APPROACHES TO THE ESTIMATION OF THE LEVEL OF FORMATION OF PROFESSIONAL COMPETENCES OF GRADUATES OF THE SPO IN MODERN CONDITIONS THE IMPLEMENTATION OF FGOS SPO

В статье рассматриваются возможности использования технологий активного обучения для формирования профессиональной компетентности будущего педагогаThe article describes the potentiality of active learning technologies for forming of professional-pedagogical competenc

Drawing bobbin lace graphs, or, Fundamental cycles for a subclass of periodic graphs

In this paper, we study a class of graph drawings that arise from bobbin lace patterns. The drawings are periodic and require a combinatorial embedding with specific properties which we outline and demonstrate can be verified in linear time. In addition, a lace graph drawing has a topological requirement: it contains a set of non-contractible directed cycles which must be homotopic to $(1,0)$, that is, when drawn on a torus, each cycle wraps once around the minor meridian axis and zero times around the major longitude axis. We provide an algorithm for finding the two fundamental cycles of a canonical rectangular schema in a supergraph that enforces this topological constraint. The polygonal schema is then used to produce a straight-line drawing of the lace graph inside a rectangular frame. We argue that such a polygonal schema always exists for combinatorial embeddings satisfying the conditions of bobbin lace patterns, and that we can therefore create a pattern, given a graph with a fixed combinatorial embedding of genus one.Comment: Appears in the Proceedings of the 25th International Symposium on Graph Drawing and Network Visualization (GD 2017

E-learning in additional educational training

The article deals with the problems of training of modern specialists for automobile dealerships, and the possibility of e-learning for the implementation of additional educational programsВ статье рассмотрены проблемы подготовки современных специалистов для автомобильных дилерских центров, и возможности электронного обучения для реализации дополнительной образовательной программ

ATF2 Proposal

ATF2 Group Accelerator Physic

Quality of life of the medium Russian city: yesterday and today (half a century Taganrog studies)

Studies of living standards of the urban population, one of the clearest examples of which are Taganrog studies, associated with name of N. Rimashevskaya, remain actual, and relevant up today. The paper deals analyses the main aspects of living standards of population such as housing conditions and properties of households and also the observing changes in this sphere of living of population in Taganrog during last fifty years

Two constructions of weight systems for invariants of knots in non-trivial 3-manifolds.

AbstractA new family of weight systems of finite type knot invariants of any positive degree in orientable 3-manifolds with non-trivial first homology group is constructed. The principal part of the Casson invariant of knots in such manifolds is split into the sum of infinitely many independent weight systems. Examples of knots separated by corresponding invariants and not separated by any other known finite type invariants are presented

Fiedler type combinatorial formulas for generalized Fiedler type invariants of knots in M2 x R1.

AbstractWe construct combinatorial formulas of Fiedler type (i.e. composed of oriented Gauss diagrams arranged by homotopy classes of loops in the base manifold, see [T. Fiedler, Gauss Diagram Invariants for Knots and Links, Math. Appl., vol. 552, Kluwer Academic Publishers, 2001; M. Polyak, O. Viro, Gauss diagram formulas for Vassiliev invariants, Int. Math. Res. Not. 11 (1994) 445–453]) for an infinite family of finite type invariants of knots in M2×R1 (M2 orientable), introduced in [S.A. Grishanov, V.A. Vassiliev, Two constructions of weight systems for invariants of knots in non-trivial 3-manifolds, Topology Appl. 155 (2008) 1757–1765]