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- ДокументGalois coverings of one-sided bimodule problems(2021) Vyacheslav Babych, Nataliya GolovashchukApplying geometric methods of 2-dimensional cell complex theory, we construct a Galois covering of a bimodule problem satisfying some structure, triangularity and finiteness conditions in order to describe the objects of finite representation type. Each admitted bimodule problem A is endowed with a quasi multiplicative basis. The main result shows that for a problem from the considered class having some finiteness restrictions and the schurian universal covering A', either A is schurian, or its basic bigraph contains a dotted loop, or it has a standard minimal non-schurian bimodule subproblem.
- ДокументOn conformally reducible pseudo-Riemannian spaces(2021) Тетяна Iванiвна Шевченко, Тетяна Сергіївна Спічак, Дмитро Миколайович ДойковThe present paper studies the main type of conformal reducible conformally flat spaces. We prove that these spaces are subprojective spaces of Kagan, while Riemann tensor is defined by a vector defining the conformal mapping. This allows to carry out the complete classification of these spaces. The obtained results can be effectively applied in further research in mechanics, geometry, and general theory of relativity. Under certain conditions the obtained equations describe the state of an ideal fluid and represent quasi-Einstein spaces. Research is carried out locally in tensor shape.
- ДокументSome applications of transversality for infinite dimensional manifolds(2021) Kaveh EftekharinasabWe present some transversality results for a category of Frechet manifolds, the so-called MCk - Frechet manifolds. In this context, we apply the obtained transversality results to construct the degree of nonlinear Fredholm mappings by virtue of which we prove a rank theorem, an invariance of domain theorem and a Bursuk-Ulam type theorem.
- ДокументDeformations of circle-valued Morse functions on 2-torus(2021) Bohdan FeshchenkoIn this paper we give an algebraic description of fundamental groups of orbits of circle-valued Morse functions on T2 with respect to the action of the group of diffeomorphisms of T2
- ДокументNUTRITIONAL PROPERTIES OF CHIA SEEDS AND THEIR SANITARY SAFETY(2020) L. Valevskaya, A. Iegorova, L. Ovsiannykova, O. Sokolovskaya, F. Marchenkov, A. ShulyanskaCurrently, there are more and more requirements not only to the quality of food, but also to the raw materials it is made from. This leads to the search for new, non-traditional products. One of these is chia seeds (Salvia hispanica). The article provides data on their useful properties. The high demand for chia seeds is due to their unique chemical composition. The main feature of the seeds of this crop is that they contain many chemical substances of high calorific and biological value, as compared with cereals and oilseeds traditionally grown in Ukraine. In chia seeds, there are 30–35% of fat, 25–41% of carbohydrates, and 20–22% of protein. Chia seeds are a valuable source of vitamin B, calcium, potassium, iron, zinc, and copper. The fatty acid composition of this crop indicates a high content of polyunsaturated fatty acids. 63.3% of them is linolenic fatty acid, which belongs to ω-3 acids and is important for the brain function, growth, and development of a living organism. That is why it is so important to find optimal ways of preparing freshly harvested chia seeds so as to extend their shelf life. These ways must take into account the biological and chemical characteristics of this crop, and make it possible to preserve its consumer properties for further targeted processing. The article presents the results of studying the quality indicators and microbiological condition of chia seeds to establish how long they can be safely stored and to assess the sanitary safety of this crop. It has been shown that within the period of 6 months, the greatest changes in the quality of chia seed oil are observed at 25°C: there is a significant increase in the acid and peroxide values and a decrease in the iodine value (the latter indicates spoilage of chia seeds). Lowering the air temperature to 5°C slows down the enzymatic processes that take place in chia seeds, and inhibits the increase of the acid and peroxide values of fat, which ensures retention of the consumer properties of seeds. It has been established that the seeds of the crop under study can be stored, without any loss of their quality, for 6 months at 5–15°C and the relative humidity 60–70%. All the beneficial properties of chia seeds are due to their unique composition, so they are supposed to be widely used for specialised and functional nutrition