Guarantees of law and problems of security in the democratic state

The article examines different approaches to the definition of "guarantees of the rule of law". Also the most relevant classification guarantees the rule of law are presented in the article

Multiple Factorizations of Bivariate Linear Partial Differential Operators

We study the case when a bivariate Linear Partial Differential Operator (LPDO) of orders three or four has several different factorizations. We prove that a third-order bivariate LPDO has a first-order left and right factors such that their symbols are co-prime if and only if the operator has a factorization into three factors, the left one of which is exactly the initial left factor and the right one is exactly the initial right factor. We show that the condition that the symbols of the initial left and right factors are co-prime is essential, and that the analogous statement "as it is" is not true for LPDOs of order four. Then we consider completely reducible LPDOs, which are defined as an intersection of principal ideals. Such operators may also be required to have several different factorizations. Considering all possible cases, we ruled out some of them from the consideration due to the first result of the paper. The explicit formulae for the sufficient conditions for the complete reducibility of an LPDO were found also

Algorithm for post-processing of tomography images to calculate the dimension-geometric features of porous structures

An algorithm for post-processing of the grayscale 3D computed tomography (CT) images of porous structures with the automatic selection of filtering parameters is proposed. The determination of parameters is carried out on a representative part of the image under analysis. A criterion for the search for optimal filtering parameters based on the count of "levitating stone" voxels is described. The stages of CT image filtering and its binarization are performed sequentially. Bilateral and anisotropic diffuse filtering is implemented; the Otsu method for unbalanced classes is chosen for binarization. Verification of the proposed algorithm was carried out on model data. To create model porous structures, we used our image generator, which implements the function of anisotropic porous structures generation. Results of the post-processing of real CT images containing noise and reconstruction artifacts by the proposed method are discussed.This work was partly supported by the RF Ministry of Science and Higher Education within the State assignment of the FSRC "Crystallography and Photonics" RAS (computed tomography measurements and data analysis) and the Russian Foundation for Basic Research (RFBR) under projects Nos. 18-29-26019 and 19-01-00790 (algorithms development)

Conjugacy in Baumslag's group, generic case complexity, and division in power circuits

The conjugacy problem belongs to algorithmic group theory. It is the following question: given two words x, y over generators of a fixed group G, decide whether x and y are conjugated, i.e., whether there exists some z such that zxz^{-1} = y in G. The conjugacy problem is more difficult than the word problem, in general. We investigate the complexity of the conjugacy problem for two prominent groups: the Baumslag-Solitar group BS(1,2) and the Baumslag(-Gersten) group G(1,2). The conjugacy problem in BS(1,2) is TC^0-complete. To the best of our knowledge BS(1,2) is the first natural infinite non-commutative group where such a precise and low complexity is shown. The Baumslag group G(1,2) is an HNN-extension of BS(1,2). We show that the conjugacy problem is decidable (which has been known before); but our results go far beyond decidability. In particular, we are able to show that conjugacy in G(1,2) can be solved in polynomial time in a strongly generic setting. This means that essentially for all inputs conjugacy in G(1,2) can be decided efficiently. In contrast, we show that under a plausible assumption the average case complexity of the same problem is non-elementary. Moreover, we provide a lower bound for the conjugacy problem in G(1,2) by reducing the division problem in power circuits to the conjugacy problem in G(1,2). The complexity of the division problem in power circuits is an open and interesting problem in integer arithmetic.Comment: Section 5 added: We show that an HNN extension G = < H, b | bab^-1 = {\phi}(a), a \in A > has a non-amenable Schreier graph with respect to the base group H if and only if A \neq H \neq

Исследование канальных блокаторов NMDA рецептора в ряду конъюгатов метиленового синего с использованием QSAR и молекулярного моделирования

29 conjugates of methylene blue and four chemical structures, including derivatives of carbazole, tetrahydrocarbazole, substituted indoles and γ-carboline, combined with a 1-oxopropylene spacer have been studied as channel blockers of the NMDA receptor (binding site of MK-801) by using four QSAR methods (multiple linear regression, random forest, support vector machine, Gaussian process) and molecular docking. QSAR models have satisfactory characteristics. The analysis of regression models at the statistical level revealed an important role of the hydrogen bond in the complex formation. This was also confirmed by the study of modeled by docking complexes. It was found that the increase in the inhibitory activity of the part of compounds could be attributed to appearance of additional H bonds between the ligands and the receptor.С использованием 4-х методов QSAR (множественная линейная регрессия, случайный лес, метод опорных векторов, гауссовский процесс) и молекулярного докинга исследованы в качестве блокаторов NMDA рецептора (сайт связывания МК-801) 29 конъюгатов метиленового синего и четырех типов соединений, включая производные карбазола, тетрагидрокарбазола, замещенных индолов и γ-карболина, объединенных 1-оксопропиленовым спейсером. Полученные QSAR модели имеют удовлетворительные характеристики. На основе анализа регрессионных моделей на статистическом уровне выявлена важная роль водородной связи при формировании комплекса. Это нашло подтверждение при исследовании моделей комплексов, полученных молекулярным докингом. Установлено, что увеличение ингибирующей способности части исследуемых соединений обусловлено появлением дополнительных Н-связей между лигандами и рецептором

Assimilation of Temperatures and Column Dust Opacities Measured by ExoMars TGO-ACS-TIRVIM During the MY34 Global Dust Storm

Funding Information: ExoMars is a space mission of ESA and Roscosmos. The Atmospheric Chemistry Suite (ACS) experiment is led by IKI, the Space Research Institute in Moscow, Russia, assisted by LATMOS in France. This work, exploiting ACS/TIRVIM data, acknowledges funding by the CNES. The science operations of ACS are funded by Roscosmos and ESA. The ACS/TIRVIM team at IKI acknowledges the subsidy of the Ministry of Science and Higher Education of Russia. The authors acknowledge Sandrine Guerlet and the ACS/TGO team for supplying the data and the data center ESPRI/IPSL for their help in accessing the data. R. M. B. Young acknowledges funding from the UAE University grants G00003322 and G00003407. Supercomputing resources were provided by the UAE University High Performance Computing, with technical support from Anil Thomas and Asma Alneyadi, and at LMD by the IPSL mesocentre. The authors thank Luca Montabone for access to processed versions of Mars Climate Sounder temperature and dust observations, and Thomas Navarro and Claus Gebhardt for useful discussions.Peer reviewe

The inverse moment problem for convex polytopes

The goal of this paper is to present a general and novel approach for the reconstruction of any convex d-dimensional polytope P, from knowledge of its moments. In particular, we show that the vertices of an N-vertex polytope in R^d can be reconstructed from the knowledge of O(DN) axial moments (w.r.t. to an unknown polynomial measure od degree D) in d+1 distinct generic directions. Our approach is based on the collection of moment formulas due to Brion, Lawrence, Khovanskii-Pukhikov, and Barvinok that arise in the discrete geometry of polytopes, and what variously known as Prony's method, or Vandermonde factorization of finite rank Hankel matrices.Comment: LaTeX2e, 24 pages including 1 appendi