Planning the forest transport systems based on the principles of sustainable development of territories

The article identifies a new method of dynamic modeling in the design of the transport system in the forest fund (TSFF), which is based on economic and mathematical modeling and fuzzy logic tools. The combination of the indicated methods is designed to reduce the disadvantages of their use and increase the benefits. The article substantiates the choice of assessing the forecast level of the impact of risks on the activities of forestry enterprises (the method of expert assessments), using the methodological tools of fuzzy logic. The indicated method makes it possible to take into account a large variety of risk factors of the internal and external environment. At the same time, methodological aspects of fuzzy logic make it possible to formulate a quantitative assessment of qualitative indicators. The article substantiates the choice of tools for economic and mathematical modeling in order to state the design problem of the planned TSFF. Since the indicated method enables the formalization of the functioning of the timber transport system in the given conditions. The article presents a developed model that correctly takes into account the influence of risk factors when planning a TSFF, through the combination of fuzzy logic methods and economic and mathematical modeling. The advantages of the developed model include: considering the multivariance of material flows, vehicles, points of overload, etc.; automated processing of input parameters and effective data; using the model for forecasting, i.e. the possibility of deriving a fuzzy estimate of the efficiency of the timber transport system by identifying cause-effect relationships between the modeling object and the influence of risk factors on its functioning. © 2019 IOP Publishing Ltd

Периодические всплески на многомерной сфере и их применение для аппроксимации функций

The author’s scheme for constructing a multiresolution analysis on a sphere in R3 with respect to the spherical coordinates, which was published in 2019, is extended to spheres in Rn (n ≥ 3). In contrast to other papers, only periodic wavelets on the axis and their tensor products are used. Approximation properties are studied only for the wavelets based on the simplest scalar wavelets of Kotel’nikov–Meyer type with the compact support of their Fourier transforms. The implementation of the idea of a smooth continuation of functions from a sphere to 2π-periodic functions in the polar coordinates analytically (without the complicated geometric interpretation made by the author earlier in R3) turned out to be very simple. © 2020 Krasovskii Institute of Mathematics and Mechanics. All rights reserved

Interpolating wavelets on the sphere

There are several works where bases of wavelets on the sphere (mainly orthogonal and wavelet-like bases) were constructed. In all such constructions, the authors seek to preserve the most important properties of classical wavelets including constructions on the basis of the lifting-scheme. In the present paper, we propose one more construction of wavelets on the sphere. Although two of three systems of wavelets constructed in this paper are orthogonal, we are more interested in their interpolation properties. Our main idea consists in a special double expansion of the unit sphere in R3 such that any continuous function on this sphere defined in spherical coordinates is easily mapped into a 2π-periodic function on the plane. After that everything becomes simple, since the classical scheme of the tensor product of one-dimensional bases of functional spaces works to construct bases of spaces of functions of several variables. © 2019, Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of Russian Academy of Sciences. All rights reserved

A numerical method for the solution of boundary value problems for a homogeneous equation with the squared Laplace operator with the use of interpolation wavelets

We present an effective numerical method for the recovery of biharmonic functions in a disk from continuous boundary values of these functions and of their normal derivatives using wavelets that are harmonic in the disk and interpolating on its boundary on dyadic rational grids. The expansions of solutions of boundary value problems into cumbersome interpolation series in the wavelet basis are folded into sequences of their partial sums that are compactly presentable in the subspace bases of the corresponding multiresolution analysis (MRA) of Hardy spaces h1(K) of functions harmonic in the disk. Effective estimates are obtained for the approximation of solutions by partial sums of any order in terms of the best approximation of the boundary functions by trigonometric polynomials of a slightly smaller order. As a result, to provide the required accuracy of the representation of the unknown biharmonic functions, one can choose in advance the scaling parameter of the corresponding MRA subspace such that the interpolation projection to this space defines a simple analytic representation of the corresponding partial sums of interpolation series in terms of appropriate compressions and shifts of the scaling functions, skipping complicated iterative procedures for the numerical construction of the coefficients of expansion of the boundary functions into series in interpolation wavelets. We write solutions using interpolation and interpolation-orthogonal wavelets based on modified Meyer wavelets, the last are convenient to apply if the boundary values of the boundary value problem are given approximately, for example, are found experimentally. In this case, one can employ the usual, well-known procedures of discrete orthogonal wavelet transformations for the analysis and refinement (correction) of the boundary values. © 2019 Trudy Instituta Matematiki i Mekhaniki UrO RAN. All rights reserved

