A smooth and unified proof of cases 6, 5 and 3 of the ringel-youngs theorem

A proof of the Heawood conjecture for Cases 6, 5, and 3 is given; “unified” means that the same “geometry” and “zigzag” are used in each of the three cases; “smooth” means that the zigzag is of simplest possible type and that the related “chord problems” are trivial or nearly so.     

Stabilization of thermal lattice Boltzmann models

A three-dimensional thermal lattice-Boltzmann model with two relaxation times to separately control viscosity and thermal diffusion is developed. Numerical stability of the model is significantly improved using Lax-Wendroff advection to provide and adjustable time step. Good agreement with a conventional fiitedifference Navier-Stokes solver is obtained in modeling compressible Rayleigh-Bénard convestion when boundary conditions are treated similarly.     

Gas-Phase Basicities of Furan Compounds. The Role of Alkyl Substitution on Proton Affinity and on the Site of Protonation

The gas-phase protonation of alkyl-substituted furan compounds is investigated in equilibrium proton-transfer reactions conducted in an ion cyclotron resonance (ICR) spectrometer. From the effects of substituents on the stability of protonated species, it is concluded that protonation of the majority of these systems occurs specifically on the C(α)-atom to form carbenium ions. Parallel MO calculations performed on different structures of the products reinforce the experimental conclusions and provide energy values for the less stable structures. The solution reactivity of these compounds towards electrophilic agents and NMR spectra of protonated species obtained in strong acidic media have been investigated.