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The effect of violation of $T$-invariance, provided that $P$-parity is preserved, is given by the total cross section of the interaction of a vector-polarized particle with a tensor-polarized target. A formalism for calculating this effect developed previously and based on the spin-dependent Glauber theory of elastic $pd$ scattering is used here to calculate the effect under discussion in the range of collision energies corresponding to the invariant mass of the $pN$ system $\sqrt{s_{pN}}=5$--$30$ GeV. The spin-dependent amplitudes of elastic $pN$ scattering required for this calculation are taken from existing phenomenological models for $pN$ scattering in the energy region considered., Comment: 8 pages, 1 figure;in Russian, presented at Scientific session of Nuclear Physics section of Physics Division of RAS, submitted to PEPAN

The author proposed an elementary derivation of the formula of Yu.V. Nesterenko expansion in continued fraction of a number 2*$\zeta(3)$., Comment: in Russian language

The paper studies the quantum action for the five-dimensional real $\phi^3$-theory in the case of a general formulation using the background field method. The three-loop renormalization is performed with the usage of a cutoff regularization in the coordinate representation. The explicit form of the first three coefficients for the renormalization constants is presented. The absence of non-local singular contributions and partial results for the fourth correction are discussed., Comment: LaTeX, 20 pages, 5 figures. Firstly appeared in Russian, April 9, 2024, see https://www.pdmi.ras.ru/preprint/2024/24-05.html

We generalize methods, developed by S. Ghilardi, and apply them to a subsystem J$_2$ of bimodal provability logic GLB. We describe projective formulas in J$_2$ in terms of Kripke semantics and prove that logic J$_2$ has finitary unification type. As an application, we show that admissibility problem for J$_2$ is decidable., Comment: In Russian, 20 pages

The paper presents various modifications of the Frank-Wolfe algorithm in the equilibrium traffic assignment problem. The Beckman model is used as a model for experiments. In this article, first of all, attention is paid to the choice of the direction of the basic step of the Frank-Wolfe algorithm. Algorithms will be presented: Conjugate Frank-Wolfe (CFW), Bi -conjugate Frank-Wolfe (BFW), Fukushima Frank-Wolfe (FFW). Each modification corresponds to different approaches to the choice of this direction. Some of these modifications are described in previous works of the authors. In this article, following algorithms will be proposed: N-conjugate Frank-Wolfe (NFW), Weighted Fukushima Frank-Wolfe (WFFW). These algorithms are some ideological continuation of the BFW and FFW algorithms. Thus, if the first algorithm used at each iteration the last two directions of the previous iterations to select the next direction conjugate to them, then the proposed algorithm NFW is using more than N previous directions. In the case of Fukushima Frank-Wolfe, the average of several previous directions is taken as the next direction. According to this algorithm, a modification WFFW is proposed, which uses a exponential smoothing from previous directions. Experiments with various modifications were carried out on several datasets representing urban structures and taken from publicly available sources. The relative gap value was taken as the quality metric. The experimental results showed the advantage of algorithms using the previous directions for step selection over the classic Frank-Wolfe algorithm. In addition, an improvement in efficiency was revealed when using more than two conjugate directions. For example, on various datasets, the modification 3FW showed the best convergence. In addition, the proposed modification WFFW often overtook FFW and CFW, although performed worse than NFW., Comment: 14 pages, in Russian language, 8 figures

The Molchanov's condition is a necessary condition for the compactness of the resolvent for a wide class of ordinary differential operators of arbitrary order, but for the Sturm-Liouville operator it is not sufficient, even if the real part of the potential is non-negative. Molchanov's criterion remains valid in the formulation closest to the original one for potentials that take values in a narrower sector than the half-plane, separated from the negative half-axis. This work is devoted to these questions., Comment: in Russian language

In a two-dimensional approximation, the probability density and current for a photoelectron near the localization of a quantum vortex are theoretically investigated. The wave function in the momentum representation, which we found earlier, is simplified near zero, corresponding to the center of the vortex. This allows us to obtain a simple analytical expression for it, which has the structure of a Gaussian wave packet and contains basic information about the vortex. It is used to analyze the temporal evolution of a quantum vortex, both in momentum and coordinate space. The effect of the intensity of an ionizing ultrashort laser pulse on the shape of a quantum vortex is also investigated., Comment: in Russian language

