Synthesis and linear and nonlinear optical properties of metal-terminated bis(dioxaborine) polymethines

Rh(III) and Ir(III) can be complexed to bipyridine groups attached to the termini of bis(dioxaborine)-capped heptamethines; these chromophores exhibit large third-order polarisabilities at 1.55 μm, while retaining good film-forming properties and linear optical transparency in the near infrared.     

Remarks on the density of sphere packings in three dimensions

This paper shows how the density of sphere packings of spheres of equal radius may be studied using the Delaunay decomposition. Using this decomposition, a local notion of density for sphere packings in ³ is defined. Conjecturally this approach should yield a bound of 0.740873... on sphere packings in ³, and a small perturbation of this approach should yield the bound of . The face-centered-cubic and hexagonal-close-packings provide local maxima (in a strong sense defined below) to the function which associates to every saturated sphere packing in ³ its density. The local measure of density coincides with the actual density for the face-centered cubic and hexagonal-close-packings.     

Sphere Packing, IV. Detailed Bounds

This paper is the fourth in a series of six papers devoted to the proof of the Kepler conjecture, which asserts that no packing of congruent balls in three dimensions has density greater than the face-centered cubic packing. In a previous paper in this series, a continuous function f on a compact space was defined, certain points in the domain were conjectured to give the global maxima, and the relation between this conjecture and the Kepler conjecture was established. The function f can be expressed as a sum of terms, indexed by regions on a unit sphere. In this paper detailed estimates of the terms corresponding to general regions are developed. These results form the technical heart of the proof of the Kepler conjecture, by giving detailed bounds on the function f. The results rely on long computer calculations.     

Using polyelectrolyte block copolymers to tune nanostructure assembly

This review presents an overview of the recent developments in polyelectrolyte block copolymer self-assembly, including charged block copolymers and random copolymers as well as polypeptidic block copolymers. Different methods for controlling micellar structures in solution are presented. In addition, the use of polyelectrolyte copolymers as responsive hydrogels, in polyelectrolyte complexes, and in layer-by-layer assemblies will be discussed.     

A Formulation of the Kepler Conjecture

This paper is the second in a series of six papers devoted to the proof of the Kepler conjecture, which asserts that no packing of congruent balls in three dimensions has density greater than the face-centered cubic packing. The top level structure of the proof is described. A compact topological space is described. Each point of this space can be described as a finite cluster of balls with additional combinatorial markings. A continuous function on this compact space is defined. It is proved that the Kepler conjecture will follow if the value of this function is never greater than a given explicit constant.     

The Honeycomb Conjecture

This article gives a proof of the classical honeycomb conjecture: any partition of the plane into regions of equal area has perimeter at least that of the regular hexagonal honeycomb tiling. Received August 30, 1999, and in revised form April 17, 2000. Online publication September 22, 2000.     

Numerical invariants and the strong product of graphs

Three numerical invariants of graphs—the independence number, the cliquecovering number, and the Rosenfeld number—are studied in relation to themselves and to the strong product of two graphs. Applications are made to limiting values, such as capacity. Some constructions exhibit the independence number of the strong product C_m ? C_n of odd cycles and of higher (strong) powers $\text{C}{}_{\mathrm{m}}{}^{\mathrm{k}}$ of certain odd cycles C_m.     

4Fe4S]2+ clusters exhibit ground-state paramagnetism

Two proteins involved in nitrogen fixation contain ferredoxin-type [4Fe4S] clusters that exist in paramagnetic ground state upon oxidation, a property never observed since the discovery of ferredoxins 50 years ago. This unique characteristic suggests a specific coupling in these clusters necessary for nitrogen fixation and implies an evolutionary connection between the clusters in the two proteins.     

Observation of Fe-H/D modes by nuclear resonant vibrational spectroscopy

Metal-hydrogen bonding is important in chemistry and catalysis, but H atoms are often difficult to observe, especially in metalloproteins. In this work we show that Fe-H interactions can be probed by nuclear resonance vibrational spectroscopy at the 14.4 keV 57Fe nuclear resonance. An important advantage of this method, compared to Raman and IR spectroscopy, is the selectivity for modes that involve 57Fe motion. We present data on the FeS4 site in rubredoxin and the [FeH(D)6]2- ion. Prospects for studying more complex systems are discussed.