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Configuration spaces of hinged mechanisms, and their projections 铰链机构的位形空间及其投影
IF 0.8 4区 数学
Sbornik Mathematics Pub Date : 2022-01-01 DOI: 10.1070/SM9542
Mikhail Dmitrievich Kovalev
{"title":"Configuration spaces of hinged mechanisms, and their projections","authors":"Mikhail Dmitrievich Kovalev","doi":"10.1070/SM9542","DOIUrl":"https://doi.org/10.1070/SM9542","url":null,"abstract":"Our subject is the geometry of planar hinged mechanisms. The article contains a formalization of basic concepts of the theory of hinged-lever constructions, as well as some information from real algebraic geometry needed for their study. We consider mechanisms with variable number of degrees of freedom and mechanisms that have more than one degree of freedom but each hinge of which moves with one degree of freedom. For the last type we find the dimension of the configuration space. We give a number of examples of mechanisms with unusual geometric properties and formulate open questions. Bibliography: 17 titles.","PeriodicalId":49573,"journal":{"name":"Sbornik Mathematics","volume":"21 1","pages":"512 - 533"},"PeriodicalIF":0.8,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90806570","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Strong convexity of reachable sets of linear systems 线性系统可达集的强凸性
IF 0.8 4区 数学
Sbornik Mathematics Pub Date : 2022-01-01 DOI: 10.1070/sm9627
M. Balashov
{"title":"Strong convexity of reachable sets of linear systems","authors":"M. Balashov","doi":"10.1070/sm9627","DOIUrl":"https://doi.org/10.1070/sm9627","url":null,"abstract":"","PeriodicalId":49573,"journal":{"name":"Sbornik Mathematics","volume":"48 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89968883","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Self-affine attractors and tiles 自仿射吸引子和瓦片
IF 0.8 4区 数学
Sbornik Mathematics Pub Date : 2022-01-01 DOI: 10.1070/sm9682
Tatyana Ivanovna Zaitseva,Vladimir Yur'evich Protasov
{"title":"Self-affine attractors and tiles","authors":"Tatyana Ivanovna Zaitseva,Vladimir Yur'evich Protasov","doi":"10.1070/sm9682","DOIUrl":"https://doi.org/10.1070/sm9682","url":null,"abstract":"","PeriodicalId":49573,"journal":{"name":"Sbornik Mathematics","volume":"49 2","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138507477","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On metrical properties of [IMG align=ABSMIDDLE alt=$ C$]tex_sm_5017_img1[/IMG]-capacities associated to solutions of second-order strongly elliptic equations in [IMG align=ABSMIDDLE alt=$ mathbb R^2$]tex_sm_5017_img2[/IMG] [IMG align=ABSMIDDLE alt=$ C$]tex_sm_5017_img1的测量性质[/IMG]- [IMG align=ABSMIDDLE alt=$ mathbb R^2$]tex_sm_5017_img2[/IMG]中二阶强椭圆方程解的相关能力
IF 0.8 4区 数学
Sbornik Mathematics Pub Date : 2022-01-01 DOI: 10.1070/sm9676
P. Paramonov
{"title":"On metrical properties of [IMG align=ABSMIDDLE alt=$ C$]tex_sm_5017_img1[/IMG]-capacities associated to solutions of second-order strongly elliptic equations in [IMG align=ABSMIDDLE alt=$ mathbb R^2$]tex_sm_5017_img2[/IMG]","authors":"P. Paramonov","doi":"10.1070/sm9676","DOIUrl":"https://doi.org/10.1070/sm9676","url":null,"abstract":"","PeriodicalId":49573,"journal":{"name":"Sbornik Mathematics","volume":"12 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90080353","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Entropy of a unitary operator on [IMG align=ABSMIDDLE alt=$ L^2(mathbb{T}^n)$]tex_sm_5018_img1[/IMG] 一元算子在[IMG align=ABSMIDDLE alt=$ L^2(mathbb{T}^n)$]tex_sm_5018_img1上的熵[/IMG]
IF 0.8 4区 数学
Sbornik Mathematics Pub Date : 2022-01-01 DOI: 10.1070/sm9679
K. Afonin, D. Treschev
{"title":"Entropy of a unitary operator on [IMG align=ABSMIDDLE alt=$ L^2(mathbb{T}^n)$]tex_sm_5018_img1[/IMG]","authors":"K. Afonin, D. Treschev","doi":"10.1070/sm9679","DOIUrl":"https://doi.org/10.1070/sm9679","url":null,"abstract":"","PeriodicalId":49573,"journal":{"name":"Sbornik Mathematics","volume":"57 9","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72612983","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Bifurcations changing the homotopy type of the closure of an invariant saddle manifold of a surface diffeomorphism 改变表面微分同构不变鞍形流形闭包的同伦类型的分岔
IF 0.8 4区 数学
Sbornik Mathematics Pub Date : 2022-01-01 DOI: 10.1070/SM9564
E. Nozdrinova, O. Pochinka
{"title":"Bifurcations changing the homotopy type of the closure of an invariant saddle manifold of a surface diffeomorphism","authors":"E. Nozdrinova, O. Pochinka","doi":"10.1070/SM9564","DOIUrl":"https://doi.org/10.1070/SM9564","url":null,"abstract":"It is well known from the homotopy theory of surfaces that an ambient isotopy does not change the homotopy type of a closed curve. Using the language of dynamical systems, this means that an arc in the space of diffeomorphisms that joins two isotopic diffeomorphisms with invariant closed curves in distinct homotopy classes must go through bifurcations. A scenario is described which changes the homotopy type of the closure of the invariant manifold of a saddle point of a polar diffeomorphism of a 2-torus to any prescribed homotopically nontrivial type. The arc constructed in the process is stable and does not change the topological conjugacy class of the original diffeomorphism. The ideas that are proposed here for constructing such an arc for a 2-torus can naturally be generalized to surfaces of greater genus. Bibliography: 32 titles.","PeriodicalId":49573,"journal":{"name":"Sbornik Mathematics","volume":"18 1","pages":"357 - 384"},"PeriodicalIF":0.8,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72801870","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Realization of Fomenko-Zieschang invariants in closed symplectic manifolds with contact singularities 具有接触奇点的闭辛流形中Fomenko-Zieschang不变量的实现
