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The normal derivative lemma and surrounding issues Russ. Math. Surv. (IF 0.9) Pub Date : 2022-04-01 D. E. Apushkinskaya, A. I. Nazarov
In this survey we describe the history and current state of one of the key areas in the qualitative theory of elliptic partial differential equations related to the strong maximum principle and the boundary point principle (normal derivative lemma).Bibliography: 234 titles.
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R. Thompson’s group and the amenability problem Russ. Math. Surv. (IF 0.9) Pub Date : 2022-04-01 V. S. Guba
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
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Effective results in the theory of birational rigidity Russ. Math. Surv. (IF 0.9) Pub Date : 2022-04-01 A. V. Pukhlikov
This paper is a survey of recent effective results in the theory of birational rigidity of higher-dimensional Fano varieties and Fano–Mori fibre spaces.Bibliography: 59 titles.
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On reduction and separation of projective sets in Tychonoff spaces Russ. Math. Surv. (IF 0.9) Pub Date : 2022-02-01 D. I. Saveliev
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Inverse function theorem on the class of holomorphic self-maps of a disc with two fixed points Russ. Math. Surv. (IF 0.9) Pub Date : 2022-02-01 O. S. Kudryavtseva,A. P. Solodov
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An observation on the Gram matrices of systems of uniformly bounded functions and a problem of Olevskii Russ. Math. Surv. (IF 0.9) Pub Date : 2022-02-01 B. S. Kashin
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On Voronoi’s conjecture for four- and five-dimensional parallelohedra Russ. Math. Surv. (IF 0.9) Pub Date : 2022-02-01 A. I. Garber,A. N. Magazinov
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Left-invariant optimal control problems on Lie groups: classification and problems integrable by elementary functions Russ. Math. Surv. (IF 0.9) Pub Date : 2022-02-01 Yu. L. Sachkov
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
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Spectrum of the Laplace operator on closed surfaces Russ. Math. Surv. (IF 0.9) Pub Date : 2022-02-01 D. A. Popov
A survey is given of classical and relatively recent results on the distribution of the eigenvalues of the Laplace operator on closed surfaces. For various classes of metrics the dependence of the behaviour of the second term in Weyl’s formula on the geometry of the geodesic flow is considered. Various versions of trace formulae are presented, along with ensuing identities for the spectrum. The case
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Structures of non-classical discontinuities in solutions of hyperbolic systems of equations Russ. Math. Surv. (IF 0.9) Pub Date : 2022-02-01 A. G. Kulikovskii, A. P. Chugainova
Discontinuity structures in solutions of a hyperbolic system of equations are considered. The system of equations has a rather general form and, in particular, can describe the longitudinal and torsional non-linear waves in elastic rods in the simplest setting and also one-dimensional waves in unbounded elastic media. The properties of discontinuities in solutions of these equations have been investigated
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What do Abelian categories form? Russ. Math. Surv. (IF 0.9) Pub Date : 2022-02-01 D. B. Kaledin
Given two finitely presentable Abelian categories and , we outline a construction of an Abelian category of functors from to , which has nice 2-categorical properties and provides an explicit model for a stable category of stable functors between the derived categories of and . The construction is absolute, so it makes it possible to recover not only Hochschild cohomology but also Mac Lane cohomology
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Dynamical phenomena connected with stability loss of equilibria and periodic trajectories Russ. Math. Surv. (IF 0.9) Pub Date : 2022-01-04 A. I. Neishtadt, D. V. Treschev
This is a study of a dynamical system depending on a parameter . Under the assumption that the system has a family of equilibrium positions or periodic trajectories smoothly depending on , the focus is on details of stability loss through various bifurcations (Poincar–Andronov– Hopf, period-doubling, and so on). Two basic formulations of the problem are considered. In the first, is constant and the
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One-dimensional dynamical systems Russ. Math. Surv. (IF 0.9) Pub Date : 2022-01-04 L. S. Efremova, E. N. Makhrova
The survey is devoted to the topological dynamics of maps defined on one-dimensional continua such as a closed interval, a circle, finite graphs (for instance, finite trees), or dendrites (locally connected continua without subsets homeomorphic to a circle). Connections between the periodic behaviour of trajectories, the existence of a horseshoe and homoclinic trajectories, and the positivity of topological
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Efficient asymptotics of solutions to the Cauchy problem with localized initial data for linear systems of differential and pseudodifferential equations Russ. Math. Surv. (IF 0.9) Pub Date : 2022-01-04 S. Yu. Dobrokhotov, V. E. Nazaikinskii, A. I. Shafarevich
We say that the initial data in the Cauchy problem are localized if they are given by functions concentrated in a neighbourhood of a submanifold of positive codimension, and the size of this neighbourhood depends on a small parameter and tends to zero together with the parameter. Although the solutions of linear differential and pseudodifferential equations with localized initial data constitute a
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3-manifolds represented by 4-regular graphs with three Eulerian cycles Russ. Math. Surv. (IF 0.9) Pub Date : 2021-12-01 A. V. Malyutin,E. A. Fominykh,E. V. Shumakova
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Non-commutative methods in additive combinatorics and number theory Russ. Math. Surv. (IF 0.9) Pub Date : 2021-12-01 I. D. Shkredov
Abstract The survey is devoted to applications of growth in non- Abelian groups to a number of problems in number theory and additive combinatorics. We discuss Zaremba’s conjecture, sum-product theory, incidence geometry, the affine sieve, and some other questions. Bibliography: 149 titles.
