The Reshetikhin-Turaev invariant, Turaev's TQFT, and many related constructions rely on the encoding of certain ribbon tangles (n-string links, or n-ribbon handles) as n-forms on the coend of a ribbon category. We introduce the monoidal category of Hopf diagrams, and describe a universal encoding of ribbon string links as Hopf diagrams. This universal encoding is an injective monoidal functor a...

This thesis begins with the study of a class of symmetric functions {x} which are generating functions for ribbon tableaux (hereon called ribbon functions), first defined by Lascoux, Leclerc and Thibon. Following work of Fomin and Greene, I introduce a set of operators called ribbon Schur operators on the space of partitions. I develop the theory of ribbon functions using these operators in an ...

In this note, I discuss a dual version of the ribbon graph decomposition of the moduli spaces of Riemann surfaces with boundary and marked points, which I introduced in the unpublished preprint [1], and used in [2] to construct open-closed topological conformal field theories. This dual version of the ribbon graph decomposition is a compact orbi-cell complex with a natural weak homotopy equival...

the objective of this study was to evaluate different pistachio hullers and determine the proper harvest time of pistachio nuts for hulling. three pistachio hulling machines (helical drum, helical- blade drum, rubber drum) at three harvest times and 15 days interval were evaluated. the hulling efficiency, percentage of damaged nuts, faulty hulled nuts and unhulled nuts were measured at each tim...

Ribbon-type presynaptic active zones are a hallmark of excitatory retinal synapses, and the ribbon organelle is thought to serve as the organizing point of the presynaptic active zone. Imaging of exocytosis from isolated retinal neurons, however, has revealed ectopic release (i.e., release away from ribbons) in significant quantities. Here, we demonstrate in an in vitro mouse retinal slice prep...

We prove that a crossing change along a double point circle on a 2-knot is realized by ribbon-moves for a knotted torus obtained from the 2-knot by attaching a 1-handle. It follows that any 2-knots for which the crossing change is an unknotting operation, such as ribbon 2-knots and twistspun knots, have trivial Khovanov-Jacobsson number. A surface-knot or -link is a closed surface embedded in 4...

W. H. Tutte’s 1947 paper on a ring generated by graphs satisfying a contraction-deletion relation is extended to ribbon graphs. This ring of ribbon graphs is a polynomial ring on an infinite set of one-vertex ribbon graphs. Acknowledgements: The LSU Research Experience for Undergraduates Program is supported by a National Science Foundation grant, DMS-0648064. Page 16 RHIT Undergrad. Math. J., ...

A ribbon is a double structure on P. The geometry of a ribbon is closely related to that of a smooth curve. In this note we consider linear series on ribbons. Our main result is an explicit determinantal description for the locus W r 2n of degree 2n line bundles with at least (r +1)-dimensional sections on a ribbon. We also discuss some results of Clifford and Brill-Noether type.

A closed duplex DNA molecule relaxed and containing nucleosomes has a different linking number from the same molecule relaxed and without nucleosomes. What does this say about the structure of the nucleosome? A mathematical study of this question is made, representing the DNA molecule by a ribbon. It is shown that the linking number of a closed ribbon can be decomposed into the linking number o...

the electronic and structural properties of pristine and carbon doped (c-doped) boron nitride nano-ribbons(bnnrs) have been studied employing density functional theory (dft) calculations. total energies, gapenergies, dipole moments, and quadrupole coupling constants (qcc) have been calculated in the optimizedstructures of the investigated bnnrs. the results indicated that the stability and gap ...