The phase formation of terbium chromium borate in melt solutions based on bismuth trimolybdate and lithium tungstate was studied. It was shown that there is no trigonal phase of terbium chromium borate in a system based on bismuth trimolybdate at all component ratios. The ratio of components of a system based on lithium tungstate has been found, at which trigonal TbCr$_3$(BO$_3$)$_4$ crystals are formed at temperatures above 1100$^\circ$C, and below this temperature only a monoclinic phase is formed. The X-ray properties of the grown crystals were studied., Comment: 12 pages, in Russian language, 1 table

The detector DANSS is located under n industrial nuclear reactor at Kalininskaya Nuclear Power Plant. This location provides ~ 50 m.w.e. reduction of the cosmic muon flux in the vertical direction, which places the experiment in an intermediate position between ground and underground experiments in terms of shielding from the cosmic rays. The detector DANSS is located under an industrial nuclear reactor at Kalininskaya Nuclear Power Plant. This location provides ~50 m.w.e. reduction of the cosmic muon flux in the vertical direction, which places the experiment in an intermediate position between ground and underground experiments in terms of shielding from the cosmic rays. The detector's sensitive area consists of 2500 plastic scintillator counters, each 100x4x1 cm$^3$ in size, making in total a 1 m$^3$ volume, which is surrounded by a muon veto system and multiple layers of passive shielding. The main goal of the DANSS experiment is to study the antineutrino spectra at different distances from the source. For this purpose the detector is placed on a lifting platform, and the data is collected at three positions: 10.9 m, 11.9 m and 12.9 m from the center of the reactor core. The detector is capable of reconstructing muon tracks passing though the sensitive volume. In this work the barometric, height and temperature correlation coefficients are calculated in three areas of the zenith angle $\theta$ using the Duperier approach. These results are based on the muon data collected during four years., Comment: 7 pages, 3 figures, submitted to JETP letters (in Russian)

The work deals with the qualification of semidiscrete hyperbolic type equations. We study a class of equations of the form $$\frac{du_{n+1}}{dx}=f\left(\frac{du_{n}}{dx},u_{n+1},u_{n}\right),$$ here the unknown function $u_n(x)$ depends on one discrete $n$ and one continuous $x$ variables. Qualification is based on the requirement of the existence of higher symmetries. The case is considered when the symmetry is of order 5 in continuous directions. As a result, a list of four equations with the required conditions is obtained. For one of the found equations, a Lax representation is constructed., Comment: 11 pages (in Russian)

We present new completeness conditions for exponential systems on the complex plane in Banach algebras of continuous functions on a compact with a connected complement that are simultaneously holomorphic in the interior of this compact if it is nonempty, as well as in spaces of holomorphic functions on a simply connected bounded domain with a topology of uniform convergence on compact subsets. These conditions are formulated in terms of the Euclidean area of the convex hull of a compact or a region on the one hand, and new characteristics of the distribution of exponential system indicators on the other., Comment: 10 pages, in Russian

The deployment of the Baikal-GVD deep underwater neutrino telescope is continuing in Lake Baikal. By April 2022, ten clusters of the telescope were put into operation, with 2880 optical modules in total. One of the relevant tasks in this context is to study the possibilities of increasing the efficiency of the detector based on the experience of its operation and the results obtained at other neutrino telescopes in recent years. In this paper, a variant of optimizing the configuration of the telescope is considered, based on the installation of additional strings of optical modules between the clusters (external strings). An experimental version of the external string was installed in Lake Baikal in April 2022. This paper presents a first estimate of the impact of adding external strings on the neutrino detection efficiency, as well as the technical implementation of the detection and data acquisition systems of the external string and first results of its in-situ tests., Comment: 12 pages, in Russian language, 7 figures, 1 Table

We present a method of creation of photonic structures whose optical spectrum of the reflection coefficient has an arbitrary shape and has predetermined features. We develop an algorithm for the construction of a photonic crystal structure, perform numerical simulation of its reflection spectra, and create an experimental sample of a photonic crystal that has a spectral response corresponding to a given shape., Comment: in Russian language