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Local groups in Delone sets: a conjecture and results Russ. Math. Surv. (IF 0.9) Pub Date : 2021-12-01 N. P. Dolbilin,M. I. Shtogrin
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Multitype branching processes in random environment Russ. Math. Surv. (IF 0.9) Pub Date : 2021-12-01 V. A. Vatutin,E. E. Dyakonova
Abstract A survey of results in the theory of multitype branching processes evolving in a random environment is presented. Bibliography: 104 titles.
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Functions with general monotone Fourier coefficients Russ. Math. Surv. (IF 0.9) Pub Date : 2021-12-01 A. S. Belov,M. I. Dyachenko,S. Yu. Tikhonov
Abstract This paper is a study of trigonometric series with general monotone coefficients in the class with . Sharp estimates are proved for the Fourier coefficients of integrable and continuous functions. Also obtained are optimal results in terms of coefficients for various types of convergence of Fourier series. For two-sided estimates are obtained for the -moduli of smoothness of sums of series
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Tetrahedron equation: algebra, topology, and integrability Russ. Math. Surv. (IF 0.9) Pub Date : 2021-10-28 D. V. Talalaev
The Zamolodchikov tetrahedron equation inherits almost all the richness of structures and topics in which the Yang–Baxter equation is involved. At the same time, this transition symbolizes the growth of the order of the problem, the step from the Yang–Baxter equation to the local Yang–Baxter equation, from the Lie algebra to the 2-Lie algebra, from ordinary knots in to 2-knots in . These transitions
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Dynamical Bethe algebra and functions on pairs of quasi-polynomials Russ. Math. Surv. (IF 0.9) Pub Date : 2021-10-28 A. N. Varchenko, A. M. Slinkin, D. Thompson
We consider the space of functions on the Cartan subalgebra of with values in the zero weight subspace of a tensor product of irreducible finite-dimensional -modules. We consider the algebra of commuting differential operators on , constructed by Rubtsov, Silantyev, and Talalaev in 2009. We describe the relations between the action of on and spaces of pairs of quasi- polynomials. Bibliography: 25 titles
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Integrable polynomial Hamiltonian systems and symmetric powers of plane algebraic curves Russ. Math. Surv. (IF 0.9) Pub Date : 2021-10-28 V. M. Buchstaber, A. V. Mikhailov
This survey is devoted to integrable polynomial Hamiltonian systems associated with symmetric powers of plane algebraic curves. We focus our attention on the relations (discovered by the authors) between the Stckel systems, Novikov’s equations for the th stationary Korteweg– de Vries hierarchy, the Dubrovin–Novikov coordinates on the universal bundle of Jacobians of hyperelliptic curves, and new systems
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Chaos and integrability in -geometry Russ. Math. Surv. (IF 0.9) Pub Date : 2021-10-28 A. V. Bolsinov, A. P. Veselov, Y. Ye
We review the integrability of the geodesic flow on a threefold admitting one of the three group geometries in Thurston’s sense. We focus on the case. The main examples are the quotients , where is a cofinite Fuchsian group. We show that the corresponding phase space contains two open regions with integrable and chaotic behaviour, with zero and positive topological entropy, respectively. As a concrete
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Solutions of a Hamiltonian system with two-dimensional control in a neighbourhood of a singular second-order extremal Russ. Math. Surv. (IF 0.9) Pub Date : 2021-10-01 M. I. Ronzhina,L. A. Manita,L. V. Lokutsievskiy
was considered. If the domain U in (1) is a triangle, then the optimal synthesis can be constructed completely (see [1]). Partial synthesis, including synthesis for the problem with a triangle, has also been constructed for a Hamiltonian system of general form with U having the shape of a convex polygon [1]. In the case when U has a smooth boundary, the question of complete optimal synthesis is still
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Lower bounds for -term approximations in the metric of the discrete space Russ. Math. Surv. (IF 0.9) Pub Date : 2021-10-01 B. S. Kashin
In applied problems m-term approximations are used extensively. The approximating m-term polynomials are usually constructed by means of various ‘greedy’ algorithms (see [1] for details). As concerns lower bounds for the quantities (1), in the case when X = L(Ω) and Φ is an orthonormal basis in X such bounds are usually obtained by using the incompressibility property of an N -dimensional cube, which