IF 0.8 4区 数学
Sbornik Mathematics Pub Date : 2022-01-01 DOI: 10.1070/SM9579
D. B. Zot’ev, V. I. Sidel'nikov
{"title":"Realization of Fomenko-Zieschang invariants in closed symplectic manifolds with contact singularities","authors":"D. B. Zot’ev, V. I. Sidel'nikov","doi":"10.1070/SM9579","DOIUrl":"https://doi.org/10.1070/SM9579","url":null,"abstract":"The topological bifurcations of Liouville foliations on invariant -manifolds that are induced by attaching toric -handles are investigated. It is shown that each marked molecule (Fomenko-Zieschang invariant) can be realized on an invariant submanifold of a closed symplectic manifold with contact singularities which is obtained by attaching toric -handles sequentially to a set of symplectic manifolds, while these latter have the structures of locally trivial fibrations over associated with atoms. Bibliography: 10 titles.","PeriodicalId":49573,"journal":{"name":"Sbornik Mathematics","volume":"23 1","pages":"443 - 465"},"PeriodicalIF":0.8,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81455810","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Values of the weight system on a family of graphs that are not the intersection graphs of chord diagrams 非弦图的交点图的一组图上的权值
IF 0.8 4区 数学
Sbornik Mathematics Pub Date : 2022-01-01 DOI: 10.1070/SM9519
P. A. Filippova
{"title":"Values of the weight system on a family of graphs that are not the intersection graphs of chord diagrams","authors":"P. A. Filippova","doi":"10.1070/SM9519","DOIUrl":"https://doi.org/10.1070/SM9519","url":null,"abstract":"The Chmutov-Lando theorem claims that the value of a weight system (a function on the chord diagrams that satisfies the four-term Vassiliev relations) corresponding to the Lie algebra depends only on the intersection graph of the chord diagram. We compute the values of the weight system at the graphs in several infinite series, which are the joins of a graph with a small number of vertices and a discrete graph. In particular, we calculate these values for a series in which the initial graph is the cycle on five vertices; the graphs in this series, apart from the initial one, are not intersection graphs. We also derive a formula for the generating functions of the projections of graphs equal to the joins of an arbitrary graph and a discrete graph to the subspace of primitive elements of the Hopf algebra of graphs. Using the formula thus obtained, we calculate the values of the weight system at projections of the graphs of the indicated form onto the subspace of primitive elements. Our calculations confirm Lando’s conjecture concerning the values of the weight system at projections onto the subspace of primitives. Bibliography: 17 titles.","PeriodicalId":49573,"journal":{"name":"Sbornik Mathematics","volume":"4 1","pages":"235 - 267"},"PeriodicalIF":0.8,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82355974","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Optimal recovery in weighted spaces with homogeneous weights 齐次权加权空间的最优恢复
IF 0.8 4区 数学
Sbornik Mathematics Pub Date : 2022-01-01 DOI: 10.1070/SM9475
K. Osipenko
{"title":"Optimal recovery in weighted spaces with homogeneous weights","authors":"K. Osipenko","doi":"10.1070/SM9475","DOIUrl":"https://doi.org/10.1070/SM9475","url":null,"abstract":"The paper concerns problems of the recovery of operators from noisy information in weighted -spaces with homogeneous weights. A number of general theorems are proved and applied to problems of the recovery of differential operators from a noisy Fourier transform. In particular, optimal methods are obtained for the recovery of powers of the Laplace operator from a noisy Fourier transform in the -metric. Bibliography: 30 titles.","PeriodicalId":49573,"journal":{"name":"Sbornik Mathematics","volume":"5 1","pages":"385 - 411"},"PeriodicalIF":0.8,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77898285","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Integrals of the difference of subharmonic functions with respect to measures and the Nevanlinna characteristic 次谐波函数对测度之差的积分及内万林纳特性
IF 0.8 4区 数学
Sbornik Mathematics Pub Date : 2022-01-01 DOI: 10.1070/sm9642
B. Khabibullin
{"title":"Integrals of the difference of subharmonic functions with respect to measures and the Nevanlinna characteristic","authors":"B. Khabibullin","doi":"10.1070/sm9642","DOIUrl":"https://doi.org/10.1070/sm9642","url":null,"abstract":"","PeriodicalId":49573,"journal":{"name":"Sbornik Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90554523","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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