The Russian consumer sector: estimation technology

The article describes the methodology for estimating the Russia’s consumer sector and the effect of its application. The monitoring procedure of the Russian consumer sector groups indicators into two units: the unit of the estimation of consumer goods and the services market estimation unit. The estimation unit of consumer goods is composed of two modules: food products and non-food products. This module offers two components that provide an estimation of the consumer sector: marketing (estimates the accessibility of retail trade and services for end users) and production (estimates the domestic manufacture). The results of the estimation show general improvements in the consumer sector in the period of 2000–2014, but overall development is evaluated as low. The analysis revealed that the financing is growing faster than the quality indices of development. As an example, the financing of agriculture has increased by 1.5 times over 15 years (against comparable prices from 2000), while agricultural production has not changed. Another most pressing challenge is the weak differentiation of the Russian economy, as evidenced by the low rates of non-food production (availability of non-foods of own production remains at a low level and averages 20 %). The results of the estimation suggest the need to reform the regulation of the sector primarily concerning priorities for its development and improvement of financial and economic mechanisms to achieve them.The research has been supported by the Russian Science Foundation Gran, the project № 15–18–10014 " Projection of optimal socio-economic systems in the turbulence of external and internal environment"

Structural phase transition and dielectric relaxation in Pb(Zn1/3Nb2/3)O3 single crystals

The structure and the dielectric properties of Pb(Zn1/3Nb2/3)O3 (PZN) crystal have been investigated by means of high-resolution synchrotron x-ray diffraction (with an x-ray energy of 32 keV) and dielectric spectroscopy (in the frequency range of 100 Hz - 1 MHz). At high temperatures, the PZN crystal exhibits a cubic symmetry and polar nanoregions inherent to relaxor ferroelectrics are present, as evidenced by the single (222) Bragg peak and by the noticeable tails at the basis of the peak. At low temperatures, in addition to the well-known rhombohedral phase, another low-symmetry, probably ferroelectric, phase is found. The two phases coexist in the form of mesoscopic domains. The para- to ferroelectric phase transition is diffused and observed between 325 and 390 K, where the concentration of the low-temperature phases gradually increases and the cubic phase disappears upon cooling. However, no dielectric anomalies can be detected in the temperature range of diffuse phase transition. The temperature dependence of the dielectric constant show the maximum at higher temperature (Tm = 417 - 429 K, depending on frequency) with the typical relaxor dispersion at T < Tm and the frequency dependence of Tm fitted to the Vogel-Fulcher relation. Application of an electric field upon cooling from the cubic phase or poling the crystal in the ferroelectric phase gives rise to a sharp anomaly of the dielectric constant at T 390 K and diminishes greatly the dispersion at lower temperatures, but the dielectric relaxation process around Tm remains qualitatively unchanged. The results are discussed in the framework of the present models of relaxors and in comparison with the prototypical relaxor ferroelectric Pb(Mg1/3Nb2/3)O3.Comment: PDF file, 13 pages, 6 figures collected on pp.12-1

Horizontal non-vanishing of Heegner points and toric periods

Let $F/\mathbb{Q}$ be a totally real field and $A$ a modular \GL_2-type abelian variety over $F$. Let $K/F$ be a CM quadratic extension. Let $\chi$ be a class group character over $K$ such that the Rankin-Selberg convolution $L(s,A,\chi)$ is self-dual with root number $-1$. We show that the number of class group characters $\chi$ with bounded ramification such that $L'(1, A, \chi) \neq 0$ increases with the absolute value of the discriminant of $K$. We also consider a rather general rank zero situation. Let $\pi$ be a cuspidal cohomological automorphic representation over \GL_{2}(\BA_{F}). Let $\chi$ be a Hecke character over $K$ such that the Rankin-Selberg convolution $L(s,\pi,\chi)$ is self-dual with root number $1$. We show that the number of Hecke characters $\chi$ with fixed $\infty$-type and bounded ramification such that $L(1/2, \pi, \chi) \neq 0$ increases with the absolute value of the discriminant of $K$. The Gross-Zagier formula and the Waldspurger formula relate the question to horizontal non-vanishing of Heegner points and toric periods, respectively. For both situations, the strategy is geometric relying on the Zariski density of CM points on self-products of a quaternionic Shimura variety. The recent result \cite{Ts, YZ, AGHP} on the Andr\'e-Oort conjecture is accordingly fundamental to the approach.Comment: Adv. Math., to appear. arXiv admin note: text overlap with arXiv:1712.0214

On gauge-invariant Green function in 2+1 dimensional QED

Both the gauge-invariant fermion Green function and gauge-dependent conventional Green function in $2+1$ dimensional QED are studied in the large $N$ limit. In temporal gauge, the infra-red divergence of gauge-dependent Green function is found to be regulariable, the anomalous dimension is found to be $\eta= \frac{64}{3 \pi^{2} N}$. This anomalous dimension was argued to be the same as that of gauge-invariant Green function. However, in Coulomb gauge, the infra-red divergence of the gauge-dependent Green function is found to be un-regulariable, anomalous dimension is even not defined, but the infra-red divergence is shown to be cancelled in any gauge-invariant physical quantities. The gauge-invariant Green function is also studied directly in Lorentz covariant gauge and the anomalous dimension is found to be the same as that calculated in temporal gauge.Comment: 8 pages, 6 figures, to appear in Phys. Rev.