Invariants of Triangular Lie Algebras

Triangular Lie algebras are the Lie algebras which can be faithfully represented by triangular matrices of any finite size over the real/complex number field. In the paper invariants ('generalized Casimir operators') are found for three classes of Lie algebras, namely those which are either strictly or non-strictly triangular, and for so-called special upper triangular Lie algebras. Algebraic algorithm of [J. Phys. A: Math. Gen., 2006, V.39, 5749; math-ph/0602046], developed further in [J. Phys. A: Math. Theor., 2007, V.40, 113; math-ph/0606045], is used to determine the invariants. A conjecture of [J. Phys. A: Math. Gen., 2001, V.34, 9085], concerning the number of independent invariants and their form, is corroborated.Comment: LaTeX2e, 16 pages; misprints are corrected, some proofs are extende

The atomic structure of large-angle grain boundaries Σ5\Sigma 5 and Σ13\Sigma 13 in YBa2Cu3O7−δ{\rm YBa_2Cu_3O_{7-\delta}} and their transport properties

We present the results of a computer simulation of the atomic structures of large-angle symmetrical tilt grain boundaries (GBs) $\Sigma 5$ (misorientation angles \q{36.87}{^{\circ}} and \q{53.13}{^{\circ}}), $\Sigma 13$ (misorientation angles \q{22.62}{^{\circ}} and \q{67.38}{^{\circ}}). The critical strain level $\epsilon_{crit}$ criterion (phenomenological criterion) of Chisholm and Pennycook is applied to the computer simulation data to estimate the thickness of the nonsuperconducting layer ${\rm h_n}$ enveloping the grain boundaries. The ${\rm h_n}$ is estimated also by a bond-valence-sum analysis. We propose that the phenomenological criterion is caused by the change of the bond lengths and valence of atoms in the GB structure on the atomic level. The macro- and micro- approaches become consistent if the $\epsilon_{crit}$ is greater than in earlier papers. It is predicted that the symmetrical tilt GB $\Sigma5$ \theta = \q{53.13}{^{\circ}} should demonstrate a largest critical current across the boundary.Comment: 10 pages, 2 figure

All solvable extensions of a class of nilpotent Lie algebras of dimension n and degree of nilpotency n-1

We construct all solvable Lie algebras with a specific n-dimensional nilradical n_(n,2) (of degree of nilpotency (n-1) and with an (n-2)-dimensional maximal Abelian ideal). We find that for given n such a solvable algebra is unique up to isomorphisms. Using the method of moving frames we construct a basis for the Casimir invariants of the nilradical n_(n,2). We also construct a basis for the generalized Casimir invariants of its solvable extension s_(n+1) consisting entirely of rational functions of the chosen invariants of the nilradical.Comment: 19 pages; added references, changes mainly in introduction and conclusions, typos corrected; submitted to J. Phys. A, version to be publishe

Computation of Invariants of Lie Algebras by Means of Moving Frames

A new purely algebraic algorithm is presented for computation of invariants (generalized Casimir operators) of Lie algebras. It uses the Cartan's method of moving frames and the knowledge of the group of inner automorphisms of each Lie algebra. The algorithm is applied, in particular, to computation of invariants of real low-dimensional Lie algebras. A number of examples are calculated to illustrate its effectiveness and to make a comparison with the same cases in the literature. Bases of invariants of the real solvable Lie algebras up to dimension five, the real six-dimensional nilpotent Lie algebras and the real six-dimensional solvable Lie algebras with four-dimensional nilradicals are newly calculated and listed in tables.Comment: 17 pages, extended versio

Study of antimicrobial activity and technology optimization of Calendulae flos galenicals

The article presents materials on optimization of manufacture technology for Calendulae flos galenicals with medium level of antibacterial activity. For antibacterial study of extracts, we used agar well diffusion method. In our research, we utilized six test-strain microorganisms: E. coli ATCC 25922, S. aureus ATCC 25923, P. vulgaris ATCC 4636, P. aeruginosa ATCC 27853, C. albicans ATCC 885/653, and B. subtilis ATCC 6633. We have found that the maximum level of extracts’ antimicrobial activity is achieved in the range of ethanol content in the extractant from 70 to 97 % v/

Sustainable Supply Chain Management in City Logistics Solutions

Abstract-The strategic supply chain processes that influences on the city management. The sustainable logistics and transportation studies constitute a primordial research axis in the enterprises’ governance. The aim of this paper arises on a reflection about the sustainable supply chain management by digitalization and smart technologies. These include product development, customers, manufacturing, vendors, and logistics. The main global introduction of digital technologies in all spheres of human and the state life continues, motivating the creation of new approaches and technological solutions. Public administration through information technologies is currently particularly relevant. The main tool of informatization and digitalization of state and municipal services are the technologies of "electronic government", in this regard, the article focuses on issues of assessing the quality and degree of functioning of electronic government

