Jordan forms for mutually annihilating nilpotent pairs

In this paper we completely characterize all possible pairs of Jordan canonical forms for mutually annihilating nilpotent pairs, i.e. pairs (A,B) of nilpotent matrices such that AB=BA=0.     

Feasibility study for cell electroporation detection and separation by means of dielectrophoresis

Electroporation is a phenomenon during which exposure of a cell to high voltage electric pulses results in a significant increase in its membrane permeability. Aside from the fact that after the electroporation the cell membrane becomes more permeable, the cells' geometrical and electrical properties change considerably. These changes enable use of the force on dielectric particles exposed to non-uniform electric field (dielectrophoresis) for separation of non-electroporated and electroporated cells. This paper reports the results of an attempt to separate non-electroporated and electroporated cells by means of dielectrophoresis. In several experiments we managed to separate the non-electroporated and electroporated cells suspended in a medium with conductivity 0.174 S/m by exposing them to a non-uniform electric field at a frequency of 2 MHz. The behaviour of electroporated cells exposed to dielectrophoresis raises the presumption that in addition to conductivity, considerable changes in membrane permittivity occur after the electroporation.     

Diameters of commuting graphs of matrices over semirings

We calculate the diameters of commuting graphs of matrices over the binary Boolean semiring, the tropical semiring and an arbitrary nonentire commutative semiring. We also find the lower bound for the diameter of the commuting graph of the semigroup of matrices over an arbitrary commutative entire antinegative semiring.     

Echo spectroscopy of atomic dynamics in a Gaussian trap via phase imprints

We present a simultaneous analysis of the X¹ Σ ⁺ and the a³ Σ ⁺ electronic ground states of the NaK molecule. Excitation of the [B ¹ Π, c³ Σ ⁺]-system made it possible to record fluorescence to rovibrational levels of both ground states simultaneously with a Fourier-transform spectrometer. For the first time high lying levels in the triplet state with v = 17 and v = 18 were seen, the highest possible v = 19 for ²³Na-³⁹K was not observed. The joint evaluation of the retrieved data leads to accurate potential energy curves, that describe the experimental data within their experimental uncertainty of 0.005 cm⁻¹. Cold collision properties like scattering length and Feshbach resonance positions are calculated with these potentials and compared to other predictions.     

Nondestructive probing of Rabi oscillations on the cesium clock transition near the standard quantum limit

We report on the nondestructive observation of Rabi oscillations on the Cs clock transition. The internal atomic state evolution of a dipole-trapped ensemble of cold atoms is inferred from the phase shift of a probe laser beam as measured using a Mach-Zehnder interferometer. We describe a single color as well as a two-color probing scheme. Using the latter, measurements of the collective pseudospin projection of atoms in a superposition of the clock states are performed and the observed spin fluctuations are shown to be close to the standard quantum limit.     

Highly substituted oxabicyclic derivatives from furan: synthesis of (±)-platensimycin

A stereocontrolled approach to a key platensimycin intermediate was achieved from a commercially available furylcarboxylate. Key to our approach is the highly efficient formal [4 + 3] cyclocondensation of a substituted furan with tetrabromocyclopropene along with an intramolecular γ-alkylation to construct the final ring of the caged intermediate.