Triaxial superdeformation in Lu

High-spin states in ¹⁶³Lu have been investigated using the Euroball spectrometer array. The previously known superdeformed band has been extended at low and high energies, and its connection to the normal-deformed states has been established. From its decay the mixing amplitude and interaction strength between superdeformed and normal states are derived. In addition, a new band with a similar dynamic moment of inertia has been found. The experimental results are compared to cranking calculations which suggest that the superdeformed bands in this mass region correspond to shapes with a pronounced triaxiality (γ≈±20°).     

Interpolation of operator ideals with an application to eigenvalue distribution problems

We derive results on the interpolation of complete quasinormed operator ideals, mainly for the absolutelyp-summing and thes-number idealsS _p ^s defined by Pietsch. By estimating theK-Functional of Peetre, we get that the interpolation ideal (S _p1 ^s ,S _p2 ^s ),_,p is contained inS _p ^s and is even equal to it in the case of the approximation numbers. A similar fact is proved for absolutely (p, q)-summing operators, interpolating the first index. We show further that the absolutelyp-summing operators onc ₀ are contained in the complex interpolation space ( _p1 (c _o), _p2 (c _o))_[].The previous results are then applied to prove summability properties for the eigenvalues of operators in Banach spaces, which are products ofS _p1 ^s -type and absolutelyp _j -summing operators. Roughly speaking, the summability order is the harmonic sum of thep _i - andp _j -indices, wherep _j 2. In the case of Hilbert spaces, this reduces to the well-known Weyl-inequality. The method uses an abstract interpolation estimate for ideal quasinorms which may be useful also for other operator ideals.     

Nanoscopic Porous Iridium/Iridium Dioxide Superstructures (15 nm): Synthesis and Thermal Conversion by In Situ Transmission Electron Microscopy

Porous particle superstructures of about 15 nm diameter, consisting of ultrasmall nanoparticles of iridium and iridium dioxide, are prepared through the reduction of sodium hexachloridoiridate(+IV) with sodium citrate/sodium borohydride in water. The water-dispersible porous particles contain about 20 wt % poly(N-vinylpyrrolidone) (PVP), which was added for colloidal stabilization. High-resolution transmission electron microscopy confirms the presence of both iridium and iridium dioxide primary particles (1–2 nm) in each porous superstructure. The internal porosity (≈58 vol%) is demonstrated by electron tomography. In situ transmission electron microscopy up to 1000 °C under oxygen, nitrogen, argon/hydrogen (all at 1 bar), and vacuum shows that the porous particles undergo sintering and subsequent compaction upon heating, a process that starts at around 250 °C and is completed at around 800 °C. Finally, well-crystalline iridium dioxide is obtained under all four environments. The catalytic activity of the as-prepared porous superstructures in electrochemical water splitting (oxygen evolution reaction; OER) is reduced considerably upon heating owing to sintering of the pores and loss of internal surface area.     

Countably determined sets and a conjecture of C.W. Henson

Partially supported by NSF grants DMS-9208071 and DMS-9100383     

Pd deposits on Ni(111): a theoretical study

The ASED-MO method has been used to gather electronic and energetic information on Pd deposits on Ni(111) and Pd atom inclusion in the first Ni layer since these model catalysts exhibit a striking catalytic efficiency towards butadiene hydrogenation. The electronic structure of Pd atoms is strongly altered compared with pure Pd. A Pd(4d)→Pd(5s) electronic transfer occurs in the case of the deposit when a slight similar transfer and a charge transfer from Pd to surrounding Ni takes place in the case of the inclusion. Those results are consistent with XPS experimental data. A low density of states, near the Fermi level, is also observed. The optimal geometrical situation for Pd deposits is found to be 2D-aggregates (in pseudoepitaxy or pseudomorphy with the underlying Ni surface, depending on the aggregate size). Small aggregates (part of the first Ni layer) are found to be the most stable in the case of a Pd inclusion in the Ni with a Pd---Pd distance of 2.64 Å, in agreement with available EXAFS experimental data.     

On the imaginary simple roots of the Borcherds algebra II9,1

In a recent paper [O. Bärwald, R.W. Gebert, M. Günaydin and H. Nicolai, preprint KCL-MTH-97-22, IASSNS-HEP-97/20, PSU-TH-178, AEI-029, hep-th/9703084, to appear in Commun. Math. Phys.] it was conjectured that the imaginary simple roots of the Borcherds algebra _II9,1 at level 1 are its only ones. We here propose an independent test of this conjecture, establishing its validity for all roots of norm − 8. However, the conjecture fails for roots of norm −10 and beyond, as we show by computing the simple multiplicities down to norm −24, which turn out to be remarkably small in comparison with the corresponding E₁₀ multiplicities. Our derivation is based on a modified denominator formula combining the denominator formulas for E₁₀ and _II9,1, and provides an efficient method for determining the imaginary simple roots. In addition, we compute the E₁₀ multiplicities of all roots up to height 231, including levels up to l = 6 and norms −42.     

On the well‐posedness of a mathematical model of quorum‐sensing in patchy biofilm communities

We analyze a system of reaction–diffusion equations that models quorum‐sensing in a growing biofilm. The model comprises two nonlinear diffusion effects: a porous medium‐type degeneracy and super diffusion. We prove the well‐posedness of the model. In particular, we present for the first time a uniqueness result for this type of problem. Moreover, we illustrate the behavior of model solutions in numerical simulations. Copyright © 2011 John Wiley & Sons, Ltd.