We prove that the complement to the caustic of a stable Lagrangian map germ of type E_6^± has seven connected components, six of which are contractible and one is homotopy equivalent to a circle. The inverse image of the noncontractible component under this map has three connected components. The restriction of the map to one of them is a two-sheeted covering; the restriction to each of the other two is a diffeomorphism.

The temperature dependences of the magnetization of La1 – xSrxFeO3 – δ samples (x = 0.33, 0.50, and 0.67) have been studied. Their Neel temperatures TN have been determined, at which non-collinear antiferromagnetism (weak ferromagnetism) is settled down in the samples. The introduction of a substituting impurity of strontium into La1 – xSrxFeO3 – δ and an increase in its content results in a considerable decrease in TN. This effect can be compensated using vacuum heat treatment, upon which, on the contrary, a noticeable increase in TN is observed.

We present a list of universal linear relations between the Euler characteristics of manifolds of multisingularities of a generic Lagrangian map to a five-dimensional space. From these relations it follows, in particular, that the numbers D5A2, A4A3 and A4A22 of isolated self-intersection points of the corresponding types on any generic compact four-dimensional caustic are even. The numbers D4+ A3 + D4-A3 + E6 and D4+ A22 + D4-A22 + 2 A4A3 are also even. 1 Bibliography: 7 titles.

It is proved that the image of a stable germ of type E_6^± of a Lagrangian map to ℝ^n is homeomorphic to the germ at zero of a closed half-space.

The changes in the substituted La0.5Sr0.5FeO3_ & gamma; orthoferrite under vacuum annealing in the temperature range of 200-650 degrees C have been studied by X-ray diffraction analysis, as well as Mo & BULL;ssbauer and Raman spectroscopy. Annealing of the as-prepared ferrite with the rhombohedral structure (R 3 c) resulted in its transition to the cubic one (Pm 3 m) at 650 degrees C. In the as-prepared ferrite being paramagnetic at room temperature, Fe ions were detected in an averaged-valence state between Fe3+ and Fe4+, which was not revealed with a decrease in the temperature down to 85 K. Gradual oxygen loss and an increase in the number of oxygen vacancies took place with an increase in the vacuum annealing temperature. Only Fe3+ ions were present in the ferrite at a vacuum annealing temperature above 500 degrees C. Several Zeeman sextets in the Mo & BULL;ssbauer spectra associated with Fe3+ ions were resulted from the presence of oxygen vacancies and Fe4+ ions in the local environment of Fe3+ ions. The variations in the ratio of the valence states of Fe ions obtained from Mo & BULL;ssbauer data depending on a vacuum annealing temperature allowed determining the content of oxygen in all the investigated samples. The contri-bution of Fe3+ ions that did not have Fe4+ ions and oxygen vacancies in their local environment was shown to increase with a vacuum annealing temperature from 12% (for the as-prepared sample) to 60% (for the sample annealed at 650 degrees C). On a whole, the process taking place under vacuum annealing can be characterized as a variation of the local environment of Fe3+ ions towards a decrease in its distortion. It was found that the width of the peaks of the Raman spectra decreased and their amplitude increased with an increase in the vacuum annealing temperature, which also demonstrated the improvement of the structural perfection of the samples.

Доказано, что образ устойчивого ростка лагранжева отображения типа $E_6^\pm$ гомеоморфен ростку в нуле замкнутого полупространства в $\mathbb{R}^5$.

