Pub Date : 2020-01-01DOI: 10.26907/2541-7746.2020.4.467-480
V. Belashov, E. Belashova, O. Kharshiladze
The influence of the rotational regime on real long-period nutational-precessional motions of the instantaneous pole of the Earth’s rotation is considered. The solar magnetospheric (through changes in the angular velocity of rotation) mechanism of action is discussed. The observed 12-month oscillations of the instantaneous axis of rotation are explained by the influence of the deforming force arising when the angular velocity changes, which causes deformation of the figure that is not uniform in the longitudinal zones, without involving baric-circulation processes as an intermediate link. Thus, free (Chandler) and forced 12-month fluctuations of the pole position are considered from a single point of view, i.e., as resulting from the variabi-lity of the rotational regime of the Earth. The analysis of heliogeophysical data for 1900–2017 confirms the validity of the proposed relationship mechanism.
{"title":"Long-Period Nutational-Precessional Motions of the Instantaneous Earth Rotation Pole","authors":"V. Belashov, E. Belashova, O. Kharshiladze","doi":"10.26907/2541-7746.2020.4.467-480","DOIUrl":"https://doi.org/10.26907/2541-7746.2020.4.467-480","url":null,"abstract":"The influence of the rotational regime on real long-period nutational-precessional motions of the instantaneous pole of the Earth’s rotation is considered. The solar magnetospheric (through changes in the angular velocity of rotation) mechanism of action is discussed. The observed 12-month oscillations of the instantaneous axis of rotation are explained by the influence of the deforming force arising when the angular velocity changes, which causes deformation of the figure that is not uniform in the longitudinal zones, without involving baric-circulation processes as an intermediate link. Thus, free (Chandler) and forced 12-month fluctuations of the pole position are considered from a single point of view, i.e., as resulting from the variabi-lity of the rotational regime of the Earth. The analysis of heliogeophysical data for 1900–2017 confirms the validity of the proposed relationship mechanism.","PeriodicalId":41863,"journal":{"name":"Uchenye Zapiski Kazanskogo Universiteta-Seriya Fiziko-Matematicheskie Nauki","volume":"27 supp1 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89851333","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-01-01DOI: 10.26907/2541-7746.2020.1.27-37
A. Aganin, M. A. Il’gamov, I. Mustafin
{"title":"Selenophysics and Models of the Lunar Three-Layered Mantle","authors":"A. Aganin, M. A. Il’gamov, I. Mustafin","doi":"10.26907/2541-7746.2020.1.27-37","DOIUrl":"https://doi.org/10.26907/2541-7746.2020.1.27-37","url":null,"abstract":"","PeriodicalId":41863,"journal":{"name":"Uchenye Zapiski Kazanskogo Universiteta-Seriya Fiziko-Matematicheskie Nauki","volume":"85 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78176521","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-01-01DOI: 10.26907/2541-7746.2020.3.335-349
S. A. Lozhkin, D.S. Kinzhikeyeva
{"title":"On the Structure, Complexity, and Depth of the Circuits over the Basis {&, ∨} Realizing Step Boolean Functions","authors":"S. A. Lozhkin, D.S. Kinzhikeyeva","doi":"10.26907/2541-7746.2020.3.335-349","DOIUrl":"https://doi.org/10.26907/2541-7746.2020.3.335-349","url":null,"abstract":"","PeriodicalId":41863,"journal":{"name":"Uchenye Zapiski Kazanskogo Universiteta-Seriya Fiziko-Matematicheskie Nauki","volume":"40 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76361493","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-01-01DOI: 10.26907/2541-7746.2020.2.111-119
A. V. Aminova, D. R. Khakimov
The five-dimensional pseudo-Riemannian spaces that admit infinitesimal projective transformations were studied. A general solution of the Eisenhart equation in the h -space H 32 of non-constant curvature was found. Necessary and sufficient conditions were established for the existence of a non-homothetic projective motion in the h- space H 32 of non-constant curvature, and, as a consequence, the structure of the non-homothetic projective Lie algebra in this space was determined.