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Regular spectral problems for systems of ordinary differential equations of the first order Russ. Math. Surv. (IF 0.9) Pub Date : 2021-10-01 A. A. Shkalikov
Here y(x) = (y1(x), . . . , yn(x)) and A(x) = {ajk(x)}j,k=1, where the ajk are complex functions in L1[0, 1], B = diag{b1, . . . , bn} with 0 ̸= bj ∈ C, ρ is a uniformly positive bounded measurable function, U0 and U1 are n × n number matrices, and λ is the spectral parameter. Special cases of such problems include spectral problems for the Dirac operator (which corresponds to n = 2, b1 = −b2 = i,
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Equivariant minimal model program Russ. Math. Surv. (IF 0.9) Pub Date : 2021-08-27 Yu. G. Prokhorov
The purpose of the survey is to systematize a vast amount of information about the minimal model program for varieties with group actions. We discuss the basic methods of the theory and give sketches of the proofs of some principal results. Bibliography: 243 titles.
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Analytic moduli for parabolic Dulac germs Russ. Math. Surv. (IF 0.9) Pub Date : 2021-08-27 P. Mardešić, M. Resman
This paper gives moduli of analytic classification for parabolic Dulac germs (that is, almost regular germs). Dulac germs appear as first return maps of hyperbolic polycycles. Their moduli are given by a sequence of calle–Voronin-type germs of analytic diffeomorphisms. The result is stated in a broader class of parabolic generalized Dulac germs having power- logarithmic asymptotic expansions. Bibliography:
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Convergence of Bieberbach polynomials: Keldysh’s theorems and Mergelyan’s conjecture Russ. Math. Surv. (IF 0.9) Pub Date : 2021-08-27 A. I. Aptekarev
Results due to Keldysh on the convergence of Bieberbach polynomials and the density of polynomials in spaces of analytic functions are considered. Their further development and relevance in the contemporary context of constructive complex analysis are discussed. Particular focus is placed on Mergelyan’s conjecture on the rate of convergence in a domain with smooth boundary, which is still open. Bibliography:
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Multipoint formulae for inverse scattering at high energies Russ. Math. Surv. (IF 0.9) Pub Date : 2021-08-01 R. G. Novikov
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Groups generated by involutions, numberings of posets, and central measures Russ. Math. Surv. (IF 0.9) Pub Date : 2021-08-01 A. M. Vershik
1. Definitions. An infinite countable ordered set {P,≻, ∅} with minimal element ∅ and no maximal elements is called a locally finite poset if all its principal ideals are finite. A monotone numbering of P (or a part of P ) is an injective map φ : N → P from the set of positive integers to P satisfying the following conditions: if φ(n) ≻ φ(m), then n > m, with φ(0) = ∅. The distributive lattice ΓP of
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Multilevel interpolation for Nikishin systems and boundedness of Jacobi matrices on binary trees Russ. Math. Surv. (IF 0.9) Pub Date : 2021-08-01 A. I. Aptekarev,V. G. Lysov
Modern applications [1] provide motivation to consider the tridiagonal Jacobi matrix (or the so-called discrete Schrödinger operator), a classical object of spectral theory, on graphs [2]. On homogeneous trees one method to implement such operators is based on Hermite–Padé interpolation problems (see [3]). Let μ⃗ = (μ1, . . . , μd) be a collection of positive Borel measures with compact supports on
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Classification of non-Khler surfaces and locally conformally Khler geometry Russ. Math. Surv. (IF 0.9) Pub Date : 2021-07-06 M. S. Verbitsky, V. Vuletescu, L. Ornea
The Enriques–Kodaira classification treats non-Khler surfaces as a special case within the Kodaira framework. We prove the classification results for non-Khler complex surfaces without relying on the machinery of the Enriques–Kodaira classification, and deduce the classification theorem for non-Khler surfaces from the Buchdahl–Lamari theorem. We also prove that all non-Khler surfaces which are not
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On the resolution of singularities of one-dimensional foliations on three-manifolds Russ. Math. Surv. (IF 0.9) Pub Date : 2021-07-02 J. C. Rebelo, H. Reis
This paper is devoted to the resolution of singularities of holomorphic vector fields and one-dimensional holomorphic foliations in dimension three, and it has two main objectives. First, within the general framework of one-dimensional foliations, we build upon and essentially complete the work of Cano, Roche, and Spivakovsky (2014). As a consequence, we obtain a general resolution theorem comparable
