Size Ramsey numbers involving stars

We calculate some size Ramsey numbers involving stars. For example we prove that for t ? k ? 2 and n sufficiently large the size Ramsey number.

$\text{r}{}_{\mathrm{n}}\text{(K}{}_{\mathrm{1,k}}\text{K}{}_{\mathrm{t}}\text{+}\text{K}{}_{\mathrm{n}}\text{=}\text{k(t?1)+1}\text{2}\text{+(k(t?1)+1)(n+k?1).}$

     

Direct writing of a conducting polymer with molecular-level control of physical dimensions and orientation

Polymer nanostructures composed of poly(3-dodecylthiophene) (PDDT) have been directly written with control of polymer strand alignment and monolayer-by-monolayer thickness down to a single molecular monolayer (2.6 nm). The molecularly ordered nanostructures were written on silicon oxide surfaces using thermal dip-pen nanolithography, where an atomic force microscope cantilever with integrated tip heater was precoated with solid PDDT. The PDDT was precisely deposited onto the surface when the tip temperature was set close to PDDT's melting temperature.     

Synthesis and polymerization of 1,5-dioxo-1-methyl-4-azaphosphepane

1,5-Dioxo-1-methyl-4-azaphosphepane was synthesized and polymeized in the presence of water, stannic chloride, or phosphoric acid. Polymers obtained by using these catalysts were shown to have lower molecular weights than nylon 6 samples prepared under identical reaction conditions. Thermal and other physical properties of the phosphorus-containing polyamide are reported and compared with those of nylon 6.     

Supramolecular Chemistry In Silico

Computational protocols capable of modelling supramolecular complexes have been evaluated. The complexation of cations by crown ethers and quaternary ammonium ions by an oxacalix[3]arene are presented as examples. In the latter case reliable qualitative results were obtained using the semi-empirical PM3 method where guest LUMO and electrostatic potential energies have been shown to correlate with experimental binding data. The optimal method for more accurate results combines semi-empirical equilibrium geometry and property calculations with single point energy calculations at the HF/6–31G* or BP/6–31G* quantum mechanical level.     

2‐factors with prescribed and proscribed edges

Let G be a finite k‐edge‐connected simple graph. We consider when a set of independent edges can be extended to a 2‐factor such that this 2‐factor avoids a fixed set of independent edges. A complete characterization is provided in those cases, where this is feasible. © 2005 Wiley Periodicals, Inc. J Graph Theory 49: 48–58, 2005     

Orthogonal Polynomials on Planar Cubic Curves

Foundations of Computational Mathematics - Orthogonal polynomials in two variables on cubic curves are considered. For an integral with respect to an appropriate weight function defined on a cubic...