Pub Date : 2021-10-01DOI: 10.17516/1997-1397-2021-14-5-566-572
D. Fedchenko, V. Stepanenko, R. V. Bikmurzin, Isaeva Victoria V.
In this paper we consider the reductant of the dihedral group Dn, consisting of a set of axial symmetries, and the sphere S2 as a reductant of the group SU(2,C) ∼= S3 (the group of unit quaternions). By introducing the Sabinin’s multiplication on the reductant of Dn, we get a quasigroup with unit
{"title":"On Reductants of Two Groups","authors":"D. Fedchenko, V. Stepanenko, R. V. Bikmurzin, Isaeva Victoria V.","doi":"10.17516/1997-1397-2021-14-5-566-572","DOIUrl":"https://doi.org/10.17516/1997-1397-2021-14-5-566-572","url":null,"abstract":"In this paper we consider the reductant of the dihedral group Dn, consisting of a set of axial symmetries, and the sphere S2 as a reductant of the group SU(2,C) ∼= S3 (the group of unit quaternions). By introducing the Sabinin’s multiplication on the reductant of Dn, we get a quasigroup with unit","PeriodicalId":43965,"journal":{"name":"Journal of Siberian Federal University-Mathematics & Physics","volume":"200 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2021-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76972143","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 : 2021-10-01DOI: 10.17516/1997-1397-2021-14-5-647-658
R. V. Ulvert
We discuss the construction of a long semi-exact Mayer–Vietoris sequence for the homology of any finite union of open subspaces. This sequence is used to obtain topological conditions of representation of the integral of a meromorphic n-form on an n-dimensional complex manifold in terms of Grothendieck residues. For such a representation of the integral to exist, it is necessary that the cycle of integration separates the set of polar hypersurfaces of the form. The separation condition in a number of cases turns out to be a sufficient condition for representing the integral as a sum of residues. Earlier, when describing such cases (in the works of Tsikh, Yuzhakov, Ulvert, etc.), the key was the condition that the manifold be Stein. The main result of this article is the relaxation of this condition
{"title":"Connecting Homomorphism and Separating Cycles","authors":"R. V. Ulvert","doi":"10.17516/1997-1397-2021-14-5-647-658","DOIUrl":"https://doi.org/10.17516/1997-1397-2021-14-5-647-658","url":null,"abstract":"We discuss the construction of a long semi-exact Mayer–Vietoris sequence for the homology of any finite union of open subspaces. This sequence is used to obtain topological conditions of representation of the integral of a meromorphic n-form on an n-dimensional complex manifold in terms of Grothendieck residues. For such a representation of the integral to exist, it is necessary that the cycle of integration separates the set of polar hypersurfaces of the form. The separation condition in a number of cases turns out to be a sufficient condition for representing the integral as a sum of residues. Earlier, when describing such cases (in the works of Tsikh, Yuzhakov, Ulvert, etc.), the key was the condition that the manifold be Stein. The main result of this article is the relaxation of this condition","PeriodicalId":43965,"journal":{"name":"Journal of Siberian Federal University-Mathematics & Physics","volume":"53 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2021-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89823863","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 : 2021-10-01DOI: 10.17516/1997-1397-2021-14-5-659-666
A. Velisevich
The identification of an unknown coefficient in the lower term of elliptic second-order differential equation Mu + ku = f with the boundary condition of the third type is considered. The identification of the coefficient is based on integral boundary data. The local existence and uniqueness of the strong solution for the inverse problem is proved
研究了具有第三类边界条件的椭圆型二阶微分方程Mu + ku = f下项中未知系数的辨识问题。系数的辨识基于积分边界数据。证明了该逆问题强解的局部存在唯一性
{"title":"On an Inverse Problem for the Stationary Equation with a Boundary Condition of the Third Type","authors":"A. Velisevich","doi":"10.17516/1997-1397-2021-14-5-659-666","DOIUrl":"https://doi.org/10.17516/1997-1397-2021-14-5-659-666","url":null,"abstract":"The identification of an unknown coefficient in the lower term of elliptic second-order differential equation Mu + ku = f with the boundary condition of the third type is considered. The identification of the coefficient is based on integral boundary data. The local existence and uniqueness of the strong solution for the inverse problem is proved","PeriodicalId":43965,"journal":{"name":"Journal of Siberian Federal University-Mathematics & Physics","volume":"276 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2021-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79139622","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 : 2021-10-01DOI: 10.17516/1997-1397-2021-14-5-547-553
P. Danchev
We study when every square matrix over an algebraically closed field or over a finite field is decomposable into a sum of a potent matrix and a nilpotent matrix of order 2. This can be related to our recent paper, published in Linear & Multilinear Algebra (2022). We also completely address the question when each square matrix over an infinite field can be decomposed into a periodic matrix and a nilpotent matrix of order 2
