Free boundary problem for a two-layer inviscid incompressible fluid

The existence of a local (in time) classical solution of a free boundary problem for a two-layer inviscid incompressible fluid is shown. The method of successive approximations and the novel approach to Lagrangian coordinates of Solonnikov are used.     

Asymptotic behaviour of solutions to semi-linear elliptic equations on the half-cylinder

Various, but closely related, forms of a Phragmén-Lindelöf principle are established for certain classes of semi-linear elliptic equations (including systems) defined on a half-cylinder. For example, it is shown that under either homogeneous Dirichlet or Neumann lateral boundary conditions, the smooth solution either fails to exist globally, or when it does exist globally it must tend asymptotically to zero with increasingly large distance along the cylinder from the base. For uniformly elliptic equations, the decay to zero is at least exponential. The method employed relies upon cross-sectional estimates and is additionally applicable to both the finite and whole cylinder. In the latter case, global existence fails for all non-trivial solutions.Dedicated to Prof. Klaus Kirchgässner on the occasion of his sixtieth birthday     

Structure of sputter-deposited Pt/Fe and Cr/Fe multilayers

Conversion electron Mössbauer spectroscopy (CEMS) and X-ray diffraction (XRD) have been used to investigate the structure of Pt/Fe and Cr/Fe multilayers deposited by magnetron sputtering. The Cr/Fe samples consisted of four samples prepared under Ar sputtering pressures of 1.3, 3.0, 5.0, and 10.0 mT, all with the same multilayer structure of 3.5 nm Cr/2.5 nm Fe, repeated 35 times onto c-Si wafer substrates. The quality of the interfaces between Cr and Fe is clearly degraded with increasing sputter pressure, as seen by changes in the relative intensities of four magnetic subspectra in the CEMS and the gradual appearance of a single-line resonance similar to Fe in solution in Cr. The low-angle XRD superlattice peaks also disappear with increasing sputter pressure, while the high-angle XRD shows a tendency for loss of the preferred (110) texture. Two films of Pt/Fe were deposited epitaxially onto MgO single crystals with bilayer periods of 1.3 nm and 2.6 nm and total thickness of 300 nm each. A transition from fcc-PtFe with near-perpendicular magnetic anisotropy to a bcc-Fe/fcc-PtFe mixture with in-plane magnetic texture is observed by CEMS for the factor of two increase in bilayer period.     

Closures of totally geodesic immersions into locally symmetric spaces of noncompact type

It is established that if and are connected locally symmetric spaces of noncompact type where has finite volume, and is a totally geodesic immersion, then the closure of in is an immersed ``algebraic' submanifold. It is also shown that if in addition, the real ranks of and are equal, then the the closure of in is a totally geodesic submanifold of The proof is a straightforward application of Ratner's Theorem combined with the structure theory of symmetric spaces.

     

A concise total synthesis of (+/-)-bakkenolide A by means of an intramolecular Diels-Alder reaction

(+/-)-Bakkenolide A was prepared in five steps from ethyl 4-benzyloxyacetoacetate by sequential alkylations with tiglyl bromide nd cis-5-bromo-1,3-pentadiene, followed by an intramolecular Diels-Alder reaction as the key step. The known 7-epibakkenolide A and novel 10-epi- and 7,10-diepibakkenolide A stereoisomers were obtained as minor byproducts.     

Studies on metal—acetylene complexes : VI. Crystal and molecular structure of [diethylbis(1-pyrazolyl)borato]methyl(1-phenylpropyne)-platinum(II), [(C2H5)2B(N2C3H3)2](CH3)Pt(C6H5CCCH3)

The crystal and molecular structure of [diethylbis(1-pyrazolyl)borato]methyl(1-phenylpropyne)platinum(II), ([(C₂H₅)₂B(N₂C₃H₃)₂](CH₃)Pt(C₆H₅CCCH₃)), has been determined by a single crystal X-ray diffraction study using diffractometer techniques. The compound crystallizes in the monoclinic space group P2₁/c with a = 13.239(6), b = 11.077(5), c = 15.619)7) Å and β = 114.53(2)°. The observed density of 1.71(2) g cm^?3 agrees well with the calculated value, 1.687 g cm^?3, assuming four molecules in the cell. A conventional agreement factor of 0.036 was obtained by least-squares refinement on F using 3289 observations and 194 variables. The coordination about the platinum atom is square planar, if the acetylene is assumed to occupy one coordination site. The substituents of the acetylene are cis-bent away from the Pt atom, the methyl substituent by 17.7(1.0)°, and the phenyl substituent by 21.2(9)°. The coordinated triple bond length is 1.227(10) Å. These results indicate that the acetylene is moderately perturbed on coordination, consistent with the observation that Δν(CC) is 211 cm^?1. The conformation of the ring formed by the bidentate polypyrazolylborate ligand is that of a “shallow” boat. One of the methylene H atoms on the ethyl substituents on the polypyrazolylborate ligand when placed in an idealized position is 2.65 Å distant from the Pt atom.