509 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
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
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 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
The development of studentsβ tolerance by means of problem-model learning
The necessarity of understanding and tolerance development of modern students in accordance with the actual problems of development of our society is discussed in this articleΠ Π΄Π°Π½Π½ΠΎΠΉ ΡΡΠ°ΡΡΠ΅ ΡΠ°ΡΡΠΌΠ°ΡΡΠΈΠ²Π°Π΅ΡΡΡ Π²ΠΎΠΏΡΠΎΡ ΠΏΠΎΡΡΠ΅Π±Π½ΠΎΡΡΠΈ Π² ΠΏΠΎΠ½ΠΈΠΌΠ°Π½ΠΈΠΈ ΠΈ ΡΠ°Π·Π²ΠΈΡΠΈΠΈ ΡΠΎΠ»Π΅ΡΠ°Π½ΡΠ½ΠΎΡΡΠΈ ΡΠΎΠ²ΡΠ΅ΠΌΠ΅Π½Π½ΡΡ
ΡΡΡΠ΄Π΅Π½ΡΠΎΠ² Π² ΡΠΎΠΎΡΠ²Π΅ΡΡΡΠ²ΠΈΠΈ Ρ Π°ΠΊΡΡΠ°Π»ΡΠ½ΡΠΌΠΈ ΠΏΡΠΎΠ±Π»Π΅ΠΌΠ°ΠΌΠΈ ΡΠ°Π·Π²ΠΈΡΠΈΡ Π½Π°ΡΠ΅Π³ΠΎ ΠΎΠ±ΡΠ΅ΡΡΠ²
The foundations of the problem-model approach in modern teaching practice
The basis of problem-model approach is described in this article, two basic types of training in modern pedagogy are discussed, problem-model approach is analyzed from the point of view of its effectiveness, the indicators of the problem-model approach in teaching are picked outΠ Π΄Π°Π½Π½ΠΎΠΉ ΡΡΠ°ΡΡΠ΅ ΡΠ°ΡΡΠΌΠ°ΡΡΠΈΠ²Π°ΡΡΡΡ ΠΎΡΠ½ΠΎΠ²Ρ ΠΈ ΠΈΡΡΠΎΠΊΠΈ ΠΏΡΠΎΠ±Π»Π΅ΠΌΠ½ΠΎ-ΠΌΠΎΠ΄Π΅Π»ΡΠ½ΠΎΠ³ΠΎ ΠΏΠΎΠ΄Ρ
ΠΎΠ΄Π° Π² ΠΎΠ±ΡΡΠ΅Π½ΠΈΠΈ, ΠΎΠΏΠΈΡΡΠ²Π°ΡΡΡΡ Π΄Π²Π° ΠΎΡΠ½ΠΎΠ²Π½ΡΡ
ΡΠΈΠΏΠ° ΠΎΠ±ΡΡΠ΅Π½ΠΈΡ Π² ΡΠΎΠ²ΡΠ΅ΠΌΠ΅Π½Π½ΠΎΠΉ ΠΏΠ΅Π΄Π°Π³ΠΎΠ³ΠΈΠΊΠ΅, Π°Π½Π°Π»ΠΈΠ·ΠΈΡΡΠ΅ΡΡΡ ΠΏΡΠΎΠ±Π»Π΅ΠΌΠ½ΠΎ-ΠΌΠΎΠ΄Π΅Π»ΡΠ½ΡΠΉ ΠΏΠΎΠ΄Ρ
ΠΎΠ΄ Ρ ΡΠΎΡΠΊΠΈ Π·ΡΠ΅Π½ΠΈΡ Π΅Π³ΠΎ ΡΡΡΠ΅ΠΊΡΠΈΠ²Π½ΠΎΡΡΠΈ, Π²ΡΠ΄Π΅Π»ΡΡΡΡΡ ΠΏΡΠΈΠ·Π½Π°ΠΊΠΈ ΠΏΡΠΎΠ±Π»Π΅ΠΌΠ½ΠΎ-ΠΌΠΎΠ΄Π΅Π»ΡΠ½ΠΎΠ³ΠΎ ΠΏΠΎΠ΄Ρ
ΠΎΠ΄Π° Π² ΠΎΠ±ΡΡΠ΅Π½ΠΈ
THE TERMS OF FORMATION OF MOTIVATION TO STUDYING A FOREIGN LANGUAGE
Π Π΄Π°Π½Π½ΠΎΠΉ ΡΡΠ°ΡΡΠ΅ ΠΎΠ±ΠΎΡΠ½ΠΎΠ²Π°Π½Π½ΠΎ, ΡΡΠΎ ΠΏΡΠ΅ΠΏΠΎΠ΄Π°Π²Π°ΡΠ΅Π»Ρ ΠΎΠ±ΡΠ·Π°Π½ Π½Π°Ρ
ΠΎΠ΄ΠΈΡΡ ΡΠ°ΠΊΠΈΠ΅ ΠΌΠ°ΡΠ΅ΡΠΈΠ°Π»Ρ Π΄Π»Ρ ΠΎΠ±ΡΡΠ΅Π½ΠΈΡ, ΠΊΠΎΡΠΎΡΡΠ΅ ΠΏΠΎΠ΄Ρ
ΠΎΠ΄ΡΡ Π΄Π»Ρ ΡΠΎΠ·Π΄Π°Π½ΠΈΡ Ρ
