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## Long-Period Oscillations of Sunspots by NoRH and SSRT Observations

Long-term oscillations of microwave emission generated in sunspot magnetospheres are detected with the Nobeyama Radioheliograph (NoRH) at a frequency of 17 GHz, and the Siberian Solar Radio Telescope (SSRT) at 5.7 GHz. Significant periodicities in the range of 22–170 min are found in the variation of the emission intensity, polarisation and the degree of circular polarisation. Periods of the oscillations are not stable: they are different in different sunspots and in the same sunspot on different days. A cross-correlation analysis shows the presence of common significant periods in both NoRH and SSRT data. The cross-correlation coefficients are typically lower than 0.5, which can be attributed to the different heights of the emission formation, and different mechanisms for the emission generation (gyroresonance and thermal bremstrahlung at 17 GHz, and pure gyroresonance at 5.7 GHz). The observational results are consistent with the global sunspot oscillation model.

Radio-observations allow us to reveal the long-lived (2–5 days) intersunspot sources (ISS), whose centers are often located above the neutral line of the magnetic field separating leading and following parts of a whole active region (the first type of ISS (ISS-I)) or above the neutral line separating magnetic polarities into complex sunspots (the second type of ISS (ISS-II)). ISS-I and ISS-II demonstrate gyrocyclotron or gyrosynchrotron spectra, more dynamic pre-flare behavior than ISS-III with bremsstrahlung in the quiet active regions. The qualitative model of “three magnetic fluxes” explaining the origin of accelerated particles in ISS and their long-lasting existence and spectral features is proposed.

We define, calculate and analyze irregularity indices λISSN of daily series of the International Sunspot Number ISSN as a function of increasing smoothing from *N* = 162 to 648 days. The irregularity indices λ are computed within 4-year sliding windows, with embedding dimensions *m* = 1 and 2. λISSN displays Schwabe cycles with ~5.5-year variations ("half Schwabe variations" HSV). The mean of λISSN undergoes a downward step and the amplitude of its variations strongly decreases around 1930. We observe changes in the ratio *R* of the mean amplitude of λ peaks at solar cycle minima with respect to peaks at solar maxima as a function of date, embedding dimension and, importantly, smoothing parameter *N*. We identify two distinct regimes, called Q1 and Q2, defined mainly by the evolution of *R* as a function of *N*: Q1, with increasing HSV behavior and *R* value as *N* is increased, occurs before 1915–1930; and Q2, with decreasing HSV behavior and *R* value as *N* is increased, occurs after ~1975. We attempt to account for these observations with an autoregressive (order 1) model with Poissonian noise and a mean modulated by two sine waves of periods *T*1 and *T*2 (*T*1 = 11 years, and intermediate *T*2 is tuned to mimic quasi-biennial oscillations QBO). The model can generate both Q1 and Q2 regimes. When *m* = 1, HSV appears in the absence of *T*2 variations. When *m* = 2, Q1 occurs when *T*2 variations are present, whereas Q2 occurs when *T*2 variations are suppressed. We propose that the HSV behavior of the irregularity index of ISSN may be linked to the presence of strong QBO before 1915–1930, a transition and their disappearance around 1975, corresponding to a change in regime of solar activity.

Numerical simulation of the oscillation thick walled shell electromagnetoelasticity

Within the framework of model calculations the possibility of occurrence of the ion-acoustic oscillation instability in a plasma without current and particle fluxes, but with an anisotropic distribution function, which corresponds to heat flux is shown. The model distribution function was selected taking into account the medium conditions. The increment of ion-acoustic oscillation is investigated as functional of the distribution function parameters. The threshold condition for the anisotropic part of the distribution function, under which the build-up of ion-acoustic oscillation with the wave vector opposite to the heat flux begins is studied. The critical heat flux, which corresponds to the threshold of ion-acoustic instability, is determined. For the solar conditions, the critical heat flux proved to be close to the heat flux from the corona into the chromosphere on the boundary of the transition region. The estimations show that outside of active regions and even in active regions with weaker magnetic fields ion-acoustic turbulence can be responsible for the formation of the sharp temperature jump. The generalized Wiedemann-Franz law for a non-isothermic quasi-neutral plasma with developed ion-acoustic turbulence is discussed. This law determines the relationship between electrical and thermal conductivities in a plasma with well-developed ion-acoustic turbulence. The anomalously low thermal conductivity responsible to the formation of high temperature gradients in the zone of the temperature jump is explained. The results are used to explain some properties of stellar atmosphere transition regions.

The dynamics of a two-component Davydov-Scott (DS) soliton with a small mismatch of the initial location or velocity of the high-frequency (HF) component was investigated within the framework of the Zakharov-type system of two coupled equations for the HF and low-frequency (LF) fields. In this system, the HF field is described by the linear Schrödinger equation with the potential generated by the LF component varying in time and space. The LF component in this system is described by the Korteweg-de Vries equation with a term of quadratic influence of the HF field on the LF field. The frequency of the DS soliton`s component oscillation was found analytically using the balance equation. The perturbed DS soliton was shown to be stable. The analytical results were confirmed by numerical simulations.

Radiation conditions are described for various space regions, radiation-induced effects in spacecraft materials and equipment components are considered and information on theoretical, computational, and experimental methods for studying radiation effects are presented. The peculiarities of radiation effects on nanostructures and some problems related to modeling and radiation testing of such structures are considered.

Let k be a field of characteristic zero, let G be a connected reductive algebraic group over k and let g be its Lie algebra. Let k(G), respectively, k(g), be the field of k- rational functions on G, respectively, g. The conjugation action of G on itself induces the adjoint action of G on g. We investigate the question whether or not the field extensions k(G)/k(G)^G and k(g)/k(g)^G are purely transcendental. We show that the answer is the same for k(G)/k(G)^G and k(g)/k(g)^G, and reduce the problem to the case where G is simple. For simple groups we show that the answer is positive if G is split of type A_n or C_n, and negative for groups of other types, except possibly G_2. A key ingredient in the proof of the negative result is a recent formula for the unramified Brauer group of a homogeneous space with connected stabilizers. As a byproduct of our investigation we give an affirmative answer to a question of Grothendieck about the existence of a rational section of the categorical quotient morphism for the conjugating action of G on itself.

Let G be a connected semisimple algebraic group over an algebraically closed field k. In 1965 Steinberg proved that if G is simply connected, then in G there exists a closed irreducible cross-section of the set of closures of regular conjugacy classes. We prove that in arbitrary G such a cross-section exists if and only if the universal covering isogeny Ĝ → G is bijective; this answers Grothendieck's question cited in the epigraph. In particular, for char k = 0, the converse to Steinberg's theorem holds. The existence of a cross-section in G implies, at least for char k = 0, that the algebra k[G]G of class functions on G is generated by rk G elements. We describe, for arbitrary G, a minimal generating set of k[G]G and that of the representation ring of G and answer two Grothendieck's questions on constructing generating sets of k[G]G. We prove the existence of a rational (i.e., local) section of the quotient morphism for arbitrary G and the existence of a rational cross-section in G (for char k = 0, this has been proved earlier); this answers the other question cited in the epigraph. We also prove that the existence of a rational section is equivalent to the existence of a rational W-equivariant map T- - - >G/T where T is a maximal torus of G and W the Weyl group.