Inverse scattering for the magnetic Schrödinger operator

We show that fixed energy scattering measurements for the magnetic Schrödinger operator uniquely determine the magnetic field and electric potential in dimensions n?3. The magnetic potential, its first derivatives, and the electric potential are assumed to be exponentially decaying. This improves an earlier result of Eskin and Ralston (1995) [5] which considered potentials with many derivatives. The proof is close to arguments in inverse boundary problems, and is based on constructing complex geometrical optics solutions to the Schrödinger equation via a pseudodifferential conjugation argument.     

Increased layer interdiffusion in polyelectrolyte films upon annealing in water and aqueous salt solutions

As-deposited films of multilayered polyelectrolytes are considered to be non-equilibrium structures. Due to the strong attraction between oppositely charged polyions, polyelectrolyte interdiffusion is thought to be suppressed during the adsorption process. Equilibration is promoted by a decrease of the electrostatic attraction between polyion pairs. We have used neutral impact collision ion scattering spectroscopy to investigate the influence of polyelectrolyte multilayer annealing in water and aqueous 1 M NaCl solutions at different temperatures (20 and 70 degrees C) on the increase in interpenetration of a single polyelectrolyte layer throughout the whole film. The multilayers were composed of poly(4-vinylpyridinium) and poly(4-styrenesulfonate). Contrast between neighboring layers was established by labelling the layer in question with the heavy atom ruthenium. It is found that both temperature and salt increase layer interpenetration, whereas salt has a stronger influence than temperature. From numerical simulations polyelectrolyte diffusion coefficients were evaluated for the different annealing conditions. The influence of temperature and salt on the equilibration of the film is interpreted in terms of increased screening of polyion charges and binding of small counterions to polyion monomeric units.     

Preparation and characterization of Cr(III), Mn(II), Fe(II), Co(II) and Ni(II) complexes of a hexaazadithiophenolate macrocycle

The ligating properties of the 24-membered macrocyclic dinucleating hexaazadithiophenolate ligand (L(Me))2- towards the transition metal ions Cr(II), Mn(II), Fe(II), Co(II), Ni(II) and Zn(II) have been examined. It is demonstrated that this ligand forms an isostructural series of bioctahedral [(L(Me))M(II)2(OAc)]+ complexes with Mn(II) (2), Fe(II) (3), Co(II) (4), Ni(II) (5) and Zn(II) (6). The reaction of (L(Me))2- with two equivalents of CrCl2 and NaOAc followed by air-oxidation produced the complex [(L(Me))Cr(III)H2(OAc)]2+ (1), which is the first example for a mononuclear complex of (L(Me))2-. Complexes 2-6 contain a central N3M(II)(mu-SR)2(mu-OAc)M(II)N3 core with an exogenous acetate bridge. The Cr(III) ion in is bonded to three N and two S atoms of (L(Me))2- and an O atom of a monodentate acetate coligand. In 2-6 there is a consistent decrease in the deviations of the bond angles from the ideal octahedral values such that the coordination polyhedra in the dinickel complex 5 are more regular than in the dimanganese compound 2. The temperature dependent magnetic susceptibility measurements reveal the magnetic exchange interactions in the [(L(Me))M(II)2(OAc)]+ cations to be relatively weak. Intramolecular antiferromagnetic exchange interactions are present in the Mn(II)2, Fe(II)2 and Co(II)2 complexes where J = -5.1, -10.6 and approximately -2.0 cm(-1) (H = -2JS1S2). In contrast, in the dinickel complex 5 a ferromagnetic exchange interaction is present with J = +6.4 cm(-1). An explanation for this difference is qualitatively discussed in terms of the bonding differences.     

Quantum and Classical Evolutions of a Nonautonomous Dynamical System—A Comparison

The influence of moving boundaries on the stability of quantum Hamiltonian systems, in particular on the dynamics of quantum versions of the classical Pustilnikov model, is investigated (the latter consists of a masspoint bouncing above an oscillating plate under the influence of constant gravity.) It is shown that, in contrast to the classical Pustilnikov model, generic time-periodic boundary conditions (including the Dirichlet condition) on the quantum models do not allow unlimited energy gain (speeding up) of these systems.     

Investigation of Contemporary Forgeries of Ancient Silver Coins

Four ancient Roman silver coins from about 200 BC to 200 AD, mainly contemporary forgeries, were investigated in order to deduce the methods and materials used in the production of the forged coins. Special attention was devoted to a Denar from the Roman Republic, a C. Mamilius Limetanus denarius serratus (approx. 82 BC), because an original coin (pure silver) as well as a forgery were available. These coins both show serrated edges, i.e. notches all around with irregular spacing. A combination of microbeam analytical techniques was applied: Scanning Electron Microscopy (SEM), Electron Probe Micro Analysis (EPMA) and Secondary Ion Mass Spectrometry (SIMS). Some of the counterfeits consist of a base metal core plated with silver. The serrated Denar exhibits a plating layer with a thickness of approx. 100µm as determined by SEM and SIMS. This is an indication for foil silvering, as well as the apparent overlapping of the outer layer in one particular area.     

Zur Reaktion der Alkin-Kupfer(I)-Komplexe [CuX(S-Alkin)] (X = Cl,Br, I; S-Alkin = 3,3,6,6-Tetramethyl-1-thia-4-cycloheptin) mit dem Chelat-Liganden N,N,N′,N′-Tetramethylethylendiamin (tmeda)

Organometallic Compounds of Copper. XVII. On the Reaction of the Alkyne-Copper(I) Complexes [CuX(S-Alkyne)] (X = Cl, Br, I; S-Alkyne = 3,3,6,6-Tetramethyl-1-thiacyclohept-4-yne) with the Chelate Ligand N,N,N′,N′-Tetramethylethylendiamine (tmeda) The alkyne copper(I) chloride complex [CuCl(S-Alkyne)]_n ( 2 a ) (S-Alkyne = 3,3,6,6–tetramethyl-1-thiacyclohept-4-yne) adds tetramethylethylene diamine (tmeda) to form the mononuclear compound [CuCl(S-Alkyne)(tmeda)] ( 4 ). The alkyne copper halide complexes [CuBr(S-Alkyne)]_n ( 2 b ) and [CuI(S-Alkyne)]_n ( 2 c ) react with tmeda to yield the complex salts [Cu(S-Alkyne)(tmeda)]⁺ [CuX₂(S-Alkyne)]^– (X = Br ( 5 a ), X = I ( 5 b )). X-ray diffraction studies on all new compounds 4 and 5 reveal distorted tetrahedral coordination of the copper atom in complex 4 and trigonal-planar coordinated copper atoms in the cations and anions of the ionic compounds 5 .