A method for solving the inverse problem of designing the structure of a one-dimensional photonic crystal is proposed and experimentally implemented. It is known that a one-dimensional photonic crystal with a spatial sinusoidal modulation of the refractive index, has a narrow photonic bandgap at a frequency related to the spatial frequency of this sinusoid. We propose a reverse engineering method for one-dimensional photonic crystals with an arbitrary given reflection spectrum by expanding this spectrum into elementary photonic band gaps and then summing them. This paper shows the application of this method to fabricate examples of photonic crystals with simple shapes of spectral reflection curves., Comment: in Russian language

Let $D$ be a domain in a finite-dimensional Euclidean space, and $H$ be a convex subcone in the convex cone of all subharmonic functions on $D$. We obtain a criterion for the existence of a lower envelope from $H$ for an arbitrary function from $H-H$., Comment: 9 pages, in Russian

We give a new scale of completeness conditions for exponential systems in two types of functional spaces on subsets of the complex plane. The first is the Banach spaces of functions that are continuous on a compact and simultaneously holomorphic in the interior of this compact, if this interior is nonempty, with a uniform norm. The second is the spaces of holomorphic functions on a bounded open set with a topology of uniform convergence on compacts. These conditions are formulated in terms of the perimeter of the convex hull of the domain of determining of functions from space and new characteristics of distribution of exponents of exponential system., Comment: 12 pages, in Russian

In this paper, a classification of semidiscrete equations of hyperbolic type is carried out. We study the class of equations of the form $$\frac{du_{n+1}}{dx}=f\left(\frac{du_{n}}{dx},u_{n+1},u_{n}\right),$$ here is the unknown function $u_n (x)$ depends on one discrete $n$ and one continuous $x$ variables. The classification is based on the requirement for the existence of higher symmetries in the discrete and continuous directions. The case is considered when the symmetries are of order 3 in both directions. As a result, a list of equations with the required conditions is obtained., Comment: 15 pages (in Russian)

Diophantine exponents are ones of the simplest quantitative characteristics responsible for the approximation properties of linear subspaces of a Euclidean space. This survey is aimed at describing the current state of the area of Diophantine approximation which studies Diophantine exponents and relations they satisfy. We discuss classical Diophantine exponents arising in the problem of approximating zero with the set of the values of several linear forms at integer points, their analogues in Diophantine approximation with weights, multiplicative Diophantine exponents, and Diophantine exponents of lattices. We pay special attention to the transference principle., Comment: v3 is in Russian, v4 is in English

We prove a version of the Beurling-Malliavin multiplier theorem. This version is formulated here in a simplified form. Let $u\not\equiv -\infty$ and $M\not\equiv -\infty$ be a pair of subharmonic functions on the complex plane $\mathbb C$ with positive parts $u^+:=\sup\{u,0\}$ and $M^+$ such that $$ \operatorname{type}[u]:=\limsup_{z\to \infty} \frac{u^+(z)}{|z|}<+\infty, \qquad \operatorname{type}[M]<+\infty, \qquad \int_{-\infty}^{+\infty}\frac{u^+(x)+M^+(x)}{1+x^2}\operatorname{d}x<+\infty. $$ If $\operatorname{type}[u]

We establish a criterion for the completeness of an exponential system in the spaces of functions continuous on a convex compact set and holomorphic in the interior of this compact set, as well as in the spaces of holomorphic functions in the convex domain in terms of the breadth of the compact set or the domain in the direction. The main results are formulated exclusively through the relations between the breadth in the direction, width or diameter of the compact set or domain on the one hand and the logarithmic submeasures or logarithmic block densities of the distribution of exponents of exponential system on the other., Comment: 10 pages, in Russian

In this paper we study the three-dimensional analogue of the relation between the irrationality exponent of a real number and the growth of its regular continued fraction partial quotients. As a multidimensional generalisation of continued fractions, we consider Klein polyhedra., Comment: In Russian

