To attack the Four Color Problem, in 1880, Tait gave a necessary and sufficient condition for plane triangulations to have a proper 4-vertex-coloring: a plane triangulation G has a proper 4-vertex-coloring if and only if the dual of G has a proper 3-edge-coloring. A cyclic coloring of a map G on a surface F 2 is a vertex-coloring of G such that any two vertices x and y receive different colors ...

Cyclic voltammetry is a fundamental experimental method for characterizing electrochemical surfaces. Despite its wide use, a way to quantitatively and directly relate cyclic voltammetry to ab initio calculations has been lacking. We derive the cyclic voltammogram for H on Pt(111) and Pt(100), based solely on density functional theory calculations and standard molecular tables. By relating the g...

This paper investigates the rigidity of bordered polyhedral surfaces. Using variational principle, we show that surfaces are determined by boundary value and discrete curvatures on interior edges. As a corollary, reprove classical result two Euclidean cyclic polygons (or hyperbolic polygons) congruent if lengths their sides equal.

We state a number of conjectures that together allow one to classify a broad class of del Pezzo surfaces with cyclic quotient singularities using mirror symmetry. We prove our conjectures in the simplest cases. The conjectures relate mutation-equivalence classes of Fano polygons with Q-Gorenstein deformation classes of del Pezzo surfaces. We explore mirror symmetry for del Pezzo surfaces with c...

In this report, we systematically investigated DNA immobilization at gold surfaces with electrochemical techniques. Comparative cyclic voltammetric and chronocoulometric studies suggested that DNA monolayers immobilized at gold surfaces were not homogeneous. Nonspecific Au-DNA interactions existed even with the treatment of mercaptohexanol, which was known to competitively remove loosely bound ...

In this work we obtain the group of conformal and anticonformal automorphisms of real cyclic p-gonal Riemann surfaces, where p ≥ 3 is a prime integer and the genus of the surfaces is at least (p − 1) + 1. We use Fuchsian and NEC groups, and cohomology of finite groups.

We give a characterization of hyperbolic Kato surfaces in terms of the existence of an automorphic Green function on a cyclic covering. This is achieved by analysing a naturally defined Levi-flat foliation, and by perturbing certain Levi-flat leaves to strictly pseudoconvex hypersurfaces. 2010 Mathematics Subject Classification: Kato surfaces, Levi-flat foliations, plurisubharmonic functions.