Some current problems in modern mathematics and education in mathematics. Papers from the 61st Scientific Conference “Gertsen Lectures – 2008”, Sankt Petersburg, Russia, April 14–19, 2008.
(Некоторые актуальные проблемы современной математики и математического образования. Материалы научной конференции “Герценовские чтения 2008”.)

*(Russian)*Zbl 1135.00008
St. Peterburg: Rossiĭskiĭ Gosudarstvennyĭ Pedagogicheskiĭ Universitet Im. A. I. Gertsena (ISBN 5-336-00055-8/pbk). 187 p. (2008).

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The 42 papers in this collection, all in Russian, include the following: A. V. Aksenov, Exact solutions of equations describing the motion of absolutely unstable media (3–9); E. A. Barova, A boundary value problem for an equation of mixed type with special conjugation conditions (9–12); A. K. Volosova and K. A. Volosov, A connection between quasilinear parabolic partial differential equation of the Burgers equation (17–20); V. N. Gorbuzov and A. F. Pronevich, First integrals of a linear multidimensional differential system in a complex domain (25–31); O. M. Dzyuba and V. F. Zaĭtsev, On nonclassical symmetries of ordinary differential equations (31–35); S. M. Evdokimov, Necessary and sufficient conditions for the existence of a limit cycle in a two-dimensional system with hysteresis (35–39); S. V. Zhestkov, On the existence of soliton solutions of a system of Redekopp equations with a power nonlinearity law and a doubled period law (39–43); V. F. Zaĭtsev and K. V. Pavlyukov, Solution of direct and inverse problems of group analysis for systems of second-order equations (44–49); V. F. Zaĭtsev and A. A. Petrushenko, On the classification of nonlocal exponential operators (49–55);

V. F. Zaĭtsev and Yu. O. Yakovleva, A three-dimensional unsolvable Lie algebra admitted by a third-order differential equation, and its subalgebras (56–58); O. M. Kechina, On a nonlocal problem with integral conditions (59–62); I. V Konopleva, B. V. Loginov and L. V. Mironova, Branching and stability of bifurcating solutions of nonlinear problems that are spectral in the sense of E. Schmidt (64–71); D. V. Kostin, Two-mode bifurcations of solutions of the von Kármán equation in the case of a weakly inhomogeneous plate (71–73); V. I. Lagno and S. V. Spichak, Group classification of quasilinear equations of elliptic type with respect to solvable Lie algebras (75–79); V. I. Lagno and V. I. Stogniĭ, Symmetry and separation of variables for the Kolmogorov equation (79–83); L. V. Linchuk, The structure of a nonlocal operator for factorizable second-order partial differential equations (83–90); L. N. Lyakhov, E. M. Merzlikina and L. B. Raĭkhel’gauz, On integral transforms associated with the Bessel transform (90–94); A. A. Migunov, Averaging of systems of differential inclusions with fast and slow variables in the case when the fast variables have different rates (95–102);

V. S. Nemets and P. B. Pavlyuchik, Properties of meromorphic solutions of algebraic differential equations (102–107); P. F. Pronevich, On singular and nonsingular powers of parametric solutions of algebraic differential equations (107–111); V. S. Fedotova, On a nonlinear Sturm-Liouville boundary value problems (115–118); O. P. Filatov, On nondegenerate differential inclusions (118–121); Yu. I. Khanukaev, An electromagnetic field as the field of quaternions (121–128); G. N. Yakovenko, Symmetries of statically linearizable systems with control (128–133); V. S. Videnskiĭ, A remark on the rational linear operators considered by A. Lupas (134–146); A. V. Koldunov, \((X,\pi)\)-Dedekind elements of vector lattices (148–152); Włodzimierz P. Odyniec, \(t\)-entropy of the Boltzmann function and properties of its restrictions (152–157); E. A. Riss, On a defining family of sets for measures on Banach spaces (160–168).

The articles of mathematical interest will be reviewed individually.