E2 strengths and transition radii difference of one-phonon 2+ states of 92Zr from electron scattering at low momentum transfer

Background: Mixed-symmetry 2+ states in vibrational nuclei are characterized by a sign change between dominant proton and neutron valence-shell components with respect to the fully symmetric 2+ state. The sign can be measured by a decomposition of proton and neutron transition radii with a combination of inelastic electron and hadron scattering [C. Walz et al., Phys. Rev. Lett. 106, 062501 (2011)]. For the case of 92Zr, a difference could be experimentally established for the neutron components, while about equal proton transition radii were indicated by the data. Method: Differential cross sections for the excitation of one-phonon 2+ and 3- states in 92Zr have been measured with the (e,e') reaction at the S-DALINAC in a momentum transfer range q = 0.3-0.6 fm^(-1). Results: Transition strengths B(E2;2+_1 -> 0+_1) = 6.18(23), B(E2; 2+_2 -> 0+_1) = 3.31(10) and B(E3; 3-_1 -> 0+_1) = 18.4(11) Weisskopf units are determined from a comparison of the experimental cross sections to quasiparticle-phonon model (QPM) calculations. It is shown that a model-independent plane wave Born approximation (PWBA) analysis can fix the ratio of B(E2) transition strengths to the 2+_(1,2) states with a precision of about 1%. The method furthermore allows to extract their proton transition radii difference. With the present data -0.12(51) fm is obtained. Conclusions: Electron scattering at low momentum transfers can provide information on transition radii differences of one-phonon 2+ states even in heavy nuclei. Proton transition radii for the 2+_(1,2) states in 92Zr are found to be identical within uncertainties. The g.s. transition probability for the mixed-symmetry state can be determined with high precision limited only by the available experimental information on the B(E2; 2+_1 -> 0+_1) value.Comment: 14 pages, 5 figures, submitted to Phys. Rev. C, revised manuscrip

Використання аліфатичних альдегідів у синтезі нових 1H-2,1-бензотіазин-4-он 2,2-діоксидів, конденсованих з пірановим ядром за допомогою доміно-взаємодій. Антимікробна активність синтезованих сполук

