The inverse problem for the Gross - Pitaevskii equation

Two different methods are proposed for the generation of wide classes of exact solutions to the stationary Gross - Pitaevskii equation (GPE). The first method, suggested by the work by Kondrat'ev and Miller (1966), applies to one-dimensional (1D) GPE. It is based on the similarity between the GPE and the integrable Gardner equation, all solutions of the latter equation (both stationary and nonstationary ones) generating exact solutions to the GPE, with the potential function proportional to the corresponding solutions. The second method is based on the "inverse problem" for the GPE, i.e. construction of a potential function which provides a desirable solution to the equation. Systematic results are presented for 1D and 2D cases. Both methods are illustrated by a variety of localized solutions, including solitary vortices, for both attractive and repulsive nonlinearity in the GPE. The stability of the 1D solutions is tested by direct simulations of the time-dependent GPE

Recognizability by Prime Graph of the Group 2 E 6(2)

It is proved that the simple group 2E6(2) is recognized by its prime graph. © 2021, Springer Science+Business Media, LLC, part of Springer Nature

Thermal and Dynamical Equilibrium in Two-Component Star Clusters

We present the results of Monte Carlo simulations for the dynamical evolution of star clusters containing two stellar populations with individual masses m1 and m2 > m1, and total masses M1 and M2 < M1. We use both King and Plummer model initial conditions and we perform simulations for a wide range of individual and total mass ratios, m2/m1 and M2/M1. We ignore the effects of binaries, stellar evolution, and the galactic tidal field. The simulations use N = 10^5 stars and follow the evolution of the clusters until core collapse. We find that the departure from energy equipartition in the core follows approximately the theoretical predictions of Spitzer (1969) and Lightman & Fall (1978), and we suggest a more exact condition that is based on our results. We find good agreement with previous results obtained by other methods regarding several important features of the evolution, including the pre-collapse distribution of heavier stars, the time scale on which equipartition is approached, and the extent to which core collapse is accelerated by a small subpopulation of heavier stars. We briefly discuss the possible implications of our results for the dynamical evolution of primordial black holes and neutron stars in globular clusters.Comment: 31 pages, including 13 figures, to appear in Ap

RECOGNITION OF THE GROUP E6(2) BY GRUENBERG–KEGEL GRAPH

The Gruenberg–Kegel graph (or the prime graph) of a finite group G is a simple graph Γ(G) whose vertices are the prime divisors of the order of G, and two distinct vertices p and q are adjacent in Γ(G) if and only if G contains an element of order pq. A finite group is called recognizable by Gruenberg–Kegel graph if it is uniquely determined up to isomorphism in the class of finite groups by its Gruenberg–Kegel graph. In this paper, we prove that the finite simple exceptional group of Lie type E6(2) is recognizable by its Gruenberg–Kegel graph. © 2021 The authors.National Natural Science Foundation of China, NSFC, (12171126)Ministry of Education and Science of the Russian Federation, MinobrnaukaWu Wen-Tsun Key Laboratory of Mathematics, Chinese Academy of Sciences, (075-02-2021-1387)The work is supported by the National Natural Science Foundation of China (project No. 12171126), by Wu Wen-Tsun Key Laboratory of Mathematics of Chinese Academy of Sciences, and by the Regional Scientific and Educational Mathematical Center “Ural Mathematical Center” under the agreement No. 075-02-2021-1387 with the Ministry of Science and Higher Education of the Russian Federation

On the pronormality of subgroups of odd index in finite simple symplectic groups

A subgroup H of a group G is pronormal if the subgroups H and Hg are conjugate in 〈H,Hg〉 for every g ∈ G. It was conjectured in [1] that a subgroup of a finite simple group having odd index is always pronormal. Recently the authors [2] verified this conjecture for all finite simple groups other than PSLn(q), PSUn(q), E6(q), 2E6(q), where in all cases q is odd and n is not a power of 2, and P Sp2n(q), where q ≡ ±3 (mod 8). However in [3] the authors proved that when q ≡ ±3 (mod 8) and n ≡ 0 (mod 3), the simple symplectic group P Sp2n(q) has a nonpronormal subgroup of odd index, thereby refuted the conjecture on pronormality of subgroups of odd index in finite simple groups. The natural extension of this conjecture is the problem of classifying finite nonabelian simple groups in which every subgroup of odd index is pronormal. In this paper we continue to study this problem for the simple symplectic groups P Sp2n(q) with q ≡ ±3 (mod 8) (if the last condition is not satisfied, then subgroups of odd index are pronormal). We prove that whenever n is not of the form 2m or 2m(22k+1), this group has a nonpronormal subgroup of odd index. If n = 2m, then we show that all subgroups of P Sp2n(q) of odd index are pronormal. The question of pronormality of subgroups of odd index in P Sp2n(q) is still open when n = 2m(22k + 1) and q ≡ ±3 (mod 8). © 2017, Pleiades Publishing, Ltd