{"title":"On the Properties of the Projective Lie Algebras of Rigid h-Spaces H32 of the Type {32}","authors":"A. V. Aminova, D. R. Khakimov","doi":"10.26907/2541-7746.2020.2.111-119","DOIUrl":"https://doi.org/10.26907/2541-7746.2020.2.111-119","url":null,"abstract":"The five-dimensional pseudo-Riemannian spaces that admit infinitesimal projective transformations were studied. A general solution of the Eisenhart equation in the h -space H 32 of non-constant curvature was found. Necessary and sufficient conditions were established for the existence of a non-homothetic projective motion in the h- space H 32 of non-constant curvature, and, as a consequence, the structure of the non-homothetic projective Lie algebra in this space was determined.","PeriodicalId":41863,"journal":{"name":"Uchenye Zapiski Kazanskogo Universiteta-Seriya Fiziko-Matematicheskie Nauki","volume":"26 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85155274","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-01-01DOI: 10.26907/2541-7746.2020.2.211-222
A. M. Shaimardanov, V. Kaurov, E. A. Petrova
The wave-corpuscle method for description of atomic photoionization by a flux of photons in the visible and X-ray range was developed and applied. Using the calculated photoionization probability in the asymptotics, we obtained the desired approximate Heitler formula for atomic photoionization probability in the final form with the angular distribution of photoelectrons. The role of the Rayleigh scattering accompanying the photoemissive effect was considered.
{"title":"A Semiclassical Approach Reproducing Asymptotically the Heitler Formula for Atomic Photoionization","authors":"A. M. Shaimardanov, V. Kaurov, E. A. Petrova","doi":"10.26907/2541-7746.2020.2.211-222","DOIUrl":"https://doi.org/10.26907/2541-7746.2020.2.211-222","url":null,"abstract":"The wave-corpuscle method for description of atomic photoionization by a flux of photons in the visible and X-ray range was developed and applied. Using the calculated photoionization probability in the asymptotics, we obtained the desired approximate Heitler formula for atomic photoionization probability in the final form with the angular distribution of photoelectrons. The role of the Rayleigh scattering accompanying the photoemissive effect was considered.","PeriodicalId":41863,"journal":{"name":"Uchenye Zapiski Kazanskogo Universiteta-Seriya Fiziko-Matematicheskie Nauki","volume":"1 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90260588","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-01-01DOI: 10.26907/2541-7746.2020.2.160-179
V. Paimushin, R. Gazizullin
Two problems of the monoharmonic sound wave transmission through a thin rectangular composite plate hinged in the opening of an absolutely stiff dividing wall were considered using the discrete layered damping model of a multilayer plate at small displacements and deformations, with account of the internal damping of layers according to the Kelvin–Voight model. In setting the first problem, it was assumed that the plate located between two semiinfinite spaces and a plane sound wave with a given amplitude value of the pressure is incident on it. In setting the second problem, it was considered that the plate is situated between two absolutely stiff barriers; one of them, owing to the harmonic vibration with a given displacement amplitude of the plate, forms an incident sound wave, while the other is stationary and coated by an energy-absorbing material with high damping properties. Behavior of the acoustic media was described by the classical wave equations based on the model of an ideal compressible fluid. Exact analytical solutions of the formulated problems were constructed. With their help, the sound insulation parameter of composite plate reinforced with carbon fiber textile was studied and the characteristics of its stress-strain state were investigated depending on the frequency of the incident sound wave. It was shown that the mechanics of the deformation of structural elements made of fiber-reinforced composites under high-frequency acoustic impact must be described by refined equations of motion, which have a high degree of accuracy and pithiness, because the stress-strain state formed in them are almost three-dimensional.
