Russian Mathematical Surveys最新文献

{"title":"R. Thompson’s group and the amenability problem","authors":"V. Guba","doi":"10.1070/RM10040","DOIUrl":"https://doi.org/10.1070/RM10040","url":null,"abstract":"This paper focuses on Richard Thompson’s group , which was discovered in the 1960s. Many papers have been devoted to this group. We are interested primarily in the famous problem of amenability of this group, which was posed by Geoghegan in 1979. Numerous attempts have been made to solve this problem in one way or the other, but it remains open. In this survey we describe the most important known properties of this group related to the word problem and representations of elements of the group by piecewise linear functions as well as by diagrams and other geometric objects. We describe the classical results of Brin and Squier concerning free subgroups and laws. We include a description of more modern important results relating to the properties of the Cayley graphs (the Belk–Brown construction) as well as Bartholdi’s theorem about the properties of equations in group rings. We consider separately the criteria for (non-)amenability of groups that are useful in the work on the main problem. At the end we describe a number of our own results about the structure of the Cayley graphs and a new algorithm for solving the word problem. Bibliography: 69 titles.","PeriodicalId":49582,"journal":{"name":"Russian Mathematical Surveys","volume":"77 1","pages":"251 - 300"},"PeriodicalIF":0.9,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43005488","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}

{"title":"Inequities in Telehealth Use Associated with Payer Type During the COVID-19 Pandemic.","authors":"Kanna N Lewis, Anthony Goudie, Jonathan C Wilson, Edward Tawiah, Jialiang Li, Joseph W Thompson","doi":"10.1089/tmj.2021.0618","DOIUrl":"10.1089/tmj.2021.0618","url":null,"abstract":"<p><p><b><i>Introduction:</i></b> <i>The COVID-19 pandemic has prompted a shift in health care delivery and compelled a heavier reliance on telehealth. The objective of this study was to determine if differences in coverage policies by payer type resulted in differential telehealth use during the first 3 months of the COVID-19 pandemic. In this population-based cohort study of low-income Arkansans, Medicaid beneficiaries enrolled in the traditional Primary Care Case Management (PCCM) program were compared with Medicaid beneficiaries covered through premium assistance in private Qualified Health Plans (QHPs).</i> <b><i>Methods:</i></b> <i>A retrospective review was conducted of insurance claims records from June 1, 2019, to June 30, 2020, for synchronous telehealth and mobile health (m-health) visits, as well as other forms of telehealth. To establish the baseline equivalence of enrollees in the two groups, propensity score matching design was used on demographic and geographic characteristics, Charlson Comorbidity Index, broadband availability, and prior service utilization.</i> <b><i>Results:</i></b> <i>Compared with enrollees in the PCCM program, Medicaid expansion enrollees in QHPs had higher odds of having had at least one telehealth visit (adjusted odds ratio [aOR] = 1.35, 95% confidence interval [CI]: 1.29-1.42) during the early phase of the COVID-19 pandemic. Categorizing utilizations by domain, QHP enrollees were more likely to use synchronous telehealth (aOR = 1.31; 95% CI: 1.25-1.37) and m-health (aOR = 5.91; 95% CI: 4.25-8.21). A higher proportion of QHP enrollees also had at least one mental or behavioral health telehealth session (aOR = 1.13; 95% CI: 1.07-1.19).</i> <b><i>Conclusions:</i></b> <i>Our study demonstrated that within low-income populations, payer type was associated with inequitable access to telehealth during the early phase of the COVID-19 pandemic.</i></p>","PeriodicalId":49582,"journal":{"name":"Russian Mathematical Surveys","volume":"35 1","pages":""},"PeriodicalIF":4.7,"publicationDate":"2022-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80552015","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}

