显示样式： 排序： IF:  GO 导出

Convergence of Trigonometric Fourier Series of Functions with a Constraint on the Fractality of Their Graphs Proc. Steklov Inst. Math. (IF 0.7) Pub Date : 20200528
M. L. GridnevFor a function f continuous on a closed interval, its modulus of fractality ν(f, ε) is defined as the function that maps any ε > 0 to the smallest number of squares of size ε that cover the graph of f. The following condition for the uniform convergence of the Fourier series of f is obtained in terms of the modulus of fractality and the modulus of continuity ω(f, δ): if $$\begin{array}{*{20}{c}} {\omega

Approximation of Functions by n Separate Wavelets in the Spaces L p (ℝ), 1 ≤ p ≤ ∞ Proc. Steklov Inst. Math. (IF 0.7) Pub Date : 20200528
E. A. PleshchevaWe consider the orthonormal bases of nseparate MRAs and wavelets constructed by the author earlier. The classical wavelet basis of the space L2(ℝ) is formed by shifts and compressions of a single function ψ. In contrast to the classical case, we consider a basis of L2(ℝ) formed by shifts and compressions of n functions ψs, s = 1,...,n. The constructed nseparate wavelets form an orthonormal basis

Linear Interpolation on a Tetrahedron Proc. Steklov Inst. Math. (IF 0.7) Pub Date : 20200528
N. V. BaidakovaThe standard method for the linear interpolation on a tetrahedron of a function with continuous secondorder partial derivatives bounded by a given constant is considered. Estimates of the approximation of firstorder derivatives that are more exact than the known estimates are derived.

Integrability Properties of Functions with a Given Behavior of Distribution Functions and Some Applications Proc. Steklov Inst. Math. (IF 0.7) Pub Date : 20200528
A. A. KovalevskyWe establish that if the distribution function of a measurable function v defined on a bounded domain Ω in ℝn (n ≥ 2) satisfies, for sufficiently large k, the estimate meas {v > k} ≤ k−αϕ(k)/ψ(k), where α > 0, ϕ: [1,+∞) → ℝ is a nonnegative nonincreasing measurable function such that the integral of the function s → ϕ(s)/s over [1,+∞) is finite, and ψ: [0,+∞) → ℝ is a positive continuous function

Harmonic Interpolating Wavelets in a Ring Proc. Steklov Inst. Math. (IF 0.7) Pub Date : 20200528
N. I. Chernykh, Yu. N. SubbotinComplementing the authors' earlier joint papers on the application of orthogonal wavelets to represent solutions of Dirichlet problems with the Laplace operator and its powers in a disk and a ring and of interpolating wavelets for the same problem in a disk, we develop a technique of applying periodic interpolating wavelets in a ring for the Dirichlet boundary value problem. The emphasis is not on

Approximation of Derivatives of Analytic Functions from One Hardy Class by Another Hardy Class Proc. Steklov Inst. Math. (IF 0.7) Pub Date : 20200528
R. R. AkopyanIn the Hardy space Hp(Dϱ), 1 ≤ p ⪯ ∞, of functions analytic in the disk Dϱ = {z ∈ ℂ}: z < ϱ, we denote by NHp(Dϱ), N > 0, the class of functions whose Lpnorm on the circle γϱ = {z ∈ ℂ: z = ϱ} does not exceed the number N and by ∂Hp(Dϱ) the class consisting of the derivatives of functions from 1Hp(Dϱ). We consider the problem of the best approximation of the class ∂Hp(Dϱ) by the class NHp(DR)N > 0

Calculation of Elements of a Guiding Program Package for Singular Clusters of the Set of Initial States in the Package Guidance Problem Proc. Steklov Inst. Math. (IF 0.7) Pub Date : 20200528
S. M. Orlov, N. V. StrelkovskiiA fixedtime package guidance problem is considered for a linear controlled dynamic system with a finite set of initial states. The control set is convex and compact and the target set is convex and closed. The paper focuses on the case where the set of initial states has singular clusters for which the existing algorithm for estimating the elements of a guiding program package is not applicable. It