In this paper, we studied substituted lanthanum orthoferrite La 0.67 Sr 0.33 FeO 3 – γ by Mössbauer spectroscopy using X-ray diffraction data. A series of vacuum annealings was performed in the temperature range of t ann = 200–650°C, after which no significant changes in the structure of the samples were detected. The Mössbauer measurements at room temperature show that the Fe ions are in an average valence state between Fe 3+ and Fe 4+ . Upon vacuum annealing, as the temperature t ann increased, the average hyperfine magnetic field on the 57 Fe nuclei and the isomer shift of the spectrum increased, which is associated with an increase in the number of vacancies and, accordingly, a decrease in the amount of Fe 4+ . Mössbauer measurements at 85 K showed that the average valence state of iron does not manifest itself. The hyperfine parameters of the low-temperature Mössbauer subspectra obtained from the model interpretation indicate that one of them belongs to Fe 4+ ions, and the rest belong to Fe 3+ . The presence in the spectra of several sextets related to Fe 3+ ions is due to the appearance of oxygen vacancies (breaking of the Fe 3+ –O 2– –Fe exchange bond) and Fe 4+ ions (weakening of the Fe 3+ –O 2– –Fe exchange bond) in the nearest ionic neighborhood of Fe atoms. Both factors cause a decrease in the hyperfine magnetic field and a change in the isomer shift of the spectrum. As a result of model interpretation of the Mössbauer spectra, the numbers of oxygen vacancies and Fe 4+ ions per formula unit depending on vacuum annealing temperature t ann were determined for all samples. It was shown that at t ann above 450°C, the process of oxygen leaving the lattice ends and only Fe 3+ ions are detected.

The valence states of Fe atoms and the formation of oxygen vacancies in substituted La0.67Sr0.33FeO3−γ orthoferrite have been studied in detail by low-temperature Mössbauer spectroscopy under oxygen removal. It has been shown that the averaged valence state of Fe atoms is not revealed with a decreasing measurement temperature. This makes it possible to reveal Fe4+ ions. The Analysis of the obtained data allows us to conclude that the presence of several Zeeman sextets associated with Fe3+ ions is related to the appearance of oxygen vacancies and Fe4+ ions in the nearest ionic surrounding of Fe ions. Using the Mössbauer data, the number of oxygen vacancies and oxygen ions has been determined for all the studied samples depending on the vacuum annealing temperature.

Sr-doped (00.2) ceramic samples of the lanthanum manganite oxides were obtained via sol-gel method to investigate the influence of doping on structural, magnetic end electronic responses, and their correlations. Synthesized samples of non-stoichiometric compositions are rhombohedral single-phase. After annealing the formation of a phase-separated system as a mixture of orthorhombic phases was found.The R-3c and PnmaI, PnmaII* and PnmaII phases have been studied using Mo spacing diaeresis ssbauer spectroscopy, XRD, SEM analysis and magnetic measurements. The magnetic temperature-concentration phase diagram of La1-xSrxMnO3+delta (x = 0.05, 0.10, 0.20) was obtained. The Jahn-Teller effect or the orbital order breaking, as well as the competition between Mn3+-O2-Mn4+ double-and Mn3+-O2--Mn3+ superexchange interaction was demonstrated under the effect of cation doping compound and interstitial oxygen value (delta). The relaxation character of the Mo spacing diaeresis ssbauer spectra and the type of magnetization dependences revealed nanosized magnetic clusters with fluctuation of their magnetic moment in all perovskite phases. Results are interpreted in terms of matrix - clusters: regions of sample with ferromagnetic type of ordering (cluster) exist in antiferromagnetically or ferromagnetically (with different exchange parameter) ordered matrix. Exchange interaction frustrations of the cluster with the matrix can lead to relaxation behavior of the magnetic moment of the cluster. The clusters size vary from about 3.9 to 5.7 nm. All samples are charac-terized by the presence of particles agglometates with a typical size about 0.4-0.8 mu m; for annealed samples additional non-conducting regions with 80-220 nm in size were found. It is shown that the annealing time significantly affects the production of materials with determined properties and be useful in the applied field in technological processes.

The valence states of Fe atoms and the formation of oxygen vacancies in substituted La 0.67 Sr 0.33 FeO 3-γ orthoferrite have been studied in detail by low-temperature Mossbauer spectroscopy under oxygen removal. It has been shown that the averaged valence state of Fe atoms is not revealed with a decreasing measurement temperature. This makes it possible to reveal Fe 4+ ions. The Analysis of the obtained data allows us to conclude that the presence of several Zeeman sextets associated with Fe 3+ ions is related to the appearance of oxygen vacancies and Fe 4+ ions in the nearest ionic surrounding of Fe ions. Using the Mossbauer data, the number of oxygen vacancies and oxygen ions has been determined for all the studied samples depending on the vacuum annealing temperature. Keywords: perovskites, substituted lanthanum ferrites, X-ray diffraction analysis, Mossbauer spectroscopy, Fe valence states, oxygen vacancies.

