On the number of two-dimensional threshold functions

A two-dimensional threshold function of k-valued logic can be viewed as coloring of the points of a k x k square lattice into two colors such that there exists a straight line separating points of different colors. For the number of such functions only asymptotic bounds are known. We give an exact formula for the number of two-dimensional threshold functions and derive more accurate asymptotics.Comment: 17 pages, 2 figure

Oxygen non-stoichiometry and defect structure of LaMn1-zCuzO3+δ

The quantitative model analysis of the defect structure of copper doped lanthanum manganites LaMn1-zCuzO3+δ (z = 0.05 and 0.1) was performed. In the framework of the model, the independent course of the three reactions of defect formation, including the electronic exchange between manganese and copper, completion of a lattice by the absorption of oxygen and the disproportionation of manganese was considered. It is shown that the increase in the dopant content leads to a change in the dominant electronic process. This is reflected in the lock and disproportionation and leads to the increase in the concentration of holes and decrease the concentration of electrons localized on the manganese atoms

Research of the plastic flow of electrolytically saturated with hydrogen (He) Al-Cu-Mg alloy

The effect of hydrogen embrittlement on the plastic flow of Al-Cu-Mg alloy was investigated (HE). The studies were performed for the test samples of aluminum alloy subjected to electrolytic hydrogenation in a three electrode electrochemical cell. It is found that the mechanical properties and plastic flow curves of aluminum alloy are affected adversely by HE. These are found to show all the plastic flow stages: the linear, parabolic and pre-failure stages. It is established that the hydrogenation enhances the localization of straining leads to significant changes in the characteristics distances between local straining zones. The patterns of localized plasticity appear to be useful for a detailed analysis of plasticity exhibited by aluminum alloys

Autowave process of the localized plastic deformation of high-chromium steel saturated with hydrogen

The deformation behavior of high-chromium stainless steel of sorbitic structure upon high-temperature tempering and of electrically saturated with hydrogen in the electrochemical cell during 12 hours is investigated. The stress-strain curves for each state were obtained. From the stress-strain curves, one can conclude that hydrogen markedly reduces the elongation to the fracture of specimen. Using double-exposed speckle photography method it was found that the plastic flow of the material is of a localized character. The pattern distribution of localized plastic flow domains at the linear hardening stage was investigated. Comparative study of autowave parameters was carried out for the tempered steel as well as the electrically saturated with hydrogen steel

Results of analyzing the passport database ‘Spring bread wheat landraces in the VIR collection’

Background. Recently, an increased interest in crop landraces has been observed among scientists working with plant genetic resources (PGR). Institutes have been organizing collecting missions to explore old varieties still cultivated locally. Attention paid to landraces is also associated with the introduction of GIS technologies into PGR studies. The N. I. Vavilov All-Russian Institute of Plant Genetic Resources (VIR) holds a unique collection of spring bread wheat landraces. One of the Institute’s top priorities is to develop and maintain a passport database, using a set of fields specifically fit for landraces.Analysis of the passport database. The passport database ‘Spring Bread Wheat Landraces in the VIR Collection’ is analyzed here. The database contains information on 5,925 accessions and has 36 fields. Statistical data are presented for the main fields: origin, collection site, botanical variety, year of registration in the collection, donor institute or expedition, and collector’s name

Ranking of spring bread wheat genotypes according to the heading date and growing season duration in different ecogeographic environments

Background. Adaptation of spring bread wheat cultivars to climate change requires a study of the factors affecting the length of their growing season in various environments. An attempt is made to analyze regularities in the effect of ecogeographic conditions on the correlations shown by the duration of the growing season and interphase periods in spring bread wheat genotypes.Materials and methods. Correlation coefficients were studied for the impact of the environment and temperature on the duration of the interphase periods from sprouting to heading (SH) and from heading to yellow ripeness (HR) versus the period from sprouting to yellow ripeness (SR) in VIR’s wheat collection across 18 sites located in Russia and Uzbekistan from 41 to 60°N and from 30 to 135°E. The effect of the genotype and year on SH and HR was studied, and agrometeorological regression models of SH and HR were constructed, based on the data obtained during the studies of the collection in St. Petersburg in 1945–2021.Results. For the sites below 52–54°N, the SR/SH correlation coefficient was generally higher than SR/HR, and in the upper latitudes it was vice versa. The change in the ratio of coefficients occurred due to an increase in the interannual variability of HR at lower temperatures. The effect of HR on SR became greater than that of SH at temperatures below 18°С during HR. The data of a long-term study in St. Petersburg demonstrated that the effect of the genotype on SH was 18.9%, with 68.9% of the year, and the effect of the factors on HR was 4.1 and 71.3%, respectively. Regression models showed that HR was determined by temperature for at least 81%, while SH had a lower coefficient of determination by weather (56%).Conclusion. Ranking of wheat genotypes according to their heading time reflected their differentiation in earliness. A significant contribution of HR was conspicuous under temperatures below 18°C after heading at latitudes above 52–54°N

