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

Energy analysis of cold-pressed vegetable oil technology with granulated oil cake producing

Through energy analysis evaluated the thermodynamic efficiency of cold pressed vegetable oils production lines. The following indicators were considered: degree of use of different types of energy used in production processes, the properties of raw materials, work carried out on the system and the total number of all types of energy, attracted from the outside

Dijkgraaf–Witten Z2{Z}_2-invariants for Seifert manifolds

In this short paper we compute the values of Dijkgraaf-Witten invariants over ${Z}_2$ for all orientable Seifert manifolds with orientable bases