{"title":"Refined Analytical Solutions of the Coupled Problems on Free and Forced Vibrations of a Rectangular Composite Plate Surrounded by Acoustic Media","authors":"V. Paimushin, R. Gazizullin","doi":"10.26907/2541-7746.2020.2.160-179","DOIUrl":"https://doi.org/10.26907/2541-7746.2020.2.160-179","url":null,"abstract":"Two problems of the monoharmonic sound wave transmission through a thin rectangular composite plate hinged in the opening of an absolutely stiff dividing wall were considered using the discrete layered damping model of a multilayer plate at small displacements and deformations, with account of the internal damping of layers according to the Kelvin–Voight model. In setting the first problem, it was assumed that the plate located between two semiinfinite spaces and a plane sound wave with a given amplitude value of the pressure is incident on it. In setting the second problem, it was considered that the plate is situated between two absolutely stiff barriers; one of them, owing to the harmonic vibration with a given displacement amplitude of the plate, forms an incident sound wave, while the other is stationary and coated by an energy-absorbing material with high damping properties. Behavior of the acoustic media was described by the classical wave equations based on the model of an ideal compressible fluid. Exact analytical solutions of the formulated problems were constructed. With their help, the sound insulation parameter of composite plate reinforced with carbon fiber textile was studied and the characteristics of its stress-strain state were investigated depending on the frequency of the incident sound wave. It was shown that the mechanics of the deformation of structural elements made of fiber-reinforced composites under high-frequency acoustic impact must be described by refined equations of motion, which have a high degree of accuracy and pithiness, because the stress-strain state formed in them are almost three-dimensional.","PeriodicalId":41863,"journal":{"name":"Uchenye Zapiski Kazanskogo Universiteta-Seriya Fiziko-Matematicheskie Nauki","volume":"206 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73968359","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-01-01DOI: 10.26907/2541-7746.2020.4.426-440
M. Norkin
The process of collapse of a cavern, which is formed following the separation impact pro-duced by a rectangular cylinder in an ideal, incompressible, and heavy liquid, was studied. Assuming that the speed of the cylinder is low, asymptotics of the main characteristics of the impact were constructed. The difficulties arising in this case are mainly related to the fact that the dynamics of the separation points is not known in advance and depends on a small parameter, i.e., on the dimensionless velocity of the cylinder. With the help of a special change of variables, the matter was reduced to the study of a problem with the dynamics of separation points corresponding to the leading approximation independent of the indicated parameter. This enabled us to determine the second term of the asymptotics with account for the nonlinear terms in the model. In the leading approximation, a problem with a free boundary, which is similar to the classical model of an impact with separation at each fixed moment of time, was formulated. On the basis of the first two terms of the asymptotics, the process of collapse of the cavern was described with allowance for the rise of the inner free boundary of the liquid. Comparison with the previously obtained results was carried out.
{"title":"Asymptotics of Slow Motions of a Rectangular Cylinder in a Liquid after a Separation Impact","authors":"M. Norkin","doi":"10.26907/2541-7746.2020.4.426-440","DOIUrl":"https://doi.org/10.26907/2541-7746.2020.4.426-440","url":null,"abstract":"The process of collapse of a cavern, which is formed following the separation impact pro-duced by a rectangular cylinder in an ideal, incompressible, and heavy liquid, was studied. Assuming that the speed of the cylinder is low, asymptotics of the main characteristics of the impact were constructed. The difficulties arising in this case are mainly related to the fact that the dynamics of the separation points is not known in advance and depends on a small parameter, i.e., on the dimensionless velocity of the cylinder. With the help of a special change of variables, the matter was reduced to the study of a problem with the dynamics of separation points corresponding to the leading approximation independent of the indicated parameter. This enabled us to determine the second term of the asymptotics with account for the nonlinear terms in the model. In the leading approximation, a problem with a free boundary, which is similar to the classical model of an impact with separation at each fixed moment of time, was formulated. On the basis of the first two terms of the asymptotics, the process of collapse of the cavern was described with allowance for the rise of the inner free boundary of the liquid. Comparison with the previously obtained results was carried out.","PeriodicalId":41863,"journal":{"name":"Uchenye Zapiski Kazanskogo Universiteta-Seriya Fiziko-Matematicheskie Nauki","volume":"12 21","pages":""},"PeriodicalIF":0.3,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72388095","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-01-01DOI: 10.26907/2541-7746.2020.3.259-268
F. Ablayev
Modern quantum technologies are NISQ (Noisy Intermediate-Scale Quantum) devices, which are used to create insufficiently accurate quantum computers with low computing power. However, quantum technologies have advanced considerably during the past years. Thus, the issue of demonstrating “quantum supremacy” in the era of NISQ technologies is on the agenda. This study demonstrates that “quantum supremacy” is forthcoming. We propose procedures for constructing a universal family of hash functions based on a quantum hashing process that maps the original sequence w to a quantum hash state and then by random trans-formation to the state | ψ (cid:105) and generating the sequence u , which is an approximate description of the state | ψ (cid:105) . We proved that the proposed procedure generates a family of nondeterministic hash functions F , which allow us to reliably distinguish between different arguments. The F family can be considered an (cid:178) -universal family of nondeterministic hash functions. We assume that the development of this research area will cast light on the effect of “quantum supremacy” and will also have a certain impact on the advance of post-quantum cryptography.