ΠΎΡΠΎΡΠ΅ΠΉ ΠΌΠΎΡΠΈΠ²Π°ΡΠΈΠΈ ΠΈ ΠΏΡΠ΅Π΄ΡΡΠ°Π²Π»ΡΡΡ ΡΠΎΠ±ΠΎΠΉ Π΄ΠΎΡΡΠ°ΡΠΎΡΠ½ΡΡ ΠΏΠΎΠ·Π½Π°Π²Π°ΡΠ΅Π»ΡΠ½ΡΡ, ΠΊΠΎΠΌΠΌΡΠ½ΠΈΠΊΠ°ΡΠΈΠ²Π½ΡΡ ΠΈ ΠΏΡΠΎΡΠ΅ΡΡΠΈΠΎΠ½Π°Π»ΡΠ½ΡΡ Π·Π½Π°ΡΠΈΠΌΠΎΡΡΡ. ΠΡΠ΅Π΄Π»ΠΎΠΆΠ΅Π½Ρ ΡΡΠ»ΠΎΠ²ΠΈΡ ΡΡΠ°Π½ΠΎΠ²Π»Π΅Π½ΠΈΡ Π½Π°Π΄Π΅ΠΆΠ½ΠΎΠΉ ΠΈ Π²ΡΡΠΎΠΊΠΎΠΉ ΠΌΠΎΡΠΈΠ²Π°ΡΠΈΠΈ ΠΊ ΠΈΠ·ΡΡΠ΅Π½ΠΈΡ ΠΈΠ½ΠΎΡΡΡΠ°Π½Π½ΠΎΠ³ΠΎ ΡΠ·ΡΠΊΠ°It is reasonable in this article that the teacher must find such materials for training that are suitable for creating good motivation and represent sufficient cognitive, communicative and professional significance. The conditions for the formation of a reliable and high motivation to learn a foreign language are propose
Stepping theories of active logic with two kinds of negation
This paper formulates a stepping theory formalism with two kinds of negation dealing with one of the areas of Active Logic, a new kind of logic aimed at performing practical tasks in real time knowledge-based AI systems. In addition to the standard logical negation, the proposed formalism uses the so-called subjective negation interpreted as inability to arrive at some conclusion through reasoning by a current time. The semantics of the proposed formalism is defined as an~argumentation structure
Problem modeling in the system of innovative approaches to learning
Π Π°ΡΡΠΌΠ°ΡΡΠΈΠ²Π°ΡΡΡΡ Π²ΠΎΠ·ΠΌΠΎΠΆΠ½ΠΎΡΡΠΈ ΠΏΡΠΈΠΌΠ΅Π½Π΅Π½ΠΈΡ ΡΠ΅Ρ
Π½ΠΎΠ»ΠΎΠ³ΠΈΠΉ ΠΏΡΠΎΠ±Π»Π΅ΠΌΠ½ΠΎΠ³ΠΎ ΠΌΠΎΠ΄Π΅Π»ΠΈΡΠΎΠ²Π°Π½ΠΈΡ, ΠΎΠΏΡΠ΅Π΄Π΅Π»ΡΡΡΡΡ ΡΠΎΠ»Ρ ΠΈ ΠΌΠ΅ΡΡΠΎ ΠΏΡΠΎΠ±Π»Π΅ΠΌΠ½ΠΎΠ³ΠΎ ΠΌΠΎΠ΄Π΅Π»ΠΈΡΠΎΠ²Π°Π½ΠΈΡ Π² ΡΠΈΡΡΠ΅ΠΌΠ΅ ΠΈΠ½Π½ΠΎΠ²Π°ΡΠΈΠΎΠ½Π½ΡΡ
ΠΏΠΎΠ΄Ρ
ΠΎΠ΄ΠΎΠ² ΠΊ ΠΎΠ±ΡΡΠ΅Π½ΠΈΡThe potential of the problem modeling training technologies for the education is described in this article. The problem modelingβs role and place in the system of innovative approaches are determine
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