{"title":"On Some Decompositions of Matrices over Algebraically Closed and Finite Fields","authors":"P. Danchev","doi":"10.17516/1997-1397-2021-14-5-547-553","DOIUrl":"https://doi.org/10.17516/1997-1397-2021-14-5-547-553","url":null,"abstract":"We study when every square matrix over an algebraically closed field or over a finite field is decomposable into a sum of a potent matrix and a nilpotent matrix of order 2. This can be related to our recent paper, published in Linear & Multilinear Algebra (2022). We also completely address the question when each square matrix over an infinite field can be decomposed into a periodic matrix and a nilpotent matrix of order 2","PeriodicalId":43965,"journal":{"name":"Journal of Siberian Federal University-Mathematics & Physics","volume":"9 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2021-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82094508","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 : 2021-08-13DOI: 10.25205/2541-9447-2021-16-2-94-104
A. Zaikin, I. Suhanov
The physics laboratory-works creating and operating computer simulations experience is described. A significant amount of laboratory works can be classified as a “black box”. The studied physical phenomenon is hidden from direct observation, the control is carried out by means of electrical measuring devices. It is difficult to distinguish physical reality from its imitation when performing such work, so the virtualization of this one does not require realistic images. The schematic representation of the laboratory installation greatly simplifies the process of creating a simulator. A unique set of installation parameters is formed for each student performing laboratory work on the simulator, which contributes to the independence of the student's work. These parameters are stored in Google Sheets. Their transfer to the laboratory work’s html-template is carried out in encrypted form through the Google Apps Script service. Virtual laboratory work is implemented as a cross-platform web application.
{"title":"The Physics Laboratory Works – Individualized Computer Simulations","authors":"A. Zaikin, I. Suhanov","doi":"10.25205/2541-9447-2021-16-2-94-104","DOIUrl":"https://doi.org/10.25205/2541-9447-2021-16-2-94-104","url":null,"abstract":"The physics laboratory-works creating and operating computer simulations experience is described. A significant amount of laboratory works can be classified as a “black box”. The studied physical phenomenon is hidden from direct observation, the control is carried out by means of electrical measuring devices. It is difficult to distinguish physical reality from its imitation when performing such work, so the virtualization of this one does not require realistic images. The schematic representation of the laboratory installation greatly simplifies the process of creating a simulator. A unique set of installation parameters is formed for each student performing laboratory work on the simulator, which contributes to the independence of the student's work. These parameters are stored in Google Sheets. Their transfer to the laboratory work’s html-template is carried out in encrypted form through the Google Apps Script service. Virtual laboratory work is implemented as a cross-platform web application.","PeriodicalId":43965,"journal":{"name":"Journal of Siberian Federal University-Mathematics & Physics","volume":"52 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2021-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76557280","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 : 2021-07-01DOI: 10.54362/1818-7919-2011-6-2-17-23
Valeriy I. Pinakov, Konstantin V. Kulik, Boris E. Grinberg
Experiments on the rotating in the air cones with vertex angle β = 120º and flat disc shown that on frequencies Ω ≥ 2.5 hertz exists a qualitative difference in movement for the particles with diameters d ≈ 1 mm and d ≈ 0.1 mm. The particles with d ≈ 0.1 mm move in the near-surface region, the particles with d ≈ 1 mm jump up to 3 cm. Comparison of the spherical and aspheric (ellipsoid with axles d, d and 4 /3 d) particles' kinematics moving shown the inevitability of the large particles jump occurrence. Large particles come to self-oscillation regime by reason of periodically appearance of the Magnus force. Small particles are localized in the velocity layer
{"title":"Analysis of the Particles’ Movement Over the Flat and Profiled Rotating Discs surface in the Velocity Layer of the Viscous Gas","authors":"Valeriy I. Pinakov, Konstantin V. Kulik, Boris E. Grinberg","doi":"10.54362/1818-7919-2011-6-2-17-23","DOIUrl":"https://doi.org/10.54362/1818-7919-2011-6-2-17-23","url":null,"abstract":"Experiments on the rotating in the air cones with vertex angle β = 120º and flat disc shown that on frequencies Ω ≥ 2.5 hertz exists a qualitative difference in movement for the particles with diameters d ≈ 1 mm and d ≈ 0.1 mm. The particles with d ≈ 0.1 mm move in the near-surface region, the particles with d ≈ 1 mm jump up to 3 cm. Comparison of the spherical and aspheric (ellipsoid with axles d, d and 4 /3 d) particles' kinematics moving shown the inevitability of the large particles jump occurrence. Large particles come to self-oscillation regime by reason of periodically appearance of the Magnus force. Small particles are localized in the velocity layer","PeriodicalId":43965,"journal":{"name":"Journal of Siberian Federal University-Mathematics & Physics","volume":"109 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2021-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78624321","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 : 2021-07-01DOI: 10.54362/1818-7919-2008-3-2-108-117
Igor A. Kotelnikov
The period of plasma physics formation as a science is mythologized. Even the birthday of plasma physics and the parentage of the word «plasma» are disputed. On the eve of 80th anniversary of the paper, where the electrically neutral region of the gas discharge has been named plasma for the first time, it is noteworthy separating the truth from archaeological stratifications.