Analytic Continuation Methods for Multivalued Functions of One Variable and Their Application to the Solution of Algebraic Equations Proc. Steklov Inst. Math. (IF 0.7) Pub Date : 20200528
L. S. MaergoizThe paper discusses several methods of analytic continuation of a multivalued function of one variable given on a part of its Riemann surface in the form of a Puiseux series generated by the power function z = w1/ρ, where ρ 1/2 and ρ ≠ 1. We present a manysheeted variant of G.Pólya’s theorem describing the relation between the indicator and conjugate diagrams for entire functions of exponential type

Best OneSided Approximation in the Mean of the Characteristic Function of an Interval by Algebraic Polynomials Proc. Steklov Inst. Math. (IF 0.7) Pub Date : 20200528
M. V. Deikalova, A. Yu. TorgashovaLet υ be a weight on (−1, 1), i.e., a measurable integrable nonnegative function nonzero almost everywhere on (−1, 1). Denote by Lυ(−1, 1) the space of realvalued functions f integrable with weight υ on (−1, 1) with the norm \(f = \int\limits_{  1}^1 {f(x)v(x)dx.} \). We consider the problems of the best onesided approximation (from below and from above) in the space Lυ(−1, 1) to the characteristic

Best Uniform Approximation of the Differentiation Operator by Operators Bounded in the Space L 2 Proc. Steklov Inst. Math. (IF 0.7) Pub Date : 20200528
V. V. ArestovWe give a solution of the problem on the best uniform approximation on the number axis of the firstorder differentiation operator on the class of functions with bounded second derivative by linear operators bounded in the space L2. This is one of the few cases of the exact solution of the problem on the approximation of the differentiation operator in some space with the use of approximating operators

Bernstein–Szegő Inequality for the Weyl Derivative of Trigonometric Polynomials in L 0 Proc. Steklov Inst. Math. (IF 0.7) Pub Date : 20200528
A. O. Leont’evaIn the set Tn of trigonometric polynomials fn of order n with complex coefficients, we consider Weyl (fractional) derivatives fn(α) of real nonnegative order α. The inequality ║Dθαfn║p ≤ Bn(α, θ)p║fn║p for the WeylSzegő operator Dθαfn(t) = fnα (t)cosθ + f͂nα (t) sin θ in the set Tn of trigonometric polynomials is a generalization of Bernstein’s inequality. Such inequalities have been studied for 90

Extremal Shift to Accompanying Points in a Positional Differential Game for a FractionalOrder System Proc. Steklov Inst. Math. (IF 0.7) Pub Date : 20200528
M. I. GomoyunovA twoperson zerosum differential game is considered. The motion of the dynamic system is described by an ordinary differential equation with a Caputo fractional derivative of order α ∈ (0, 1). The quality index consists of two terms: the first depends on the motion of the system realized by the terminal time and the second includes an integral estimate of the realizations of the players’ controls

A Feller Transition Kernel with Measure Supports Given by a SetValued Mapping Proc. Steklov Inst. Math. (IF 0.7) Pub Date : 20200528
S. N. SmirnovAssume that X is a topological space and Y is a separable metric space. Let these spaces be equipped with Borel σalgebras BX and BY, respectively. Suppose that P(x, B) is a stochastic transition kernel; i.e., the mapping x ↦ P(x,B) is measurable for all B ∈ BY and the mapping B ↦ P(x, B) is a probability measure for any x ∈ X. Denote by supp(P(x, ·) the topological support of the measure B ↦ P(x,B)

Convergence of Quartic Interpolating Splines Proc. Steklov Inst. Math. (IF 0.7) Pub Date : 20200528
Yu. S. VolkovThe problem of interpolation by quartic splines according to Marsden’s scheme is considered. It is shown that the calculation of an interpolating spline in terms of the coefficients of expansion of its second derivative in L1normalized quadratic Bsplines yields a system of linear equations for the chosen parameters. The matrix of the system is pentadiagonal and has a column diagonal dominance, which

Relaxation of the Pursuit–Evasion Differential Game and Iterative Methods Proc. Steklov Inst. Math. (IF 0.7) Pub Date : 20200528
A. G. Chentsov, D. M. KhachayA variant of the program iteration method called stability iterations is used for a differential game of pursuit–evasion. The successful solvability set of one of the problems generating the game is found as a limit of the iterative procedure in the space of sets whose elements are positions of the game. The game is defined by a pair of closed sets, one of the which is the target set in the pursuit

