Matrix solutions of a noncommutative KP equation and a noncommutative mKP equation

Matrix solutions of a noncommutative KP and a noncommutative mKP equation which can be expressed as quasideterminants are discussed. In particular, we investigate interaction properties of two-soliton solutions.Comment: 2 figure

Poisson Yang-Baxter maps with binomial Lax matrices

A construction of multidimensional parametric Yang-Baxter maps is presented. The corresponding Lax matrices are the symplectic leaves of first degree matrix polynomials equipped with the Sklyanin bracket. These maps are symplectic with respect to the reduced symplectic structure on these leaves and provide examples of integrable mappings. An interesting family of quadrirational symplectic YB maps on $\mathbb{C}^4 \times \mathbb{C}^4$ with $3\times 3$ Lax matrices is also presented.Comment: 22 pages, 3 figure

On multidimensional analogs of Melvin's solution for classical series of Lie algebras

A multidimensional generalization of Melvin's solution for an arbitrary simple Lie algebra $\cal G$ is presented. The gravitational model contains n 2-forms and $l \geq n$ scalar fields, wheren is the rank of $\cal G$. The solution is governed by a set of n functions obeying n ordinary differential equations with certain boundary conditions. It was conjectured earlier that these functions should be polynomials (the so-called fluxbrane polynomials). A program (in Maple) for calculating of these polynomials for classical series of Lie algebras is suggested (see Appendix). The polynomials corresponding to the Lie algebra D_4 are obtained. It is conjectured that the polynomials for A_n-, B_n- and C_n-series may be obtained from polynomials for D_{n+1}-series by using certain reduction formulas.Comment: 6 pages, based on a report at RUSGRAV-13 (23-28 June, 2008, PFUR, Moscow

Exchange coupling in Eu monochalcogenides from first principles

Using a density functional method with explicit account for strong Coulomb repulsion within the 4f shell, we calculate effective exchange parameters and the corresponding ordering temperatures of the (ferro)magnetic insulating Eu monochalcogenides (EuX; X=O,S,Se,Te) at ambient and elevated pressure conditions. Our results provide quantitative account of the many-fold increase of the Curie temperatures with applied pressure and reproduce well the enhancement of the tendency toward ferromagnetic ordering across the series from telluride to oxide, including the crossover from antiferromagnetic to ferromagnetic ordering under pressure in EuTe and EuSe. The first and second neighbor effective exchange are shown to follow different functional dependencies. Finally, model calculations indicate a significant contribution of virtual processes involving the unoccupied f states to the effective exchange.Comment: 4 pages, 6 figure

Ionospheric response to the 2009 sudden stratospheric warming over the equatorial, low, and middle latitudes in the South American sector

The present study investigates the ionospheric total electron content (TEC) and F-layer response in the Southern Hemisphere equatorial, low, and middle latitudes due to major sudden stratospheric warming (SSW) event, which took place during January-February 2009 in the Northern Hemisphere. In this study, using 17 ground-based dual frequency GPS stations and two ionosonde stations spanning latitudes from 2.8°N to 53.8°S, longitudes from 36.7°W to 67.8°W over the South American sector, it is observed that the ionosphere was significantly disturbed by the SSW event from the equator to the midlatitudes. During day of year 26 and 27 at 14:00 UT, the TEC was two times larger than that observed during average quiet days. The vertical TEC at all 17 GPS and two ionosonde stations shows significant deviations lasting for several days after the SSW temperature peak. Using one GPS station located at Rio Grande (53.8°S, 67.8°W, midlatitude South America sector), it is reported for the first time that the midlatitude in the Southern Hemisphere was disturbed by the SSW event in the Northern Hemisphere.Fil: Fagundes, P. R.. Universidade do Vale do Paraíba; BrasilFil: Goncharenko, L. P.. Massachusetts Institute of Technology; Estados UnidosFil: De Abreu, A. J.. Universidade do Vale do Paraíba; BrasilFil: Venkatesh, K.. Universidade do Vale do Paraíba; BrasilFil: Pezzopane, M.. Istituto Nazionale Di Geofisica E Vulcanologia; ItaliaFil: De Jesus, R.. Universidade do Vale do Paraíba; BrasilFil: Gende, Mauricio Alfredo. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Coster, A. J.. Massachusetts Institute of Technology; Estados UnidosFil: Pillat, V. G.. Universidade do Vale do Paraíba; Brasi

Development and support of small innovative entrepreneurship in Europe and the USA

Modern business practice shows that small innovative entrepreneurship needs special support in the context of rapid development of science and technology. To implement the outlined, various business support programs are being developed at a rapid pace, which are being actively implemented in practice. The aim of the article is to present the conceptual features of the development and support of small innovative entrepreneurship in Europe and the United States. The purpose of the academic paper is to present the conceptual features of supporting small innovative entrepreneurship in Europe and the United States of America

