Defining relations of a free modular lattice of rank 3

For a 3-generated free modular lattice we obtain a set of 11 defining relations and prove that this set is minimal. © 2013 Allerton Press, Inc

On Chromatic Uniqueness of Some Complete Tripartite Graphs

Let P(G,x) be a chromatic polynomial of a graph G. Two graphs G and H are called chromatically equivalent iff P(G,x)=H(G,x). A graph G is called chromatically unique if G≃H for every H chromatically equivalent to G. In this paper, the chromatic uniqueness of complete tripartite graphs K(n1,n2,n3) is proved for n1⩾n2⩾n3⩾2 and n1−n3⩽5.The author is grateful to his scientific advisor prof. V. A. Baransky for constant attention and remarks

ON GARLANDS IN x-UNIQUELY COLORABLE GRAPHS

a graph G is called x-uniquely colorable, if all its x-colorings induce the same partion of the vertex set into one-color components. For x-uniquely colorable graphs new bound of the number of vertex set partions into x + 1 cocliques is found. © 2019 gein p.a

Computer learning tests as the diagnostic method of development methacognitive competences

Предлагается использовать технологию обучающих тестов, дополненную рефлексивным компонентом, для диагностики у студентов вузов уровня развития метакогнитивных компетенций.It is proposed to use the technology of training tests, supplemented by reflexive component for the diagnosis of the level of development of metacognitive skills

Роль метапредметных конструктов в формировании когнитивных компетенций студентов ВУЗа

Discussed is a psychological and pedagogical basis for metasubject structures application and given are examples of their employment to form higher school students’ cognitive competences.Дано психолого-педагогическое обоснование использованию метапредметных конструктов и приведены примеры их применения для формирования когнитивных компетенций у студентов вузов

Design, Synthesis, and Structure−Activity Relationship Exploration of 1-Substituted 4-Aroyl-3-hydroxy-5-phenyl-1H-pyrrol-2(5H)-one Analogues as Inhibitors of the Annexin A2−S100A10 Protein Interaction

This research was supported by grants from Cancer Research UK. H.K.M. was funded by a Biotechnology and Biological Sciences Research Council studentship.S100 proteins are small adaptors that regulate the activity of partner proteins by virtue of direct protein interactions. Here, we describe the first small molecule blockers of the interaction between S100A10 and annexin A2. Molecular docking yielded candidate blockers that were screened for competition of the binding of an annexin A2 peptide to S100A10. Several inhibitory clusters were identified with some containing compounds with potency in the lower micromolar range. We chose 3-hydroxy-1-(2-hydroxypropyl)-5-(4-isopropylphenyl)-4-(4-methylbenzoyl)-1H-pyrrol-2(5H)-one (1a) as a starting point for structure-activity studies. These confirmed the hypothetical binding mode from the virtual screen for this series of molecules. Selected compounds disrupted the physiological complex of annexin A2 and S100A10, both in a broken cell preparation and inside MDA-MB-231 breast cancer cells. Thus, this class of compounds has promising properties as inhibitors of the interaction between annexin A2 and S100A10 and may help to elucidate the cellular function of this protein interaction.Peer reviewe