Extremal Shift in a Problem of Tracking a Solution of an Operator Differential Equation Proc. Steklov Inst. Math. (IF 0.7) Pub Date : 20200528
V. I. MaksimovA control problem for an operator differential equation in a Hilbert space is considered. The problem consists in constructing an algorithm generating a feedback control and guaranteeing that the solution of the equation follows a solution of another equation, which is subject to an unknown disturbance. We assume that both equations are given on an infinite time interval and the unknown disturbance

Extraction of Several Harmonics from Trigonometric Polynomials. FejerType Inequalities Proc. Steklov Inst. Math. (IF 0.7) Pub Date : 20200525
D. G. Vasilchenkova, V. I. DanchenkoGiven a trigonometric polynomial \({T_n}(t) = \sum\nolimits_{k = 1}^n {{\tau _k}\left( t \right),{\tau _k}\left( t \right): = {a_k}\cos kt + {b_k}\sin kt}\) we consider the problem of extracting the sum of harmonics \(\sum \tau_{\mu_s}(t)\) prescribed orders µs by the method of amplitude and phase transformations. Such transformations map the polynomials Tn(t) into similar ones using two simple operations:

Knot Invariants in Geodesic Flows Proc. Steklov Inst. Math. (IF 0.7) Pub Date : 20200525
P. M. Akhmet’evThe mean value of an asymptotic invariant of a knotted trajectory of a GhysDehornoy geodesic flow is calculated. The result is important for investigating the magnetostatic equilibrium state of a magnetic field in a liquid conducting medium.

Singularities of Multivalued Solutions of Quasilinear Hyperbolic Systems Proc. Steklov Inst. Math. (IF 0.7) Pub Date : 20200525
I. A. Bogaevsky, D. V. TunitskyWe study the singularities of multivalued solutions of a quasilinear hyperbolic system with two independent and two dependent variables that satisfies the strong nonlinearity condition. For such solutions we obtain a local leftright classification of their projections onto the plane of independent variables at points of finite multiplicity of rank 1.

Tracking the Solution of a Linear Parabolic Equation Using Feedback Laws Proc. Steklov Inst. Math. (IF 0.7) Pub Date : 20200525
V. I. MaksimovWe consider the problem of tracking the solution of a parabolic equation with an unknown righthand side by the solution of a similar parabolic equation. To solve this problem, we propose two noiseresistant algorithms based on the extremal shift method known in guaranteed control theory. The first algorithmpertains to the case of continuousmeasurement of solutions to the equations, and the second

Fredholm Property of Integral Operators with Homogeneous Kernels of Compact Type in the L 2 Space on the Heisenberg Group Proc. Steklov Inst. Math. (IF 0.7) Pub Date : 20200525
V. V. Denisenko, V. M. DeundyakWe consider the Heisenberg group ℍn with Korányi norm. In the space L2(ℍn), we introduce integral operators with homogeneous kernels of compact type and multiplicatively weakly oscillating coefficients. For the unital C*algebra \(\mathfrak{W}\)(ℍn) generated by such operators, we construct a symbolic calculus and in terms of this calculus formulate necessary and sufficient conditions for an operator

On Some Sufficient Hyperbolicity Conditions Proc. Steklov Inst. Math. (IF 0.7) Pub Date : 20200525
S. D. Glyzin, A. Yu. Kolesov, N. Kh. RozovAbstract—We consider an arbitrary C1 diffeomorphism f that acts from an open subset U of a Riemannian manifold M of dimension m, m ≥ 2, to f(U) ⊂ M. Let A be a compact finvariant (i.e., f(A) = A) subset in U. We propose various sufficient conditions under which A is a hyperbolic set of f.

On Sufficient Optimality Conditions for Infinite Horizon Optimal Control Problems Proc. Steklov Inst. Math. (IF 0.7) Pub Date : 20200525
Anton O. BelyakovWe consider the Seierstad sufficiency theorem in comparison with the Mangasarian and Arrow sufficiency theorems for optimal control problems with infinite time horizon. Both finite and infinite values of the objective functional are allowed, since the concepts of overtaking and weakly overtaking optimality are implied. We extend the conditions under which the Seierstad sufficiency theorem can be applied

