Naoko Kamada

ABSTRACT LINK DIAGRAMS AND VIRTUAL KNOTS

The notion of an abstract link diagram is re-introduced with a relationship with Kauffmans virtual knot theory. It is prove that there is a bijection from the equivalence classes of virtual link diagrams to those of abstract link diagrams. Using abstract link diagrams, we have a geometric interpretation of the group and the quandle of a virtual knot. A generalization to higher dimensional cases is introduced, and the state-sum invariants are treated.

Span of the Jones polynomial of an alternating virtual link

For an oriented virtual link, L.H. Kauffman defined the f-polynomial (Jones polynomial). The supporting genus of a virtual link diagram is the minimal genus of a surface in which the diagram can be embedded. In this paperwe show that the span of the /-polynomial of an alternating virtual link L is determined by the number of crossings of any alternating diagram of L and the supporting genus of the diagram. It is a generalization of Kauffman-Murasugi-Thistlethwaites theorem. We also prove a similar result for a virtual link diagram that is obtained from an alternating virtual link diagram by virtualizing one real crossing. As a consequence, such a diagram is not equivalent to a classical link diagram.

BIQUANDLES WITH STRUCTURES RELATED TO VIRTUAL LINKS AND TWISTED LINKS

We introduce two kinds of structures, called v-structures and t-structures, on biquandles. These structures are used for colorings of diagrams of virtual links and twisted links such that the numbe...

INDEX POLYNOMIAL INVARIANTS OF TWISTED LINKS

Bourgoin defined the notion of a twisted link. In a sense, it is a non-orientable version of a virtual link. Im, Lee and Lee defined a polynomial invariant of a virtual link by using the virtual intersection index. In this paper, we give an alternative definition of index polynomial by using indices of real crossings and extend it to a twisted links.

BRIDGE PRESENTATIONS OF VIRTUAL KNOTS

We study bridge presentations of virtual knots, and determine the virtual bridge numbers of pseudo-prime virtual knots with real crossing numbers less than 5, except two virtual knots.

Double coverings of twisted links

Twisted links are a generalization of virtual links. As virtual links correspond to abstract links on orientable surfaces, twisted links correspond to abstract links on (possibly non-orientable) surfaces. In this paper, we introduce the notion of the double covering of a twisted link. It is defined by considering the orientation double covering of an abstract link or alternatively by constructing a diagram called a double covering diagram. We also discuss links in thickened surfaces, their diagrams and their stable equivalence classes. Bourgoin’s twisted knot group is understood as the virtual knot group of the double covering.

THE VIRTUAL MAGNETIC KAUFFMAN BRACKET SKEIN MODULE AND SKEIN RELATIONS FOR THE f-POLYNOMIAL

We introduce the virtual magnetic Kauffman bracket skein module, and show how to find a skein relation for the f-polynomial through the module. Furthermore, we give a unified approach to constructions of skein relations which hold under certain conditions.

Biomarkers of Radiosensitivity in A-Bomb Survivors Pregnant at the Time of Bombings in Hiroshima and Nagasaki

Purpose. There is evidence in the literature of increased maternal radiosensitivity during pregnancy. Materials and Methods. We tested this hypothesis using information from the atomic-bomb survivor cohort, that is, the Adult Health Study database at the Radiation Effects Research Foundation, which contains data from a cohort of women who were pregnant at the time of the bombings of Hiroshima and Nagasaki. Previous evaluation has demonstrated long-term radiation dose-response effects. Results/Conclusions. Data on approximately 250 women were available to assess dose-response rates for serum cholesterol, white blood cell count, erythrocyte sedimentation rate, and serum hemoglobin, and on approximately 85 women for stable chromosome aberrations, glycophorin A locus mutations, and naïve CD4 T-cell counts. Although there is no statistically significant evidence of increased radiosensitivity in pregnant women, the increased slope of the linear trend line in the third trimester with respect to stable chromosome aberrations is suggestive of an increased radiosensitivity.

A twisted link invariant derived from a virtual link invariant

Virtual knot theory is a generalization of knot theory which is based on Gauss chord diagrams and link diagrams on closed oriented surfaces. A twisted knot is a generalization of a virtual knot, which corresponds to a link diagram on a possibly non-orientable surface. In this paper, we discuss an invariant of twisted links which is obtained from the JKSS invariant of virtual links by use of double coverings. We also discuss some properties of double covering diagrams.