European Workshop "Nonlinear Maps and Applications" - 2017, Nizhni Novgorod, Russia

Regular European Workshops "Nonlinear Maps and Applications" (NOMA) are held biannually in those European Universities where successful researchers in the area of nonlinear maps and their applications work. In far 1973 year French scientist Christian Mira organized Colloquium "Point Mappings and Applications" in the University of Toulouse, where he worked. According to Christian Mira, his mathematical preferences were formed under the influence of works of the founder of the Nizhni Novgorod nonlinear oscillations school A.A. Andronov

State and prospects of the linac of nuclear-physics complex with energy of electrons up to 100 MeV

The paper describes the results of the work on improvement of electron linac LUE-40. This linac has been designed for nuclear physics research in the electron energy range 40…100 MeV. The main purpose is to reduce the energy spread, emittance and long-term instability of the beam characteristics. For this purpose the system of klystron high voltage stabilization and the beam loading compensation system have been developed. The improved injector has been put into operation. A new DC power supply system of the magnetic spectrometer has been installed and tested.Приведено описание результатов работы по усовершенствованию линейного ускорителя ЛУЭ-40, предназначенного для проведения ядерно-физических исследований в диапазоне энергий электронов 40…100 МэВ. Основной целью работы является уменьшение энергетического разброса, эмиттанса и долговременной нестабильности характеристик пучка. Для этого установлен и введен в эксплуатацию более совершенный инжектор. Разработаны системы стабилизации высокого напряжения клистронов и схема компенсации энергетического разброса, вызываемого токовой нагрузкой секции. Разработана и испытана новая система питания магнитного спектрометра.Наведено опис результатів роботи з удосконалення лінійного прискорювача електронів ЛУЕ-40, призначеного для проведення ядерно-фізичних досліджень у діапазоні енергій електронів 40…100 МеВ. Основною метою роботи є зменшення енергетичного розкиду, еміттансу і довготривалої нестабільності характеристик пучка. Для цього встановлено та введено в експлуатацію більш досконалий інжектор. Розроблені системи стабілізації високої напруги клістронів і схема компенсації енергетичного розкиду, що спричиняється струмовим навантаженням секції. Розроблена і випробувана нова система живлення магнітного спектрометра

Group measure space decomposition of II_1 factors and W*-superrigidity

We prove a "unique crossed product decomposition" result for group measure space II_1 factors arising from arbitrary free ergodic probability measure preserving (p.m.p.) actions of groups \Gamma in a fairly large family G, which contains all free products of a Kazhdan group and a non-trivial group, as well as certain amalgamated free products over an amenable subgroup. We deduce that if T_n denotes the group of upper triangular matrices in PSL(n,Z), then any free, mixing p.m.p. action of the amalgamated free product of PSL(n,Z) with itself over T_n, is W*-superrigid, i.e. any isomorphism between L^\infty(X) \rtimes \Gamma and an arbitrary group measure space factor L^\infty(Y) \rtimes \Lambda, comes from a conjugacy of the actions. We also prove that for many groups \Gamma in the family G, the Bernoulli actions of \Gamma are W*-superrigid.Comment: Final version. Some extra details have been added to improve the expositio

Spectral boundary value problems for Laplace–Beltrami operator: Moduli of continuity of eigenvalues under domain deformation

The paper is pertaining to the spectral theory of operators and boundary value problems for differential equations on manifolds. Eigenvalues of such problems are studied as functionals on the space of domains. Resolvent continuity of the corresponding operators is established under domain deformation and estimates of continuity moduli of their eigenvalues/eigenfunctions are obtained provided the boundary of nonperturbed domain is locally represented as a graph of some continuous function and domain deformation is measured with respect to the Hausdorff–Pompeiu metric. © 2017 American Mathematical Society

Spectral boundary value problems for Laplace–Beltrami operator: Moduli of continuity of eigenvalues under domain deformation

The paper is pertaining to the spectral theory of operators and boundary value problems for differential equations on manifolds. Eigenvalues of such problems are studied as functionals on the space of domains. Resolvent continuity of the corresponding operators is established under domain deformation and estimates of continuity moduli of their eigenvalues/eigenfunctions are obtained provided the boundary of nonperturbed domain is locally represented as a graph of some continuous function and domain deformation is measured with respect to the Hausdorff–Pompeiu metric. © 2017 American Mathematical Society

Spectral boundary value problems for Laplace-Beltrami operator: moduli of continuity of eigenvalues under domain deformation

Let M be a compact Riemannian manifold, possibly with non-empty boundary partial M, let Cal{A} be a strongly elliptic operator with Lipschitz coefficients and consider the eigenvalue problem Cal{A} u= lambda u, quad uin ocirc{H}{}^1(Omega) on a domain Omegasubseteq M with overline{Omega}cap partial M=emptyset. par Under suitable assumptions on the domains, the authors establish the resolvent continuity of the boundary value problem with respect to domain perturbations (Theorem 4.2). As a consequence, they obtain an estimate for the moduli of continuity of the eigenvalues relative to different domains Omega_1 and Omega_2 in terms of their Hausdorff-Pompeiu distance (Theorem 4.1)

Plasma flow injector based on an open coaxial microwave resonator [Инжектор плазменного потока на основе открытого коаксиального СВЧ-резонатора]

The possibility of using an open coaxial microwave resonator as an element of an injector of a plasma flow with accelerated ions has been established. A diagram of a plasma flow injector consisting of an open coaxial resonator and an additional ring electrode is presented. The characteristic dependences of the energy spectra of the plasma ion component on the potential at the ring electrode for fixed values of the mass flow of gas (argon) and the microwave power input into the resonator are obtained. © 2020 Federal Informational-Analytical Center of the Defense Industry. All rights reserved