High dose iron implantation into silicon and metals

High dose implantations of Fe into metals and semiconductors have been performed with beam energies up to 1 MeV at the UNILAC-injector at GSI. Unusual high concentrations of 70 atomic % for Si and 20 atomic % for Cu have been obtained, with doses of 10¹⁸ Fe/cm² in the case of Si and several 10¹⁷ Fe/cm² in the case of Cu. For Si the thickness of the layers were determined by Rutherford backscattering to be 4500 Å. These results are consistent with calculations, which show that these high concentrations are due to the reduction of the sputter yield at the relative high particle energies. Samples have been characterized using several complementary methods (Mössbauer Spectroscopy (MS), Rutherford Backscattering Spectroscopy (RBS), Auger electron Spectroscopy (AES). Scanning Electron Microscopy (SEM), X-ray diffraction (XRD)).     

Sub-megabar Mössbauer studies using diamond anvil cells

The development and the use of the diamond anvil cell for Mössbauer Spectroscopy (MS) to pressures nearing 100 GPa are discussed. Three types of cells and their typical performance are given. Pressure calibration, hydrostatic media, gasketing, collimation, -ray absorption, and sample size for MS are reviewed. New MS results showing hysteresis in the room temperature high pressure transition in iron and showing the rapid rise ofT _N in NiI₂ with pressure are presented.     

Plunger measurements on highly stripped O-ions as tool for detecting electron polarization on emergence from thin ferromagnetic layers

From hyperfine interaction studles on free single electron¹⁶O(3⁻) ions. in a time differential mode using the recoil distance technique. It is shown that these ions are polarized when emerging from magnetized thin layers of Fe. The observed degree of polarization , however, is smaller than expected from transient field measurements.     

Determinants of Laplacians in real line bundles over hyperbolic manifolds connected with quantum geometry of membranes

The possibility is discussed of generalizing the Polyakov approach to strings on membranes and the connection of such a generalization with Thurston's classification of three-dimensional geometries. The important ingredients for computing a membrane path integral are the determinants of scalar Laplacians acting in real line bundles over three-dimensional closed manifolds. In the closed bosonic membrane case, such determinants are evaluated for a class of closed 3-manifolds of the H ³/ form with a discrete subgroup of isometries of the three-dimensional Lobachevsky space H ³ and they are expressed in terms of the Selberg zeta function. Some further possible implications of the results obtained are also discussed.     

Multiple local solutions to nonlinear control processes

We use the topological tool of Nielsen fixed-point theory to study the controllability of perturbed linear control processes whose control space can be reduced to a finite-dimensional one. These methods produce a lower bound on the number of controls that achieve a given target. We concentrate particularly on the case where the perturbation has sublinear growth, and we exhibit examples of multiple controls of various types that are detected by the Nielsen theory method.This research was partly supported by the Research Grant Teoria del Controllo dei Sistemi Dinamici, Ministero della Pubblica Istruzione, Roma, Italy.     

Equivalence of regularity for the Bergman projection and the\bar \partial-neumann operator

A necessary and sufficient condition for regularity of the -Neumann operator on (0,q)-forms in a smooth bounded pseudoconvex domain in Cⁿ is that the orthogonal projections onto -closed forms of degrees (0,q−1), (0,q), and (0,q+1) all be regular. The first author partially supported by NSF Grant DMS-8701038     

Asymptotics of solutions of a linear singularity perturbed system with degeneracy

Asymptotic expansions with respect to a small parameter e are constructed for a fundamental system of solutions of a linear singularity perturbed system of equations of the form

Extending an edge-coloring

When can a k-edge-coloring of a subgraph K of a graph G be extended to a k-edge-coloring of G? One necessary condition is that for all X ? E(G) - E(K), where μ_i(X) is the maximum cardinality of a subset of X whose union with the set of edges of K colored i is a matching. This condition is not sufficient in general, but is sufficient for graphs of very simple structure. We try to locate the border where sufficiency ends.     

The Choquet-Deny convolution equation μ=μ*σ for probability measures on Abelian semigroups

In this note, we characterize the regular probability measures satisfying the Choquet-Deny convolution equation =* on Abelian topological semigroups for a given probability measure .