Authors:E. A. Alekhno; E. M. Semenov; F. A. Sukochev; A. S. Usachev Pages: 305 - 307 Abstract: Abstract Banach limits invariant with respect to the Cesàro transform are studied. New functional characteristics of Banach limits are introduced and studied. PubDate: 2017-07-01 DOI: 10.1134/s1064562417040019 Issue No:Vol. 96, No. 1 (2017)

Authors:V. N. Denisov Pages: 308 - 311 Abstract: Abstract Sharp sufficient conditions on the coefficients of a second-order parabolic equation are examined under which the solution of the corresponding Cauchy problem with a power-law growing initial function stabilizes to zero. An example is presented showing that the found sufficient conditions are sharp. Conditions on the coefficients of a parabolic equation are obtained under which the solution of the Cauchy problem with a bounded initial function stabilizes to zero at a power law rate. PubDate: 2017-07-01 DOI: 10.1134/s1064562417040020 Issue No:Vol. 96, No. 1 (2017)

Authors:V. L. Popov Pages: 312 - 314 Abstract: Abstract For connected simple algebraic groups defined over an algebraically closed field of characteristic zero, the classifications of irreducible algebraic representations of modalities 0, 1, and 2 are obtained. PubDate: 2017-07-01 DOI: 10.1134/s1064562417040032 Issue No:Vol. 96, No. 1 (2017)

Authors:V. D. Stepanov; G. E. Shambilova Pages: 315 - 320 Abstract: Abstract Necessary and sufficient conditions for the weighted boundedness of a class of positive quasilinear two-kernel integral operators of iterated type on the real half-line are given. PubDate: 2017-07-01 DOI: 10.1134/s1064562417040056 Issue No:Vol. 96, No. 1 (2017)

Authors:M. E. Zhukovskii; A. D. Matushkin Pages: 326 - 328 Abstract: Abstract Spectra of first-order formulas are studied. The spectrum of a first-order formula is the set of all positive α such that either this formula is true for the random graph G(n, n −α) with an asymptotic probability being neither 0 nor 1 or the limit does not exist. It is well known that there exists a first-order formula with an infinite spectrum. The minimum number of quantifier alternations in such a formula is found. PubDate: 2017-07-01 DOI: 10.1134/s1064562417040093 Issue No:Vol. 96, No. 1 (2017)

Authors:V. G. Zvyagin; V. P. Orlov Pages: 329 - 331 Abstract: Abstract The existence of a weak solution of a boundary value problem for a viscoelasticity model with memory on an infinite time interval is proved. The proof relies on an approximation of the original boundary value problem by regularized ones on finite time intervals and makes use of recent results concerning the solvability of Cauchy problems for systems of ordinary differential equations in the class of regular Lagrangian flows. PubDate: 2017-07-01 DOI: 10.1134/s106456241704010x Issue No:Vol. 96, No. 1 (2017)

Authors:V. P. Platonov; G. V. Fedorov Pages: 332 - 335 Abstract: Abstract Article [1] raised the question of the finiteness of the number of square-free polynomials f ∈ ℚ[h] of fixed degree for which \(\sqrt f \) has periodic continued fraction expansion in the field ℚ((h)) and the fields ℚ(h)( \(\sqrt f \) ) are not isomorphic to one another and to fields of the form ℚ(h) \(\left( {\sqrt {c{h^n} + 1} } \right)\) , where c ∈ ℚ* and n ∈ ℕ. In this paper, we give a positive answer to this question for an elliptic field ℚ(h)( \(\sqrt f \) ) in the case deg f = 3. PubDate: 2017-07-01 DOI: 10.1134/s1064562417040068 Issue No:Vol. 96, No. 1 (2017)

Authors:R. I. Prosanov; A. M. Raigorodskii; A. A. Sagdeev Pages: 336 - 338 Abstract: Abstract The Frankl–Rödl classical bound for the number of edges in a hypergraph with forbidden intersections is improved. The improvements are used to obtain new results in Euclidean Ramsey theory and in combinatorial geometry. PubDate: 2017-07-01 DOI: 10.1134/s106456241704007x Issue No:Vol. 96, No. 1 (2017)

Authors:M. N. Zubova; T. A. Shaposhnikova Pages: 344 - 347 Abstract: Abstract The asymptotic behavior of solutions to a boundary value problem in a domain periodically perforated by small holes with a rapidly oscillating nonhomogeneous Robin-type condition on their boundaries is investigated in the case of critical parameter values. PubDate: 2017-07-01 DOI: 10.1134/s1064562417040159 Issue No:Vol. 96, No. 1 (2017)

Authors:L. E. Shabanov; A. M. Raigorodskii Pages: 351 - 353 Abstract: Abstract A lower bound is obtained for the number of edges in a distance graph G in an infinitesimal plane layer ℝ2 × [0, ε] d , which relates the number of edges e(G), the number of vertices ν(G), and the independence number α(G). It is proved that \(e\left( G \right) \geqslant \frac{{19\nu \left( G \right) - 50\alpha \left( G \right)}}{3}\) . This result generalizes a previous bound for distance graphs in the plane. It substantially improves Turán’s bound in the case where \(\frac{1}{5} \leqslant \frac{{\alpha \left( G \right)}}{{\nu \left( G \right)}} \leqslant \frac{2}{7}\) . PubDate: 2017-07-01 DOI: 10.1134/s1064562417040135 Issue No:Vol. 96, No. 1 (2017)

Authors:V. A. Polunin; A. P. Soldatov Pages: 358 - 361 Abstract: Abstract A new integral representation of the general solution of the Moisil–Théodorescu system in a bounded multiply connected domain with a smooth boundary is obtained. PubDate: 2017-07-01 DOI: 10.1134/s1064562417040172 Issue No:Vol. 96, No. 1 (2017)

