Orthogonal modules and nonlinear cohomologies

Ordinary cohomologies in an algebra most often exhibit themselves either as objects that describe extensions (of algebras, groups, or modules) or as subjects hindering the existence of algebraic constructions. We introduce the notion of nonlinear cohomologies at a level of cochain complexes, furnish particular examples for Lie algebras, and give an interpretation of first nonlinear cohomologies in terms of “quasiextensions” of orthogonal modules. Translated fromAlgebra i Logika, Vol. 37, No. 5, pp. 522–541, September–October, 1998.     

Thermal gradient induced sidebranching in directional solidification

The polycrystalline perovskitelike manganese oxides La_1-xA_xMnO (A = Na, and K, ) have been fabricated by sol-gel technique. For all the compositions explored in this work, the average manganese oxidation state is practically constant, at for A = Na, and for A = K, respectively. A close relationship is confirmed to hold between the Curie temperature (T_c) and the bond distance of Mn-O. Results of magnetic measurements show that these materials can be utilized as suitable candidates for magnetic refrigerants with wide applied temperature span, for their significant entropy change and the easily tuned Curie temperature. Received: 12 September 1997 / Revised: 18 December 1997 / Accepted: 21 January 1998     

Loss and non-linearity saturation effects on the bistability of non-linear distributed feedback structures

We investigate theoretically the effects of optical absorption and saturation of the non-linear index of refraction on the bistability of non-linear distributed feedback structures (NLDFBs). By assuming that the Kerr non-linearity saturates in an exponential fashion, we obtain for the first time closed-form expressions for the so-called self-phase and cross-phase modulation terms. Our investigation shows that both absorption and, in particular, saturation significantly affect the bistable properties of this structure and in many cases eliminate this response completely. In some cases, however, saturation alters the NLDFB's transfer characteristics in a potentially useful manner. We find that weak levels of saturation may increase the contrast ratio between the intensities of the high and low bistable states. At increasing levels of saturation, where bistability is no longer observed, we find regimes where the NLDFB structure could possibly be used for optical amplification. This revised version was published online in November 2006 with corrections to the Cover Date.     

Mössbauer study of Martian regolith analogues

Terrestrial basalt rocks considered to be a good analogues of the Martian regolith were studied by using the Mössbauer spectroscopy and X-ray diffraction. The weathering of basalts was followed by the changes of the Fe²⁺/Fe³⁺ ratio. The basalt rock undergoes alteration from primary mineral composition (olivine+pyroxene+plagioclase) through smectite to kaolinite clay with oxides and hydroxides with the increase of the Fe²⁺/Fe³⁺ ratio.     

129Xe NMR study of the homogeneity and the size distribution of small sodium metal particles in NaY zeolite

NaY zeolite samples loaded with sodium metal by vapor phase deposition have been investigated using¹²⁹Xe NMR spectroscopy. At low sodium concentration, the¹²⁹Xe NMR spectrum showed three resonance lines which clearly indicate the existence of distinct domains in the zeolite sample. Such an observation suggests that the diffusion of the xenon atoms into each domain only occurs with respect to the NMR time scale (2.9 ms). As the sodium concentration increases, observation of a single broad line indicate a macroscopic homogenization of the system. The shift of this line is explained in part due to a paramagnetic interaction between the xenon atoms and the unpaired electrons of particles containing an odd number of sodium atoms. The linewidth is due to the distribution of the local magnetic fields partially averaged by the rapid motion of the xenon atoms and to the statistical distribution of the sodium particles in the supercage cavities. The paramagnetic interaction vanishes with the oxidation of the sample leading to a narrowing and a shift of the line to higher magnetic fields.     

Alloying by high dose ion implantation of iron into magnesium and aluminium

Alloys of the systems Fe–Al (mixable over the whole concentration range) and Fe–Mg (insoluble with each other) were produced by implantation of Fe ions into Al and Mg, respectively. The implantation energy was 200 keV and the ion doses ranged from 1 × 10₁₄ to 9 × 10₁₇cm^-2The obtained implantation profiles were determined by Auger electron spectroscopy depth profiling. Maximum iron concentrations reached were up to 60 at.% for implantation into Al and 94 at.% for implantation into Mg. Phase analysis of the implanted layers was performed by conversion electron Mössbauer spectroscopy and X‐ray diffraction. For implantation into Mg, two different kinds of Mössbauer spectra were obtained: at low doses paramagnetic doublets indicating at least two different iron sites and at high doses a dominant ferromagnetic six‐line‐pattern with a small paramagnetic fraction. The X‐ray diffraction pattern concluded that in the latter case a dilated αiron lattice is formed. For implantation into Al, the Mössbauer spectra were doublet structures very similar to those obtained at amorphous Fe–Al alloys produced by rapid quenching methods. They also indicated at least two different main iron environments. For the highest implanted sample a ferromagnetic six‐line‐pattern with magnetic field values close to those of Fe₃Al appeared.     

Logarithmic temperature dependence of the conductivity of the two-dimensional metal

We report on the first observation and studies of a weak delocalizing logarithmic temperature dependence of the conductivity, which causes the conductivity of the 2D metal to increase as T decreases down to 16 mK. The prefactor of the logarithmic dependence is found to decrease gradually with density, to vanish at a critical density n _c , 2∼2×10¹² cm⁻², and then to have the opposite sign at n>n _c ,2. The second critical density sets the upper limit on the existence region of the 2D metal, whereas the conductivity at the critical point, G _c ,2∼120e ²/h, sets an upper (low-temperature) limit on its conductivity. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 6, 497–501 (25 September 1998) Published in English in the original Russian journal. Edited by Steve Torstveit.     

The signature theorem and some related questions

Some corollaries of the Hirzebruch-Thom signature theorem are discussed. The multiplicativity of the signature and the naturalness of the Pontryagin classes for coverings in the case of ℚ-homology manifolds is proved. A geometric proof of Hirzebruch’s well-known “functional equation” for the virtual signature is outlined. Bibliography: 25 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 231, 1995, pp. 197–209. Translated by N. Yu. Netsvetaev.     

Investigation of the chemical state of copper in Cu/SiO2 composite films by x-ray photoelectron spectroscopy

The concentration and chemical state of copper in the subsurface region of Cu/SiO₂ composite films obtained by simultaneous magnetron sputtering from two sources (Cu and SiO₂) are determined by x-ray photoelectron spectroscopy (XPS). It is established that copper in the as-grown film is primarily in the form of unoxidized atoms dispersed in a SiO₂ matrix. Annealing of the film results in practically no oxidation, but about 70% of the copper atoms condense into metallic clusters with sizes below 10 Å in the subsurface region and about 50 Å in the bulk of the film. The changes in the binding energy of core electrons, and especially in the energies of Auger electrons, are so large in this situation that photoelectron and Auger spectroscopy are efficient methods for monitoring the chemical state of this composite material.