Domino-type Knoevenagel-Michael-hetero-Thorpe-Ziegler and Knoevenagel-hetero-Diels-Alder interactions using 1-ethyl-1H-2,1-benzothiazin-4(3H)-one 2,2-dioxide and aliphatic aldehydes as initial compounds have been studied. These reactions have led to 2-amino-3-cyano-4H-pyran and 2H-3,4-dihydropyran derivatives, respectively. It has been shown that the three-component one-pot interaction of 1-ethyl-1H-2,1-benzothiazin-4(3H)one 2,2-dioxide with saturated aliphatic aldehydes and malononitrile proceeds under rather mild conditions and results in formation of 2-amino-6-ethyl-4-alkyl-4,6-dihydropyrano[3,2-c][2,1]benzothiazin-3-carbonitrile 5,5-dioxides with moderate and high yields. At the same time, the yields of target products decrease with the increase of the length of the aliphatic aldehyde carbon chain. In this regard, the use of citronellal allowed us to obtain the product of the three-component interaction with a low yield. To date, there is no information in the literature about the possible application of aliphatic dialdehydes in such three-component interactions. It has been found that the use of glutaric aldehyde results in the synthesis of a new class of bis-derivatives of 2-amino-4H-pyran, in which two fragments are linked by the polymethylene bridge. The use of α,β-unsaturated aldehydes in the three-component interaction with 1-ethyl-1H-2,1-benzothiazin-4(3H)-one 2,2-dioxide and malononitrile was accompanied by decrease in the process efficiency compared to saturated aliphatic aldehydes. The target fused 2-amino-3-cyano-4H-pyran was obtained only when α-methylcinnamic aldehyde was used in the reaction. A two-component interaction of 1-ethyl-1H-2,1-benzothiazin-4(3H)-one 2,2-dioxide with citronellal has been also studied. It has been shown that this reaction is stereospecific. It proceeds through domino Knoevenagel-heteroDiels-Alder sequence resulting in a new heterocyclic system – 2,2a,3,4,5,6,6a,8-octahydroisochromeno[4,3-c] [2,1]benzothiazine 7,7-dioxide. The study of the antimicrobial activity of the compounds synthesized has allowed finding compounds with a moderate activity against P. aeruginosa і C. albicans.Изучены домино-взаимодействия Кневенагеля-Михаэля-гетеро-Торпа-Циглера и Кневенагеля-гетеро-Дильса-Альдера с участием 1-этил-2,1-бензотиазин-4(3Н)-он 2,2-диоксида и алифатических альдегидов, приводящих соответственно к образованию производных 2-амино-3-циано-4Н-пирана и 2Н-3,4-дигидропирана. Показано, что трехкомпонентное одностадийное взаимодействие 1-этил-2,1-бензотиазин-4(3Н)-он 2,2-диоксида с насыщенными алифатическими альдегидами и малонодинитрилом протекает в очень мягких условиях и приводит к образованию 2-амино-6-этил-4-алкил-4,6-дигидропирано[3,2-c][2,1]бензотиазин-3-карбонитрил 5,5-диоксидов с высокими и умеренными выходами. В то же время увеличение длины углеродной цепи алифатических альдегидов приводит к уменьшению выхода целевых продуктов. Так, при использовании цитронеллаля продукт трехкомпонентного взаимодействия удалось получить только с невысоким выходом. Алифатические диальдегиды не были ранее использованы в данных взаимодействиях; показано, что применение глутарового альдегида приводит к новому классу бис-производных 2-амино-4Н-пирана, в котором фрагменты соединены полиметиленовым мостиком. Использование α,β-ненасыщенных альдегидов в трехкомпонентном взаимодействии с 1-этил-2,1-бензотиазин-4(3Н)-он 2,2-диоксидом и малонодинитрилом сопровождалось уменьшением эффективности процесса по сравнению с насыщенными алифатическими альдегидами. Целевой продукт взаимодействия конденсированный 2-амино-3-циано-4Н-пиран был получен только в случае применения α-метилкоричного альдегида. Изучено взаимодействие между 1-этил-2,1-бензотиазин-4(3Н)-он 2,2-диоксидом и цитронеллалем; показано, что данная реакция протекает исключительно как стерео-специфичное домино-взаимодействие Кневенагеля-гетеро-Дильса-Альдера и приводит к образованию новой гетероциклической системы – 2,2a,3,4,5,6,6a,8-октагидроизохромено[4,3-c][2,1]бензотиазин 7,7-диоксида. Изучение антимикробной активности синтезированных соединений позволило обнаружить производные, проявляющие умеренную активность против P. aeruginosa и C. albicansВивчені доміно-взаємодії Кньовенагеля-Міхаеля-гетеро-Торпа-Ціглера та Кньовенагеля-гетеро-Дільса-Альдера за участю 1-етил-1Н-2,1-бензотіазин-4(3Н)-ону 2,2-діоксиду та аліфатичних альдегідів, що приводять до утворення відповідно похідних 2-аміно-3-ціано-4Н-пірану та 2Н-3,4-дигідропірану. Показано, що трикомпонентна одностадійна взаємодія 1-етил-1Н-2,1-бензотіазин-4(3Н)-ону 2,2-діоксиду з насиченими аліфатичними альдегідами і малонодинітрилом перебігає у дуже м’яких умовах і приводить до утворення 2-аміно-6-етил-4-алкіл-4,6-дигідропірано[3,2 c][2,1]бензотіазин-3-карбонітрил 5,5-діоксидів з високими та помірними виходами. У той же час збільшення довжини вуглецевого ланцюга аліфатичного альдегіду приводить до зменшення виходу цільових продуктів. Так, при використанні цитронелалю продукт трикомпонентної взаємодії вдалося одержати тільки з невисоким виходом. Аліфатичні діальдегіди не були раніше використані у даних взаємодіях; показано, що використання глутарового альдегіду дозволяє отримати новий клас біс-похідних 2-аміно-4Н-пірану, в якому фрагменти з’єднані поліметиленовим містком. Використання α,β-ненасичених альдегідів у трикомпонентній взаємодії з 1-етил-1Н-2,1-бензотіазин-4(3Н)-ону 2,2-діоксидом і малонодинітрилом супроводжувалося зменшенням ефективності процесу в порівнянні з насиченими аліфатичними альдегідами. Цільовий продукт взаємодії конденсований 2-аміно-3-ціано-4Н-піран був отриманий тільки у випадку застосування α-метилкоричного альдегіду. Вивчена взаємодія між 1-етил-1Н-2,1-бензотіазин-4(3Н)-ону 2,2-діоксидом і цитронелалем; показано, що така реакція перебігає винятково як стереоспецифічна доміно-взаємодія Кньовенагеля-гетеро-Дільса-Альдера і приводить до утворення нової гетероциклічної системи – 2,2a,3,4,5,6,6a,8-октагідроізохромено[4,3-c][2,1]бензотіазин 7,7-діоксиду. Вивчення антимікробної активності синтезованих сполук дозволило виявити похідні, що проявляють помірну активність проти P. aeruginosa і C. albicans