Localized Asymptotic Solution of a VariableVelocity Wave Equation on the Simplest Decorated Graph Proc. Steklov Inst. Math. (IF 0.7) Pub Date : 20200525
A. V. Tsvetkova, A. I. ShafarevichWe consider a variablevelocity wave equation on the simplest decorated graph obtained by gluing a ray to the threedimensional Euclidean space, with localized initial conditions on the ray. The wave operator should be selfadjoint, which implies some boundary conditions at the gluing point. We describe the leading part of the asymptotic solution of the problem using the construction of the Maslov

On the Structure of Solutions to a Model System That Is Nonstrictly Hyperbolic in the Sense of Petrovskii Proc. Steklov Inst. Math. (IF 0.7) Pub Date : 20200525
V. V. PalinWe construct solutions to the Cauchy problem for a model system that is not hyperbolic in the sense of Friedrichs. To this end, we apply a new geometric method for constructing solutions to the Riemann problem.

Stabilization of Statistical Solutions for an Infinite Inhomogeneous Chain of Harmonic Oscillators Proc. Steklov Inst. Math. (IF 0.7) Pub Date : 20200525
T. V. DudnikovaAn infinite inhomogeneous harmonic chain of particles with different force constants of interaction is considered. The large time behavior of distributions of the solutions to the Cauchy problem with random initial data is studied. The main result of the paper establishes the convergence of these distributions to a limiting measure.

Multiple Mixing with Respect to Noncoinciding Sets Proc. Steklov Inst. Math. (IF 0.7) Pub Date : 20200525
S. V. TikhonovWe introduce a class of systems without multiple mixing. The sets with respect to which the mixing is considered are not assumed to coincide. This class contains Ledrappier’s example as a particular case. We prove that there are no multidimensional flows among such systems.

Hölder Continuity and Harnack’s Inequality for p ( x )Harmonic Functions Proc. Steklov Inst. Math. (IF 0.7) Pub Date : 20200525
Yu. A. Alkhutov, M. D. SurnachevA sufficient condition for a measurable exponent p(x) is obtained that implies the Hölder continuity and Harnack’s inequality for p(x)harmonic functions.

Qualitative Properties of a Duffing System with Polynomial Nonlinearity Proc. Steklov Inst. Math. (IF 0.7) Pub Date : 20200525
A. N. Kanatnikov, A. P. KrishchenkoThe paper is devoted to the qualitative analysis of a nonautonomous Duffing equation with nonlinearity in the form of a monomial of odd degree. For all values of the parameters, compact localizing sets containing all compact invariant sets of the system are constructed. The behavior of the trajectories of the system outside the localizing set is analyzed, and it is shown that the trajectories of the

On the Solvability of a Class of Nonlinear Hammerstein—Stieltjes Integral Equations on the Whole Line Proc. Steklov Inst. Math. (IF 0.7) Pub Date : 20200525
Kh. A. Khachatryan, H. S. PetrosyanWe consider a nonlinear integral equation on the whole line with a HammersteinStieltjes integral operator whose prekernel is a continuous distribution function. Under certain conditions imposed on the nonlinearity, we prove constructive existence and uniqueness theorems for nonnegative monotone bounded solutions. Some qualitative properties of the constructed solution are also studied. In particular

Derivation Algebra in Noncommutative Group Algebras Proc. Steklov Inst. Math. (IF 0.7) Pub Date : 20200525
A. A. ArutyunovFor a generally infinite noncommutative discrete group G, we study derivation algebras in the group algebra of G in terms of characters on a groupoid associated with the group. We obtain necessary conditions for a character to define a derivation. Using these conditions, we analyze some examples. In particular, we describe a derivation algebra in the case when the group is a nilpotent group of rank

Three Types of Attractors and Mixed Dynamics of Nonholonomic Models of Rigid Body Motion Proc. Steklov Inst. Math. (IF 0.7) Pub Date : 20200525
S. V. Gonchenko, A. S. Gonchenko, A. O. KazakovWe survey recent results on the theory of dynamical chaos from the point of view of topological dynamics. We present the concept of three types of dynamics: conservative, dissipative, and mixed dynamics, and also show several simple examples of attractors and repellers of all three types. Their similarities and differences with other known types of attractors and repellers (maximal and Milnor ones)