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Theory of homotopes with applications to mutually unbiased bases, harmonic analysis on graphs, and perverse sheaves Russ. Math. Surv. (IF 0.9) Pub Date : 2021-07-02 A. I. Bondal, I. Yu. Zhdanovskiy
This paper is a survey of contemporary results and applications of the theory of homotopes. The notion of a well-tempered element of an associative algebra is introduced, and it is proved that the category of representations of the homotope constructed by a well-tempered element is the heart of a suitably glued -structure. The Hochschild and global dimensions of homotopes are calculated in the case
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Chaplygin ball in a solenoidal field Russ. Math. Surv. (IF 0.9) Pub Date : 2021-06-01 A. V. Borisov,A. V. Tsiganov
According to Dirac, changes in the equations of motion related to additional external forces performing no work can be described in terms of deformations of the Poisson bracket. It is natural to ask whether or not Dirac’s ideas are valid in non-holonomic mechanics. We discuss this question here by taking the Chaplygin ball as an example. We consider the linear Lie–Poisson bracket on the Lie algebra
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Landau–Ginzburg models of complete intersections in Lagrangian Grassmannians Russ. Math. Surv. (IF 0.9) Pub Date : 2021-06-01 V. V. Przyjalkowski,K. Rietsch
Let LG(n) be the Lagrangian Grassmannian parameterizing the Lagrangian linear subspaces of the 2n-dimensional complex symplectic vector space. It has a Plücker embedding to a projective space P, so that for H = OP(1) we have Pic(LG(n)) = ZH. Let X ⊂ LG(n) be a smooth Fano complete intersection of degrees d1, . . . , dk. We have ∑k i=1 di < n + 1, and dk+1 = n + 1 − ∑k i=1 di is the Fano index of X
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Interpolation properties of Hermite–Padé polynomials Russ. Math. Surv. (IF 0.9) Pub Date : 2021-06-01 S. P. Suetin
where σ1 is a positive measure with support supp σ1 on a compact set E ⊂ R and h ∈ H (E) is a holomorphic function on E. If h(z) = σ̂2(z), where σ2 is a positive measure with support supp σ2 ⊂ F , where F ⊂ R \ E is a compact set, then the pair of functions f1, f2 forms a Nikishin system (see [6], and also [7], [5], [10], and the bibliography therein). Let Qn,j , j = 0, 1, 2, be the Hermite–Padé polynomials
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Newton polytopes and tropical geometry Russ. Math. Surv. (IF 0.9) Pub Date : 2021-04-27 B Ya Kazarnovskii, A G Khovanskii, A I Esterov
The practice of bringing together the concepts of `Newton polytopes', `toric varieties', `tropical geometry', and `Grbner bases' has led to the formation of stable and mutually beneficial connections between algebraic geometry and convex geometry. This survey is devoted to the current state of the area of mathematics that describes the interaction and applications of these concepts. Bibliography: 68
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On the tensor rank of multiplication in finite extensions of finite fields and related issues in algebraic geometry Russ. Math. Surv. (IF 0.9) Pub Date : 2021-04-27 S. Ballet, J. Pieltant, M. Rambaud, H. Randriambololona, R. Rolland, J. Chaumine
In this paper, we give a survey of the known results concerning the tensor rank of multiplication in finite extensions of finite fields, enriched with some unpublished recent results, and we analyze these to enhance the qualitative understanding of the research area. In particular, we identify and clarify certain partially proved results and emphasise links with open problems in number theory, algebraic
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Questions in algebra and mathematical logic. Scientific heritage of S. I. Adian Russ. Math. Surv. (IF 0.9) Pub Date : 2021-04-27 V. S. Atabekyan, L. D. Beklemishev, V. S. Guba, I. G. Lysenok, A. A. Razborov, A. L. Semenov
This is a survey of results on the Burnside problem and properties of Burnside groups, the finite basis problem for group identities, periodic products of groups and Malcev’s problem, construction of groups with special properties (Tarski monsters), constructive bounds in the Burnside- Magnus problem, and algorithmic problems: the problem of recognition of group properties, the word problem for semigroups
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Separation of variables for type Hitchin systems on a hyperelliptic curve Russ. Math. Surv. (IF 0.9) Pub Date : 2021-04-01 P. I. Borisova
