The Grothendieck group of the stable category of symmetric special biserial algebras

Cartan matrices of symmetric special biserial algebras are described, and the order of the Grothendieck group for the stable category of these algebras is computed. In particular, a criterion for the existence of a free summand in these groups is obtained. Bibliography: 3 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 321, 2005, pp. 5–12.     

Optical echo in photonic crystals

The dynamics of a photonic wavepacket in the effective oscillator potential is studied. The oscillator potential is constructed on the base of one-dimensional photonic crystal with a period of unit cell adiabatically varied in space. The structure has a locally equidistant discrete spectrum. This leads to an echo effect, i.e., the periodical reconstruction of the packet shape. The effect can be observed in the nonlinear response of the system. Numerical estimations for porous-silicon based structures are presented for a femtosecond Ti:sapphire laser pump. The text was submitted by the authors in English.     

Crystal structure and high-temperature electrical conductivity of novel perovskite-related gallium and indium oxides

Novel complex oxides Sr₂Ga_1+x In_1?x O₅, x?=?0.0–0.2 with brownmillerite-type structure were prepared in air at T?=?1,273 K, 24 h. Study of the crystal structure of Sr₂Ga_1.1In_0.9O₅ refined using X-ray powder diffraction data (S.G. Icmm, a?=?5.9694(1) Å, b?=?15.2091(3) Å, c?=?5.7122(1) Å, χ ²?=?2.48, R _F ²? ₌?0.0504, R _p?=?0.0458) revealed ordering of Ga³⁺ and In³⁺ cations over tetrahedral and octahedral positions, respectively. A partial replacement of Sr²⁺ by La³⁺ according to formula Sr_1?y La _y Ga_0.5In_0.5O_2.5+y/2, leads to the formation of a cubic perovskite (a?=?4.0291(5) Å) for y?=?0.3. No ordering of oxygen vacancies or cations was observed in Sr_0.7La_0.3Ga_0.5In_0.5O_2.65 as revealed by electron diffraction study. The trace diffusion coefficient (D _T) of oxygen for cubic perovskite Sr_0.7La_0.3Ga_0.5In_0.5O_2.65 is in the range 2.0?×?10^?9–6.3?×?10^?8 cm²/s with activation energy 1.4(1)?eV as determined by isotopic exchange depth profile technique using secondary ion mass spectrometry at 973–1,223 K. These values are close to those reported for Ca-doped ZrO₂. High-temperature electrical conductivity of Sr_0.7La_0.3Ga_0.5In_0.5O_2.65 studied by AC impedance was found to be nearly independent on oxygen partial pressure. Calculated values of activation energy at T?<?1,073 K for hole and oxide-ion conductivities are 0.96 and 1.10 eV, respectively.     

The possibility of applying a titanium-magnesium nanocatalyst in the polymerization filling of polyolefins and some properties of the obtained composites

The possibility of applying a titanium-magnesium nanocatalyst during in situ polymerization of ethylene and propylene in the presence of organomodified aluminum silicates and diatomite under mild conditions is investigated. How the substantial (2- to 3-fold) increase in the catalytic activity of the system depends on the type and amount of filler is shown. The activity of the titanium-magnesium nanocatalyst-filler system during polymerization of propylene is 3–4 times higher than that during the polymerization of ethylene. Composites based on ultrahigh-molecular-mass polyethylene (M = (1.4–1.7) × 10⁶) with 3.5–13.0 wt % filler are obtained. According to DSC and X-ray structural-analysis data, the polyethylene matrix differs by its high crystallinity and a T _m of 143–144°C. The physicochemical characteristics of the composites are 1.5–2.0 times greater than those of unfilled polyethylene; the nanocomposite containing 11 wt % mont-morillonite modified with vinyltrimethoxysilane has the best properties. It is shown that during the propylene polymerization, the effect of the type of filler affects not only the catalytic activity of the system, increasing it three times in the case of diatomite, but also the stereospecificity of the effect. Isotactic high-molecularmass (up to 390 × 10³) polypropylene is obtained in the presence of montmorillonite containing vinyltrimethoxysilane, while a low-molecular-mass ((65–75) × 10³) polymer with lower isotacticity is formed on diatomite. The deformation-strength characteristics of composites based on polypropylene testify the formation of an elastomeric material with T _m = 156–158°C.     

Spatial Separation of Covalent,Ionic, and Metallic Interactions in Mg11Rh18B8 and Mg3Rh5B3

The crystal structures of Mg₁₁Rh₁₈B₈ and Mg₃Rh₅B₃ have been investigated by using single‐crystal X‐ray diffraction. Mg₁₁Rh₁₈B₈: space group P4/mbm; a=17.9949(7), c=2.9271(1) Å; Z=2. Mg₃Rh₅B₃: space group Pmma; a=8.450(2), b=2.8644(6), c=11.602(2) Å; Z=2. Both crystal structures are characterized by trigonal prismatic coordination of the boron atoms by rhodium atoms. The [BRh₆] trigonal prisms form arrangements with different connectivity patterns. Analysis of the chemical bonding by means of the electron‐localizability/electron‐density approach reveals covalent B? Rh interactions in these arrangements and the formation of B? Rh polyanions. The magnesium atoms that are located inside the polyanions interact ionically with their environment, whereas, in the structure parts, which are mainly formed by Mg and Rh atoms, multicenter (metallic) interactions are observed. Diamagnetic behavior and metallic electron transport of the Mg₁₁Rh₁₈B₈ and Mg₃Rh₅B₃ phases are in agreement with the bonding picture and the band structure.     

Λ(1520) → Λγ radiative-decay width

The radiative decay Λ(1520) → Λγ was recorded in the exclusive reaction p + N → Λ(1520)K ⁺ + N at the SPHINX facility. The branching ratio for this decay and the corresponding partial width were found to be, respectively, Br[Λ(1520) → Λγ] = (1.02 ± 0.21) × 10^?2 and Γ[Λ(1520) → Λγ] = 159 ± 35 keV (the quoted errors are purely statistical, the systematic errors being within 15%).     

Spin-glass, antiferromagnetism and kondo behavior in Ce2Au1−x Co x Si3 alloys

Recently, the solid solution Ce₂Au_{1− x Co} xSi₃ has been shown to exhibit many magnetic anomalies associated with the competition between magnetic ordering and the Kondo effect. Here we report high pressure electrical resistivity of Ce₂AuSi₃, ac susceptibility (X) and magnetoresistance of various alloys of this solid solution in order to gain better knowledge of the magnetism of these alloys. High pressure resistivity behavior is consistent with the proposal that Ce₂AuSi₃ lies at the left-hand side of the maximum in Doniach’s magnetic phase diagram. The ac X data reveal that there are in fact two magnetic transitions, one at 2 K and the other at 3 K for this compound, both of which are spin-glass-like. However, as the Co concentration is increased, antiferromagnetism is stabilized for intermediate compositions before attaining non-magnetism for the Co end member.     

Role of rotational symmetry in magnetism of multiband models

The role of the complete Coulomb interaction matrix in the determination of the magnetic susceptibility of the two-band Hubbard model has been investigated in the dynamical mean-field theory. The off-diagonal component of the U-matrix has been found to reduce the Néel temperature, which agrees with the available experimental data. The magnitude of the effect upon a change in the dimension of the U-matrix is discussed. The results have been compared with the thermodynamic characteristics of an isolated Hubbard atom.