Class preserving automorphisms of unitriangular groups

Let $\textrm{UT}_n (K)$ be a unitriangular group over a field $K$ and $\Gamma_{n,k} := \textrm{UT}_n (K)/ \gamma_k(\textrm{UT}_n (K))$, where $\gamma_k (\mathrm{UT}_n(K))$ denotes the $k$-th term of the lower central series of $\mathrm{UT}_n (K)$, $2 \le k \le n$. We prove that the group of all class preserving automorphisms of $\Gamma_{n,k}$ is equal to \Inn(\Gamma_{n,k}) if and only if $K$ is a prime field. Let $G_n^{(m)} := \mathrm{UT}_n (\mathbb{F}_{p^m}) / \gamma_3 (\mathrm{UT}_n(\mathbb{F}_{p^m}))$. We calculate the group of all class preserving automorphisms and class preserving outer automorphisms of $G_n^{(m)}$.Comment: 19 pages, accepted for publication in International Journal of Algebra and Computatio

Factors affecting the quality of life of patients with chronic obstructive pulmonary disease

The aim of the study - to study the correlation between the indicators of physical health of patients with COPD and the results of CAT and PF–10 questionnaires, to determine the influence of additional factors on the nature of the course of the disease.Цель исследования – изучение корреляции между показателями физического здоровья пациентов с ХОБЛ и результатами опросников CAT и PF-10, определение влияния дополнительных факторов на характер течения заболевания

Ionospheric Disturbances and Irregularities During the 25-26 August 2018 Geomagnetic Storm

International audienceWe use ground-based (GNSS, SuperDARN, and ionosondes) and space-borne (Swarm, CSES, and DMSP) instruments to study ionospheric disturbances due to the 25-26 August 2018 geomagnetic storm. The strongest large-scale storm-time enhancements were detected over the Asian and Pacific regions during the main and early recovery phases of the storm. In the American sector, there occurred the most complex effects caused by the action of multiple drivers. At the beginning of the storm, a large positive disturbance occurred over North America at low and high latitudes, driven by the storm-time reinforcement of the equatorial ionization anomaly (at low latitudes) and by particle precipitation (at high latitudes). During local nighttime hours, we observed numerous medium-scale positive and negative ionospheric disturbances at middle and high latitudes that were attributed to a storm-enhanced density (SED)-plume, mid-latitude ionospheric trough, and particle precipitation in the auroral zone. In South America, total electron content (TEC) maps clearly showed the presence of the equatorial plasma bubbles, that, however, were not seen in data of Rate-of-TEC-change index (ROTI). Global ROTI maps revealed intensive small-scale irregularities at high latitudes in both hemispheres within the auroral region. In general, the ROTI disturbance "imaged" quite well the auroral oval boundaries. The most intensive ionospheric fluctuations were observed at low and mid-latitudes over the Pacific Ocean. The storm also affected the positioning accuracy by GPS receivers: during the main phase of the storm, the precise point positioning error exceeded 0.5 m, which is more than five times greater as compared to quiet days