For Hitchin systems Darboux variables were until recently known only in the case of genus 2 and rank 2 (see [2]). For arbitrary simple Lie algebras a description of the class of spectral curves for Hitchin systems on hyperelliptic curves of any genus was given in [5]. For Lie algebras of types An, Bn, Cn Darboux variables were found in an explicit form using separation of variables. The goal of this
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Quantization of linear systems of differential equations with a quadratic invariant in a Hilbert space Russ. Math. Surv. (IF 0.9) Pub Date : 2021-04-01 V. V. Kozlov
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On families of constrictions in the model of an overdamped Josephson junction Russ. Math. Surv. (IF 0.9) Pub Date : 2021-04-01 Yu. P. Bibilo,A. A. Glutsyuk
The tunnelling effect predicted by Josephson [8] in 1962 (Nobel Prize in Physics, 1973) relates to a system of two superconductors separated by a thin dielectric layer. This phenomenon is as follows: if the dielectric is sufficiently thin, then there is a superconducting current through the system (called a Josephson junction) which is described by Josephson’s equations. In this note we investigate
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Hyperbolic Roussarie fields with degenerate quadratic part Russ. Math. Surv. (IF 0.9) Pub Date : 2021-04-01 N. G. Pavlova,A. O. Remizov
In many problems in analysis and geometry there is a need to investigate vector fields with singular points that are not isolated but rather form a submanifold of the phase space, which most often has codimension 2. Of primary interest are the local orbital normal forms of such fields. ‘Orbital’ means that we may multiply vector fields by scalar functions with constant sign. In what follows, all vector
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Spinning tops and magnetic orbits Russ. Math. Surv. (IF 0.9) Pub Date : 2021-03-04 S. P. Novikov
A number of directions were initiated by the author and his students in their papers of 1981–1982. However, one of them, concerning the properties of closed orbits on the sphere and in the groups and , has not been sufficiently developed. This paper revives the discussion of these questions, states unsolved problems, and explains what was regarded as fallacies in old papers. In general, magnetic orbits
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The Dickman–Goncharov distribution Russ. Math. Surv. (IF 0.9) Pub Date : 2021-03-04 S. A. Molchanov, V. A. Panov
In the 1930s and 40s, one and the same delay differential equation appeared in papers by two mathematicians, Karl Dickman and Vasily Leonidovich Goncharov, who dealt with completely different problems. Dickman investigated the limit value of the number of natural numbers free of large prime factors, while Goncharov examined the asymptotics of the maximum cycle length in decompositions of random permutations
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Iterated Laurent series over rings and the Contou-Carrre symbol Russ. Math. Surv. (IF 0.9) Pub Date : 2021-03-01 S. O. Gorchinskiy, D. V. Osipov
This article contains a survey of a new algebro-geometric approach for working with iterated algebraic loop groups associated with iterated Laurent series over arbitrary commutative rings and its applications to the study of the higher-dimensional Contou-Carrre symbol. In addition to the survey, the article also contains new results related to this symbol. The higher-dimensional Contou-Carrre symbol
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Quasi-classical approximation for magnetic monopoles Russ. Math. Surv. (IF 0.9) Pub Date : 2021-03-01 Yu. A. Kordyukov, I. A. Taimanov
A quasi-classical approximation is constructed to describe the eigenvalues of the magnetic Laplacian on a compact Riemannian manifold in the case when the magnetic field is given by a non-exact 2-form. For this, the multidimensional WKB method in the form of the Maslov canonical operator is applied. In this case, the canonical operator takes values in sections of a non-trivial line bundle. The constructed
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Fenchel–Nielsen coordinates and Goldman brackets Russ. Math. Surv. (IF 0.9) Pub Date : 2021-02-23 L. O. Chekhov
It is explicitly shown that the Poisson bracket on the set of shear coordinates defined by V. V. Fock in 1997 induces the Fenchel–Nielsen bracket on the set of gluing parameters (length and twist parameters) for pair-of-pants decompositions of Riemann surfaces with holes. These structures are generalized to the case of Riemann surfaces with holes and bordered cusps. Bibliography: 49 titles.