Indexed articles:

Aksenov, A. V., Exact solutions of equations describing the motion of absolutely unstable media, 3-9 [Zbl 1238.35004]

Barova, E. A., A boundary value problem for an equation of mixed type with special conjugation conditions, 9-12 [Zbl 1238.35063]

Volosova, A. K.; Volosov, K. A., A connection between quasilinear parabolic partial differential equation of the Burgers equation, 17-20 [Zbl 1238.35049]

Gorbuzov, V. N.; Pronevich, A. F., First integrals of a linear multidimensional differential system in a complex domain, 25-31 [Zbl 1238.34154]

Dzyuba, O. M.; Zaĭtsev, V. F., On nonclassical symmetries of ordinary differential equations, 31-35 [Zbl 1238.34060]

Evdokimov, S. M., Necessary and sufficient conditions for the existence of a limit cycle in a two-dimensional system with hysteresis, 35-39 [Zbl 1238.34094]

Zhestkov, S. V., On the existence of soliton solutions of a system of Redekopp equations with a power nonlinearity law and a doubled period law, 39-43 [Zbl 1238.35123]

Zaĭtsev, V. F.; Pavlyukov, K. V., Solution of direct and inverse problems of group analysis for systems of second-order equations, 44-49 [Zbl 1238.34063]

Zaĭtsev, V. F.; Petrushenko, A. A., On the classification of nonlocal exponential operators, 49-55 [Zbl 1238.34149]

Zaĭtsev, V. F.; Yakovleva, Yu. O., A three-dimensional unsolvable Lie algebra admitted by a third-order differential equation, and its subalgebras, 56-58 [Zbl 1238.34064]

Kechina, O. M., On a nonlocal problem with integral conditions, 59-62 [Zbl 1238.35053]

Konopleva, I. V; Loginov, B. V.; Mironova, L. V., Branching and stability of bifurcating solutions of nonlinear problems that are spectral in the sense of E. Schmidt, 64-71 [Zbl 1238.47041]

Kostin, D. V., Two-mode bifurcations of solutions of the von Kármán equation in the case of a weakly inhomogeneous plate, 71-73 [Zbl 1238.35154]

Lagno, V. I.; Spichak, S. V., Group classification of quasilinear equations of elliptic type with respect to solvable Lie algebras, 75-79 [Zbl 1238.35005]

Lagno, V. I.; Stogniĭ, V. I., Symmetry and separation of variables for the Kolmogorov equation, 79-83 [Zbl 1238.35006]

Linchuk, L. V., The structure of a nonlocal operator for factorizable second-order partial differential equations, 83-90 [Zbl 1238.35007]

Lyakhov, L. N.; Merzlikina, E. M.; Raĭkhel’gauz, L. B., On integral transforms associated with the Bessel transform, 90-94 [Zbl 1238.44002]

Migunov, A. A., Averaging of systems of differential inclusions with fast and slow variables in the case when the fast variables have different rates, 95-102 [Zbl 1238.34087]

Nemets, V. S.; Pavlyuchik, P. B., Properties of meromorphic solutions of algebraic differential equations, 102-107 [Zbl 1238.34016]

Pronevich, P. F., On singular and nonsingular powers of parametric solutions of algebraic differential equations, 107-111 [Zbl 1238.34153]

Fedotova, V. S., On a nonlinear Sturm-Liouville boundary value problems, 115-118 [Zbl 1238.34036]

Filatov, O. P., On nondegenerate differential inclusions, 118-121 [Zbl 1238.34028]

Khanukaev, Yu. I., An electromagnetic field as the field of quaternions, 121-128 [Zbl 1238.78002]

Yakovenko, G. N., Symmetries of statically linearizable systems with control, 128-133 [Zbl 1238.34062]

Videnskiĭ, V. S., A remark on the rational linear operators considered by A. Lupas, 134-146 [Zbl 1238.41015]

Koldunov, A. V., \((X,\pi)\)-Dedekind elements of vector lattices, 148-152 [Zbl 1238.46004]

Odyniec, Włodzimierz P., \(t\)-entropy of the Boltzmann function and properties of its restrictions, 152-157 [Zbl 1238.82031]

Riss, E. A., On a defining family of sets for measures on Banach spaces, 160-168 [Zbl 1238.28012]

##### MSC:

00B20 | Proceedings of conferences of general interest |

34-06 | Proceedings, conferences, collections, etc. pertaining to ordinary differential equations |

34C14 | Symmetries, invariants of ordinary differential equations |

35-06 | Proceedings, conferences, collections, etc. pertaining to partial differential equations |

35A30 | Geometric theory, characteristics, transformations in context of PDEs |

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\textit{V. F. Zaĭtsev} (ed.), Некоторые актуальные проблемы современной математики и математического образования. Материалы научной конференции ``Герценовские чтения 2008'' (Russian). St. Peterburg: Rossiĭskiĭ Gosudarstvennyĭ Pedagogicheskiĭ Universitet Im. A. I. Gertsena (2008; Zbl 1135.00008)