Poincaré series of semi-invariants of 2×2 matrices

The Poincaré series of the algebra of -invariants of m-tuples of 2×2 matrices is presented both as a rational function and as a series of Schur functions. We show that this algebra of invariants is generated by the determinants, the mixed discriminants and the discriminants of 2×2 matrices. Consequences on invariants of three-dimensional matrices of the shape 2×2×m are discussed. For arbitrary n2, we prove an explicit functional equation for the Poincaré series of the -invariants of m-tuples of n×n matrices.     

Increment sizes of the principal value of Brownian local time

Let W be a standard Brownian motion, and define Y(t)= ∫₀ ^t ds/W(s) as Cauchy's principal value related to local time. We determine: (a) the modulus of continuity of Y in the sense of P. Lévy; (b) the large increments of Y. Received: 1 April 1999 / Revised version: 27 September 1999 / Published online: 14 June 2000     

The spectral projections and the resolvent for scattering metrics

In this paper, we consider a compact manifold with boundaryX equipped with a scattering metricg as defined by Melrose [9]. That is,g is a Riemannian metric in the interior ofX that can be brought to the formg=x ⁻⁴ dx²+x^{−2 h’} near the boundary, wherex is a boundary defining function andh’ is a smooth symmetric 2-cotensor which restricts to a metrich on ϖX. LetH=Δ+V, whereV∈x ²C^∞ (X) is real, soV is a ‘short-range’ perturbation of Δ. Melrose and Zworski started a detailed analysis of various operators associated toH in [11] and showed that the scattering matrix ofH is a Fourier integral operator associated to the geodesic flow ofh on ϖX at distance π and that the kernel of the Poisson operator is a Legendre distribution onX×ϖX associated to an intersecting pair with conic points. In this paper, we describe the kernel of the spectral projections and the resolvent,R(σ±i0), on the positive real axis. We define a class of Legendre distributions on certain types of manifolds with corners and show that the kernel of the spectral projection is a Legendre distribution associated to a conic pair on the b-stretched productX _b ² (the blowup ofX ² about the corner, (ϖX)²). The structure of the resolvent is only slightly more complicated. As applications of our results, we show that there are ‘distorted Fourier transforms’ forH, i.e., unitary operators which intertwineH with a multiplication operator and determine the scattering matrix; we also give a scattering wavefront set estimate for the resolventR(σ±i0) applied to a distributionf.     

Nonlocal boundary value problems for discrete systems

Our goal in this paper is to provide sufficient conditions for the existence of solutions to discrete, nonlinear systems subject to multipoint boundary conditions. The criteria we present depends on the size of the nonlinearity and the set of solutions to the corresponding linear, homogeneous boundary value problems. Our analysis is based on the Lyapunov–Schmidt Procedure and Brouwer?s Fixed Point Theorem. The results presented extend the previous work of D. Etheridge and J. Rodríguez (1996, 1998) [5], [6] and J. Rodríguez and P. Taylor (2007) [18], [19].     

Passivation of aluminium–n+ silicon contacts for solar cells by ultrathin Al2O3 and SiO2 dielectric layers

Ultra‐thin thermally grown SiO₂ and atomic‐layer‐deposited (ALD) Al₂O₃ films are trialled as passivating dielectrics for metal–insulator–semiconductor (MIS) type contacts on top of phosphorus diffused regions applicable to high efficiency silicon solar cells. An investigation of the optimum insulator thickness in terms of contact recombination factor J_{0_cont} and contact resistivity ρ_c is undertaken on 85 Ω/□ and 103 Ω/□ diffusions. An optimum ALD Al₂O₃ thickness of ～22 Å produces a J_{0_cont} of ～300 fAcm^–2 whilst maintaining a ρ_c lower than 1 mΩ cm² for the 103 Ω/□ diffusion. This has the potential to improve the open‐circuit voltage by a maximum 15 mV. The thermally grown SiO₂ fails to achieve equivalently low J_{0_cont} values but exhibits greater thermal stability, resulting in slight improvements in ρ_c when annealed for 10 minutes at 300 °C without significant changes in J_{0_cont}. The after‐anneal J_{0_cont} reaches ～600 fAcm^–2 with a ρ_c of ～2.5 mΩ cm² for the 85 Ω/□ diffusion amounting to a maximum gain in open‐circuit voltage of 6 mV. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