{"title":"Universal Hash Functions from Quantum Procedures","authors":"F. Ablayev","doi":"10.26907/2541-7746.2020.3.259-268","DOIUrl":"https://doi.org/10.26907/2541-7746.2020.3.259-268","url":null,"abstract":"Modern quantum technologies are NISQ (Noisy Intermediate-Scale Quantum) devices, which are used to create insufficiently accurate quantum computers with low computing power. However, quantum technologies have advanced considerably during the past years. Thus, the issue of demonstrating “quantum supremacy” in the era of NISQ technologies is on the agenda. This study demonstrates that “quantum supremacy” is forthcoming. We propose procedures for constructing a universal family of hash functions based on a quantum hashing process that maps the original sequence w to a quantum hash state and then by random trans-formation to the state | ψ (cid:105) and generating the sequence u , which is an approximate description of the state | ψ (cid:105) . We proved that the proposed procedure generates a family of nondeterministic hash functions F , which allow us to reliably distinguish between different arguments. The F family can be considered an (cid:178) -universal family of nondeterministic hash functions. We assume that the development of this research area will cast light on the effect of “quantum supremacy” and will also have a certain impact on the advance of post-quantum cryptography.","PeriodicalId":41863,"journal":{"name":"Uchenye Zapiski Kazanskogo Universiteta-Seriya Fiziko-Matematicheskie Nauki","volume":"68 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80267213","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-01-01DOI: 10.26907/2541-7746.2020.3.359-366
G. Temerbekova, D. S. Romanov
Detection testing of Boolean functions implemented by Boolean circuits, which are affected by single replacements of gates with inverters, was discussed. The relevance of the study is determined by the fact that replacements of gates with inverters is a type of malfunction that occurs in the development and production of VLSI. The study was carried out in order to prove the possibility of constructing easily testable circuits under replacing elements with inverters. To achieve this goal, special methods for the synthesis of easily testable circuits were developed. Based on the results of the study, the following conclusions were drawn: for an arbitrary Boolean function implemented over a Zhegalkin basis B 1 = { x & y, x ⊕ y, 1} , there is an irredundant circuit that allows a single detection test set consisting of one vector; for an arbitrary Boolean function implemented over a standard basis B 0 = { x & y, x ∨ y, x ¯} , there is an irredundant circuit that allows a single detection test set consisting of two vectors.
