Induced representations and a new proof of the imprimitivity theorem

We present a brief and elementary proof of the Imprimitivity Theorem for an arbitrary locally compact group.     

The Coulomb correction to electron pair production by intermediate-energy photons

The Coulomb correction to the total cross section for intermediate-energy pair production is evaluated in terms of a high-energy-expansion formula, with the Davies-Bethe-Maximon correction as the leading term, followed by terms proportional to k^?1ln²k, k^?1lnk, k^?1 etc., the coefficients of which are determined by fitting to the Øverb?-Mork-Olsen exact low-energy results. The formula is estimated to be accurate within a few tenths of a per cent for photon energies between 3.5 m_ec² and infinity.     

Relativistic description of Marinov's modification of the Harress experiment

It is shown that Marinov's modification of the Harress experiment does not provide a means of giving an experimental decision between the theory of space-time absoluteness and the special theory of relativity     

Electron Wavefunctions and Densities for Atoms

With a special 'Ansatz' we analyse the regularity properties of atomic electron wavefunctions and electron densities. In particular we prove an a priori estimate, sup _y∈B(x,R) |∇ψ (y)| ≤C(R) sup_y∈B(x,2R) |ψ (y)| and obtain for the spherically averaged electron density, p(r), that p"(0) exists and is non-negative.     

Radical addition of nitrones to acrylates mediated by SmI2: asymmetric synthesis of gamma-amino acids employing carbohydrate-based chiral auxiliaries

Alkyl nitrones possessing N-substituted sugars as chiral auxiliaries were found to effectively undergo an SmI(2)-mediated radical addition to n-butyl acrylate affording gamma-amino acid derivatives with high diastereomeric control.     

Vortex imaging in the pi band of magnesium diboride

We report scanning tunneling spectroscopy imaging of the vortex lattice in single crystalline MgB2. By tunneling parallel to the c axis, a single superconducting gap (Delta=2.2 meV) associated with the pi band is observed. The vortices in the pi band have a large core size compared to estimates based on H(c2) and show an absence of localized states in the core. Furthermore, superconductivity between the vortices is rapidly suppressed by an applied field. These results suggest that superconductivity in the pi band is, at least partially, induced by the intrinsically superconducting sigma band.     

Scanning tunneling spectroscopy of Bi(2)Sr(2)CuO(6+delta): new evidence for the common origin of the pseudogap and superconductivity

Using scanning tunneling spectroscopy, we investigated the temperature dependence of the quasiparticle density of states of overdoped Bi(2)Sr(2)CuO(6+delta) between 275 mK and 82 K. Below T(c) = 10 K, the spectra show a gap with well-defined coherence peaks at +/-Delta(p) approximately 12 meV, which disappear at T(c). Above T(c), the spectra display a clear pseudogap of the same magnitude, gradually filling up and vanishing at T(*) approximately 68 K. The comparison with Bi(2)Sr(2)CaCu(2)O(8+delta) demonstrates that the pseudogap and the superconducting gap scale with each other, providing strong evidence that they have a common origin.     

Buckling driven debonding in sandwich columns

A compression loaded sandwich column that contains a debond is analyzed using a geometrically non-linear finite element model. The model includes a cohesive zone along one face sheet/core interface whereby the debond can extend by interface crack growth. Two geometrical imperfections are introduced; a global imperfection of the sandwich column axis and a local imperfection of the debonded face sheet axis. The model predicts the sandwich column to be very sensitive to the initial debond length and the local face sheet imperfection. The study shows that the sensitivity to the face sheet imperfection results from two mechanisms: (a) interaction of local debond buckling and global buckling and (b) the development of a damaged zone at the debond crack tip. Based on the pronounced imperfection sensitivity, the author predicts that an experimental measurement of the strength of sandwich structures may exhibit a large scatter caused by geometrical variations between test specimens.     

Forward–Backward Stochastic Differential Games and Stochastic Control under Model Uncertainty

We study optimal stochastic control problems with jumps under model uncertainty. We rewrite such problems as stochastic differential games of forward–backward stochastic differential equations. We prove general stochastic maximum principles for such games, both in the zero-sum case (finding conditions for saddle points) and for the nonzero sum games (finding conditions for Nash equilibria). We then apply these results to study robust optimal portfolio-consumption problems with penalty. We establish a connection between market viability under model uncertainty and equivalent martingale measures. In the case with entropic penalty, we prove a general reduction theorem, stating that a optimal portfolio-consumption problem under model uncertainty can be reduced to a classical portfolio-consumption problem under model certainty, with a change in the utility function, and we relate this to risk sensitive control. In particular, this result shows that model uncertainty increases the Arrow–Pratt risk aversion index.