growth rate is less than that for a monochromatic wave. For a “meander spectrum”, the growth rate is increased with the width of the spectrum in the first stage then decreased for further increase of the width.     

Book reviews

Ohne Zusammenfassung

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Book reviews

     

Deformation of doped NaCl crystals during uniaxial compression at temperatures of 4.2–293 K

The impurity weakening of crystalline NaCl:Mg and NaCl:Mn associated with purification of the matrix in a melt is demonstrated. This effect is manifested in a consistent change in the yield strength and mobility of dislocations. Its unusual temperature dependence is determined: in a number of cases weakening becomes greater as the temperature is lowered within the interval 293–4.2 K. A deviation in the elastic region of the stress-strain curves is observed to increase as the temperature is lowered. Plasticizing of crystalline NaCl is established: when the deformation temperature is lowered from 293 to 77 and 4.2 K the rate of rise in the yield strength of Cd²⁺ and Sr²⁺ doped samples is lower than that of undoped samples. An explanation for this fact is proposed. Fiz. Tverd. Tela (St. Petersburg) 39, 313–317 (February 1997) Deceased.     

Short-range order in miscible polymer blends: A monte carlo study

Local ordering in miscible binary polymer blends with strong attractive interactions between the two types of chains was investigated by computer simulation of allowable conformations on an incompressible cubic lattice. A tendency toward maximum ordering (in which chains pack in alternate parallel rows) is shown by the calculation of pair correlations and in “snapshots” of the mixtures. A specific directional interaction is not necessarily required for ordering. A comparison of these results with those recently obtained using mean-field theory is presented. The heat capacity of mixing was also calculated and found to be positive, with a value close to that reported experimentally.