{"title":"Effect of excise tax on sugar-sweetened beverages in Catalonia, Spain, three and a half years after its introduction.","authors":"Miguel Ángel Royo-Bordonada, Carlos Fernández-Escobar, Carlos José Gil-Bellosta, Elena Ordaz","doi":"10.1186/s12966-022-01262-8","DOIUrl":"10.1186/s12966-022-01262-8","url":null,"abstract":"<p><strong>Background: </strong>The World Health Organisation urges countries to levy specific excise taxes on SSBs. Currently, more than 50 countries have introduced some type of tax on SSBs. In March 2017, the Autonomous Region of Catalonia approved the introduction of a tiered excise tax on SSBs for public health reasons. To evaluate the effect of the Catalonian excise tax on the price and purchase of sugar-sweetened beverages (SSBs) and their possible substitutes, i.e., non-sugar-sweetened beverages (NSSBs) and bottled water, three and half years after its introduction, and 1 year after the outbreak of the COVID-19 pandemic.</p><p><strong>Methods: </strong>We analysed purchase data on soft drinks, fruit drinks and water, sourced from the Ministry of Agriculture food-consumption panel, in a random sample of 12,500 households across Spain. We applied the synthetic control method to infer the causal impact of the intervention, based on a Bayesian structural time-series model which predicts the counterfactual response that would have occurred in Catalonia, had no intervention taken place.</p><p><strong>Results: </strong>As compared to the predicted (counterfactual) response, per capita purchases of SSBs fell by 0.17 l three and a half years after implementing the SSB tax in Catalonia, a 16.7% decline (95% CI: - 23.18, - 8.74). The mean SSB price rose by 0.11 €/L, an 11% increase (95% CI: 9.0, 14.1). Although there were no changes in mean NSSB prices, NSSB consumption rose by 0.19 l per capita, a 21.7% increase (95% CI: 18.25, 25.54). There were no variations in the price or consumption of bottled water. The effects were progressively greater over time, with SSB purchases decreasing by 10.4% at 1 year, 12.3% at 2 years, 15.3% at 3 years, and 16.7% at three and a half years of the tax's introduction.</p><p><strong>Conclusions: </strong>The Catalonian SSB excise tax had a sustained and progressive impact over time, with a fall in consumption of as much as 16.7% three and half years after its introduction. The observed NSSB substitution effect should be borne in mind when considering the application of this type of tax to the rest of Spain.</p>","PeriodicalId":49582,"journal":{"name":"Russian Mathematical Surveys","volume":"55 1","pages":"24"},"PeriodicalIF":5.6,"publicationDate":"2022-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8917362/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80873733","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Elements of hyperbolic theory on an infinite-dimensional torus","authors":"S. Glyzin, A. Kolesov","doi":"10.1070/rm10058","DOIUrl":"https://doi.org/10.1070/rm10058","url":null,"abstract":"","PeriodicalId":49582,"journal":{"name":"Russian Mathematical Surveys","volume":"1 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"59014106","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}

{"title":"On a canonical basis of a pair of compatible Poisson brackets on a symplectic Lie algebra","authors":"A. A. Garazha","doi":"10.1070/RM10035","DOIUrl":"https://doi.org/10.1070/RM10035","url":null,"abstract":"Every reductive complex Lie algebra g is equipped with the canonical Poisson structure {φ,ψ}(x) = (x, [dxφ, dxψ]), where φ and ψ are smooth functions on g, while dxφ and dxψ are treated as elements of g, which is identified with g∗ using the invariant inner product. Moreover, for every a ∈ g, a Poisson structure ‘with frozen argument’ is defined: {φ,ψ}a(x) = (a, [dxφ, dxψ]). An approach described in [1] makes it possible to work with Poisson structures using the language of linear algebra. The Poisson brackets { · , · }a and { · , · } are regarded as skew-symmetric bilinear forms fa and fx over the field K = C(g) on the space g⊗K of rational vector fields on g, where the element a is fixed and x is a generic element. Namely, if φ and ψ are polynomials, then dφ and dψ can be regarded as elements of g⊗K, and then {φ,ψ}(x) = fx(dφ, dψ) and {φ,ψ}a(x) = fa(dφ, dψ). The above approach can be used to solve an important problem in Hamiltonian mechanics, namely, the search for complete families of functions in bi-involution, that is, maximal families of functions commuting with respect to both Poisson brackets. The polynomials φ1, . . . , φs define a complete family of functions in bi-involution with respect to { · , · }a and { · , · } if and only if their differentials dφ1, . . . , dφs form a basis of a bi-Lagrangian subspace (that is, a maximal subspace which is isotropic with respect to both bilinear forms). Thus, to obtain a complete family of functions in bi-involution, it suffices to find a basis for a bi-Lagrangian subspace and ‘integrate with respect to x’. If a basis is found (we call it canonical) in which the matrices of both forms fa and fx are reduced simultaneously to the canonical Jordan–Kronecker form (with blocks of two types, Jordan and Kronecker, see [1]), then a basis of the bi-Lagrangian subspace is formed by the second halves of the bases in each block. The second (‘larger’) halves of the bases in Kronecker blocks span a subspace L, which is the intersection of all bi-Lagrangian subspaces for the forms fa and fx. In [4] a basis of the subspace L and the corresponding functions in bi-involution were constructed for the Lie algebras gln and sp2n. In [3] the Kronecker part of a canonical basis and the corresponding part of the complete system of functions in bi-involution were constructed for the Lie algebra gln. Now we introduce our notation and formulate the result. Let {λ1, . . . , λs} be distinct eigenvalues of a matrix A ∈ gln. Assume that Jordan cells of order nk,1 ⩾ · · · ⩾ nk,ik correspond to an eigenvalue λk. We write","PeriodicalId":49582,"journal":{"name":"Russian Mathematical Surveys","volume":"77 1","pages":"375 - 377"},"PeriodicalIF":0.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"59012690","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}

