The exotic quantum double and its universal R-matrix for quantum Yang-Baxter equation are constructed in terms of Drinfeld’s quantum double theory.As a new quasi-triangular Hopf algebra, it is much different from those standard quantum doubles that are the q-deformations for Lie algebras or Lie superalgebras. By studying its representation theory,many-parameter representations of the exotic qua...

We introduce and study the triple of a quasitriangular Lie bialgebra as a natural extension of the Drinfeld double. The triple is itself a quasitriangular Lie bialgebra. We prove several results about the algebraic structure of the triple, analogous to known results for the double. Among them, we prove that in the factorisable case the triple is isomorphic to a twisting of g ⊕ g ⊕ g by a certai...

Dendrotoxin proteins isolated from Mamba snake venom block potassium channels with a high degree of specificity and selectivity. Using site-directed mutagenesis we have identified residues that constitute the functional interaction surfaces of delta-dendrotoxin and its voltage-gated potassium channel receptor. delta-Dendrotoxin uses a triangular patch formed by seven side-chains (Lys3, Tyr4, Ly...

Using Monte Carlo simulations of a touching-bead model of double-stranded DNA, we show that DNA extension is enhanced in isosceles triangular nanochannels (relative to a circular nanochannel of the same effective size) due to entropic depletion in the channel corners. The extent of the enhanced extension depends non-monotonically on both the accessible area of the nanochannel and the apex angle...

We propose the set of coupled ordinary differential equations dnj/dt = n 2 j−1 − n 2 j as a discrete analog of the classic Burgers equation. We focus on traveling waves and triangular waves, and find that these special solutions of the discrete system capture major features of their continuous counterpart. In particular, the propagation velocity of a traveling wave and the shape of a triangular...

We prove that, for any n, the monoid of all $$n \times n$$ supertropical matrices extending tropical satisfies nontrivial semigroup identities; in particular, such triangular admit exactly same identities satisfied by matrices. These are carried over to labeled-weighted digraphs with double arcs.

This paper describes a new structure of a six-DOF parallel robot. First, a known planar three-DOF double-triangular structure is modified by replacing the stationary triangle with a circle. It increases the work envelope considerably especially when rotational motions are required. The ability for unlimited rotational motion allows extending the structure into six-DOF by using two sets of stati...