Fundamentals of Plasma Polymerization

The plasma polymerization of ethylene is used as an example through which to discuss the elementary steps involved in forming a polymer in an electric discharge. The relationship of the experimentally controlled variables to the rate of formation of first generation active species is discussed. These species are related, in turn, to the overall rate of polymerization through a simple model. Two asymptotic conditions are discussed which correspond to minimal and total conversion of monomer to polymer. The dependence of polymer deposition rate on monomer flow rate predicted by the model is found to correspond very closely to that observed experimentally. The predicted effect of gas pressure on polymer deposition rate also agrees with that found experimentally.     

Extending Martin-Löf Type Theory by one Mahlo-universe

We define a type theory MLM, which has proof theoretical strength slightly greater then Rathjen's theory KPM. This is achieved by replacing the universe in Martin-L?f's Type Theory by a new universe V having the property that for every function f, mapping families of sets in V to families of sets in V, there exists a universe inside V closed under f. We show that the proof theoretical strength of MLM is . This is slightly greater than , and shows that V can be considered to be a Mahlo-universe. Together with [Se96a] it follows . Received: 8 February 1996     

The aΔg→XΣg magnetic dipole transition of S2

Emission spectra of the 0-0 band of the a¹Δ_g→X³Σ⁻_g magnetic dipole transition of S₂ have been observed in the near-infrared spectral region near 4400 cm⁻¹. The S₂ molecules were generated in a fast-flow system by passing S_x or S₂Cl₂ vapor in Ar carrier gas through a microwave discharge and were excited by electronic-to-electronic energy transfer from metastable singlet oxygen O₂(a¹Δ_g). Medium-resolution spectra of the b¹Σ⁺_g→X³Σ⁻_g and a¹Δ_g→X³Σ⁻_g transitions of S₂ were measured with a Fourier-transform spectrometer. By comparing the bandshape of the 0-0 band of the a→X system with a computer simulation calculated with literature data of the rotational constants of the X and a states, the origin of the 0-0 band was determined to be ν₀=4394.25±0.2 cm⁻¹.     

A new proof of partial regularity of solutions to Navier-Stokes equations

In this paper we give a new proof of the partial regularity of solutions to the incompressible Navier-Stokes equation in dimension 3 first proved by Caffarelli, Kohn and Nirenberg. The proof relies on a method introduced by De Giorgi for elliptic equations. This work was supported in part by NSF Grant DMS-0607953.