A major breakthrough in the theory of topological algorithms occurred in 1992 when Hyam Rubinstein introduced the idea of an almost normal surface. We explain how almost normal surfaces emerged naturally from the study of geodesics and minimal surfaces. Patterns of stable and unstable geodesics can be used to characterize the 2-sphere among surfaces, and similar patterns of normal and almost no...

Headed for a membrane: Continuous, polycrystalline ZIF-90 membranes (picture, left) can be grown at 65 °C from methanolic precursor solutions on nanocrystal-seeded surfaces of poly(amide-imide) macroporous hollow fibers (right). The ZIF-90 membranes exhibit good separation properties for linear over cyclic hydrocarbons, as well as gas permeation selectivities higher than Knudsen values.

A covalence sequence of a vertex-transitive map is a cyclic sequence of covalences around a vertex of the map. We explain the algebraic background for a study of the relationship between covalence sequences of maps on compact orientable surfaces and covalence sequences of (infinite) plane tessellations that both exhibit the same ‘level of transitivity’ of automorphism groups on vertices or edges.

In this note, we consider K3 surfaces X with an action by the alternating group A 5. We show that if a cyclic extension A 5 .C n acts on X then n = 1, 2, or 4. We also determine the A 5-invariant sublattice of the K3 lattice and its discriminant form.

Let X be a non-Gorenstein Q-Fano 3-fold with only cyclic quotient terminal singularities such that the class of −KX generates the group of numerical equivalence classes of divisors, and | −KX | contains Du Val K3 surfaces. We prove that g(X) := h(−KX)− 2 ≤ 8 and give the classification of X with g(X) ≥ 6.

For r = 7 and 8 we consider an action of the Weyl group of type E r on a unimodular lattice of rank r + 1. We give the tables of the first cohomology groups for all cyclic subgroups of the Weyl group with respect to this action. These are important in the arithmetic theory of Del Pezzo surfaces.

Acetylene-linked macrocycles incorporating multiple perylene tetracarboxylic acid bisimide (PBI) chromophores have been synthesised and separated by recycling GPC. The very first example of such macrocycles, i.e., cyclic trimer 5, containing three PBI dyes self-assembles into highly ordered donut-shaped unique hexagonal nanopatterns on HOPG surfaces as revealed by atomic force microscopy (AFM).

A new design for microelectrode array (MEA) devices fabricated by semiconductor-processing techniques is presented. The microelectrode surfaces consist of gold and are surrounded by an insulating silicon nitride layer. Each chip of these so-called Multi MEAs contains regular arrays with circular-shaped electrodes of eight different sizes: 1, 3, 5, 10, 50, 100, 500 and 1000μm. The Multi MEAs wer...

We present three types of polyhedral surfaces, which are continuously flexible and have not only an initial pose, where all faces are coplanar, but pass during their self-motion through another pose with coplanar faces (“flat pose”). These surfaces are examples of so-called rigid origami, since we only admit exact flexions, i.e., each face remains rigid during the motion; only the dihedral angl...

In this work, the electropolymerization of polyaniline (PANI) is explored for its action as either a suitable coating or substrate Nickel (Ni) and Magnetite (Fe3O4) surfaces. PANI has been achieved through cyclic voltammetry (CV), potentiostatic galvanostatic electrochemical methods. The interaction between obtained surfaces ferromagnetic layers (Ni Fe3O4) investigated function pH electrolytic ...