Isoperimetric numbers of graph bundles

The main aim of this paper is to give some upper and lower bounds for the isoperimetric numbers of graph coverings or graph bundles, with exact values in some special cases. In addition, we show that the isoperimetric number of any covering graph is not greater than that of the base graph. Mohar's theorem for the isoperimetric number of the cartesian product of a graph and a complete graph can be extended to a more general case: The isoperimetric numberi(G × K _2n) of the cartesian product of any graphG and a complete graphK _2n on even vertices is the minimum of the isoperimetric numberi(G) andn, and it is also a sharp lower bound of the isoperimetric numbers of all graph bundles over the graphG with fiberK _2n. Furthermore, ifn 2i(G) then the isoperimetric number of any graph bundle overG with fibreK _n is equal to the isoperimetric numberi(G) ofG. Partially supported by The Ministry of Education, Korea.     

Electrochemically induced and controlled one-step covalent coupling reaction on self-assembled monolayers

We report on a novel covalent coupling method using electrochemical activation of hydroquinone monoester self-assembled monolayers. The reaction generates benzoquinone as a good leaving group, followed by nucleophilic acyl substitution with a primary amine to form an amide in high yield. The method allows the site-selective and the reaction-controlled positioning of biotin on the individually addressable microelectrode array and, subsequently, density-differentiated patterning of streptavidin on the biotin surfaces. Because the electrochemical coupling method provides a very rapid, mild, and quantitatively controllable reaction pathway for covalent bond formation on organic surfaces, it will be used as a versatile molecular anchoring tool in fields such as molecular electronics and biochip technology.     

Synthesis of highly crosslinked monodisperse polymer particles: Effect of reaction parameters on the size and size distribution

Monodisperse polystyrene particles crosslinked with different concentrations of divinylbenzene were synthesized in the 3.2–9.1 μm size range by dispersion polymerization in an isopropyl alcohol/toluene mixed‐dispersion medium with poly(N‐vinylpyrrolidone) as a steric stabilizer and 2,2′‐azobisisobutyronitrile as a radical initiator. The effects of the reaction parameters such as the crosslinking agent concentration, media solvency (controlled by varying the amount of toluene addition), the initiator concentration, and the stabilizer concentration on the particle size and size distribution were investigated with reference particles with a monodisperse size distribution and crosslinked by 1.5 wt % divinylbenzene. The appropriate increase in media solvency was a prerequisite for preparing crosslinked particles without coagulated and/or odd‐shaped particles. The investigation of the effects of the polymerization parameters also shows that only specific sets of conditions produce particles with a monodisperse size distribution. The glass‐transition temperatures of the particles increased with increasing divinylbenzene concentration. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 40: 4368–4377, 2002