370 research outputs found

    Reflection groups in hyperbolic spaces and the denominator formula for Lorentzian Kac--Moody Lie algebras

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    This is a continuation of our "Lecture on Kac--Moody Lie algebras of the arithmetic type" \cite{25}. We consider hyperbolic (i.e. signature (n,1)(n,1)) integral symmetric bilinear form S:M×MZS:M\times M \to {\Bbb Z} (i.e. hyperbolic lattice), reflection group WW(S)W\subset W(S), fundamental polyhedron \Cal M of WW and an acceptable (corresponding to twisting coefficients) set P({\Cal M})\subset M of vectors orthogonal to faces of \Cal M (simple roots). One can construct the corresponding Lorentzian Kac--Moody Lie algebra {\goth g}={\goth g}^{\prime\prime}(A(S,W,P({\Cal M}))) which is graded by MM. We show that \goth g has good behavior of imaginary roots, its denominator formula is defined in a natural domain and has good automorphic properties if and only if \goth g has so called {\it restricted arithmetic type}. We show that every finitely generated (i.e. P({\Cal M}) is finite) algebra {\goth g}^{\prime\prime}(A(S,W_1,P({\Cal M}_1))) may be embedded to {\goth g}^{\prime\prime}(A(S,W,P({\Cal M}))) of the restricted arithmetic type. Thus, Lorentzian Kac--Moody Lie algebras of the restricted arithmetic type is a natural class to study. Lorentzian Kac--Moody Lie algebras of the restricted arithmetic type have the best automorphic properties for the denominator function if they have {\it a lattice Weyl vector ρ\rho}. Lorentzian Kac--Moody Lie algebras of the restricted arithmetic type with generalized lattice Weyl vector ρ\rho are called {\it elliptic}Comment: Some corrections in Sects. 2.1, 2.2 were done. They don't reflect on results and ideas. 31 pages, no figures. AMSTe

    Creating a virtual device for processing the results of sorption measurements in the study of zinc oxide nanorods

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    The work is devoted to the creation of a virtual device (computer program) for processing the results of sorption analysis of nanomaterials, including for estimating the size of nanoparticles based on the specific surface area. The obtained evaluation results were compared with the scanning electron microscopy data. Photocatalytically active zinc oxide samples were chosen as the object of the study

    Синтез і комп’ютерний скринінг нових 2-метилхінолін-4-онів, зв’язаних з піразолон-5-оновим фрагментом

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    The 1,3-dicarbonyl derivatives of 2-methyl-1,4-dihydroquinoline-4-one have been synthesized by alkylation of methylene active compounds with 3-dimethylaminomethyl-2-methyl-1,4-dihydroquinoline-4-one. These compounds are the convenient starting material for creating the new chemical libraries in the series of 3-heteryl substituted 2-methyl-1,4-dihydroquinoline-4-ones. In this work the examples of the synthesis of new quinolone-pyrazolone systems are presented. Their condensation with hydrazine hydrate resulted in the new derivatives of 2-methyl-3-[(5-oxo-4,5-dihydro-1H-pyrazol-4-yl)methyl]-1,4-dihydroquinolin-4-ones. The estimation of novelty of the compounds obtained in such chemical databases as PubChem, ChemBl, Spresi has shown that these substances are not present in these sources, and the chemical scaffold – quinolone bound via the methylene bridge with azoles is new. Determination of 2D similarity of the compounds synthesized by standard molecular descriptors with the biologically active structures in the ChemBl_20 database has shown the uniqueness of a new quinolone scaffold and the potential anti-inflammatory activity for compounds of this series. The molecular similarity has been determined using the ChemAxon software (JKlustor, Instant JChem).Алкилированием 3-диметиламинометил-2-метил-1,4-дигидрохинолин-4-оном метиленактивных соеди- нений были синтезированы 1,3-дикарбонильные производные 2-метил-1,4-дигидрохинолин-4-она. Дан- ные соединения являются удобным стартовым материалом для создания библиотек в ряду 3-гетерилзамещенных 2-метил-1,4-дигидрохинолин-4-онов. В работе приведены примеры синтеза новых хинолон-пиразолоновых систем. Конденсацией алкилированных метиленактивных соединений с гидразин гидратом получены новые производные 2-метил-3-[(5-оксо-4,5-дигидро-1H-пиразол-4-ил)метил]-1,4- дигидрохинолин-4-онов. Проведенная оценка новизны полученных соединений по химическим базам PubChem, ChemBl и Spresi показала, что данные соединения совсем не представлены в этих источниках, а химический скаффолд – хинолон, соединенный через метиленовый мостик с азолами, является новым. Определение 2D подобия синтезированных соединений по стандартным молекулярным дескрипторам с биологически активными структурами базы данных ChemBl_20 показало уникальность и перспективность нового хинолонового скаффолда в дизайне лекарственных веществ, а также вероятность проявления противовоспалительной активности среди соединений данного ряда. Молекулярное подобие было определено с помощью программного обеспечения ChemAxon (JKlustor, Instant JChem).Алкілуванням 3-диметиламінометил-2-метил-1,4-дигідрохінолін-4-оном метиленактивних сполук були синтезовані 1,3-дикарбонільні похідні 2-метил-1,4-дигідрохінолін-4-ону. Дані сполуки є зручним стар- товим матеріалом для створення хімічних бібліотек в ряду 3-гетерилзаміщених 2-метил-1,4-ди- гідрохінолін-4-онів. У роботі наведені приклади синтезу нових хінолон-піразолонових систем. Конден- сацією алкілованих метиленактивних сполук з гідразин гідратом отримані нові похідні 2-метил-3-[(5- оксо-4,5-дигідро-1H-піразол-4-іл)метил]-1,4-дигідрохінолін-4-онів. Проведена оцінка новизни отриманих сполук за хімічними базами PubChem, ChemBl і Spresi показала, що дані сполуки зовсім не представлені в цих джерелах; а хімічний скаффолд – хінолон, з’єднаний через метиленовий місток з азолами, є новим. Визначення 2D схожості синтезованих речовин за стандартними молекулярними дескрипторами з біологічно активними структурами бази даних ChemBl_20 показало унікальність і перспективність нового хінолонового скаффолда в дизайні лікарських речовин, а також імовірність прояву протизапальної активності серед сполук даного ряду. Молекулярну схожість було визначено за допомогою програмного забезпечення ChemAxon (JKlustor, Instant JChem)