On the pronormality of subgroups of odd index in finite simple groups

We prove the pronormality of subgroups of finite index for many classes of simple groups. © 2015, Pleiades Publishing, Ltd

Giant Pulses -- the Main Component of the Radio Emission of the Crab Pulsar

The paper presents an analysis of dual-polarization observations of the Crab pulsar obtained on the 64-m Kalyazin radio telescope at 600 MHz with a time resolution of 250 ns. A lower limit for the intensities of giant pulses is estimated by assuming that the pulsar radio emission in the main pulse and interpulse consists entirely of giant radio pulses; this yields estimates of 100 Jy and 35 Jy for the peak flux densities of giant pulses arising in the main pulse and interpulse, respectively. This assumes that the normal radio emission of the pulse occurs in the precursor pulse. In this case, the longitudes of the giant radio pulses relative to the profile of the normal radio emission turn out to be the same for the Crab pulsar and the millisecond pulsar B1937+21, namely, the giant pulses arise at the trailing edge of the profile of the normal radio emission. Analysis of the distribution of the degree of circular polarization for the giant pulses suggests that they can consist of a random mixture of nanopulses with 100% circular polarization of either sign, with, on average, hundreds of such nanopulses within a single giant pulse.Comment: 13 pages, 6 figures (originally published in Russian in Astronomicheskii Zhurnal, 2006, vol. 83, No. 1, pp. 62-69) translated by Denise Gabuzd

Мультиспиральная компьютерная томография сердца: оптимизация протокола сканирования при проведении неинвазивного картирования сердца перед катетерной абляцией фибрилляции предсердий

