Structural and electronic properties of graphite layers grown on SiC(0 0 0 1)

Photoelectron spectroscopy, low-energy electron diffraction, and scanning probe microscopy were used to investigate the electronic and structural properties of graphite layers grown by solid state graphitization of SiC(0 0 0 1) surfaces. The process leads to well-ordered graphite layers which are rotated against the substrate lattice by 30°. On on-axis 6H-SiC(0 0 0 1) substrates we observe graphitic layers with up to several 100 nm wide terraces. ARUPS spectra of the graphite layers grown on on-axis 6H-SiC(0 0 0 1) surfaces are indicative of a well-developed band structure. For the graphite/n-type 6H-SiC(0 0 0 1) layer system we observe a Schottky barrier height of ?_B,n = 0.3 ± 0.1 eV. ARUPS spectra of graphite layers grown on 8° off-axis oriented 4H-SiC(0 0 0 1) show unique replicas which are explained by a carpet-like growth mode combined with a step bunching of the substrate.     

Smart Geodesic Tracing in GRworkbench

We have developed a new tool for numerical work in General Relativity: GRworkbench. We discuss how GRworkbench's implementation of a numerically-amenable analogue to Differential Geometry facilitates the development of robust and chart-independent numerical algorithms. We consider, as an example, geodesic tracing on two charts covering the exterior Schwarzschild space-time.     

Algebraic K-theory of non-linear projective spaces

In the spirit of “The Fundamental Theorem for the algebraic K-theory of spaces: I” (J. Pure Appl. Algebra 160 (2001) 21–52) we introduce a category of sheaves of topological spaces on n-dimensional projective space and present a calculation of its K-theory, a “non-linear” analogue of Quillen's isomorphism K_i(P_Rⁿ)₀ⁿK_i(R).     

Non‐standard Stokes and Navier–Stokes problems: existence and regularity in stationary case

This paper is devoted to Stokes and Navier–Stokes problems with non‐standard boundary conditions: we consider, in particular, the case where the pressure is given on a part of the boundary. These problems were studied by Bégue, Conca, Murat and Pironneau. They proved the existence of variational solutions, indicating that these were solutions of the initial non‐standard problems, if they are regular enough, but without specifying the conditions on the data which would imply this regularity. In this paper, first we show that the variational solutions, on supposing pressure on the boundary Γ₂ of regularity H^1/2 instead of H^?1/2, have their Laplacians in L² and, therefore, are solutions of non‐standard Stokes problem. Next, we give a result of regularity H², which we generalize, obtaining regularities W^{m, r}, m∈?, m?2, r?2. Finally, by a fixed‐point argument, we prove analogous results for the Navier–Stokes problem, in the case where the viscosity νis large compared to the data. Copyright © 2002 John Wiley & Sons, Ltd.     

A note on minimum degree conditions for supereulerian graphs

A graph is called supereulerian if it has a spanning closed trail. Let G be a 2-edge-connected graph of order n such that each minimal edge cut SE(G) with |S|3 satisfies the property that each component of G−S has order at least (n−2)/5. We prove that either G is supereulerian or G belongs to one of two classes of exceptional graphs. Our results slightly improve earlier results of Catlin and Li. Furthermore, our main result implies the following strengthening of a theorem of Lai within the class of graphs with minimum degree δ4: If G is a 2-edge-connected graph of order n with δ(G)4 such that for every edge xyE(G) , we have max{d(x),d(y)}(n−2)/5−1, then either G is supereulerian or G belongs to one of two classes of exceptional graphs. We show that the condition δ(G)4 cannot be relaxed.     

Structural evolution in amorphous silicon and germanium thin films.

The structural evolution in amorphous silicon and germanium thin films has been investigated by high-resolution transmission electron microscopy (HRTEM) in conjunction with autocorrelation function (ACF) analysis. The results established that the structure of as-deposited semiconductor films is of a high density of nanocrystallites embedded in the amorphous matrix. In addition, from ACF analysis, the structure of a-Ge is more ordered than that of a-Si. The density of embedded nanocrystallites in amorphous films was found to diminish with annealing temperature first, then to increase. The conclusions also corroborate well with the results of diminished medium-range order in annealed amorphous films determined previously by a variable coherence microscopy method.     

Operations in A-theory

A construction for Segal operations for K-theory of categories with cofibrations, weak equivalences and a biexact pairing is given and coherence properties of the operations are studied. The model for K-theory, which is used, allows coherence to be studied by means of (symmetric) monoidal functors. In the case of Waldhausen A-theory it is shown how to recover the operations used in Waldhausen (Lecture Notes in Mathematics, Vol. 967, Springer, Berlin, 1982, pp. 390-409) for the A-theory Kahn-Priddy theorem. The total Segal operation for A-theory, which assembles exterior power operations, is shown to carry a natural infinite loop map structure. The basic input is the un-delooped model for K-theory, which has been developed from a construction by Grayson and Gillet for exact categories in Gunnarsson et al. (J. Pure Appl. Algebra 79 (1992) 255), and Grayson's setup for operations in Grayson (K-theory (1989) 247). The relevant material from these sources is recollected followed by observations on equivariant objects and pairings. Grayson's conditions are then translated to the context of categories with cofibrations and weak equivalences. The power operations are shown to be well behaved w.r.t. suspension and are extended to algebraic K-theory of spaces. Staying close with the philosophy of Waldhausen (1982) Waldhausen's maps are found. The Kahn-Priddy theorem follows from splitting the “free part” off the equivariant theory. The treatment of coherence of the total operation in A-theory involves results from Laplaza (Lecture Notes in Mathematics, Vol. 281, Springer, Berlin, 1972, pp. 29-65) and restriction to spherical objects in the source of the operation.     

Nielsen realization for 3-manifolds containing two-sided projective planes

For compact irreducible sufficiently large 3-manifolds containing 2-sided projective planes, we consider the following Realization Problem: Given a finite subgroup of the outer automorphism group of the fundamental group, is there a finite group of homeomorphisms, which induces this subgroup? Received: 16 November 1999; in final form: 18 January 2001 / Published online: 8 November 2002     

Locally Periodic Versus Globally Periodic Infinite Words

We call a one-way infinite word w over a finite alphabet (ρ,l)-repetitive if all long enough prefixes of w contain as a suffix a ρth power (or more generally a repetition of order ρ) of a word of length at most l. We show that each (2,4)-repetitive word is ultimately periodic, as well as that there exist continuum many, and hence also nonultimately periodic, (2,5)-repetitive words. Further, we characterize nonultimately periodic (2,5)-repetitive words both structurally and algebraically.