Nernst-Ettingshausen effect in two-component electronic liquids

A simple model describing the Nernst-Ettingshausen effect (NEE) in two-component electronic liquids is formulated. The examples considered include graphite, where the normal and Dirac fermions coexist, superconductor in fluctuating regime, with coexisting Cooper pairs and normal electrons, and the inter-stellar plasma of electrons and protons. We give a general expression for the Nernst constant and show that the origin of a giant NEE is in the strong dependence of the chemical potential on temperature in all cases

Synthesis, Single Crystal Growth, and Properties of Cobalt Deficient Double Perovskite EuBaCo2-xO6-delta (x=0-0.1)

The cobalt deficient double perovskites EuBaCo2−xO6−δ with x=0–0.1 were obtained both as powders and as single crystal. Formation of cobalt vacancies in their crystal lattice was shown to be accompanied by the formation of oxygen ones. Chemical lattice strain caused by this cooperative disordering of cobalt and oxygen sublattices was found to be isotropic contrary to that caused by the formation of oxygen vacancies only. Cobalt deficiency was also shown to lead to lowering overall conductivity and Seebeck coefficient of EuBaCo2−xO6−δ double perovskites as a result of simultaneous decrease of charge carriers’ concentration and their mobility as well as number of sites available for electrons and holes transfer. Strong anisotropy of the overall conductivity of the single crystal double perovskites EuBaCo2−xO6−δ was found and explained on the basis of preferential location of oxygen vacancies in the rare-earth-oxygen- (REO-) planes

Thermodynamics of Formation of Solid Solutions between BaZrO3 and BaPrO3

Received: 30.03.2020. Accepted: 11.05.2020. Published: 30.06.2020.A linear relationship between the standard enthalpy of formation from binary oxides, ΔfH°ox, and the Goldschmidt tolerance factor, t, for some AIIBIVO3 (A = Ca, Sr, Ba; B = Ti, Zr, Hf, Ce, Pr, Tb, U, Pu, Am) perovskite oxides was used for estimation of ΔfH°ox of Pr-substituted barium zirconates BaZr1–xPrxO3. A dependence of the relative change of the standard entropies, S°298, on the relative change of the molar volumes in the reactions of formation of AIIBIVO3 (A = Ca, Sr, Ba; B = Ti, Zr, Hf, Ce) from binary oxides was also found to be linear. Using this dependence, a relatively precise method of estimating S°298 was proposed, and S°298 of BaPrO3 was calculated as (162.8 ± 2.8) J·mol–1·K–1. Knowing S°298 of BaPrO3 and using the literature data for S°298 of BaZrO3, the values of S°298 of BaZr1–xPrxO3 were predicted on the assumption that BaZr1–xPrxO3 is a regular or ideal solution of BaPrO3 in BaZrO3 as evidenced by the very small enthalpy of mixing calculated based on the estimated ΔfH°ox. The values of standard entropy changes, ΔfS°ox, and Gibbs energy changes, ΔfG°ox, for the reactions of formation of BaZr1–xPrxO3 from BaO, ZrO2 and PrO2 were also estimated. Substituting Pr for Zr in BaZr1–xPrxO3 results in ΔfH°ox and ΔfG°ox becoming more positive, indicating the decrease of the relative stability with respect to the corresponding binary oxides. Expanded uncertainties of the estimated values of ΔfH°ox and ΔfG°ox are equal to 14 kJ · mol–1, and those of S°298 and ΔfS°ox — less than 2.8 J · mol–1·K–1 and 3.5 J · mol–1·K–1, respectively, for BaZr1–xPrxO3 (x = 0.0–1.0).This work was supported by the Russian Science Foundation (project No. 18‑73‑00022)