New Method of Reflector Surface Shaping to Produce a Prescribed Contour Beam

In this paper a simple iterative synthesis method is presented for the formation of the shape of the reflector surface with a single feed element to produce the desired contour beam. This is the method of the optimal phase synthesis of the appropriate field in the reflector aperture similar to other works. But unlike them, we solve the problem in a very simple way using the properties of complex-valued functions and Fourier transforms and not applying complicated methods of numerical minimization theory.This work was supported by the Program for State Support of Leading Scientific Schools of the Russian Federation (projectno.NSh-9356.2016.1) and by RAS Presidium programm “Mathematical Problems of Modern Control Theory”.The authors are grateful to N.A. Baraboshkina for collaboration in the work on this paper

A New Algorithm for Analysis of Experimental Mössbauer Spectra

A new approach to analyze the nuclear gamma resonance (NGR) spectra is presented and justified in the paper. The algorithm successively spots the Lorentz lines in the experimental spectrum by a certain optimization procedures. In Mössbauer spectroscopy, the primary analysis is based on the representation of the transmission integral of an experimental spectrum by the sum of Lorentzians. In the general case, a number of lines and values of parameters in Lorentzians are unknown. The problem is to find them. In practice, before the experimental data processing, one elaborates a model of the Mössbauer spectrum. Such a model is usually based on some additional information. Taking into account physical restrictions, one forms the shape of the lines which are close to the normalized experimental Mössbauer spectrum. This is done by choosing the remaining free parameters of the model. However, this approach does not guarantee a proper model. A reasonable way to construct a structural NGR spectrum decomposition should be based on its model-free analysis. Some model-free methods of the NGR spectra analysis have been implemented in a number of known algorithms. Each of these methods is useful but has a limited range of application. In fact, the previously known algorithms did not react to hardly noticeable primary features of the experimental spectrum, but identify the dominant components only. In the proposed approach, the difference between the experimental spectrum and the known already determined part of the spectral structure defines the next Lorentzian. This method is effective for isolation of fine details of the spectrum, although it requires a well-elaborated algorithmic procedure presented in this paper

OMPEGAS: Optimized Relativistic Code for Multicore Architecture

The paper presents a new hydrodynamical code, OMPEGAS, for the 3D simulation of astrophysical flows on shared memory architectures. It provides a numerical method for solving the three-dimensional equations of the gravitational hydrodynamics based on Godunov’s method for solving the Riemann problem and the piecewise parabolic approximation with a local stencil. It obtains a high order of accuracy and low dissipation of the solution. The code is implemented for multicore processors with vector instructions using the OpenMP technology, Intel SDLT library, and compiler auto-vectorization tools. The model problem of simulating a star explosion was used to study the developed code. The experiments show that the presented code reproduces the behavior of the explosion correctly. Experiments for the model problem with a grid size of (Formula presented.) were performed on an 16-core Intel Core i9-12900K CPU to study the efficiency and performance of the developed code. By using the autovectorization, we achieved a 3.3-fold increase in speed in comparison with the non-vectorized program on the processor with AVX2 support. By using multithreading with OpenMP, we achieved an increase in speed of 2.6 times on a 16-core processor in comparison with the vectorized single-threaded program. The total increase in speed was up to ninefold. © 2022 by the authors.Russian Science Foundation, RSF: 18-11-00044The work of the third author (I.M.K.) and fourth author (I.G.C.) was supported by the Russian Science Foundation (project no. 18-11-00044). The first author (E.N.A.) and second author (V.E.M.) received no external funding

Consistent alpha-cluster description of the 12C (0^+_2) resonance

The near-threshold 12C (0^+_2) resonance provides unique possibility for fast helium burning in stars, as predicted by Hoyle to explain the observed abundance of elements in the Universe. Properties of this resonance are calculated within the framework of the alpha-cluster model whose two-body and three-body effective potentials are tuned to describe the alpha - alpha scattering data, the energies of the 0^+_1 and 0^+_2 states, and the 0^+_1-state root-mean-square radius. The extremely small width of the 0^+_2 state, the 0_2^+ to 0_1^+ monopole transition matrix element, and transition radius are found in remarkable agreement with the experimental data. The 0^+_2-state structure is described as a system of three alpha-particles oscillating between the ground-state-like configuration and the elongated chain configuration whose probability exceeds 0.9