Sufficient Optimality Conditions for Hybrid Systems of Variable Dimension Proc. Steklov Inst. Math. (IF 0.7) Pub Date : 20200525
A. S. BortakovskiiWe consider an optimal control problem for a hybrid system whose continuous motion alternates with discrete variations (switchings) under which the dimension of the state space changes. The moments and the number of switchings are not specified in advance. They are determined as a result of minimizing a functional that incorporates the cost of each switching. The state space may change, for example

Coincidence Points and Generalized Coincidence Points of Two SetValued Mappings Proc. Steklov Inst. Math. (IF 0.7) Pub Date : 20200525
A. V. Arutyunov, E. S. Zhukovskiy, S. E. ZhukovskiyWe consider setvalued mappings acting in metric spaces and show that, under natural general assumptions, the set of coincidence points of two such mappings one of which is covering and the other is Lipschitz continuous is dense in the set of generalized coincidence points of these mappings. We use this result to study the coincidence points and generalized coincidence points of a setvalued covering

Linear Pfaffian Systems and Classical Solutions of Triangular Schlesinger Equations Proc. Steklov Inst. Math. (IF 0.7) Pub Date : 20200525
V. P. LeksinIn this paper, by classical solutions we mean solutions to Fuchsian type meromorphic linear integrable Pfaffian systems dy = Ωy on the complex linear spaces ℂn, n ≥ 1, where y(z) = (y1(z),..., yn(z)T ∈ ℂn is a column vector and Ω is a meromorphic matrix differential 1form such that Ω = ∑1≤i

Scenario of a Simple Transition from a Structurally Stable 3Diffeomorphism with a TwoDimensional Expanding Attractor to a DA Diffeomorphism Proc. Steklov Inst. Math. (IF 0.7) Pub Date : 20200525
V. Z. Grines, E. V. Kruglov, O. V. PochinkaThe Smale surgery on the threedimensional torus allows one to obtain a socalled DA diffeomorphism from the Anosov automorphism. The nonwandering set of a DA diffeomorphism consists of a single twodimensional expanding attractor and a finite number of source periodic orbits. As shown by V. Z. Grines, E. V. Zhuzhoma, and V. S. Medvedev, the dynamics of an arbitrary structurally stable 3diffeomorphism

On Automorphism Groups of AT4(7, 9, r )Graphs and of Their Local Subgraphs Proc. Steklov Inst. Math. (IF 0.7) Pub Date : 20200322
L. Yu. TsiovkinaThe paper is devoted to the problem of classification of AT4(p, p + 2, r)graphs. An example of an AT4(p, p + 2, r)graph with p = 2 is provided by the Soicher graph with intersection array {56, 45, 16, 1; 1, 8, 45, 56}. The question of existence of AT4(p, p + 2, r)graphs with p > 2 is still open. One task in their classification is to describe such graphs of small valency. We investigate the automorphism

One Approach to the Solution of Problems in Plasma Dynamics Proc. Steklov Inst. Math. (IF 0.7) Pub Date : 20200322
L. I. Rubina, O. N. Ul’yanovA system of equations for the motion of an ionized ideal gas is considered. An algorithm for the reduction of this system of nonlinear partial differential equations (PDEs) to systems of ordinary differential equations (ODEs) is presented. It is shown that the independent variable ψ in the systems of ODEs is determined from the relation ψ = t + xf1(ψ) + yf2(ψ) + zf3(ψ) after choosing (setting or finding)

PolynomialTime Approximation Scheme for the Capacitated Vehicle Routing Problem with Time Windows Proc. Steklov Inst. Math. (IF 0.7) Pub Date : 20200322
M. Yu. Khachai, Yu. Yu. OgorodnikovThe capacitated vehicle routing problem with time windows (CVRPTW) is a wellknown NPhard combinatorial optimization problem. We present a further development of the approach first proposed by M. Haimovich and A. H. G. Rinnooy Kan and propose an algorithm that, for an arbitrary ε > 0, finds a (1 + ε)approximate solution for the Euclidean CVRPTW in \(\text{TIME}\;(\text{TSP},\;\rho ,n)\; + \;O({n^2})

On a Control Problem under Disturbance and Possible Breakdown Proc. Steklov Inst. Math. (IF 0.7) Pub Date : 20200322
V. I. UkhobotovA linear control problem is considered in the presence of an uncontrolled disturbance. It is only known that the values of the disturbance belong to a given connected compact set. The terminal time of the control process is fixed. The terminal component of the payoff depends on the modulus of a linear function of the phase variables, and the integral component is given by an integral of a power of