讨论了由布尔电路实现的布尔函数的检测测试，该测试受逆变器单次更换门的影响。该研究的相关性取决于这样一个事实，即用逆变器替换栅极是一种在超大规模集成电路的开发和生产中发生的故障。本研究是为了证明在用逆变器代替元件的情况下，构建易于测试的电路的可能性。为了实现这一目标，开发了易于测试的电路合成的特殊方法。根据研究结果，得出以下结论:对于在Zhegalkin基上实现的任意布尔函数b1 = {x & y, x⊕y, 1}，存在允许由一个向量组成的单个检测测试集的非冗余电路;对于在标准基B 0 = {x & y, x, x¯}上实现的任意布尔函数，存在一个允许由两个向量组成的单个检测测试集的不冗余电路。
{"title":"On Single Detection Test Sets under Replacements of Gates with Inverters","authors":"G. Temerbekova, D. S. Romanov","doi":"10.26907/2541-7746.2020.3.359-366","DOIUrl":"https://doi.org/10.26907/2541-7746.2020.3.359-366","url":null,"abstract":"Detection testing of Boolean functions implemented by Boolean circuits, which are affected by single replacements of gates with inverters, was discussed. The relevance of the study is determined by the fact that replacements of gates with inverters is a type of malfunction that occurs in the development and production of VLSI. The study was carried out in order to prove the possibility of constructing easily testable circuits under replacing elements with inverters. To achieve this goal, special methods for the synthesis of easily testable circuits were developed. Based on the results of the study, the following conclusions were drawn: for an arbitrary Boolean function implemented over a Zhegalkin basis B 1 = { x & y, x ⊕ y, 1} , there is an irredundant circuit that allows a single detection test set consisting of one vector; for an arbitrary Boolean function implemented over a standard basis B 0 = { x & y, x ∨ y, x ¯} , there is an irredundant circuit that allows a single detection test set consisting of two vectors.","PeriodicalId":41863,"journal":{"name":"Uchenye Zapiski Kazanskogo Universiteta-Seriya Fiziko-Matematicheskie Nauki","volume":"1 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86428464","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-01-01DOI: 10.26907/2541-7746.2020.1.77-90
V. I. Pan’zhenskii, B. A. Rastrepina
Among the known eight-dimensional Thurston geometries, there is a geometry of the Sol manifold – a Lie group consisting of real special matrices. For a left-invariant Riemannian metric on the Sol manifold, the left shift group is a maximal simple transitive group of isometry. In this paper, we found all left-invariant differential 1-forms and proved that on the oriented Sol manifold there is only one left-invariant differential 1-form, such that this form and the left-invariant Riemannian metric together define the contact metric structure on the Sol manifold. We identified all left-invariant contact metric connections and distinguished flat connections among them. A completely non-holonomic contact distribution along with the restriction of a Riemannian metric to this distribution define the contact metric structure on the Sol manifold, and an orthogonal projection of the Levi-Chivita connection is a truncated connection. We obtained geodesic parameter equations of the truncated connection, which are the sub-geodesic equations, using a non-holonomic field of frames adapted to the contact metric structure. We revealed that these geodesics are a part of the geodesics of the flat contact metric connection.
{"title":"The Left-Invariant Contact Metric Structure on the Sol Manifold","authors":"V. I. Pan’zhenskii, B. A. Rastrepina","doi":"10.26907/2541-7746.2020.1.77-90","DOIUrl":"https://doi.org/10.26907/2541-7746.2020.1.77-90","url":null,"abstract":"Among the known eight-dimensional Thurston geometries, there is a geometry of the Sol manifold – a Lie group consisting of real special matrices. For a left-invariant Riemannian metric on the Sol manifold, the left shift group is a maximal simple transitive group of isometry. In this paper, we found all left-invariant differential 1-forms and proved that on the oriented Sol manifold there is only one left-invariant differential 1-form, such that this form and the left-invariant Riemannian metric together define the contact metric structure on the Sol manifold. We identified all left-invariant contact metric connections and distinguished flat connections among them. A completely non-holonomic contact distribution along with the restriction of a Riemannian metric to this distribution define the contact metric structure on the Sol manifold, and an orthogonal projection of the Levi-Chivita connection is a truncated connection. We obtained geodesic parameter equations of the truncated connection, which are the sub-geodesic equations, using a non-holonomic field of frames adapted to the contact metric structure. We revealed that these geodesics are a part of the geodesics of the flat contact metric connection.","PeriodicalId":41863,"journal":{"name":"Uchenye Zapiski Kazanskogo Universiteta-Seriya Fiziko-Matematicheskie Nauki","volume":"51 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86017513","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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