Unique Continuation with Weak Type Lower Order Terms

This paper proves a unique continuation property for the elliptic differential inequality|u| A|u| + B|u|,where the coefficients A and B are functions in the Lorentz space with small weak type norm.     

A remark on unique continuation

In this paper a unique continuation result is proved for differential inequality of second order.     

Eine Methode, um im Laboratorium einen continuirlichen und gleichm?ssigen Strom von Acetylen

Ohne Zusammenfassung     

A definition for the covalent and ionic bond index in a molecule

Formulae for hermitian operators representing covalent, ionic, and total bond indices are derived. The eigenstates of these operators come in pairs, and can be considered as bonding, anti-bonding and lone-pair orbitals. The form of these operators is derived by generalising the rule that the bond order be defined as the net number of bonding electron pairs. The percentage of covalency and ionicity of a chemical bond may be obtained, and bond indices can also be defined between groups of atoms. The calculation of the bond indices depends only on the electron density operator, and certain projection operators used to represent each atom in the molecule. Bond indices are presented for a series of first and second row hydrides and fluorides, hydrocarbons, a metal complex, a Diels–Alder reaction and a dissociative reaction. In general the agreement between the bond indices is in accord with chemical intuition. The bond indices are shown to be stable to basis set expansion.     

Thermally induced mixing of water dominated interstellar ices

Despite considerable attention in the literature being given to the desorption behaviour of smaller volatiles, the thermal properties of complex organics, such as ethanol (C(2)H(5)OH), which are predicted to be formed within interstellar ices, have yet to be characterized. With this in mind, reflection absorption infrared spectroscopy (RAIRS) and temperature programmed desorption (TPD) have been used to probe the adsorption and desorption of C(2)H(5)OH deposited on top of water (H(2)O) films of various thicknesses grown on highly oriented pyrolytic graphite (HOPG) at 98 K. Unlike many other molecules detected within interstellar ices, C(2)H(5)OH has a comparable sublimation temperature to H(2)O and therefore gives rise to a complicated desorption profile. RAIRS and TPD show that C(2)H(5)OH is incorporated into the underlying ASW film during heating, due to a morphology change in both the C(2)H(5)OH and H(2)O ices. Desorption peaks assigned to C(2)H(5)OH co-desorption with amorphous, crystalline (CI) and hexagonal H(2)O-ice phases, in addition to C(2)H(5)OH multilayer desorption are observed in the TPD. When C(2)H(5)OH is deposited beneath ASW films, or is co-deposited as a mixture with H(2)O, complete co-desorption is observed, providing further evidence of thermally induced mixing between the ices. C(2)H(5)OH is also shown to modify the desorption of H(2)O at the ASW-CI phase transition. This behaviour has not been previously reported for more commonly studied volatiles found within astrophysical ices. These results are consistent with astronomical observations, which suggest that gas-phase C(2)H(5)OH is localized in hotter regions of the ISM, such as hot cores.     

Photochemical fixation of structures in binary polymer brushes-influence of layer thickness and grafting method

Polymer brushes consisting of hydrophilic and hydrophobic polymer components (poly-4-vinylpyridine, polymethacrylic acid and polystyrene, respectively) change their surface properties (as revealed by contact angles) when they are exposed to various solvents. In brushes prepared via grafting-from methods (using a specific surface initiator) layer thicknesses up to 300 nm were obtained. Copolymerization of the brush component monomers with 2-(4'-styryl)-indene yielded photo-cross-linkable brushes, which were used to fix the brushes in either the hydrophilic or hydrophobic state. Structural patterns differing in surface properties were produced and fixed by photo-cross-linking the hydrophobic component in that samples were irradiated through a mask. The patterns turned out most stable in moderately thick layers. AFM pictures confirm the contact angle results but reveal micro-domains of the two immiscible polymers in the grafted layers.