On the Problem of Global Localization of Discontinuity Lines for a Function of Two Variables Proc. Steklov Inst. Math. (IF 0.7) Pub Date : 20200322
A. L. Ageev, T. V. AntonovaWe consider the illposed problem of localizing (finding the position of) the discontinuity lines of a function of two variables that is smooth outside the discontinuity lines and has a discontinuity of the first kind at each point of such lines. A uniform square grid with step τ is considered, and it is assumed that the mean values of a perturbed function over squares with side τ are known at each

Minimal Submanifolds of Spheres and Cones Proc. Steklov Inst. Math. (IF 0.7) Pub Date : 20200322
M. I. Zelikin, Yu. S. OsipovIntersections of cones of index zero with spheres are investigated. Fields of the corresponding minimal manifolds are found. In particular, the cone \(\mathbb{K} = \left\{ {x_0^2 + x_1^2 + x_2^2 + x_3^2} \right\}\) is considered. Its intersection with the sphere \(\mathbb{S}^{3}=\sum\nolimits_{i=0}^{3} x_{i}^{2}\) is often called the Clifford torus \(\mathbb {T}\), because Clifford was the first to

Polynomials Least Deviating from Zero on a Square of the Complex Plane Proc. Steklov Inst. Math. (IF 0.7) Pub Date : 20200322
E. B. BayramovThe Chebyshev problem on the square Π = {z = x + iy ∈ ℂ: max{∣x∣, ∣y∣} ≤ 1} of the complex plane ℂ is studied. Let \(p_{n} \in \mathfrak{P}_{n}\) be the set of algebraic polynomials of a given degree n with the unit leading coefficient. The problem is to find the smallest value τn(Π) of the uniform norm ∥pn∥C(π) of polynomials \(\mathfrak{P}_{n}\) on the square Π and a polynomial with the smallest

Optimal Stopping Strategies in the Game “The Price Is Right” Proc. Steklov Inst. Math. (IF 0.7) Pub Date : 20200322
T. V. Seregina, A. A. Ivashko, V. V. MazalovThe popular TV show “The Price Is Right” is an attractive source of modeling the strategic behavior in a competitive environment for a specific reward. In this study, the structure of the show is used as a basis for several gametheoretic settings. We consider a noncooperative optimal stopping game for a finite number of players. Each player earns points by observing the sums of independent random

Inverse Problems in the Theory of DistanceRegular Graphs Proc. Steklov Inst. Math. (IF 0.7) Pub Date : 20200322
A. A. Makhnev, D. V. PaduchikhFor a distanceregular graph Γ of diameter 3, the graph Γi can be strongly regular for i = 2 or 3. Finding the parameters of Γi from the intersection array of Γ is a direct problem, and finding the intersection array of Γ from the parameters of Γi is the inverse problem. The direct and inverse problems were solved earlier by A. A. Makhnev and M. S. Nirova for i = 3. In the present paper, we solve the

Shilla DistanceRegular Graphs with b 2 = sc 2 Proc. Steklov Inst. Math. (IF 0.7) Pub Date : 20200322
I. N. BelousovA Shilla graph is a distanceregular graph Γ of diameter 3 whose second eigenvalue is a = a3. A Shilla graph has intersection array {ab, (a + 1)(b − 1), b2; 1, c2, a(b − 1)}. J. Koolen and J. Park showed that, for a given number b, there exist only finitely many Shilla graphs. They also found all possible admissible intersection arrays of Shilla graphs for b ∈ {2, 3}. Earlier the author together with

On Finite Simple Linear and Unitary Groups of Small Size over Fields of Different Characteristics with Coinciding Prime Graphs Proc. Steklov Inst. Math. (IF 0.7) Pub Date : 20200322
M. R. Zinov’evaSuppose that G is a finite group, π(G) is the set of prime divisors of its order, and ω(G) is the set of orders of its elements. A graph with the following adjacency relation is defined on π(G): different vertices r and s from π(G) are adjacent if and only if rs ∈ ω(G). This graph is called the Gruenberg—Kegel graph or the prime graph of G and is denoted by GK(G). In A. V. Vasil’ev’s Question 16.26