The goal of the paper is establishing the approximation of mixed partial derivatives of the second order of a function of several variables via modified Bernstein polynomials in the $L_1$ norm under the minimal regularity., Comment: 28 pages, in Russian language, 21 references; in comparison to the v2 version, the text was rearranged and polished significantly, and one important historical reference was added

Let $Z$ and $W$ are distributions of points on the complex plane $\mathbb C$. The following problem goes back to the studies of F. Carlson, T. Carleman, L. Schwartz, A. F. Leont'ev, B. Ya. Levin, J.-P. Kahane and others. For which $Z$ and $W$ for an entire function $g\neq 0$ of exponential type vanishing on $W$, there is an entire function $f\neq 0$ of exponential type vanishing on $Z$ such that $|f|\leq |g|$ on the imaginary axis? The classical Malliavin-Rubel theorem of the early 1960s completely solves this problem for "positive" $Z$ and $W$ lying only on the positive semiaxis. A number of generalizations of this criterion were established by us in the late 1980s for "complex" $Z\subset\mathbb C$ and $W\subset\mathbb C$ separated by angles from the imaginary axis, with some advances in the 2020s. In this paper, tougher problems are solved in a more general subharmonic framework for distributions of masses on $\mathbb C$. All the previously mentioned results can be obtained from the main results of the paper in a much stronger form even in the initial formulation for distributions of points $Z$ and $W$ and entire functions $f$ and $g$ of exponential type. Some of the results of the article are closely related to the famous Beurling-Malliavin theorems on the radius of completeness and the multiplier., Comment: 49 pages, in Russian

We consider two balayage constructions on the complex plane $\mathbb C$ with real axis $\mathbb R$ for $0\leq b\in \mathbb R$. Let $u\not\equiv -\infty$ be a subharmonic function on $\mathbb C$ of order $$\operatorname{ord}[u]:=\limsup_{z\to \infty} \frac{\ln \max\{1,u(z)\}}{\ln |z|}\leq 1,$$ $U=u-v$ be the difference of subharmonic functions $u$ and $v\not\equiv -\infty$ on $\mathbb C$ with $\operatorname{ord}[v]\leq 1$, i.e., $\delta$-subharmonic function on $\mathbb C$ of order $\operatorname{ord}[U]\leq 1$. Then there is a $\delta$-subharmonic function $V\not\equiv \pm\infty$ on $\mathbb C$ of order $\operatorname{ord}[V]\leq 1$ such that $V$ is harmonic on $\bigl\{ z \in \mathbb C\bigm| |\Re z|> b\bigr\}$ and $U(z)\equiv V(z)$ for all $z\in \bigl\{ z \in \mathbb C\bigm| |\Re z|\leq b\bigr\}\setminus E$ where $E\subset \mathbb C$ is polar. If $u$ is a subharmonic function of finite type under order $1$, i.e., $$\limsup_{z\to \infty} \frac{u(z)}{|z|}<+\infty,$$ then there exist subharmonic functions $u_{\mathbb R}$ and $u_b$ of finite type under order $1$ that are harmonic respectively on $\mathbb C\setminus \mathbb R$ and $\bigl\{ z \in \mathbb C\bigm| |\Re z|> b\bigr\}$ such that $$\begin{cases} u(z)\equiv u_{\mathbb R}(z)+u_b(z) \text{ for all $z\in {\mathbb R}\bigcup \bigl\{ z \in \mathbb C\bigm| |\Re z|\leq b\bigr\}$},\\ u(z)\leq u_{\mathbb R}(z) + u_b(z) \text{ for each $z\in \mathbb C$.}\end{cases}$$ At the same time, we trace special relationships between the various logarithmic characteristics of the Riesz mass and charge distributions of subharmonic and $\delta$-subharmonic functions., Comment: 13 pages, in Russian

Let $\nu$ be a charge distribution on the complex plane $\mathbb C$, i.e. the real Radon measure on $\mathbb C$ with total variation $|\nu|$. The charge distribution $\nu$ is of finite upper density under order of $1$ if $$ \limsup_{0