Authors:I. G. Tsar’kov Pages: 362 - 364 Abstract: Abstract The paper studies approximation and structural geometric-topological properties of sets in normed and more general (asymmetric) spaces for which there exists a continuous selection for the best and near-best approximation operators. Sufficient conditions on the metric projection of sets which ensure the existence of a continuous selection for this projection are obtained, and the structural properties of such sets are determined. The existence of a continuous selection for the near-best approximation operator on a finite-dimensional space more general than a normed space is investigated. It is shown that the lower semicontinuity of the metric projection is sufficient for the existence of a continuous selection for the near-best approximation operator in the general case. PubDate: 2017-07-01 DOI: 10.1134/s1064562417040196 Issue No:Vol. 96, No. 1 (2017)

Authors:A. D. Baev; V. V. Pankov Pages: 365 - 367 Abstract: Abstract Problems in a strip for high-order elliptic equations that degenerate into an odd-order equation on the strip boundary are studied. Coercive a priori estimates and existence and uniqueness theorems for solutions of such problems are obtained in special weighted Sobolev-type spaces. The norms in these spaces are defined with the help of a special integral transform. PubDate: 2017-07-01 DOI: 10.1134/s1064562417040214 Issue No:Vol. 96, No. 1 (2017)

Authors:J. Montaldi; O. G. Smolyanov Pages: 368 - 372 Abstract: Abstract The definition of Feynman path integrals (Feynman functional integrals) as integrals with respect to a generalized measure, called the Lebesgue–Feynman measure in the paper and being an infinite-dimensional analogue of the classical Lebesgue measure on finite-dimensional Euclidean space, is discussed. This definition, which is a formalization of Feynman’s original definition, is different from those used previously in the mathematical literature. It makes it possible to give a description of the origin of quantum anomaly which is a mathematically correct version of the description given in the book Path Integrals and Quantum Anomalies by K. Fujikawa and H. Suzuki (Oxford, 2004) (and erroneously qualified as wrong in the book Functional Integration: Action and Symmetries by P. Cartier and C. DeWitt-Morette (Cambridge Univ. Press, Cambridge, 2006)). PubDate: 2017-07-01 DOI: 10.1134/s1064562417040226 Issue No:Vol. 96, No. 1 (2017)

Authors:V. S. Samovol Pages: 373 - 376 Abstract: Abstract The Riccati equation is considered. Both continuable and noncontinuable solutions of this equation are studied. Asymptotic representations of its solutions are obtained by power geometry methods. PubDate: 2017-07-01 DOI: 10.1134/s106456241704024x Issue No:Vol. 96, No. 1 (2017)

Authors:D. V. Tunitsky Pages: 377 - 379 Abstract: Abstract The communication concerns a theory of global solvability of initial value problem for nonlinear hyperbolic equations with two independent variables that is an immediate analog of a theory of global solvability of ordinary differential equations. PubDate: 2017-07-01 DOI: 10.1134/s1064562417040263 Issue No:Vol. 96, No. 1 (2017)

Authors:A. A. Polosin Pages: 389 - 392 Abstract: Abstract An asymptotic representation of the eigenfunctions of a convolution-type completely continuous operator for which the image of the kernel is the characteristic function of the interval is constructed. PubDate: 2017-07-01 DOI: 10.1134/s1064562417040305 Issue No:Vol. 96, No. 1 (2017)

Authors:V. V. Ternovskii; T. M. Khapaeva; M. M. Khapaev Pages: 403 - 405 Abstract: Abstract Interest in the inverse Sturm–Liouville problem is motivated by its numerous applications in mathematics and computational physics. To solve a complete inverse problem, one needs two exact spectra, which are usually not known in experimental spectroscopy. Accordingly, a problem of interest is to restore the potential from a finite set of noisy spectral data. A new variational method for solving inverse spectral problems is proposed, which is based on the regularization of ill-posed problems. The method takes into account the measurement error of the spectrum and restores the potential without using simplifying assumptions that it belongs to a certain functional class. The method has been tested on potentials involving smooth segments and jump discontinuities. PubDate: 2017-07-01 DOI: 10.1134/s1064562417040251 Issue No:Vol. 96, No. 1 (2017)

Authors:A. A. Vasin; O. M. Grigoryeva; N. I. Tsyganov Pages: 411 - 414 Abstract: Abstract The optimization of a transportation system in terms of an increase in social welfare is considered. A new algorithm for solving this problem is described in the case where the welfare function is supermodular on the set of lines, and the efficiency of the algorithm is demonstrated. The sub- and supermodularity properties are generalized in the form of complementary and competitive transportation lines. For tree-structured markets, the conditions are indicated under which, for any pair of lines, it can be determined whether they are competitive or complementary. PubDate: 2017-07-01 DOI: 10.1134/s1064562417040202 Issue No:Vol. 96, No. 1 (2017)

Authors:V. V. Pozdyayev Pages: 419 - 422 Abstract: Abstract The computation of the H ∞ and H 2 norms of 2D systems (systems whose dynamic state depends on two independent variables) can be reduced to algebraic problems underlain by parametrized linear matrix inequalities, which have to hold for all parameter values. Available methods for solving such problems based on their interpretation in terms of nonnegative polynomials are poorly scaled since the sizes of auxiliary problems grow rapidly. In this paper, solution methods are presented that are simpler and more efficient as compared with well-known results. PubDate: 2017-07-01 DOI: 10.1134/s1064562417040184 Issue No:Vol. 96, No. 1 (2017)