Rook placements in G2G_2 and F4F_4 and associated coadjoint orbits

Let $\mathfrak{n}$ be a maximal nilpotent subalgebra of a simple complex Lie algebra with root system $\Phi$. A subset $D$ of the set $\Phi^+$ of positive roots is called a rook placement if it consists of roots with pairwise non-positive scalar products. To each rook placement $D$ and each map $\xi$ from $D$ to the set $\mathbb{C}^{\times}$ of nonzero complex numbers one can naturally assign the coadjoint orbit $\Omega_{D,\xi}$ in the dual space $\mathfrak{n}^*$. By definition, $\Omega_{D,\xi}$ is the orbit of $f_{D,\xi}$, where $f_{D,\xi}$ is the sum of root covectors $e_{\alpha}^*$ multiplied by $\xi(\alpha)$, $\alpha\in D$. (In fact, almost all coadjoint orbits studied at the moment have such a form for certain $D$ and $\xi$.) It follows from the results of Andr\`e that if $\xi_1$ and $\xi_2$ are distinct maps from $D$ to $\mathbb{C}^{\times}$ then $\Omega_{D,\xi_1}$ and $\Omega_{D,\xi_2}$ do not coincide for classical root systems $\Phi$. We prove that this is true if $\Phi$ is of type $G_2$, or if $\Phi$ is of type $F_4$ and $D$ is orthogonal.Comment: 16 pages, 4 figure

Combined Cracking Residue and Mechanical Activation Oil Shale

Исследован совместный крекинг механоактивированного горючего сланца и нефтяного остатка. Введение горючего сланца позволило интенсифицировать процесс деструкции высокомолекулярных компонентов нефтяного остатка. При увеличении доли горючего сланца в реакционной смеси в продуктах крекинга снижается количество асфальтенов с 4,2 до 2,8 % мас., смол с 6,7 до 4,8 % мас. В полученных жидких продуктах термолиза преобладают масла от 40,2 до 81,1 % мас. В газообразных продуктах увеличивается доля углекислого газа и монооксида углерода. Введение механоактивированного горючего сланца влияет на фракционный состав продуктов термолиза, изменяя количественное соотношение бензиновых (НК – 200 °С) и дизельных фракций (200–360 °С)The joint cracking of mechanically activated oil shale and petroleum residue was studied. The introduction of oil shale allowed to intensify the process of destruction of high-molecular components of the petroleum residue. In the obtained liquid thermolysis products, oils predominate from 40,2 to 81,1% wt. With an increase in the share of oil shale in the cracking products, the proportion of asphaltenes decreases from 4,2 to 2,8% wt, and of tar from 6,7 to 4,8% wt. In gaseous products, the proportion of carbon dioxide and carbon monoxide increases markedly. The introduction of mechanically activated oil shale also affects the fractional composition of thermolysis products; the proportion of gasoline (IPB – 200 °С) and diesel fractions (200–360 °С) change

Development of topological method for calculating current distribution coefficients in complex power networks

The author of this research developed a modified topological method for calculating distribution coefficients of main currents. Main currents are represented as functions of electrical network parameters based on possible trees of directed graphs. Algorithms can be realized in the MATLAB environment. This method can increase load automation of complex electrical networks and systems. Keywords: Urban power network, Topology of electrical networks, Load flow analysis, Reactive power, Power transmissio

Incidence of severe critical events in paediatric anaesthesia (APRICOT): a prospective multicentre observational study in 261 hospitals in Europe