X‐ray absorption study of the local structure at the NiO/oxide interfaces

This work reports an X‐ray absorption near‐edge structure (XANES) spectroscopy study at the Ni K‐edge in the early stages of growth of NiO on non‐ordered SiO₂, Al₂O₃ and MgO thin films substrates. Two different coverages of NiO on the substrates have been studied. The analysis of the XANES region shows that for high coverages (80 Eq‐ML) the spectra are similar to that of bulk NiO, being identical for all substrates. In contrast, for low coverages (1 Eq‐ML) the spectra differ from that of large coverages indicating that the local order around Ni is limited to the first two coordination shells. In addition, the results also suggest the formation of cross‐linking bonds Ni—O—M (M = Si, Al, Mg) at the interface.     

Semiempirical fine-tuning for Hartree–Fock ionization potentials of atomic ions with non-integral atomic number

Amovilli and March (2006) [8] used diffusion quantum Monte Carlo techniques to calculate the non-relativistic ionization potential I(Z)$I(Z)$ in He-like atomic ions for the range of (fractional) nuclear charges Z   lying between the known critical value _Zc=0.911$Z_{\mathrm{c}}=0.911$ at which I(Z)$I(Z)$ tends to zero and Z=2$Z=2$. They showed that it is possible to fit I(Z)$I(Z)$ to a simple quadratic expression. Following that idea, we present here a semiempirical fine-tuning of Hartree–Fock ionization potentials for the isoelectronic series of He, Be, Ne, Mg and Ar-like atomic ions that leads to excellent estimations of _Zc$Z_{\mathrm{c}}$ for these series. The empirical information involved is experimental ionization and electron affinity data. It is clearly demonstrated that Hartree–Fock theory provides an excellent starting point for determining I(Z)$I(Z)$ for these series.     

Validation and generalization of DEA and its uses

Summary Rapidly expanding uses of DEA have been accompanied by developments which have enhanced its power and enlarged its utility for additional applications. Developments covered in the present paper include simulation studies comparing DEA with competing forms of statistical regressions. Other studies covered show how these two approaches can be combined in complementary fashion. Another part of this paper deals with Chance Constrained Programming formulations which incorporate probabilistic elements into DEA. Included also are discussions of statistical characterizations with accompanying tests of statistical significance for DEA efficiency evaluations. This paper concludes with uses of DEA in “discovery processes”-processes that need strengthening (and encouragemnt) in contemporary social science and management science research. Suggestions are made for additional research on further developments which extend to uses of DEA to provide new approaches in economics (including econometrics), management and psychology and an Appendix introduces new or recently developed efficiency measures for use in DEA. Invited by J. T. Pastor     

Determination of the spacetime from local time measurements

We consider an inverse problem for a Lorentzian spacetime (M, g), and show that time measurements, that is, the knowledge of the Lorentzian time separation function on a submanifold \(\Sigma \subset M\) determine the \(C^\infty \)-jet of the metric in the Fermi coordinates associated to \(\Sigma \). We use this result to study the global determination of the spacetime (M, g) when it has a real-analytic structure or is stationary and satisfies the Einstein-scalar field equations. In addition to this, we require that (M, g) is geodesically complete modulo scalar curvature singularities. The results are Lorentzian counterparts of extensively studied inverse problems in Riemannian geometry—the determination of the jet of the metric and the boundary rigidity problem. We give also counterexamples in cases when the assumptions are not valid, and discuss inverse problems in general relativity.