Nicotinic acetylcholine receptors (nAChR) play important neurophysiological roles and are of considerable medical relevance. They have been studied extensively, greatly facilitated by the gastropod acetylcholine-binding proteins (AChBP) which represent soluble structural and functional homologues of the ligand-binding domain of nAChR. All these proteins are ring-like pentamers. Here we report t...

(a) Describe the conjugacy classes of D and use this to prove that D is simple. [Hint: Any normal subgroup is a union of conjugacy classes.] (b) Compute the number of distinguishable ways to color the faces of a dodecahedron with k colors. [Hint: Let X be the set of all colorings, so that |X| = k12. Many of these colorings are indistinguishable after rotation so we really want to know the numbe...

BACKGROUND Bleomycin (BLM) is an anticancer antibiotic used in many cancer regimens. Its utility is limited by systemic toxicity and dose-dependent pneumonitis able to progress to lung fibrosis. The latter can affect up to nearly 50% of the total patient population, out of which 3% will die. We propose to improve BLM delivery by tethering it to an efficient delivery vector. Adenovirus (Ad) dode...

We consider tilings of the sphere by congruent pentagons. The basic example is dodecahedron, which has 12 pentagonal tiles. To simplify the problem, we assume the tiling is edge-to-edge and all vertices have degree ≥ 3.

An n-fullerene is an n-dimensional cell complex where the stars of the points are (n − 1)-dimensional simplices and the 2-cells are pentagons or hexagons. We say that an n-fullerene is uniform if the number of hexagonal faces containing a given vertex p (and, when n¿ 3, contained in a given 3-face X on p) does not depend on the choice of p (and X ). For instance, the dodecahedron, the truncated...

A Dirichlet k-partition of a closed d-dimensional surface is a collection of k pairwise disjoint open subsets such that the sum of their first Laplace-BeltramiDirichlet eigenvalues is minimal. In this paper, we develop a simple and efficient diffusion generated method to compute Dirichlet k-partitions for d-dimensional flat tori and spheres. For the 2d flat torus, for most values of k = 3–9,11,...

As part of a study to characterize the detailed coordination behavior of Pu(IV), single crystal X-ray diffraction structures have been determined for Pu(IV) and Ce(IV) complexes with the naturallyoccurring ligand maltol (3-hydroxy-2-methyl-pyran-4-one) and its derivative bromomaltol (5-bromo-3-hydroxy-2-methyl-pyran-4-one). Although Ce(IV) is generally accepted as a structural analog for Pu(IV)...

Any convex polytope whose combinatorial automorphism group has two orbits on the flags is isomorphic to one whose group of Euclidean symmetries has two orbits on the flags (equivalently, to one whose automorphism group and symmetry group coincide). Hence, a combinatorially two-orbit convex polytope is isomorphic to one of a known finite list, all of which are 3-dimensional: the cuboctahedron, i...

Motivated by applications in numerical analysis, we investigate balanced triangulations, i.e. triangulations where all angles are strictly larger than π/6 and strictly smaller than π/2, giving the optimal lower bound for the number of triangles in the case of the square. We also investigate platonic surfaces, where we find for each one its respective optimal bound. In particular, we settle (aff...

[Abstract] A PC code based on the quantum mechanical Langevin equation to simulate dynamic motion of deuterium (or hydrogen) cluster with three dimensional symmetry has been developed for studying very fast condensation or oscillation behavior in time-step of 0.001 as (1.0E-21 second) for overall time interval of several fs to 500 fs. Some numerical results are typically shown for two cases of ...