Massey products in symplectic manifolds

The paper is devoted to study of Massey products in symplectic manifolds. Theory of generalized and classical Massey products and a general construction of symplectic manifolds with nontrivial Massey products of arbitrary large order are exposed. The construction uses the symplectic blow-up and is based on the author results, which describe conditions under which the blow-up of a symplectic manifold X along its submanifold Y inherits nontrivial Massey products from X ot Y. This gives a general construction of nonformal symplectic manifolds.Comment: LaTeX, 48 pages, 2 figure

Special Moduli of Continuity and the Constant in the Jackson-Stechkin Theorem

We consider a special 2k-order modulus of continuity W 2k(f,h) of 2π-periodic continuous functions and prove an analog of the Bernstein-Nikolsky-Stechkin inequality for trigonometric polynomials in terms of W 2k. We simplify the main construction from the paper by Foucart et al. (Constr. Approx. 29(2), 157-179, 2009) and give new upper estimates of the Jackson-Stechkin constants. The inequality W2k(f,h)≤3∥f∥∞ and the Bernstein-Nikolsky-Stechkin type estimate imply the Jackson-Stechkin theorem with nearly optimal constant for approximation by periodic splines. © 2013 The Author(s)

Priming winter wheat seeds with the bacterial quorum sensing signal N-hexanoyl-L-homoserine lactone (C6-HSL) shows potential to improve plant growth and seed yield

Several model plants are known to respond to bacterial quorum sensing molecules with altered root growth and gene expression patterns and induced resistance to plant pathogens. These compounds may represent novel elicitors that could be applied as seed primers to enhance cereal crop resistance to pathogens and abiotic stress and to improve yields. We investigated whether the acyl-homoserine lactone N-hexanoyl-L-homoserine lactone (C6-HSL) impacted winter wheat (Triticum aestivum L.) seed germination, plant development and productivity, using two Ukrainian varieties, Volodarka and Yatran 60, in both in vitro experiments and field trials. In vitro germination experiments indicated that C6-HSL seed priming had a small but significant positive impact on germination levels (1.2x increase, p < 0.0001), coleoptile and radicle development (1.4x increase, p < 0.0001). Field trials over two growing seasons (2015-16 and 2016-17) also demonstrated significant improvements in biomass at the tillering stage (1.4x increase, p < 0.0001), and crop structure and productivity at maturity including grain yield (1.4 – 1.5x increase, p < 0.0007) and quality (1.3x increase in good grain, p < 0.0001). In some cases variety effects were observed (p ≤ 0.05) suggesting that the effect of C6-HSL seed priming might depend on plant genetics, and some benefits of priming were also evident in F1 plants grown from seeds collected the previous season (p ≤ 0.05). These field-scale findings suggest that bacterial acyl-homoserine lactones such as C6-HSL could be used to improve cereal crop growth and yield and reduce reliance on fungicides and fertilisers to combat pathogens and stress

Reflection of hydrogen and deuterium atoms from the beryllium, carbon, tungsten surfaces

Particle reflection coefficients for scattering of hydrogen and deuterium atoms from amorphous beryllium, carbon and tungsten were obtained, which are of interest for thermonuclear reactor physics. For the case of deuterium scattering from tungsten the data were also calculated for polycrystalline and crystalline target. The calculations were carried out by two methods: by modeling the trajectories of the incident particles and by using the binary collision approximation. Interaction potentials between hydrogen and helium atoms and the selected materials were calculated in the scope of the density function theory using program DMol for choosing wave functions. The dependence of the reflection coefficient RN on the potential well depth was found. The results demonstrate a good agreement with the available experimental values.Peer reviewe