The physicochemical properties of siderites (FeCO 3 ) of different origin have attracted attention due to challenges in the diagnostics with the aim of evaluating the involvement of bacteria in the formation of iron-rich sedimentary deposits. A comparative study of siderites of chemical and bacterial origin was performed by Mӧssbauer spectroscopy, X-ray diffraction, and scanning electron microscopy for the purpose of determining the possible characteristics, which will allow the identification of biogenic siderite. It was found that all the characterized siderites have significant differences in the crystal morphology associated with the physicochemical conditions of their formation. Siderites of bacterial origin are characterized by a smaller crystal size compared to siderites of hydrothermal or sedimentary origin. The inhomogeneity of the nearest environment of the iron atoms, which was found for siderites of bacterial origin and which is manifested in the Mӧssbauer spectra as a larger width of the quadrupole shift distribution, can be used as a diagnostic indication of biogenic siderites.

Transformations of polycrystalline La 0.5 Sr 0.5 FeO 3 – γ ferrites subjected to vacuum annealing in the temperature range of 400–650°C were studied by Raman spectroscopy at ambient conditions. It was shown that the homogeneity of the sample and its local ordering depended on the vacuum annealing temperature. An increase in the vacuum annealing temperature resulted in a gradual loss of oxygen and a transition of all iron ions to the oxidation state Fe 3+ . These ferrites demonstrated a shift of the whole Raman spectra (including two-magnon modes) to higher frequencies with increasing Sr content of 0 < x < 0.5. The possible reasons for the observed effects are discussed.

The substituted orthoferrite La0.67Sr0.33FeO3_gamma was studied using scanning electron microscopy, X-ray diffraction (XRD), and Mo center dot ssbauer and Raman spectroscopy. A series of vacuum annealing in the temperature range of 200-650 degrees C was performed, resulting in negligible changes in the crystal structure of samples. The volume of the pseudocubic unit cell increased continuously with raising temperature up to 450 degrees C. It follows from the Mo center dot ssbauer measurements that at room temperature Fe ions were characterized by an averaged-valence state. The vacuum annealing induced oxygen vacancies and changed the averaged-valence state of Fe ions. Sufficiently good correlations among the Mo center dot ssbauer, XRD, and Raman spectroscopy data were obtained.

The article for the first time deals with the issues of natural regeneration of the forest in blown sands – a kind of deserts of the northern taiga and forest-tundra of Western Siberia, which arose on the site of automorphic pine stands, destroyed by natural and technogenic impacts. During the reconnaissance survey of several blows, it was found, that the main factor hindering the natural regeneration of forests in these peculiar deserts of the North is the wind. In this regard, forest formation on them is carried out only in areas adjacent to the leeward side of the forest walls and in low places, as well as in voids between large-sized logging residues covered with sand.

Crystal structure, short range order, lattice dynamics and valence state of polycrystalline single-phase strontium ferrites SrFeO3-delta (with 3-6 = 2.87 divided by 2.5) were studied by Raman and Mossbauer spectroscopy at normal conditions. Valence states of Fe ions and their fractions were determined from Mossbauer spectroscopy and concentrations of oxygen in all phases were estimated. For all studied SrFeO3-delta phases only five (or less) bands were observed above 200 cm(-1) in spite of numerous Raman active phonon modes predicted by a factor group analysis. For the antiferromagnetic Brownmillerite phase (3-delta = 2.5), a broad band observed at -1350-1400 cm(-1), was attributed to the two-magnon scattering. This band was found also for the SrFeO3-delta samples with 3-6 = 2.87 divided by 2.725 which are in paramagnetic state at room temperature. This fact indicates an existence of the unusual magnetic correlations in all SrFeO3-delta perovskites.

Geometric analysis of the flow path in pipeline gate and ball valves permits identification of the zone where the abrasive pollutant flux is most intense. The speed of this flux contributes greatly to its aggressiveness. Recommendations are made for more effective protection of the moving parts in shutoff valves.

We prove that the manifold of non-singular points of a stable real caustic germ of type E-6 and the manifolds of points of transversal intersection of its smooth branches consist only of contractible connected components. We also calculate the number of these components.