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...

This paper explores the effect of impeller design on the chaotic mixing in a helical ribbon mixer. Numerical simulations using the Smoothed Particle Hydrodynamics (SPH) method are used to solve for the fluid flow around the moving impellor. The mixing flow is visualised by extracting the hyperbolic Lagrangian Coherent Structures (LCS) of the flow from the Finite-Time Lyapunov Exponent (FTLE) fi...

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 ...

An overview is provided of some of the basic facts concerning rim hook lattices and ribbon tableaux, using a representation of partitions by their edge sequences. An action is defined of the affine Coxeter group of type Ãr−1 on the r-rim hook lattice, and thereby on the sets of standard and semistandard r-ribbon tableaux, and this action is related to the concept of chains in r-ribbon tableaux....

Ribbon tiles are polyominoes consisting of n squares laid out in a path, each step of which goes north or east. Tile invariants were rst introduced in P1], where a full basis of invariants of ribbon tiles was conjectured. Here we present a complete proof of the conjecture, which works by associating ribbon tiles with certain polygons in the complex plane, and deriving invariants from the signed...

Recent works in algebraic combinatorics have brought up to date the importance of certain planar structures, called ribbon tableaux, which are generalizations of Young tableaux. This paper gives an algorithm to eeciently distribute, using PVM, the computation of the set of all ribbon tableaux of given shape and weight. It also provides a way to compute the spin polynomials associated to those s...

INTRODUCTION Four species of seals live in association with sea ice in Alaska; these are the ringed seal (Phoca hispida), spotted seal (P. largha), bearded seal (Erignathus barbatus), and ribbon seal (Histriophoca fasciata or Phoca fasciata). Ribbon seals, the focus of this paper, range from the Sea of Japan and the Sea of Okhotsk eastward into the Bering Sea and northward into the Chukchi Sea....