    Response calculations based on an independent particle system with the exact one-particle density matrix: Excitation energies

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    Adiabatic response time-dependent density functional theory (TDDFT) suffers from the restriction to basically an occupied → virtual single excitation formulation. Adiabatic time-dependent density matrix functional theory allows to break away from this restriction. Problematic excitations for TDDFT, viz. bonding-antibonding, double, charge transfer, and higher excitations, are calculated along the bond-dissociation coordinate of the prototype molecules

    Facile Low-Cost Synthesis of Highly Photocatalitycally Active Zinc Oxide Powders

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    The industrial waste can cause significant harm to human health and to the environment. Organic dyes in particular are environmentally dangerous since they may cause the death of aquatic life or contaminate the feed chain. Thus, one of the current research fields consists of the development of an inexpensive and environmentally friendly method to purify wastewater from organic contaminants. Among the others, Zinc oxide (ZnO) is considered one of the most effective photocatalysts for the decomposition of organic pollutants in water. In this work, we developed a highly efficient low-temperature and environmentally safe synthesis method to obtain photocatalytically active nanostructured ZnO by chemical precipitation from a solution. The effect of the technological conditions of synthesis on the photocatalytic properties is considered in detail, the correlation with the morphology, structural, and optical properties of the synthesized ZnO samples is determined. It was found that the maximum photocatalytic activity with respect to the decomposition of the dye rhodamine-B (RhB) is achieved for samples synthesized at NaOH molar concentration from 0.4 to 0.7 M; in this case, the sizes of crystallites along the crystallographic direction 002 reach maximum values of ∼42 nm. On the contrary, the sizes of crystallites along the directions 100 and 101 decrease monotonically from 30 to 25 nm with an increase in the molar concentration of NaOH from 0.14 to 1 M

    Classification of hyperbolic Dynkin diagrams, root lengths and Weyl group orbits

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    We give a criterion for a Dynkin diagram, equivalently a generalized Cartan matrix, to be symmetrizable. This criterion is easily checked on the Dynkin diagram. We obtain a simple proof that the maximal rank of a Dynkin diagram of compact hyperbolic type is 5, while the maximal rank of a symmetrizable Dynkin diagram of compact hyperbolic type is 4. Building on earlier classification results of Kac, Kobayashi-Morita, Li and Sa\c{c}lio\~{g}lu, we present the 238 hyperbolic Dynkin diagrams in ranks 3-10, 142 of which are symmetrizable. For each symmetrizable hyperbolic generalized Cartan matrix, we give a symmetrization and hence the distinct lengths of real roots in the corresponding root system. For each such hyperbolic root system we determine the disjoint orbits of the action of the Weyl group on real roots. It follows that the maximal number of disjoint Weyl group orbits on real roots in a hyperbolic root system is 4.Comment: J. Phys. A: Math. Theor (to appear

    On The 100th Anniversary Of The Founder Of The Odessa Scientific School Of Economic Thought A. K. Pokrytan

