We show that a null–homologous transverse knot K in the complement of an overtwisted disk in a contact 3–manifold is the boundary of a Legendrian ribbon if and only if it possesses a Seifert surface S such that the self–linking number of K with respect to S satisfies sl(K,S) = −χ(S). In particular, every null–homologous topological knot type in an overtwisted contact manifold can be represented...

In this paper, we present some of our recent experiences with a data visualization tool and offer some use cases where the visualization tool can potentially drive programmatic change in universities. The Ribbon Tool provides an interactive visualization of student flows through academic programs, progressing over time to either successful completion (graduation) or attrition. Through effective...

One of the most important applications of the RT-functor is the construction of invariants of (closed, connected, oriented) 3-manifolds, the so-called Reshetikhin-Turaev-Witten invariants of 3-manifolds. However, the RT-invariants of ribbon links associated with colorings of links with objects of a ribbon category C in week 46 and week 47 are far too general for this purpose. For this more ambi...

We study Kauffman’s model of folded ribbon knots: knots made of a thin strip of paper folded flat in the plane. The ribbonlength is the length to width ratio of such a ribbon, and it turns out that the way the ribbon is folded influences the ribbonlength. We give an upper bound of n cot(π/n) for the ribbonlength of n-stick unknots. We prove that the minimum ribbonlength for a 3-stick unknot wit...

the multiple reference frames (mrf) method is the most suitable method tosimulate impeller rotation in mixing systems. precise determination of stationaryand moving zones in mrf method leads to accurate results in mixing performance.in this research, the entire volume of mixing system was divided into two zones.the kinetic energy values were used to distinguish the zones with differentvelocitie...

the relationship between altitude, slope and tree age with the red heartwood of beech (fagusorientalis lipsky) were investigated. transect sampling method was used to collect the data. theresults showed that in the 476 sampled trees, 132 trees were suffering the phenomenon of red heartswith deferent shape and size. the results indicate that the tree with red heartwoods in shafa-roudforest area,...

The Arc repressor of bacteriophage P22 is a dimeric member of the ribbon-helix-helix family of transcription factors. Residues 9-14 of each wild-type Arc subunit pair to form two antiparallel beta-strands and have the alternating pattern of polar and nonpolar residues expected for a beta-ribbon with one solvent-exposed face and one face that forms part of the hydrophobic core. Simultaneously sw...