Let $u\not\equiv -\infty$ be a subharmonic function on the complex plane $\mathbb C$. Then for any function $r\colon\mathbb C\to (0,1]$ satisfying the condition $$\inf_{z\in\mathbb C}\frac{\ln r(z)}{\ln(2+|z|)}>-\infty,$$ there is an entire function $f\not\equiv 0$ such that $$ \ln |f(z)|\leq \frac{1}{2\pi}\int_0^{2\pi}u(z+r(z)e^{i\theta})\,{\mathrm d}\theta\quad\text{for all $z\in\mathbb C$.}$$ A similar result is established for subharmonic functions of finite order with inequalities of the form $\ln|f(z)|\leq u(z)$ at all points $z\in\mathbb C\setminus E$, where the exceptional set $E$ is small in terms of $d$-dimensional Hausdorff content of $E$ with variable radius $r$., Comment: 11 pages, in Russian

The article provides a review of the publications on the current trends and developments in Dempster-Shafer theory and its different applications in science, engineering, and technologies. The review took account of the following provisions with a focus on some specific aspects of the theory. Firstly, the article considers the research directions whose results are known not only in scientific and academic community but understood by a wide circle of potential designers and developers of advanced engineering solutions and technologies. Secondly, the article shows the theory applications in some important areas of human activity such as manufacturing systems, diagnostics of technological processes, materials and products, building and construction, product quality control, economic and social systems. The particular attention is paid to the current state of research in the domains under consideration and, thus, the papers published, as a rule, in recent years and presenting the achievements of modern research on Dempster-Shafer theory and its application are selected and analyzed., Comment: 11 pages, in Russian. Artificial intelligence and decision making. 2018. N 4

We obtaine the full characterization of proper closed invariant subspaces of a generalized backward shift operator (Pommiez operator) in the Frechet space of all holomorphic functions on a simply connected domain $\Omega$ of the complex plane, containing the origin. In the case when the function, which defines this operator, is not has zeros in $\Omega$ all such subspaces are finite-dimensional. If additionally $\Omega $ coincides with the complex plane, then the considered operator is unicellular. If this function has zeros in $\Omega $, then the family of mentioned invariant subspaces splits into two classes: the first consists of finite-dimensional subspaces, and the second of infinite-dimensional ones., Comment: 19 pages, in Russian

Let $G$ be a nonempty bounded domain in a finite-dimensional Euclidean space. The main results are general estimates from below at points from $G$ for an arbitrary subharmonic function $u\not\equiv -\infty$ on the closure of the domain $G$ through the maximum of the function $u$ on the boundary of the domain $G$. These results are new for planar domains $G$, and for intervals of $G$ on the numerical line have also not been previously noted. They show that the Harnack distance plays a key role in these estimates. Further applications to subharmonic, convex, holomorphic functions, as well as to meromorphic functions and differences of subharmonic functions in domains of a particular type are supposed to be outlined in the continuation of this article., Comment: 11 pages, in Russian

A new algorithm for estimating the time-varying frequency of a noiseless sinusoidal signal is considered. It is assumed that the amplitude and frequency of the sinusoidal signal are unknown functions of time, but are solutions of linear stationary differential equations with known parameters. The problem is solved using gradient tuning algorithms based on a linear regression equation obtained by parameterizing the original nonlinear sinusoidal signal. The example presented in the article and the results of computer modeling illustrate the efficiency of the proposed algorithm, as well as explain the procedure for its synthesis., Comment: in Russian

In this note, we consider two types of estimates for the Harnack distance in bounded domains of a finite-dimensional Euclidean space. The first type is based on the geometric concept of the entropy of arcwise connectedness. We used this concept earlier to study zero sets of holomorphic functions in weighted classes of holomorphic functions. The second type is based on the concept of separatedness for subsets in domain, which is introduced in this note. The latter concept, generally speaking, can be more subtle., Comment: 7 pages, in Russian

Additional integral inequalities are obtained for integrals of the differences of subharmonic functions by Borel measures on balls in a multidimensional Euclidean space. These integrals are still estimated from above through the Nevanlinna characteristic and various characteristics of the Borel measure and its support. All the results are also new for logarithms of modules of meromorphic functions on discs in the complex plane. Integration by Borel measures with a support on fractal sets is allowed, and estimates in these cases are given by the Hausdorff measure and the Hausdorff content for the support of the Borel measure. We consider separately important for applications special cases of functions in the entire complex plane and space, in the unit disc or ball, as well as cases of integration over length on subsets of Lipschitz curves and over area on subsets of Lipschitz hypersurfaces., Comment: 16 pages, in Russian