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    The partnership between the Odessa National University of Economics and "D. A. Tsenov” Academy of Economics is an example of a successful model for adding value in the field of scientific research. With its annual scientific conferences, the Odessa National University of Economics has provided dozens of scientists from the Svishtov Academy and other foreign researchers with the opportunity to publish their papers abroad. Prof. Mihail Zveryakov himself is a Doctor Honoris Causa (Zastrahovatel.com, 2010) of D. A. Tsenov Academy and a prominent co-author in collaborative research publications indexed in SCOPUS Q1/WoS (Zahariev, et al., 2020). The paper commemorates and pays due respect to Prof. Anatoly Karpovich Pokrytan - one of the most prominent scientists in the field of economics whose centenary provided his scientific followers with the opportunity to reflect on his scientific legacy. The 100th anniversary of the establishment of the Odessa National Economic University in Ukraine (founded under the name Odessa Institute of National Economy) on 16 May 1921 is another evidence for our Ukrainian partner’s tenacity during the decades of intense socio-economic and ideological changes of the 20th and the 21st century

    Profibrotic genetic polymorphisms as possible risk factors for the development of diastolic dysfunction in patients with epicardial adiposity

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    Aim. To determine the associations of variable sites of fibrogenesis genes with the risk of left ventricular (LV) diastolic dysfunction (DD) in patients with epicardial adiposity (EA).Material and methods. The study included 101 men with general obesity (Altai Territory) without cardiovascular diseases, diabetes and documented LVDD, of which, after determining the epicardial fat thickness (EFT), 2 groups were formed: group 1 — with EA (EA+), EFT ≥7 mm or more (n=70); group 2 — without EA (EA-), EFT <7 mm (n=31). The control group was formed from Kemerovo region residents of the corresponding sex and age and without a history of cardiovascular diseases and general obesity. Polymorphisms of the MMP9 rs17576, TGFB1 rs1800469, MMP3 rs6796620, MMP3 rs626750, MMP1 rs514921, LOC101927143 rs4290029, TIMP2 rs2277698 genes were determined in all patients using the polymerase chain reaction. After 4,7±0,3 years, all patients with general obesity underwent repeated echocardiography to assess LVDD.Results. We found that in the group with EA for rs626750 MMP3, the carriage of the homozygous T allele is 2 times more common (recessive inheritance, p=0,0022). After 4,7±0,3 years, LVDD was registered in 18 patients in the EA+ group and in 2 patients in the EA- group. When analyzing inheritance patterns, as well as comparing genotypes in groups of patients with EA with developed LVDD (n=20) and without LVDD (n=78), we found that patients with EA and LVDD are 3,4 times more likely to be a carrier of the homozygous T allele (recessive inheritance, p=0,02) for rs1800469 TGFB1.Conclusion. In patients with EA and LVDD, the carriage of the T rs1800469 TGFB1 allele is more common, which probably contributes to cardiac fibrosis and LVDD according to a recessive inheritance

    Immunological substantiation of complex therapy in patients with mild HPV-associated cervical intraepithelial neoplasia

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    Introduction. As is known, the development of invasive cervical cancer is preceded by cervical intraepithelial neoplasia of varying severity, which is a pathological process in which cells with varying degrees of atypia and impaired differentiation appear in the thickness of the stratified squamous epithelium of the cervix.Objective. To study the  effect of  complex therapy in  patients with mild HPV-associated cervical intraepithelial neoplasia on the dynamics of local cytokine status and autoimmunity parameters.Materials and methods. The study included 86 patients aged 35 to 40 years with morphologically verified mild cervical intraepithelial neoplasia. The main group consisted of 52 patients who, along with radio wave destruction of the cervix, were prescribed an immunostimulating drug with antiviral activity “Groprinosin-Richter” 1000 mg 3 times a day for 10 days 10–14 days before destruction and similar 2 courses after 10–14 days after it. The comparison group included 34 patients who underwent only radio wave destruction of the cervix.Results. An analysis of the outcomes of low-grade squamous intraepithelial lesions after 6 months showed that in the main group, CIN I regression was observed in 92.3% of patients, persistence – in 7.7% of cases, while in the comparison group, CIN I regression was noted in 73,5% of cases, persistence – in 26.5% of patients.Conclusions. Conducting complex therapy, including radio wave destruction and the use of a drug with immunostimulating and antiviral activity “Groprinosin-Richter” in  patients with low-grade HPV-associated cervical intraepithelial neoplasia, leads to the elimination of the initial imbalance of cytokines and normalization of autoantibody levels, helping to reduce the likelihood of HPV persistence and CIN progression to invasive cervical cancer uterus
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