Convergence of series of dependent φ-subgaussian random variables

The almost sure convergence of weighted sums of φ-subgaussian m-acceptable random variables is investigated. As corollaries, the main results are applied to the case of negatively dependent and m-dependent subgaussian random variables. Finally, an application to random Fourier series is presented.     

Relaxations in chitin: Evidence for a glass transition

Relaxations in chitin have been investigated in the temperature range 298–523 K using impedance spectroscopy in the frequency range 10⁻¹–10⁸ Hz. The objective was to detect a glass‐transition temperature for this naturally occurring, semicrystalline polysaccharide. The impedance study was complemented with X‐ray diffraction, thermogravimetric, and differential scanning calorimetry measurements. Preliminary impedance data treatment includes the subtraction of the dc conductivity contribution, the exclusion of contact and interfacial polarization effects, and obtaining a condition of minimum moisture content for further analysis. When all these aspects are taken into account, two relaxations are clearly revealed in the impedance data. For the first time, evidence is presented for a relaxation process, which exhibits a non‐Arrhenius temperature dependence, in dry α‐chitin (∼0.1% moisture content), and likely represents the primary α‐relaxation. This evidence suggests a glass transition temperature for chitin of 335 ± 10 K estimated on the basis of the temperature dependence of the conductivity and of the relaxation time. A second relaxation in dry α‐chitin, not previously reported in the literature, is observed from 353 K to the onset of thermal degradation (∼483 K) and is identified as the σ‐relaxation often associated with proton mobility. It exhibits a normal Arrhenius‐type temperature dependence with activation energy of 113 ± 3 kJ/mol. The latter has not been previously reported in the literature. A high frequency secondary β‐relaxation is also observed with Arrhenius activation energy of 45 ± 1 kJ/mol. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 932–943, 2009     

Nanoparticle enabled thermal control of ions in liquid crystals

Typically, ionic species in thermotropic liquid crystals are nearly fully ionised. Therefore, the concentration of mobile ions practically does not depend on the temperature. Interestingly, the same liquid crystals doped with nanoparticles exhibit totally different behaviour. The concentration of mobile ions become temperature dependent. This paper reports the effects of the temperature on the concentration of ions in liquid crystal nanocolloids. Liquid crystals doped with both 100% pure and contaminated nanoparticles are considered. Regardless the ionic purity of nanodopants, the concentration of mobile ions in liquid crystal nanocolloids increases towards the saturation as their temperature goes up. The magnitude of this saturation level equals the initial concentration of ions in liquid crystals doped with 100% pure nanoparticles. The temperature induced release of ions by contaminated nanoparticles in liquid crystals increases the above-mentioned saturation level. While the dispersion of 100% pure nanoparticles in liquid crystals leads to the temperature-dependent purification only, the use of contaminated nanoparticles results in the temperature-driven switching between the purification and contamination regimes enabling thermal control of ions.     

Effect of Pumping Pulse Duration on Echo Signal Amplitude in Four-Pulse PELDOR

The impact of pumping pulse duration on four-pulse pulsed electron?Celectron double resonance (PELDOR) data was experimentally studied. For biradicals with known distances between two spin labels, it is shown that refocused echo amplitude decreases with increasing the pumping pulse duration and decreasing the distance between spin labels. The effect becomes substantial when the pumping pulse duration is comparable or exceeds the inverse value of the dipole?Cdipole interaction between spin labels. This effect is essential for determination of distance distribution between labels in double-labeled molecules and for determination of the number of labels in clusters of spin-labeled molecules. PELDOR signal distortion was observed when the pumping pulse position in the time scale coincided with those of the detecting pulses. An approach of signal correction to eliminate this distortion is proposed.     

On Cohen-Macaulay modules over non-commutative surface singularities

We generalize the results of Kahn about a correspondence between Cohen-Macaulay modules and vector bundles to non-commutative surface singularities. As an application, we give examples of non-commutative surface singularities which are not Cohen-Macaulay finite, but are Cohen-Macaulay tame.     

The Neumann boundary problem for axisymmetric fractional heat conduction equation in a solid with?cylindrical hole and associated thermal stress

The theory of thermoelasticity based on the heat conduction equation with the Caputo time-fractional derivative of order α is used to study thermal stress in an infinite medium with a cylindrical hole. Two types of Neumann boundary conditions are considered: the constant value of the normal derivative of the temperature and constant heat flux at the surface of a cavity. The solution is obtained applying Laplace and Weber integral transforms. Numerical results are illustrated graphically.     

On the closure of the first Grigorchuk group

We consider the closure (in the natural topology) of the well-known periodic self-similar group. A finitely generated group that is not isomorphic to the Grigorchuk group and has the same closure is constructed.