We supplement the result of the first part of the work with estimates of the integrals of the difference of subharmonic functions in measure with some deterioration of the absolute constants, but these estimates have the form of a criterion, which is formulated exclusively in terms of the measure and its potential. This criterion is also new for meromorphic functions on the complex plane., Comment: 12 pages, in Russian

We obtain new integral inequalities for the integrals of the difference of subharmonic functions in measure through their Nevanlinna characteristic and some functional characteristic of the measure. These results are new also for meromorphic functions. Let us illustrate the main result for the case of a meromorphic function. We denote by $D_z(r)$ a closed disc of radius $r$ centered at $z$ in the complex plane $\mathbb C$. Let $\mu\geq 0$ be a Borel measure on $D_0(r)$, and $M:=\mu(D_0(r))<+\infty$. The modulus of continuity of measure $\mu$ is the function $h(t):=\sup_{z\in \mathbb C}\mu(D_z(t)), \quad t\geq 0.$ Suppose that $\int_0\frac{h(t)}{t} dt<+\infty$. Let $f\neq 0$ be a meromorphic function on a neighbourhood of $D_0(R)$ of radius $R>r$ with $f(0)\in \mathbb C$ and the Nevanlinna characteristic $T_f$ . Then there is $$\int \ln^+|f| \,d\mu \leq 2\frac{R+r}{R-r}T_f(R)M\biggl(1+\int_0^{R+r}\frac{h(t)}{t} dt\biggr).$$, Comment: 14 pages, in Russian

Let $Z$ and $W$ be a pair of point distributions of finite upper density on the complex plane $\mathbb C$ with the real axis $\mathbb R$. We give several variants of necessary and at the same time sufficient conditions for their arrangement, under which for every entire function of exponential type $g\neq 0$ vanishing on $W$, there is, respectively, either an entire function of exponential type $f\neq 0$ vanishing on $Z$ and satisfies one of the two variants of the constraints: 1) $|f(iy)|\leq |g(iy)|$ at each $y\in \mathbb R$, i.e. everywhere on the imaginary axis $i\mathbb R$, 2) $\ln |f(iy)|\leq \ln |g(iy)|+o(|y|)$ as $y\to \pm \infty$, or for any number $\varepsilon >0$ there is an entire function of exponential type $f\neq 0$ vanishing on $Z$ and satisfies the inequality $\ln \bigl|f(iy)\bigr|\leq \ln \bigl|g(iy)\bigr|+\varepsilon |y|$ for all $y\in \mathbb R\setminus E$, where $E\subset \mathbb R$ is a set of finite linear Lebesgue measure. Our study is carried out within the framework of generalization of the development of the classical theorem of P. Malliavin and L.A. Rubel of the 1960s, where the case of the location of $Z\subset \mathbb R^+$ and $W\subset \mathbb R^+$ on the positive semiaxis $\mathbb R^+\subset \mathbb R$ is considered. Our criteria are given in terms of special logarithmic characteristics and (sub)measures for $Z$ and $W$. At the same time, in the third variant, there are no additional requirements for $Z$ and $W$, but in the first and second variants, we require the asymptotic separation of $Z$ and $W$ by angles from the imaginary axis together with the Lindel\"of-type condition for $W$ along the imaginary axis $iR$ on a certain symmetry of the imaginary parts of $1/w$ for $w\in W$ in the form $\Bigl|\sum_{1\leq |w|\leq r}\Im (1/w)\Bigr|=O(1)$ as $r\to +\infty$., Comment: 14 pages, in Russian

In the early 1960s, P. Malliavin and L. A. Rubel gave a complete description of pairs of distributions of positive points $Z$ and $W$ such that for each entire function of exponential type $g\neq 0$ that vanishes on $W$, there is an entire function of exponential type $f\neq 0$ such that $f$ vanishes on $Z$ and satisfies the inequality $|f|\leq |g|$ everywhere on the imaginary axis. We extend this result to much more general distributions of complex points $Z$ and $W$ lying outside of some pair of vertical angles containing the imaginary axis as the points approach $\infty$., Comment: 6 pages, in Russian

