Chain enumeration and non-crossing partitions

A formula is established for the number of chains with designated ranks in the non-crossing partition lattice. As corollaries, certain results of Kreweras are obtained. Non-crossing partitions are then generalized in two ways, and similar problems are solved.     

A note on the Stokes resistance tensors of multiparticle systems in shear fields

The Stokes resistance tensors (material tensors) of a multiparticle system subjected to a general shear flow depends on the spatial configuration of the particles, their shape, size and location of some arbitrarily fixed set of points locked to the particles by which their linear velocities are traced. The objective of this work is the determination of some symmetry properties of the material tensors and the transformation laws which govern them under translation of the set of points fixed to the particles.     

On a fixed point theorem for partially ordered sets

An elementary combinatorial proof is presented of the following fixed point theorem: Let P be a finite partially ordered set with a cut-set X. If every subset of X has either a meet or a join, then P has the fixed point property. This theorem is strengthened to include a certain class of infinite partially ordered sets, as well.     

Kinetics and mechanism of acrylonitrile polymerization by p-toluenesulfinic acid. III. Initiation through disproportionation

A mechanism for radical formation from aromatic sulfinic acids through the disproportionation reaction is suggested. It is postulated that two parallel steps, one a bimolecular reaction and the other involving a trimer of sulfinic acid, yield sulfenyl sulfonate. This labile compound decomposes into free radicals or reacts with another molecule of sulfinic acid producing thiol sulfonate and sulfonic acid. This mechanism explains the variety and unusually high orders encountered in polymerization initiated by sulfinic acid initiators. The proposed kinetic scheme is in agreement with the proton dependence found for both the initiation as well as the disproportionation reactions.     

Magneto-optical spectroscopy of Yb ions in huntite structure

We report the first measurements of magnetic circular dichroism (MCD) and magneto-optical activity (ratio of zero moments of MCD and absorption bands) of Yb³⁺ ion in the trigonal single crystals Yb_xTm_1−xAl₃(BO₃)₄ as a function of temperature in the range of 100-293 K. Magneto-optical activity follows the Curie-Weiss law with the Weiss constant θ=−55 K for Yb_0.1Tm_0.9Al₃(BO₃)₄ crystal. The value and origin of the magneto-optical activity is theoretically analyzed.     

A note on regular Ramsey graphs

We prove that there is an absolute constant C>0 so that for every natural n there exists a triangle‐free regular graph with no independent set of size at least \({{C}}\sqrt{{{n}}\log{{n}}}\). © 2009 Wiley Periodicals, Inc. J Graph Theory 64: 244–249, 2010     

Linear and quadratic magneto-optical effects observed in La0.7Sr0.3MnO3 thin films in transmitted light

Magnetic linear dichroism (MLD) is observed in polycrystalline La_0.7Sr_0.3MnO₃ films in transmitted light. The spectral and temperature dependences of the MLD are determined for the energy E of the light wave ranging from 1.5 to 3.5 eV. The experimental spectra are fitted by a sum of Lorentzian curves. The MLD spectrum exhibits more features in comparison to the spectra of magnetic circular dichroism (MCD), which we measured earlier using the same film samples. Various temperature behaviors of the intensities of the Lorentzian components centered at different E values have been revealed. This can be related to the effect of the surface states on the magneto-optical characteristics of the samples.     

Emission characteristics of a glow discharge plasma based on a mixture of helium with chlorine molecules

We present the results of a study of the emission characteristics of a longitudinal glow discharge based on a mixture of helium and chlorine. Study of the emission characteristics of the discharge showed that it emits most efficiently in the bands of the chlorine molecule with maxima at 200 nm and 258 nm in an He-Cl₂ mixture (P = 0.2–0.3 kPa). We present the optimization of the average emission power of a UV emitter as a function of the glow discharge parameters, the pressure, and the composition of the working gas mixture. Based on solution of the Boltzmann equation for the electron energy distribution function in a discharge based on the optimal mixture (according to experimental data), we calculated the power losses per unit pressure going toward elementary processes, the electron transport characteristics, the ionization and attachment coefficients as a function of the parameter E/P. The calculated parameters of the plasma for the UV emitter allowed us to provide a basis for the qualitative pattern of physicochemical processes in the studied plasma. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 75, No. 1, pp. 121–124, January–February, 2008.     

Macroscopic Polarization Change of Mononuclear Valence Tautomeric Cobalt Complexes Through the Use of Enantiopure Ligand

The crystallization of a complex having electron transfer properties in a polar space group can induce the polarization switching of a crystal in a specific direction, which is attractive for the development of sensors, memory devices, and capacitors. Unfortunately, the probability of crystallization in a polar space group is usually low. Noticing that enantiopure compounds crystallize in Sohncke space groups, this paper reports a strategy for the molecular design of non-ferroelectric polarization switching crystals based on the use of intramolecular electron transfer and chirality. In addition, this paper describes the synthesis of a mononuclear valence tautomeric (VT) cobalt complex bearing an enantiopure ligand. The introduction of enantiomer enables the crystallization of the complex in the polar space group (P2₁). The polarization of the crystals along the b-axis direction is not canceled out and the VT transition is accompanied by a change in the macroscopic polarization of the polar crystal. Polarization switching via electron transfer is realized at around room temperature.