6,872 research outputs found
Lattice sites of ion-implanted Li in diamond
Published in: Appl. Phys. Lett. 66 (1995) 2733-2735
citations recorded in [Science Citation Index]
Abstract: Radioactive Li ions were implanted into natural IIa diamonds at temperatures between 100 K and 900 K. Emission channelling patterns of a-particles emitted in the nuclear decay of 8Li (t1/2 = 838 ms) were measured and, from a comparison with calculated emission channelling and blocking effects from Monte Carlo simulations, the lattice sites taken up by the Li ions were quantitatively determined. A fraction of 40(5)% of the implanted Li ions were found to be located on tetrahedral interstitial lattice sites, and 17(5)% on substitutional sites. The fractions of implanted Li on the two lattice sites showed no change with temperature, indicating that Li diffusion does not take place within the time window of our measurements.
Constructing Invariant Subspaces as Kernels of Commuting Matrices
Given an n by n matrix A over the complex numbers and an invariant subspace
L, this paper gives a straightforward formula to construct an n by n matrix N
that commutes with A and has L equal to the kernel of N. For Q a matrix putting
A into Jordan canonical form J = RAQ with R the inverse of Q, we get N = RM$
where the kernel of M is an invariant subspace for J with M commuting with J.
In the formula M = P ZVW with V the inverse of a constructed matrix T and W the
transpose of P, the matrices Z and T are m by m and P is an n by m row
selection matrix. If L is a marked subspace, m = n and Z is an n by n block
diagonal matrix, and if L is not a marked subspace, then m > n and Z is an m by
m near-diagonal block matrix. Strikingly, each block of Z is a monomial of a
finite-dimensional backward shift. Each possible form of Z is easily arranged
in a lattice structure isomorphic to and thereby displaying the complete
invariant subspace lattice L(A) for A.Comment: 12 pages with two illustrations of invariant subspace lattice
diagram
Constructing invariant subspaces as kernels of commuting matrices
Given an n n matrix A over C and an invariant subspace N, a straightforward formula
constructs an n n matrix N that commutes with A and has N = kerN. For Q a matrix putting A into Jordan canonical form, J = Q1AQ, we get N = Q1M where M= ker(M) is an invariant subspace for J with M commuting with J. In the formula J = PZT1Pt, the matrices Z and T are m m and P is an n m row selection matrix. If N is a marked subspace, m = n and Z is an n n block diagonal matrix, and if N is not a marked subspace, then m > n and Z is an m m near-diagonal block matrix. Strikingly, each block of Z is a monomial of a nite-dimensional backward shift. Each possible form of Z is easily arranged in a lattice structure isomorphic to and thereby displaying the complete invariant subspace lattice L(A) for A
On the first Gaussian map for Prym-canonical line bundles
We prove by degeneration to Prym-canonical binary curves that the first
Gaussian map of the Prym canonical line bundle is
surjective for the general point [C,A] of R_g if g >11, while it is injective
if g < 12.Comment: To appear in Geometriae Dedicata. arXiv admin note: text overlap with
arXiv:1105.447
Kondo temperature of magnetic impurities at surfaces
Based on the experimental observation, that only the close vicinity of a
magnetic impurity at metal surfaces determines its Kondo behaviour, we
introduce a simple model which explains the Kondo temperatures observed for
cobalt adatoms at the (111) and (100) surfaces of Cu, Ag, and Au. Excellent
agreement between the model and scanning tunneling spectroscopy (STS)
experiments is demonstrated. The Kondo temperature is shown to depend on the
occupation of the d-level determined by the hybridization between adatom and
substrate with a minimum around single occupancy.Comment: 4 pages, 2 figure
Equianalytic and equisingular families of curves on surfaces
We consider flat families of reduced curves on a smooth surface S such that
each member C has the same number of singularities of fixed singularity types
and the corresponding (locally closed) subscheme H of the Hilbert scheme of S.
We are mainly concerned with analytic resp. topological singularity types and
give a sufficient condition for the smoothness of H (at C). Our results for
S=P^2 seem to be quite sharp for families of cuves of small degree d.Comment: LaTeX v 2.0
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