{"title":"Origin of «Plasma», or The History of a Word","authors":"Igor A. Kotelnikov","doi":"10.54362/1818-7919-2008-3-2-108-117","DOIUrl":"https://doi.org/10.54362/1818-7919-2008-3-2-108-117","url":null,"abstract":"The period of plasma physics formation as a science is mythologized. Even the birthday of plasma physics and the parentage of the word «plasma» are disputed. On the eve of 80th anniversary of the paper, where the electrically neutral region of the gas discharge has been named plasma for the first time, it is noteworthy separating the truth from archaeological stratifications.","PeriodicalId":43965,"journal":{"name":"Journal of Siberian Federal University-Mathematics & Physics","volume":"14 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2021-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78370378","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 : 2021-06-01DOI: 10.17516/1997-1397-2021-14-3-313-325
Ahmed A. Hamoud
In this paper, we established some new results concerning the uniqueness and Ulam’s stability results of the solutions of iterative nonlinear Volterra-Fredholm integro-differential equations subject to the boundary conditions. The fractional derivatives are considered in the Caputo sense. These new results are obtained by applying the Gronwall–Bellman’s inequality and the Banach contraction fixed point theorem. An illustrative example is included to demonstrate the efficiency and reliability of our results
{"title":"Uniqueness and Stability Results for Caputo Fractional Volterra-Fredholm Integro-Differential Equations","authors":"Ahmed A. Hamoud","doi":"10.17516/1997-1397-2021-14-3-313-325","DOIUrl":"https://doi.org/10.17516/1997-1397-2021-14-3-313-325","url":null,"abstract":"In this paper, we established some new results concerning the uniqueness and Ulam’s stability results of the solutions of iterative nonlinear Volterra-Fredholm integro-differential equations subject to the boundary conditions. The fractional derivatives are considered in the Caputo sense. These new results are obtained by applying the Gronwall–Bellman’s inequality and the Banach contraction fixed point theorem. An illustrative example is included to demonstrate the efficiency and reliability of our results","PeriodicalId":43965,"journal":{"name":"Journal of Siberian Federal University-Mathematics & Physics","volume":"119 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77689995","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 : 2021-06-01DOI: 10.17516/1997-1397-2021-14-3-287-300
U. Safarov
We study a conjugacy between two critical circle homeomorphisms with irrational rotation number. Let fi, i = 1, 2 be a C3 circle homeomorphisms with critical point x(i) cr of the order 2mi + 1. We prove that if 2m1 + 1 ̸= 2m2 + 1, then conjugating between f1 and f2 is a singular function. Keywords: circle homeomorphism, critical point, conjugating map, rotation number, singular function
{"title":"A Note on the Conjugacy Between Two Critical Circle Maps","authors":"U. Safarov","doi":"10.17516/1997-1397-2021-14-3-287-300","DOIUrl":"https://doi.org/10.17516/1997-1397-2021-14-3-287-300","url":null,"abstract":"We study a conjugacy between two critical circle homeomorphisms with irrational rotation number. Let fi, i = 1, 2 be a C3 circle homeomorphisms with critical point x(i) cr of the order 2mi + 1. We prove that if 2m1 + 1 ̸= 2m2 + 1, then conjugating between f1 and f2 is a singular function. Keywords: circle homeomorphism, critical point, conjugating map, rotation number, singular function","PeriodicalId":43965,"journal":{"name":"Journal of Siberian Federal University-Mathematics & Physics","volume":"319 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78384591","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 : 2021-06-01DOI: 10.17516/1997-1397-2021-14-3-360-368
D. Pochekutov
We describe branch points of complete q-diagonals of Laurent series for rational functions in several complex variables in terms of the logarithmic Gauss mapping. The sufficient condition of non-algebraicity of such a diagonal is proven
{"title":"Analytic Continuation of Diagonals of Laurent Series for Rational Functions","authors":"D. Pochekutov","doi":"10.17516/1997-1397-2021-14-3-360-368","DOIUrl":"https://doi.org/10.17516/1997-1397-2021-14-3-360-368","url":null,"abstract":"We describe branch points of complete q-diagonals of Laurent series for rational functions in several complex variables in terms of the logarithmic Gauss mapping. The sufficient condition of non-algebraicity of such a diagonal is proven","PeriodicalId":43965,"journal":{"name":"Journal of Siberian Federal University-Mathematics & Physics","volume":"35 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86006684","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：