Background Little is known about the incidence of severe critical events in children undergoing general anaesthesia in Europe. We aimed to identify the incidence, nature, and outcome of severe critical events in children undergoing anaesthesia, and the associated potential risk factors. Methods The APRICOT study was a prospective observational multicentre cohort study of children from birth to 15 years of age undergoing elective or urgent anaesthesia for diagnostic or surgical procedures. Children were eligible for inclusion during a 2-week period determined prospectively by each centre. There were 261 participating centres across 33 European countries. The primary endpoint was the occurence of perioperative severe critical events requiring immediate intervention. A severe critical event was defined as the occurrence of respiratory, cardiac, allergic, or neurological complications requiring immediate intervention and that led (or could have led) to major disability or death. This study is registered with ClinicalTrials.gov, number NCT01878760. Findings Between April 1, 2014, and Jan 31, 2015, 31â127 anaesthetic procedures in 30â874 children with a mean age of 6·35 years (SD 4·50) were included. The incidence of perioperative severe critical events was 5·2% (95% CI 5·0â5·5) with an incidence of respiratory critical events of 3·1% (2·9â3·3). Cardiovascular instability occurred in 1·9% (1·7â2·1), with an immediate poor outcome in 5·4% (3·7â7·5) of these cases. The all-cause 30-day in-hospital mortality rate was 10 in 10â000. This was independent of type of anaesthesia. Age (relative risk 0·88, 95% CI 0·86â0·90; p<0·0001), medical history, and physical condition (1·60, 1·40â1·82; p<0·0001) were the major risk factors for a serious critical event. Multivariate analysis revealed evidence for the beneficial effect of years of experience of the most senior anaesthesia team member (0·99, 0·981â0·997; p<0·0048 for respiratory critical events, and 0·98, 0·97â0·99; p=0·0039 for cardiovascular critical events), rather than the type of health institution or providers. Interpretation This study highlights a relatively high rate of severe critical events during the anaesthesia management of children for surgical or diagnostic procedures in Europe, and a large variability in the practice of paediatric anaesthesia. These findings are substantial enough to warrant attention from national, regional, and specialist societies to target education of anaesthesiologists and their teams and implement strategies for quality improvement in paediatric anaesthesia. Funding European Society of Anaesthesiology

Incidence of severe critical events in paediatric anaesthesia (APRICOT): a prospective multicentre observational study in 261 hospitals in Europe

Background Little is known about the incidence of severe critical events in children undergoing general anaesthesia in Europe. We aimed to identify the incidence, nature, and outcome of severe critical events in children undergoing anaesthesia, and the associated potential risk factors. Methods The APRICOT study was a prospective observational multicentre cohort study of children from birth to 15 years of age undergoing elective or urgent anaesthesia for diagnostic or surgical procedures. Children were eligible for inclusion during a 2-week period determined prospectively by each centre. There were 261 participating centres across 33 European countries. The primary endpoint was the occurence of perioperative severe critical events requiring immediate intervention. A severe critical event was defined as the occurrence of respiratory, cardiac, allergic, or neurological complications requiring immediate intervention and that led (or could have led) to major disability or death. This study is registered with ClinicalTrials.gov, number NCT01878760. Findings Between April 1, 2014, and Jan 31, 2015, 31 127 anaesthetic procedures in 30 874 children with a mean age of 6.35 years (SD 4.50) were included. The incidence of perioperative severe critical events was 5.2% (95% CI 5.0-5.5) with an incidence of respiratory critical events of 3.1% (2.9-3.3). Cardiovascular instability occurred in 1.9% (1.7-2.1), with an immediate poor outcome in 5.4% (3.7-7.5) of these cases. The all-cause 30-day in-hospital mortality rate was 10 in 10 000. This was independent of type of anaesthesia. Age (relative risk 0.88, 95% CI 0.86-0.90; p<0.0001), medical history, and physical condition (1.60, 1.40-1.82; p<0.0001) were the major risk factors for a serious critical event. Multivariate analysis revealed evidence for the beneficial effect of years of experience of the most senior anaesthesia team member (0.99, 0.981-0.997; p<0.0048 for respiratory critical events, and 0.98, 0.97-0.99; p=0.0039 for cardiovascular critical events), rather than the type of health institution or providers. Interpretation This study highlights a relatively high rate of severe critical events during the anaesthesia management of children for surgical or diagnostic procedures in Europe, and a large variability in the practice of paediatric anaesthesia. These findings are substantial enough to warrant attention from national, regional, and specialist societies to target education of anaesthesiologists and their teams and implement strategies for quality improvement in paediatric anaesthesia