Let $U\not\equiv \pm\infty$ be a $\delta$-subharmonic function on a closed disc of radius $R$ centered at zero. In the previous two parts of our paper, we obtained general and explicit estimates of the integral of the positive part of the radial maximum growth characteristic ${\mathsf M}_U(t):= \sup\bigl\{U(z)\bigm| |z|=r\bigr\}$ over the increasing integration function $m$ on the segment $[0, r]\subset [0,R)$ through the difference characteristic of Nevanlinna and the quantities associated with the integration function $m$. The third part of our paper contains estimates of these quantities in terms of the Hausdorff $h$-measure and $h$-content of compact subset $S\subset [0, r]$ such that the integration function $m$ is constant on each open component of the connectivity of the complement $[0, r]\setminus S$. The case of the d-dimensional Hausdorff measure is highlighted separately., Comment: 9 pages, in Russian

Let $U\not\equiv \pm\infty$ be the difference of subharmonic functions, i.e., a $\delta$-subharmonic function, on a closed disc of radius $R$ centered at zero. In the preceding first part of our paper, we obtained general estimates for the integral of the positive part of the radial maximum growth characteristic ${\mathsf M}_U(t):=\sup\bigl\{U(z)\bigm| |z|=r\bigr\}$ over the increasing integration function $m$ on the segment $[0, r]$ via the Nevanlinna difference characteristic and the modulus of continuity of the function $m$. The second part of the work gives an explicit view for such estimates, provided that the modulus of continuity of the function $m$ does not exceed some differentiable function $h$ on the open interval $(0,r)$ with the only condition $\sup\limits_{t\in (0,r)}\dfrac{h(t)}{th'(t)}<+\infty$. This condition is satisfied by any power functions $t\mapsto t^d$ of degree $d>0$. The estimates are optimal in a certain sense., Comment: 7 pages, in Russian

Let $f$ be a meromorphic function on the complex plane $\mathbb C$ with the maximum function of its modulus $M(r,f)$ on circles centered at zero of radius $r$. A number of classical, well-known and widely used results allow us to estimate from above the integrals of the positive part of the logarithm $\ln^+M(t,f)$ over subsets of $E\subset [0,r]$ via the Nevanlinna characteristic $T(r,f)$ and the linear Lebesgue measure of the set $E$. The paper gives similar estimates for the Lebesgue-Stieltjes integrals of $\ln^+M (t,f)$ over the increasing integration function of $m$. The main part of the presentation is conducted immediately for the differences of subharmonic functions on closed discs with the center at zero, i.e, $\delta$-subharmonic functions. The only condition in the main theorem is the Dini condition for the modulus of continuity of the integration function $m$. This condition is, in a sense, necessary. Thus, the first part of the work to a certain extent completes in a general form the research on the upper estimates of the integrals of the radial maximum growth characteristics of arbitrary meromorphic and $\delta$-subharmonic functions through the Nevanlinna characteristic with its versions and through the characteristics of the integration function $m$., Comment: 15 pages, in Russian

The paper presents a solution for the problem of choosing a method for analytical determining of weight factors for a genetic algorithm additive fitness function. This algorithm is the basis for an evolutionary process, which forms a stable and effective query population in a search engine to obtain highly relevant results. The paper gives a formal description of an algorithm fitness function, which is a weighted sum of three heterogeneous criteria. The selected methods for analytical determining of weight factors are described in detail. It is noted that expert assessment methods are impossible to use. The authors present a research methodology using the experimental results from earlier in the discussed project "Data Warehouse Support on the Base Intellectual Web Crawler and Evolutionary Model for Target Information Selection". There is a description of an initial dataset with data ranges for calculating weights. The calculation order is illustrated by examples. The research results in graphical form demonstrate the fitness function behavior during the genetic algorithm operation using various weighting options., Comment: 9 pages, in Russian

