The most significant feature in the transition from the quasicrystalline to the amorphous state is the loss of long-range bond-orientational order. Disclinations are candidates for elementary excitations which destroy angular correlations. Genera lizing the topological defect classification, we investigate point singularities in two-dimensional pentagonal quasicrystals and construct disclinatio...

We describe a rapid and quantitative method to generate DNA cages of deliberately designed geometry from readily available starting strands. Balancing the incorporation of sequence uniqueness and symmetry in a face-centered approach to 3D construction can result in triangular (TP), rectangular (RP), and pentagonal prisms (PP) without compromising the potential for nanostructure addressability.

The PM3 quantum-mechanical method is able to model the magic water clusters (H20),, and (H20)&+. Results indicate that the H30+ ion is tightly bound within the (H20),, cluster by multiple hydrogen bonds, causing deformation to the symmetric (HzO),, pentagonal dodecahedron structure. The structures, energetics, and hydrogen bond patterns of six local minima (H20)21H+ clusters are presented.

The moduli spaceMg of compact Riemann surfaces of genus g has orbifold structure, and the set of singular points of such orbifold is the branch locus Bg. For g 6≡ 3 mod 4, g ≥ 26, g 6= 37, there exists isolated strata corresponding to families of pentagonal Riemann surfaces.

If A is a set of natural numbers containing 0, then there is a unique nonempty “reciprocal” set B of natural numbers (containing 0) such that every positive integer can be written in the form a+ b, where a ∈ A and b ∈ B, in an even number of ways. Furthermore, the generating functions for A and B over F2 are reciprocals in F2[[q]]. We consider the reciprocal set B for the set A containing 0 and...

The eigenvalues of a graph is the root of its characteristic polynomial. A fullerene F is a 3- connected graphs with entirely 12 pentagonal faces and n/2 -10 hexagonal faces, where n is the number of vertices of F. In this paper we investigate the eigenvalues of a class of fullerene graphs.

The crystal structure of bergenite, ideally Ca2Ba4[(UO2)3O2(PO4)2]3(H2O)16, monoclinic, space group P21/c, a 10.092(1), b 17.245(2), c 17.355(2) Å, 113.678(2)°, V 2766.2(3) Å3, Z = 2, Dcalc 4.82 g/cm3, was solved by direct methods and refined by full-matrix least-squares techniques on the basis of F2 to agreement indices R1 of 5.0% calculated for 4118 unique observed reflections (|Fo| ≥ 4 F), a...

A novel nonadecanuclear silver double cage was isolated, in which a square antiprism and a pentacapped pentagonal prism templated by a chloride ion share a tetragonal face to form a snowman-like cluster that is held together by bridging alkynyl groups and trifluoroacetates.

Two different interpretations have been recently proposed to rationalize the stabilization of some hosting cages in endohedral metallofullerenes as a consequence of the larger localization of the negative charge on pentagonal rather than on hexagonal faces. We try to figure out the physical origin that mainly governs the stability of charged fullerenes; is it aromaticity or electrostatics?

A decanuclear Cd complex has been found as a carbonate-containing capsule. The structure strongly resembles a ten-blade waterwheel with a central carbonate ligand surrounded by two superimposed Cd(5)O(5) crowns with a pentagonal antiprism-like disposition. The capsule is doubly capped by two pentadentate perchlorate anions.