{"title":"Left-invariant optimal control problems on Lie groups: classification and problems integrable by elementary functions","authors":"Y. Sachkov","doi":"10.1070/RM10019","DOIUrl":"https://doi.org/10.1070/RM10019","url":null,"abstract":"Left-invariant optimal control problems on Lie groups are an important class of problems with a large symmetry group. They are theoretically interesting because they can often be investigated in full and general laws can be studied by using these model problems. In particular, problems on nilpotent Lie groups provide a fundamental nilpotent approximation to general problems. Also, left-invariant problems often arise in applications such as classical and quantum mechanics, geometry, robotics, visual perception models, and image processing. The aim of this paper is to present a survey of the main concepts, methods, and results pertaining to left-invariant optimal control problems on Lie groups that can be integrated by elementary functions. The focus is on describing extremal trajectories and their optimality, the cut time and cut locus, and optimal synthesis. Questions concerning the classification of left-invariant sub-Riemannian problems on Lie groups of dimension three and four are also addressed. Bibliography: 91 titles.","PeriodicalId":49582,"journal":{"name":"Russian Mathematical Surveys","volume":"77 1","pages":"99 - 163"},"PeriodicalIF":0.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"59012963","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}

{"title":"On Voronoi’s conjecture for four- and five-dimensional parallelohedra","authors":"A. Garber, A. Magazinov","doi":"10.1070/RM10020","DOIUrl":"https://doi.org/10.1070/RM10020","url":null,"abstract":"1. Parallelohedra and Voronoi’s conjecture. A convex d-dimensional polytope is called a parallelohedron or a d-parallelohedron if there is a tiling of the space R into parallel copies of P . In particular, all parallelograms and all hexagons with a centre of symmetry are 2-parallelohedra. All five types of 3-parallelohedra were classified by Fedorov at the end of the 19th century. The theory of parallelohedra has its origins in the works by Fedorov, Minkowski, Voronoi, and Delone. Parallelohedra are closely connected with mathematical crystallography, the classification of crystallographic groups, algorithmic and geometric questions relating to integer lattices, and, in particular, with Hilbert’s 18th problem. Voronoi’s conjecture [1] is one of the central conjectures in the theory of parallelohedra. It states that for each d-parallelohedron P , there is a d-dimensional lattice Λ such that P is affinely equivalent to the Dirichlet–Voronoi cell of Λ. If Voronoi’s conjecture holds for P , then we call it a V-parallelohedron. Voronoi’s conjecture has been proved fully for d ⩽ 5. The cases d = 1, 2, 3 are common wisdom. The proof for d = 4 was given by Delone [2] in 1929. For d = 5, the proof was obtained by the authors of the present paper in 2019; see [3]. A review of key results in the theory of parallelohedra can be found in [4], Chap. 3, and in [5]. In this note we present a new proof of Voronoi’s conjecture in R, which uses ideas from [3] adapted for d = 4. For instance, our proof relies on a combinatorial approach, in contrast to Delone’s geometric methods. Both approaches use a number of general properties of parallelohedra, and, in particular, a classification of the types of coincidence of parallelohedra at faces of codimension three and the existence of a layered structure of tilings into parallelohedra under certain constraints. However, we rely on combinatorial methods developed long after Delone’s publication. In conclusion, we present a sketch of the proof of Voronoi’s conjecture for d = 5 from [3].","PeriodicalId":49582,"journal":{"name":"Russian Mathematical Surveys","volume":"77 1","pages":"174 - 176"},"PeriodicalIF":0.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"59013080","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}

