Изменение дефектной структуры поверхности ленты металлического стекла Fe-=SUB=-77-=/SUB=-Ni-=SUB=-1-=/SUB=-Si-=SUB=-9-=/SUB=-B-=SUB=-13-=/SUB=- при воздействии гидростатического давления и изотермического отжига

The features and generality of the effect of hydrostatic pressure and annealing on the surface relief of the contact and non-contact side of the Fe77Ni1Si9B13 metal glass ribbon are revealed. The relationship between transformation of the ribbon surface inhomogeneities under these effects and possible formation of nanocrystalline regions are analyzed. We found that the evolution of the surface inhomogeneities at the contact side of the ribbon after annealing procedure leads to appearing of discrete-sized fractions in these regions

Ribbon-clasp T2-knots and semi-welded knots

The notion of ribbon-clasp surface-links is a generalization of ribbon surface-links. It is known that any ribbon [Formula: see text]-knot is presented by a welded knot, and then its knot group is isomorphic to the group of the welded knot. In this paper, we define the group of a semi-welded knot. We show that any ribbon-clasp [Formula: see text]-knot is presented by a semi-welded knot and that the knot group of the ribbon-clasp [Formula: see text]-knot is isomorphic to the group of the semi-welded knot.

Faithful equivalence of equivalent ribbon surface-links

A chord graph in [Formula: see text]-space is constructed from a ribbon surface-link in [Formula: see text]-space. In earlier papers, the three moves on the diagrams of chord graphs (namely, the chord diagrams) were introduced to describe the faithful equivalence of a ribbon surface-link. In this paper, it is shown that any two equivalent ribbon surface-links are faithfully equivalent, so that any chord diagrams of any two equivalent ribbon surface-links are connected by a finite number of these three moves. By combining it with an earlier result, it is shown that any two TOP-equivalent ribbon surface-links are equivalent. In other words, there is no exotic ribbon surface-link, generalizing an earlier result on the trivial ribbon surface-knot. In another earlier result, the three moves on the chord diagrams were modified into the 16 moves on the chord diagrams without base crossing. In this paper, further modified moves of the 16 moves on the chord diagrams without base crossing are also introduced to describe how the set of ribbon torus-links is produced from the set of welded virtual links.

Supplement to a chord diagram of a ribbon surface-link

A revised proof is given to an assertion on chord diagrams of a ribbon surface-link.

A chord diagram of a ribbon surface-link

A ribbon chord diagram, or simply a chord diagram, of a ribbon surface-link in the 4-space is introduced. Links, virtual links and welded virtual links can be described naturally by chord diagrams with the corresponding moves, respectively. Some moves on chord diagrams are introduced by overseeing these special moves. Then the faithful equivalence on ribbon surface-links is stated in terms of the moves on chord diagrams. This answers questions by Nakanishi and Marumoto affirmatively. The faithful TOP-equivalence on ribbon surface-links derives the same result. By combining a previous result on TOP-triviality of a surface-knot, a ribbon surface-knot is DIFF-trivial if and only if the fundamental group is an infinite cyclic group. This corrects an erroneous proof in Yanagawa's old paper.