933 research outputs found
4-colored graphs and knot/link complements
A representation for compact 3-manifolds with non-empty non-spherical
boundary via 4-colored graphs (i.e., 4-regular graphs endowed with a proper
edge-coloration with four colors) has been recently introduced by two of the
authors, and an initial classification of such manifolds has been obtained up
to 8 vertices of the representing graphs. Computer experiments show that the
number of graphs/manifolds grows very quickly as the number of vertices
increases. As a consequence, we have focused on the case of orientable
3-manifolds with toric boundary, which contains the important case of
complements of knots and links in the 3-sphere. In this paper we obtain the
complete catalogation/classification of these 3-manifolds up to 12 vertices of
the associated graphs, showing the diagrams of the involved knots and links.
For the particular case of complements of knots, the research has been extended
up to 16 vertices.Comment: 19 pages, 6 figures, 3 tables; changes in Lemma 6, Corollaries 7 and
About the notion of problem-model learning
The notion of problem-model learning is described in this article. The notions of the similar types of learning are givenΠ Π΄Π°Π½Π½ΠΎΠΉ ΡΡΠ°ΡΡΠ΅ ΡΠ°ΡΡΠΌΠ°ΡΡΠΈΠ²Π°Π΅ΡΡΡ ΠΏΠΎΠ½ΡΡΠΈΠ΅ ΠΏΡΠΎΠ±Π»Π΅ΠΌΠ½ΠΎ-ΠΌΠΎΠ΄Π΅Π»ΡΠ½ΠΎΠ³ΠΎ ΠΎΠ±ΡΡΠ΅Π½ΠΈΡ. ΠΠ°Π΅ΡΡΡ ΠΎΠΏΡΠ΅Π΄Π΅Π»Π΅Π½ΠΈΠ΅ ΡΡ
ΠΎΠΆΠΈΡ
Π²ΠΈΠ΄ΠΎΠ² ΠΎΠ±ΡΡΠ΅Π½ΠΈ
The foundation of forming the professional thinking of the educational specialist of vocational education
The problem of specific feature of the foundation of professional thinking of educational specialist of vocational education is discussed in the articleΠ Π°ΡΡΠΌΠΎΡΡΠ΅Π½Ρ Π²ΠΎΠΏΡΠΎΡΡ ΡΠΎΡΠΌΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΠΏΡΠΎΡΠ΅ΡΡΠΈΠΎΠ½Π°Π»ΡΠ½ΠΎΠ³ΠΎ ΠΌΡΡΠ»Π΅Π½ΠΈΡ ΠΏΠ΅Π΄Π°Π³ΠΎΠ³Π° ΠΏΡΠΎΡΠ΅ΡΡΠΈΠΎΠ½Π°Π»ΡΠ½ΠΎΠ³ΠΎ ΠΎΠ±ΡΡΠ΅Π½ΠΈ
Game modeling as a new approach to higher pedagogical education
The article is about game modeling - the new technology of education in universities. The notion of game modeling, its backgrounds and importance of usage are examinedΠ‘ΡΠ°ΡΡΡ ΠΏΠΎΡΠ²ΡΡΠ΅Π½Π° ΠΈΠ³ΡΠΎΠ²ΠΎΠΌΡ ΠΌΠΎΠ΄Π΅Π»ΠΈΡΠΎΠ²Π°Π½ΠΈΡ β Π½ΠΎΠ²ΠΎΠΉ ΡΠ΅Ρ
Π½ΠΎΠ»ΠΎΠ³ΠΈΠΈ Π² ΠΏΡΠΎΡΠ΅ΡΡΠ΅ ΠΎΠ±ΡΡΠ΅Π½ΠΈΡ ΡΡΡΠ΄Π΅Π½ΡΠΎΠ² ΡΠ½ΠΈΠ²Π΅ΡΡΠΈΡΠ΅ΡΠΎΠ². Π Π°ΡΡΠΌΠ°ΡΡΠΈΠ²Π°Π΅ΡΡΡ ΠΏΠΎΠ½ΡΡΠΈΠ΅ ΠΌΠΎΠ΄Π΅Π»ΠΈΡΠΎΠ²Π°Π½ΠΈΡ, Π΅Π³ΠΎ ΠΈΡΡΠΎΠΊΠΈ ΠΈ Π²Π°ΠΆΠ½ΠΎΡΡΡ ΠΏΡΠΈΠΌΠ΅Π½Π΅Π½ΠΈ
The main directions of the development of education and training in the context of the problem-model of training
The potential of the problem-model training technologies for the education is described in this articleΠ Π°ΡΡΠΌΠ°ΡΡΠΈΠ²Π°ΡΡΡΡ Π²ΠΎΠ·ΠΌΠΎΠΆΠ½ΠΎΡΡΠΈ ΠΏΡΠΈΠΌΠ΅Π½Π΅Π½ΠΈΡ ΡΠ΅Ρ
Π½ΠΎΠ»ΠΎΠ³ΠΈΠΉ ΠΏΡΠΎΠ±Π»Π΅ΠΌΠ½ΠΎ-ΠΌΠΎΠ΄Π΅Π»ΡΠ½ΠΎΠ³ΠΎ ΠΎΠ±ΡΡΠ΅Π½ΠΈΡ Π² ΠΎΠ±ΡΠ°Π·ΠΎΠ²Π°Π½ΠΈ
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