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Dynamics and spectral stability of soliton-like structures in fluid-filled membrane tubes Russ. Math. Surv. (IF 0.9) Pub Date : 2021-02-23 A. T. Il’ichev
This survey presents results on the stability of elevation solitary waves in axisymmetric elastic membrane tubes filled with a fluid. The elastic tube material is characterized by an elastic potential (elastic energy) that depends non-linearly on the principal deformations and describes the compliant elastic media. Our survey uses a simple model of an inviscid incompressible fluid, which nevertheless
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Yang–Baxter algebras, convolution algebras, and Grassmannians Russ. Math. Surv. (IF 0.9) Pub Date : 2021-02-23 V. G. Gorbunov, C. Korff, C. Stroppel
This paper surveys a new actively developing direction in contemporary mathematics which connects quantum integrable models with the Schubert calculus for quiver varieties: there is a purely geometric construction of solutions to the Yang–Baxter equation and their associated Yang–Baxter algebras which play a central role in quantum integrable systems and exactly solvable (integrable) lattice models
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The law of large numbers for the bigraded Betti numbers of a random simplicial complex Russ. Math. Surv. (IF 0.9) Pub Date : 2021-02-01 D. Baralić,V. Limic
This note announces recent exciting progress on the frontier between algebraic topology and probability theory. It is intended for a journal which publishes such announcements (without an abstract, typically in Russian). A description of a larger work in progress is included in the concluding remarks.
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Extreme points of the set of quantum states with bounded energy Russ. Math. Surv. (IF 0.9) Pub Date : 2021-02-01 S. W. Weis,M. E. Shirokov
We show that for any energy observable every extreme point of the set of quantum states with bounded energy is a pure state. This allows us to write every state with bounded energy in terms of a continuous convex combination of pure states of bounded energy. Furthermore, we prove that any quantum state with finite energy can be represented as a continuous convex combination of pure states with the
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Adjunction in 2-categories Russ. Math. Surv. (IF 0.9) Pub Date : 2021-01-05 D. B. Kaledin
The aim of the paper is to introduce an approach to the theory of 2-categories which is based on systematic use of the Grothendieck construction and the Segal Machine and to show how adjunction questions can be investigated by means of this approach and what its connections are with more traditional approaches. As an application, the derived Morita 2-category and the Fourier–Mukai 2-category over a
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Slide complexes and subword complexes Russ. Math. Surv. (IF 0.9) Pub Date : 2020-12-01 E. Yu. Smirnov,A. A. Tutubalina
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Bifurcations in spatially distributed chains of two-dimensional systems of equations Russ. Math. Surv. (IF 0.9) Pub Date : 2020-12-01 S. A. Kaschenko
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Quantisation ideals of nonabelian integrable systems Russ. Math. Surv. (IF 0.9) Pub Date : 2020-10-01 A. V. Mikhailov
We consider dynamical systems on the space of functions taking values in a free associative algebra. The system is said to be integrable if it possesses an infinite dimensional Lie algebra of commuting symmetries. In this paper we propose a new approach to the problem of quantisation of dynamical systems, introduce the concept of quantisation ideals and provide meaningful examples.
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The spectral radius of a certain parametric family of functional operators Russ. Math. Surv. (IF 0.9) Pub Date : 2020-10-01 N. B. Zhuravlev,L. E. Rossovskii