Uniqueness of embeddings of the affine line into algebraic groups

Let $Y$ be the underlying variety of a connected affine algebraic group. We prove that two embeddings of the affine line $\mathbb{C}$ into $Y$ are the same up to an automorphism of $Y$ provided that $Y$ is not isomorphic to a product of a torus $(\mathbb{C}^\ast)^k$ and one of the three varieties $\mathbb{C}^3$, $\operatorname{SL}_2$, and $\operatorname{PSL}_2$

Process for the preparation of ethylene

Process for the preparation of ethylene by pyrolysis of low molecular weight hydrocarbons, by contacting a flow of gas, consisting of low molecular weight hydrocarbons with an inert particulate carrier material having a surface area of > 0.01 and /g, at a temperature in the range of from 1000 to 1400 DEG C and at a GHSV of from 100 to 6000 hr, during a period in the range of from 1 minute to 60 minutes, followed by recovering ethylene gas produced in said reaction from the product stream, and calcination of said inert particulate carrier material in a flow of an oxidizing gas to remove the carbonaceous deposits on the carrier material surface, at a temperature in the range of from 600 DEG C to 1000 DEG C and a GHSV of from 100 to 6000 hr, for at least one minute

Molecular dynamics study of vesicle deformation mechanisms

Lipid bilayer membranes are known to form various structures like large sheets or vesicles. When both bilayer leaflets have equal composition, membranes preferentially form flat sheets or spherical vesicles. However, vesicles with a wide variety of shapes, including ellipsoids, discoids, pear-shaped, cup-shaped and budded vesicles, have been shown experimentally. Such shapes were predicted theoretically from energy minimization of continuous sheets as well. We show, using coarse-grained molecular dynamics simulations, how relatively small asymmetry in composition between the two leaflets may result in spontaneously curved bilayers and all these vesicle shapes. Three types of bilayer asymmetry are considered. Firstly, the situation where the headgroup-solvent interaction and thus the lipid packing alters due to a change in pH or ion-concentration of the vesicle interior/exterior (A). Secondly, where asymmetry arises from phase separation of two lipid types (B). And thirdly, where asymmetry arises from growth of one of the bilayer leaflets by incorporation of additional lipids from the solvent (C)

Influence of aging and dilution on the crystallization of silicate-1

The correlation between the formation of colloidal aggregates and the crystallization of silicalite-l from a clear solution has been investigated with in situ combined small-angle X-ray scattering and wide-angle X-ray scattering, and in situ ultra- small-angle X-ray scattering using synchrotron radiation. Increasing the aging time at room temperature of the synthesis mixture prior to heating to the reaction temperature reduced the induction period and increased the crystal growth rate without affecting the formation of colloidal aggregates. Dilution of the synthesis mixtures did not influence the nucleation and crystal growth rate, and did not affect the formation of colloidal aggregate

NO structures adsorbed on Rh(111) : theoretical approach to high-coverage STM images

Theoretical modeling of scanning tunneling microscopy (STM) measurements is used for the interpretation of images of nitrogen monoxide on Rh(111) surfaces in order to gain insight into the factors which control the contrast of an STM image, especially in the case of high coverage overlayers. Topographic images of NO/Rh(111) for different coverages and adsorption positions were calculated. These results were used to analyze the experimental images obtained for the p(2×2)-3NO and p(3×3)-7NO high coverage structures. The theoretical calculations confirm that not all NO molecules present on the surface can be observed experimentally, the image being dominated by the contribution of top NO molecules in the adlayer. In addition, the calculations reveal that destructive interference effects between molecular contributions in the tunnel current play a decisive role for the different contrast of the two high coverage structures. A general discussion of why and how the differences in the adsorbate surface configuration reflect the experimental STM images is given