In this paper the Mittag-Leffler function is given through the exponential functions for any rational derivatives of m/n order, where m1 are natural irreducible numbers (if n=1 then m is also equal to unity). Unlike the previous papers the given formulas do not contain integrals., Comment: in Russian

An exact discretization method is being developed for solving linear systems of ordinary fractional-derivative differential equations with constant matrix coefficients (LSOFDDECMC). It is shown that the obtained linear discrete system in this case does not have constant matrix coefficients. Further, this method is compared with the known approximate method. The above scheme is developed for arbitrary linear systems with piecewise constant perturbations. The results are applied to the discretization of linear controlled systems and are illustrated with numerical examples., Comment: in Russian

The article examines Nikolskii and Besov spaces with norms defined using $L_p$-averaged mixed moduli of continuity of functions of appropriate orders, instead of mixed moduli of continuity of known orders for certain mixed derivative functions. The author builds continuous linear mappings of such spaces of functions defined in domains of certain type to ordinary Nikolskii and Besov spaces of mixed smoothness in $ \mathbb R^d, $ that are function extension operators, thus incurring coincidence of both kinds of spaces in the said domains. It also significantly broadens the class of Nikolskii and Besov spaces of mixed smoothness for which the theorems of those kind of extension have been derived. Under certain conditions, operators of partial differentiation from the aforementioned function spaces of mixed smoothness to Lebesgue spaces have been established to be continuous., Comment: in Russian. 87 pages

Theory of spin noise in low dimensional systems and bulk semiconductors is reviewed. Spin noise is usually detected by optical means, continuously measuring the rotation angle of the polarization plane of the probe beam passing through the sample. Spin noise spectra yield rich information about the spin properties of the system including, for example, $g$-factors of the charge carriers, spin relaxation times, parameters of the hyperfine interaction, spin-orbit interaction constants, frequencies and widths of the optical resonances. The review describes basic models of spin noise, methods of its theoretical description, and their relation with the experimental results. We also discuss the relation between the spin noise spectroscopy, the strong and weak quantum measurements and the spin flip Raman scattering, and analyze similar effects including manifestations of the charge, current and valley polarization fluctuations in the optical response. Possible directions for further development of the spin noise spectroscopy are outlined., Comment: Accepted to Phys. Usp. The original manuscript in Russian is available in the supplementary files at arXiv and at this URL: https://www.dropbox.com/s/kz5uyz3btgocf8l/UFN_spin_noise_review_rus.pdf?dl=1

We prove that subharmonic functions of finite order on finite dimensional real space, bounded from above outside of some asymptotically small sets on spheres, are bounded from above everywhere. It follows that subharmonic functions of finite order on the complex plane, entire and plurisubharmonic functions of finite order, and convex or harmonic functions of finite order bounded from above outside of such sets on spheres are constant. Our results and methods of proof are also new for functions of one complex variable., Comment: 9 pages, in Russian

We prove that convex functions of finite order on the real line and subharmonic functions of finite order on finite dimensional real space, bounded from above outside of some set of zero relative Lebesgue density, are bounded from above everywhere. It follows that subharmonic functions of finite order on the complex plane, entire and plurisubharmonic functions of finite order, and convex or harmonic functions of finite order bounded from above outside some set of zero relative Lebesgue density are constant., Comment: 5 pages, in Russian

We present a new, short and independent proof of the Liouville-type theorem for entire and subharmonic functions of finite order bounded outside some set of zero planar density., Comment: 4 pages, in Russian

Modern methods for studying wetting in nanodisperse systems based on the use of electron microscopy and experimental results on the size effects in the interaction of highly dispersed phases are presented. For students of physical and Physics and Technology specialties of higher educational institutions. ----- Izlozheny sovremennye metody issledovaniya smachivaniya v nanodispersnyh sistemah, osnovannye na primenenii elektronnoj mikroskopii, i eksperimentalnye rezultaty o proyavlenii razmernyh effektov pri kontaktnom vzaimodejstvii vysokodispersnyh faz. Dlya studentov fizicheskih i fiziko-tehnicheskih specialnostej vysshih uchebnyh zavedenij., Comment: in Russian