Purpose: to develop optimal technique of cardiac multidetector computed tomography (MDCT) before noninvasive cardiac mapping before cateter ablation of atrial fibrillation.Materials and methods. 94 patients with atrial fibrillation were included in study (60 males, 34 females; mean age = 58.3 ± 10 years; mean body mass index (BMI) = 29.9 ± ± 4.8). The patients were divided into 2 groups: I – 80 patients who underwent computer tomography (CT)-protocol for noninvasive cardiac mapping with standard contrast enhancement (single-bolus protocol); II – 14 patients who underwent CT with modified contrast enhancement technique with preliminary contrast injection (prebolus). To detect thrombotic masses in the left auricle the low-dose delayed phase was performed. The analysis of individual features of pulmonary veins, left atrium and adjacent structures was performed. Contrast enhancement of heart chambers was assessed by mean attenuation and homogeneity measurement.Results and discussion. The typical anatomy of the right pulmonary veins was in 93.6% of cases; right middle pulmonary vein in 5.3%; right segmental veins in 1.1%. The typical anatomy at the left side was in 57.4% of cases; common vestibulum of the left pulmonary veins in 18.1%; common left trunk in 24.5%. Volume enlargement of the left atrium (LA) was in 96.8% of patients. In 6 cases left auricle thrombosis was suspected, low-dose delayed phase was performed. In 2 cases filling defects in left auricle persisted, thrombosis was proved by transesophageal echocardiography. With the single-bolus injection protocol the contrast enhancement of left heart chambers was best (mean attenuation of blood in LA = 296 ± 84 HU, in left ventricle (LV) = 286 ± 83 HU), but the contrast enhancement and homogeneity of the chambers were insufficient (mean attenuation of blood in right atrium (RA) = 179 ± 97 HU, in right ventricle (RV) = 176 ± 80 HU). With prebolus protocol the contrast enhancement and homogeneity of all chambers were optimal (mean attenuation of blood in LA = 259 ± 31 HU, in LV = 286 ± 83 HU, in RA = 270 ± 92 HU, in RV = 253 ± 80 HU). This allowed making more accurate epi-endocardial heart models in the noninvasive cardiac mapping and operation planning. Conclusion. MDCT with standard contrast enhancement protocol provides detailed information about anatomy and size of pulmonary veins, the left atrium volume, the presence of intracardiac masses (including thrombotic masses), the anatomy of adjacent structures. The modified contrast enhancement technique with preliminary contrast injection (prebolus) allows to receive optimal contrast enhancement of all heart chambers and to make high accurate epi-endocardial models of both the right and left sides of the heart in case of noninvasive cardiac mapping.Цель исследования: разработать оптимальную методику сканирования для мультиспиральной компьютерной томографии (МСКТ) сердца при проведении неинвазивного картирования сердца (НКС) перед катетерной абляцией фибрилляции предсердий.Материал и методы. В исследование включено 94 случая фибрилляции предсердий (60 мужчин и 34 женщины, средний возраст 58,3 ± 10 лет, средний индекс массы тела 29,9 ± 4,8 кг/м2). Пациенты разделены на 2 группы: 1-я (n = 80) – МСКТ выполнялась по специальному протоколу для НКС со стандартным контрастированием (сингл-болюс), 2-я (n = 14) – МСКТ сердца выполнялась по модифицированной методике предболюса. Для выявления тромбов в ушке левого предсердия (ЛП) выполнялась низкодозовая отсроченная фаза контрастирования. Проанализированны индивидуальные особенности легочных вен (ЛВ), ЛП и соседних структур. Проведена оценка контрастирования камер сердца по результатам измерения средней плотности и гомогенности заполнения контрастом.Результаты. Справа типичная анатомия ЛВ встречалась в 93,6%, впадение средней вены отдельным стволом – в 5,3%, отсутствие формирования крупных стволов – в 1,1%. Слева типичное впадение ЛВ отмечено в 57,4% случаев, вестибюль ЛВ – в 18,1%, общий ствол – в 24,5%. Увеличение объема ЛП определялось у 96,8% пациентов. В 6 случаях по МСКТ был заподозрен тромбоз ушка ЛП, исследование было дополнено отсроченной фазой, в 2 случаях дефекты контрастирования сохранялись; далее тромбоз подтвержден при чреспищеводной эхокардиографии. При протоколе сингл-болюс отмечалось наилучшее контрастирование левых отделов сердца (средняя плотность крови в ЛП 296 ± 84 HU, в левом желудочке (ЛЖ) 286 ± 83 HU), но неудовлетворительное контрастирование и недостаточная гомогенность правых отделов (средняя плотность крови в правом предсердии (ПП) 179 ± 97 HU, правом желудочке (ПЖ) 176±80 HU). При использовании модифицированного протокола контрастирования с предварительным болюсом контрастного средства отмечалось оптимальное контрастирование и гомогенность всех отделов сердца (средняя плотность крови в ЛП = 259 ± 31 HU, ЛЖ= 286 ± 83 HU, ПП = 270 ± 92 HU, ПЖ = 253 ± 80 HU). Это позволило построить более точные эпи-эндокардиальные модели сердца при неинвазивном картировании для анализа высокочастотной драйверной активности и выбора тактики интервеционнного лечения.Заключение. МСКТ с использованием стандартного протокола контрастирования предоставляет детальную информацию об анатомии и диаметре устьев ЛВ, размерах ЛП, наличии внутрисердечных образований (в том числе тромботических масс), анатомии соседних структур. Использование модифицированного протокола контрастирования с введением предварительного болюса контрастного средства позволяет получить оптимальное контрастирование и построить с высокой точностью эпи-эндокардиальные модели как правых, так и левых отделов сердца в целях неинвазивного картирования

ВНЕЗАПНАЯ СМЕРТЬ ПРИ СИНДРОМЕ БРУГАДА: УСПЕШНАЯ РЕАНИМАЦИЯ, ЭКГ-ДИАГНОСТИКА И ТРЕТИЧНАЯ ПРОФИЛАКТИКА

The articles describes the clinical follow-up and the data of one-year prospective follow-up of the patient suffering from the Brugada syndrome complicated by clinical death. Приведены клиническое наблюдение и данные одногодичного катамнеза пациента с синдромом Бругада, осложненным клинической смертью.