ОТДАЛЕННЫЕ РЕЗУЛЬТАТЫ ЛЕЧЕНИЯ ХОЛАНГИОКАРЦИНОМЫ

С 2010 по 2016 г. в клинике оперированы 72 больных по поводу холангиокарциномы различной локализации. Радикальное (R-0) вмешательство выполнено у 33 (45,8%) больных, условно-радикальное (R-1) – у 39 (54,2%). Больным выполняли изолированную резекцию общего печеночного протока (ОПП), сегментарную, долевую и расширенную резекцию печени. Резекция воротной вены  выполнена у 8 (11,1%) больных. После операции 25 (34,7%) больным проведена внутриартериальная химиотерапия. Показатели общей 5-летней выживаемости больных после R-0 резекции составили 20%, медиана выживаемости 29 мес, после R-1 резекции - 12 мес. Радикальная операция (R-0) по поводу холангиокарциномы имеет преимущества по сравнению с условно-радикальной (R-1) резекцией

СОЦІАЛЬНИЙ МОНІТОРИНГ ЧИННИКІВ РИЗИКУ ВИНИКНЕННЯ ПЕРИНАТАЛЬНИХ УСКЛАДНЕНЬ У ЖІНОК, ЗАЛЕЖНИХ ВІД ТЮТЮНОКУРІННЯ

Purpose: to determine the socio-medical factors of the perinatal risk complications in pregnant women under the conditions of tobacco smoking. Materials and Methods. We examined 75 pregnant women who were divided into 2 subgroups: group 1-A consisted of 45 pregnant women who smoked cigarettes during pregnancy; group 1-B – 30 pregnant women who smoked cigarettes before pregnancy and did not abuse tobacco during their current pregnancies. The control group consisted of 40 healthy pregnant women non-smokers. Results. It is shown that smoking pregnant women belong to a high social risk group. It was established that the risk of tobacco smoking during gestation increases the incidence of perinatal complications, but part of pregnant women is not able to abandon smoking during gestation and breastfeeding. It was proved that the intro­duction of a comprehensive correction and rehabilitation program for such women contributes to a decrease in tobacco smoking among pregnant women and a decrease in the frequency of perinatal complications. Conclusions. Tobacco smoking is a risk factor for perinatal complications, and pre-birth training for such women is crucial for reducing perinatal pathology.Мета: визначити соціально-медичні чинники ризику виникнення перинатальних ускладнень у вагітних за умов тютюнокуріння. Матеріали і методи. Обстежено 75 вагітних (основна група), яких поділено на 2 підгрупи: 1-А групу склали 45 вагітних, які курили сигарети протягом вагітності; 1-Б групу – 30 вагітних, які курили сигарети до вагітності й не зловживали тютюном упродовж теперішньої вагітності. Контрольну групу склали 40 здорових вагітних, які не курили. Результати. Показано, що вагітні, залежні від тютюнокуріння, належать до високої групи соціального ризику. Встановлено, що ризик тютюнокуріння впродовж гестації підвищує частоту перинатальних ускладнень, проте частина вагітних жінок не в змозі відмовитися від куріння впродовж  гестації та вигодовування немовля грудьми. Доведено, що впровадження комплексної корекційно-реабілітаційної програми для таких жінок сприяє зниженню тютюнокуріння серед вагітних і зменшенню частоти перинатальних ускладнень. Висновки. Тютюнокуріння є чинником ризику перинатальних ускладнень, а прегравідарна підготовка таких жінок має вирішальне значення щодо зниження перинатальної патології

Invariants of Lie Algebras with Fixed Structure of Nilradicals

An algebraic algorithm is developed for computation of invariants ('generalized Casimir operators') of general Lie algebras over the real or complex number field. Its main tools are the Cartan's method of moving frames and the knowledge of the group of inner automorphisms of each Lie algebra. Unlike the first application of the algorithm in [J. Phys. A: Math. Gen., 2006, V.39, 5749; math-ph/0602046], which deals with low-dimensional Lie algebras, here the effectiveness of the algorithm is demonstrated by its application to computation of invariants of solvable Lie algebras of general dimension $n<\infty$ restricted only by a required structure of the nilradical. Specifically, invariants are calculated here for families of real/complex solvable Lie algebras. These families contain, with only a few exceptions, all the solvable Lie algebras of specific dimensions, for whom the invariants are found in the literature.Comment: LaTeX2e, 19 page

САМОСТІЙНА РОБОТА СТУДЕНТІВ НА КАФЕДРІ ВНУТРІШНЬОЇ МЕДИЦИНИ № 3

The question of the organization of student’s self-work at the Inner Medicine Department number 3 is reported in the article. Self-work has a special importance in the study of medical students, as the usage of the knowledge gained during the seminars to make a diagnosis on their own is very important for the improvement of clinical thinking of the future doctor.У статті висвітлено питання організації самостійної роботи студентів на кафедрі внутрішньої медицини № 3. Працювати самостійно особливе значення має в навчанні студентів-медиків, оскільки, використовувати знання, отримані на практичних заняттях, для постановки діагнозу самостійно є дуже важливим для покращення клінічного мислення майбутнього лікаря.