Modern possibilities of preterm birth prediction

Purpose of the study is to improve the method of preterm deliveries onset predicting in pregnant women at 24–34 weeks. Materials and methods. 49 pregnant women with gestational age 24–34 weeks and with diagnosis of “threatening premature deliveries" were comprehensively examined using transvaginal ultrasound. Pregnant women with a shortened cervix ≤25 mm were given a qualitative determination of fetal fibronectin. The average age of pregnant women ranged from 26–34 years and averaged out 31.2 ± 0,6 years. Study results. Clinically significant structural changes in the cervix were only in 21 (42.9%) pregnant women. The average value of the cervix length varied between 16–24 mm and averaged 18.2 ± 0.4 mm. Positive test on fetal fibronectin in vaginal secretions was in 7 (33.3%) of 21 pregnant women with clinically significant structural changes in the cervix. During 10 days premature birth occurred in 3 (42.9%) of 7 pregnant women with clinically significant cervix shortening and a positive test for fetal fibronectin in the gestation period of 32 weeks. Hospitalization in an obstetric hospital was found to be unjustified in 28 (57.1%) cases. Conclusions. Combination of a comprehensive assessment of the cervix state and vaginal fetal fibronectin evaluation in pregnant women with risk of preterm deliveries at the outpatient stage allows to predict the manifestation of preterm birth in critical terms also determine the volume and direction of therapy in obstetric department. Combination of this methods help to prevent unwarranted hospitalization of a pregnant woman in an obstetric hospital and as a result it limits the conduct of glucocorticoid therapy and prevent a prolong stay of a pregnant woman in a hospital and the associated contamination with nosocomial bacteria strains

Концепція мультифункціонального розвитку сільських територій регіону

Priorities of conception of regional rural areas multifunctional development are revealed in the article. Experience in European Union countries and European Green Deal policy is taken into account  for rural areas development in regional level. Priorities of sustainable development policy in rural areas and regional agri-food industry are certainly in ground  of strategy development due to cluster initiatives in the Lviv Region. Certainly priorities and advantages of cluster development strategy in rural areas recognition experience and prospects of transborder cooperation initiative. Possibility in farms economic development providing is examined within the framework of clusters for achievement of synergy effect and positive influence on the economic, ecological and social sphere in region. Cluster conception of development is realized in the Lviv Region  allowed to provide economic support of farms, develop infrastructural ecosystem of business support and complex to define priorities of multifunctional rural areas  development in regional level. Perspective directions of integrated development of craft food producers within the framework in regional clusters at the level of counties in Lviv Area are grounded. Offered approach of institutional development in regional level with the purpose of multifunctional rural areas development with balance between  economy, ecological and social constituents within the framework to the cluster for realization of farms competitive edges during the correct keeping of products in the internal market. Certainly priorities of state business support in regional agri-food  industry during realization of cluster development initiatives and measures of stimulant influence are for providing modernization changes on principles of Smart Specialization.У статті актуалізовано пріоритети концепції мультифункціонального  розвитку сільських територій. Враховано досвід країн Європейського Союзу та політики Європейського зеленого курсу для розвитку сільських територій на регіональному рівні. Пріоритети політики збалансованого розвитку сільських територій та регіонального агропродовольчого підкомплексу визначено в основі розробки стратегії реалізації кластерних ініціатив у Львівській області. Визначено пріоритети та переваги кластерної стратегії розвитку сільських територій із врахуванням досвіду Львівської області і перспектив транскордонного співробітництва. Розглядається можливість забезпечення економічного розвитку фермерських господарств в рамках кластерів для досягнення ефекту синергії та позитивного впливу на економічну,екологічну та соціальну сферу регіону. Кластерна концепція розвитку реалізована у Львівській області дозволила забезпечити економічну підтримку фермерських господарств, розвинути інфраструктурну екосистему підтримки підприємництва та комплексно визначити пріоритети мультифункціонального розвитку сільських територій на регіональному рівні. Обгрунтовано перспективні напрями інтегрованого розвитку виробників крафтової продукції в рамках регіональний кластерів на рівні районів Львівської області. Запропоновано підходи до інституційного розвитку на регіональному рівні з метою мультифункціонального розвитку сільських територій із збалансуванням економічної, екологічної та соціальної складових в рамках кластеру для реалізації конкурентних переваг фермерських господарств при правильному позиціонуванні продукції на національному ринку. Визначено пріоритети державної підтримки суб’єктів господарювання в агропродовольчому підкомплексі регіону при реалізації кластерних розвиткових ініціатив та заходи стимулюючого впливу для забезпечення модернізаційних змін на засадах смарт-спеціалізації