{"title":"Spectrum of a convolution operator with potential","authors":"D. Borisov, E. Zhizhina, Andrey L. Piatnitski","doi":"10.1070/rm10038","DOIUrl":"https://doi.org/10.1070/rm10038","url":null,"abstract":"","PeriodicalId":49582,"journal":{"name":"Russian Mathematical Surveys","volume":"1 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"59012783","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}

{"title":"Boris Abramovich Trakhtenbrot","authors":"S. Artemov, J. Bārzdiņš, L. A. Bokut', Yuri Gurevich, A. M. Dekhtyar', L. Levin, I. Lomazova, Y. Matiyasevich, V. A. Nepomnyashchii, S. P. Novikov, A. Rabinovich, V. Sazonov, A. O. Slisenko, V. Sokolov, M. Trakhtenbrot, N. V. Shilov","doi":"10.1070/RM10048","DOIUrl":"https://doi.org/10.1070/RM10048","url":null,"abstract":"Boris Abramovich Trakhtenbrot (20.02.1921– 19.09.2016), the centenary of whose birth was celebrated on 20 February 2021, was one of the founders of theoretical computer science, who was widely recognised both in the Soviet Union and all over the world. His scientific biography is also interesting in both its humanistic and historical aspects. He was born on 20 February 1921 in Bessarabia, in the village of Brichevo (which during various periods of time belonged to Russia, Romania, USSR, and Moldova). In 1940 he started studying mathematics at the Kishinev Pedagogical Institute (now Ion Creangă State Pedagogical University). At the beginning of World War II he was evacuated to the Urals with the Institute. By that time Kishinev was already under bombardment. Until 1943 he was completely out of touch with his family, which was separated and deported from Bessarabia to the Urals and Siberia during the large-scale eviction in June of 1941 (paradoxically, this exile saved his family from the Holocaust). Trakhtenbrot was disqualified from active military service because of his weak eyesight. During that period he combined intermittent studies with working at a footwear factory and in a gas trust company. In 1944 he returned from evacuation. For a year he worked as a teacher of mathematics in the town of Beltsy (now Moldovan Bălţi). He completed his mathematical studies at the University of Chernovtsy (now Ukrainian Chernivtsi) in 1945–1947. Parallel to his studies, he took an active part in the restoration of the well-stocked mathematical library of Chernovtsy State University, and this activity played an important role in his education and familiarization with science. A number of teachers at Chernovtsy State University were disciples of Moscow mathematical schools. Among those who had great influence on Trakhtenbrot was A.A. Bobrov, a former student of A. N. Kolmogorov. It was at Bobrov’s seminar on Hausdorff’s monograph that Trakhtenbrot became fascinated by descriptive set theory. On the","PeriodicalId":49582,"journal":{"name":"Russian Mathematical Surveys","volume":"77 1","pages":"183 - 188"},"PeriodicalIF":0.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"59013218","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}

{"title":"Evgenii Vital'evich Shchepin (on his seventieth birthday)","authors":"V. Buslaev, V. Buchstaber, A. Dranishnikov, Vitalii Mendelevich Kliatskin, S. A. Melikhov, L. Montejano, S. Novikov, P. Semenov","doi":"10.1070/rm10043","DOIUrl":"https://doi.org/10.1070/rm10043","url":null,"abstract":"","PeriodicalId":49582,"journal":{"name":"Russian Mathematical Surveys","volume":"1 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"59013431","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}