ЦИТОГЕНЕТИЧНА ХАРАКТЕРИСТИКА КОРІВ МОЛОЧНОЇ ХУДОБИ

With the help of cytogenetic analysis in breeding herds of cattle found that most of the cows tested karyotype as normal, but in the third part of the cows found in the mutant cells and aberrant chromosome karyotype. It was also found that in the investigated cows of herds from the Shchors pedigree plant the total percentage of mutative cells is 17,0 % and in cows of herds from «Agrosvit» this data is twice higher – 35,8 % (Р < 0,001). Low correlation was found between the number of cell mutation and performance (r = 0,108–0,299, P > 0,05). Cytogenetic indicators characterize chromosomal status of animals and is a marker of the intensity of metabolism in animals that cause an increase in milk yield of cows. Evaluation kariotypovoyi variability of breeding stock will help in the short term to detect and remove carriers a high level of chromosomal disorders.  Цитогенетическим анализом в племенных стадах молочного скота установлено, что в большей части протестированных коров кариотип соответствует норме, однако в третьей части этих коров обнаружили мутационные клетки и в кариотипе аберрантные хромосомы.В протестированных коров стада СПК им. Щорса общий процент мутационных клеток составляет 17,0 %, в СООО «Агросвит» – 35,8 % при достоверной разнице Р<0,001.Установлена низкая связь между количеством мутационных клеток и молочной производительностью (r = 0,108–0,299, Р > 0,05). Цитогенетические показатели отражают хромосомный статус животных и являются определенным маркером интенсивности обменных процессов в организме животных, которые приводят к увеличению удоевкоров. Оценка кариотипической изменчивости маточного поголовья позволит в короткие сроки выявить и изъять носителей высокого уровня хромосомных нарушений.Цитогенетичним аналізом у племінних стадах молочної худоби встановлено, що у більшої частини протестованих корів каріотип відповідає нормі, однак у третьої частини цих корів виявили мутаційні клітини та у каріотипі аберантні хромосоми. У протестованих корів стада СВК ім. Щорса загальний відсоток мутаційних клітин становить 17,0 %, у СТОВ «Агросвіт» – 35,8 % за вірогідної різниці Р0,05). Цитогенетичні показники характеризують хромосомний статус тварин і є маркером інтенсивності обмінних процесів в організмі тварин, які зумовлюють збільшення надоїв корів. Оцінка каріотипової мінливості маточного поголів’я дасть змогу в короткі строки виявити і вилучити носіїв високого рівня хромосомних порушень

Asymptotic description of solutions of the exterior Navier Stokes problem in a half space

We consider the problem of a body moving within an incompressible fluid at constant speed parallel to a wall, in an otherwise unbounded domain. This situation is modeled by the incompressible Navier-Stokes equations in an exterior domain in a half space, with appropriate boundary conditions on the wall, the body, and at infinity. We focus on the case where the size of the body is small. We prove in a very general setup that the solution of this problem is unique and we compute a sharp decay rate of the solution far from the moving body and the wall

Weed plants of oilseed rape agrocoenoses in Tomsk Oblast

The species composition of weed plants in the oilseed rape agrocoenoses in the south part of Western Siberia (Tomsk region) have been studied. There are more than 80 species of weed plants occupied oilseed rape fields on this territory. Euphorbia virgata, Convolvulus arvensis, Stachys palustris, Cirsium setosum and Sonchus arvensis belongs to the most common and widely distributed species of perennial weeds. In the seed lots of Brassica napus L. Metzg. Cultivated in Tomsk Oblast the fruit and seeds of more than 40 weed seeds have been founded

NATURE OF LEGAL BEHAVIOR: THE CONCEPTS OF DEFINITION AND THEIR EVOLUTION

Purpose: The purpose of the study is determining nature of legal behavior: the concepts of definition and their evolution Methodology: This is intellectual research and we used here historical methods for analyzing. Result: The genesis of the concept of legal behavior implies a link between research and the praxeological dimension of the legal system in which the legal personality is a central element. Applications: This research can be used for universities, teachers, and students. Novelty/Originality: In this research, the model of nature of legal behavior: the concepts of definition and their evolution are presented in a comprehensive and complete manner

The Hilbert-Schmidt Theorem Formulation of the R-Matrix Theory

Using the Hilbert-Schmidt theorem, we reformulate the R-matrix theory in terms of a uniformly and absolutely convergent expansion. Term by term differentiation is possible with this expansion in the neighborhood of the surface. Methods for improving the convergence are discussed when the R-function series is truncated for practical applications.Comment: 16 pages, Late