An Algorithm for the Polyhedral Cycle Cover Problem with Constraints on the Number and Length of Cycles Proc. Steklov Inst. Math. (IF 0.7) Pub Date : 20200322
V. V. ShenmaierA cycle cover of a graph is a spanning subgraph whose connected components are simple cycles. Given a complete weighted directed graph, consider the intractable problem of finding a maximumweight cycle cover which satisfies an upper bound on the number of cycles and a lower bound on the number of edges in each cycle. We suggest a polynomialtime algorithm for solving this problem in the geometric

Coalitional Stability Conditions in Multicriteria Dynamic Games Proc. Steklov Inst. Math. (IF 0.7) Pub Date : 20200322
A. N. RettievaWe study the stability of coalitions in multicriteria dynamic games. We use the bargaining construction (Nash product) to obtain a noncooperative equilibrium and the Nash bargaining scheme for the entire duration of the game to find a cooperative solution. Conditions for the internal and external stability are extended to dynamic games with vector payoff functions. The notion of coalitional stability

On a Singularly Perturbed TimeOptimal Control Problem with Two Small Parameters Proc. Steklov Inst. Math. (IF 0.7) Pub Date : 20200322
A. R. Danilin, O. O. KovrizhnykhIn this paper, we investigate a timeoptimal control problem for a singularly perturbed linear autonomous system with two independent small parameters and smooth geometric constraints on the control in the form of a ball. The main difference between this case and the case of systems with fast and slow variables studied earlier is that the matrix at the fast variables is a multidimensional analog of

Stabilizers of Vertices of Graphs with Primitive Automorphism Groups and a Strong Version of the Sims Conjecture. IV Proc. Steklov Inst. Math. (IF 0.7) Pub Date : 20200322
A. S. Kondrat’ev, V. I. TrofimovThis is the fourth in a series of papers whose results imply the validity of a strong version of the Sims conjecture on finite primitive permutation groups. In this paper, the case of primitive groups with a simple socle of orthogonal Lie type and nonparabolic point stabilizer is considered. Let G be a finite group, and let M1 and M2 be distinct conjugate maximal subgroups of G. For any i ∈ ℕ, we define

An Example of a Fractal Finitely Generated Solvable Group Proc. Steklov Inst. Math. (IF 0.7) Pub Date : 20200322
Roman V. MikhailovA fractal group is a group with unbounded iterated identity. In this paper a finitely generated fractal solvable group is constructed.

Orbit Closures of the Witt Group Actions Proc. Steklov Inst. Math. (IF 0.7) Pub Date : 20200322
Vladimir L. PopovWe prove that for any prime p there exists an algebraic action of the twodimensional Witt group W2 (p) on an algebraic variety X such that the closure in X of the W2(p)orbit of some point x ∈ X contains infinitely many W2(p)orbits. This is related to the problem of extending, from the case of characteristic zero to the case of characteristic p, the classification of connected affine algebraic groups

Classification of Degenerations and Picard Lattices of Kählerian K3 Surfaces with Symplectic Automorphism Group C 4 Proc. Steklov Inst. Math. (IF 0.7) Pub Date : 20200322
Viacheslav V. NikulinIn the author’s papers of 2013–2018, the degenerations and Picard lattices of Kählerian K3 surfaces with finite symplectic automorphism groups of high order were classified. For the remaining groups of small order—D6, C4, (C2)2, C3, C2, and C1—the classification was not completed because each of these cases requires very long and difficult considerations and calculations. The case of D6 was recently

Monotonic Lagrangian Tori of Standard and Nonstandard Types in Toric and Pseudotoric Fano Varieties Proc. Steklov Inst. Math. (IF 0.7) Pub Date : 20200322
Nikolai A. TyurinIn recent papers we constructed examples of nonstandard Lagrangian tori in compact simply connected toric symplectic manifolds. Using a new “pseudotoric” technique, we explained the appearance of nonstandard Lagrangian tori of Chekanov type and proposed a topological obstruction which separates them from the standard ones. In the present paper we construct nonstandard tori satisfying the BohrSommerfeld

Automorphisms of Weighted Complete Intersections Proc. Steklov Inst. Math. (IF 0.7) Pub Date : 20200322
Victor V. Przyjalkowski, Constantin A. ShramovWe show that smooth wellformed weighted complete intersections have finite automorphism groups, with several obvious exceptions.