A tight colored Tverberg theorem for maps to manifolds

We prove that any continuous map of an N-dimensional simplex ΔN with colored vertices to a d-dimensional manifold M must map r points from disjoint rainbow faces of ΔN to the same point in M: For this we have to assume that N?(r−1)(d+1), no r vertices of ΔN get the same color, and our proof needs that r is a prime. A face of ΔN is a rainbow face if all vertices have different colors.This result is an extension of our recent “new colored Tverberg theorem”, the special case of M=Rd. It is also a generalization of Volovikov?s 1996 topological Tverberg theorem for maps to manifolds, which arises when all color classes have size 1 (i.e., without color constraints); for this special case Volovikov?s proof, as well as ours, works when r is a prime power.     

On biquadratic fields that admit unit power integral basis

We consider biquadratic number fields whose maximal orders have power integral bases consisting of units. We prove an effective and efficient criteria to decide whether the maximal order of a biquadratic field has a unit power integral basis or not. In particular we can determine all trivial biquadratic fields whose maximal orders have a unit power integral basis.     

Controllable and reversible inversion of the electronic structure in nickel N-confused porphyrin: a case when MCD matters

Nickel N-confused tetraphenylporphyrin, 1, and nickel 2-N-methyl-N-confused tetraphenylporphyrin, 1-Me, exhibit unusual sign-reversed (positive-to-negative intensities in ascending energy) MCD spectra in the Q-type band region, suggesting a rare ΔHOMO < ΔLUMO relationship between π and π* MOs in the porphyrin core. Simple and reversible deprotonation of the external NH proton in 1 dramatically changes the electronic structure of the porphyrin core into the ΔHOMO > ΔLUMO combination characteristic for the meso-(tetraaryl)porphyrins. DFT, time-dependent DFT, and semiempirical ZINDO/S calculations on 1, 1-Me, and 1(-) confirm the experimental finding and successfully explain the MCD pattern in the target compounds.     

Distribution of Ir and Pt isotopes produced as fragments of 1 A GeV Au projectiles: a thermometer for peripheral nuclear collisions

Cross sections of iridium and platinum isotopes have been measured, which were produced as fragments from ¹⁹⁷Au projectiles interacting with aluminum target nuclei at 1 A GeV. The fragments were identified by a kinematic analysis (ΔE−Bρ-time-of-flight) and by an ion-optical separation at the projectile-fragment separator FRS at GSI. Indications are found for high excitation energies and weak proton-neutron correlations in the peripheral nuclear-collision process.     

Effect of indium doping on Ge2Sb2Te5 thin films for phase-change optical storage

The influence of In doping on the crystallization kinetics of Ge₂Sb₂Te₅ has been investigated using four-point-probe electrical resistance measurements, grazing incidence X-ray diffraction (XRD), X-ray reflectometry (XRR), variable incident angle spectroscopic ellipsometry, a static tester, and atomic force microscopy. For a stoichiometric Ge₂Sb₂Te₅ alloy doped with 3% In, the amorphous-to-crystalline transition is observed at 150 °C in the sheet resistance measurements. XRD reveals the formation of a predominant NaCl-type Ge₂Sb₂Te₅ phase during the amorphous-to-crystalline transition together with small amounts of crystalline In₂Te₃. Density values of 5.88±0.05 g cm^-3 and 6.22±0.05 g cm^-3 are measured by XRR for the film in the amorphous and crystalline states, respectively. Perfect erasure can be achieved by laser pulses longer than 165 ns. The retarded crystallization, as compared with the undoped Ge₂Sb₂Te₅ alloy, is attributed to the observed phase segregation. Sufficient optical contrast is exhibited and can be correlated with the large density change upon crystallization. PACS 68.55.-a; 78.20.-e; 78.66.Jg     

On a Family of Thue Equations Over Function Fields

Many families of parametrized Thue equations over number fields have been solved recently. In this paper we consider for the first time a family of Thue equations over a polynomial ring. In particular, we calculate all solutions of X(X-Y)(X-(T+x)Y)+Y³=1+xT(1-T)X(X-Y)(X-(T+\xi)Y)+Y^3=1+\xi T(1-T) over \Bbb C[T]{\Bbb C}[T] for all x ? \Bbb C\xi\in{\Bbb C} .