Matching subsequences in trees

Given two rooted, labeled trees P and T the tree path subsequence problem is to determine which paths in P are subsequences of which paths in T. Here a path begins at the root and ends at a leaf. In this paper we propose this problem as a useful query primitive for XML data, and provide new algorithms improving the previously best known time and space bounds.     

Optical pump - nuclear resonance probe experiments on spin crossover complexes

A novel sample environment enabling optical pump – nuclear resonance probe experiments has been installed at the beamline P01, Petra III, DESY Hamburg. This set-up has been used to investigate optically induced spin state changes of spin crossover (SCO) complexes by nuclear resonant scattering immediately after excitation by an optical laser pulse. Here, we report the technical details as well as first results of the experiments performed at 290 K and 80 K on the SCO complexes [Fe (NH₂trz)₃]Cl₂ and [Fe(PM-BiA)₂(NCS)₂], respectively. The ⁵⁷Fe-enriched SCO complexes were excited by a 531 nm laser with a pulse length <?100 ps. Evaluation of the nuclear forward scattering data clearly indicate the presence of high spin (HS) states when the complexes are excited by laser pulses and a pure low spin (LS) state in the absence of any laser pulse. Furthermore, the dependence of the optically excited HS-fraction has been determined as a function of the average optical power.     

Reinvestigation of the sign problem in the two-dimensional Hubbard model

We reinvestigate the sign problem in the two-dimensional Hubbard model using the projector ground state Quantum Monte Carlo scheme with Langevin dynamics. Our interest is mainly motivated by the question: what is the parameter space in which simulations may be performed with reliable results and how does the average sign scales with inverse temperature? In the parameter space in which one may omit the sign problem we have studied the ground state properties: momentum distribution and spin structure. We find an exponential decay of the average sign. At half filling, we find evidence for an antiferromagnetic insulating ground state. At off half band fillings, the antiferromagnetic state is destroyed leaving place to an incommensurate spin density state.     

Bounds on Weights of Nearby Cycles and Wakimoto Sheaves on Affine Flag Manifolds

We study certain nearby cycles sheaves on an affine flag manifold which arise naturally in the Beilinson–Gaitsgory deformation of the affine flag manifold to the affine Grassmannian. We study the multiplicity functions we introduced in an earlier paper, which encode the data of the Jordan-Hölder series. We prove the multiplicity functions are polynomials in q, and we give a sharp bound for their degrees. Our results apply as well to the nearby cycles in the p-adic deformation of Laumon–Haines–Ngô, and also to Wakimoto sheaves.     

Dimensions of some affine Deligne-Lusztig varieties

This paper concerns the dimensions of certain affine Deligne-Lusztig varieties, both in the affine Grassmannian and in the affine flag manifold. Rapoport conjectured a formula for the dimensions of the varieties Xμ(b) in the affine Grassmannian. We prove his conjecture for b in the split torus; we find that these varieties are equidimensional; and we reduce the general conjecture to the case of superbasic b. In the affine flag manifold, we prove a formula that reduces the dimension question for Xx(b) with b in the split torus to computations of dimensions of intersections of Iwahori orbits with orbits of the unipotent radical. Calculations using this formula allow us to verify a conjecture of Reuman in many new cases, and to make progress toward a generalization of his conjecture.     

1. Allgemeine Analytische Chemie

Analytical and Bioanalytical Chemistry -     

A connection between deterministic motion and the steady-state probability distribution

We start with a given deterministic equation of motion for a set of macrovariables. Suppose that we can construct a corresponding master equation which has the following properties. In the limit of large systems the deterministic equation can be derived from the master equation for not too long times and the steady-state probability distribution is the exponential of an extensive quantity. Then, using a theorem concerning the solutions of master equations, we can show that the solutions of the deterministic equations evolve into the direction of a nondecreasing steady-state probability.     

Surface characterization of fluorinated polymers (PTFE, PVDF, PFA) for use in ultratrace analysis

Surface characterization of new unused PTFE, PFA and PVDF labware has been carried out by light microscopy, scanning electron microscopy, profilometry and atomic force microscopy. It has been found that in spite of higher micro-roughness, PFA exhibits the lowest nano-roughness and hence seems best suited as vessel material for relatively mild pressureless chemical operations for sample preparation of ultrapure substances, as container material for storage of ultrapure liquids, and for transport of such liquids, e.g., from the producer in the chemical to the end user in the microelectronics industry. This suitability refers only to the surface quality of the investigated materials. PTFE-surfaces, due to the sintering process of production, exhibit the most unfavourable surface quality of the investigated fluorinated polymers.     

Laser systems specialized for laser spectroscopy at storage rings

Laser spectroscopy at storage rings often suffers from a limited resolution due to Doppler-broadened resonances. Broadening is caused by the velocity spread of the ions stored in the beam. In the following, the present status of our work on laser systems specialized on the specific needs of laser spectroscopy at storage rings is reported. Two pulsed laser systems were developed. One is a dye laser whose spectral bandwidth can be switched by inserting different Littrow-prisms into the resonator. An increase in bandwidth up to a factor of 45 was achieved. This laser was used for fast qualitative scans and high resolution measurements. The other laser system is a Nd : YAG laser pumped optical parametric oscillator. It is a tunable laser system covering the spectral range from 410 to 4000 nm. Furthermore, a continuous wave laser with a frequency shifted feedback cavity is described. It shows broadband emission with an adjustable bandwidth of up to 4.5 GHz. This laser can be advantageous for laser cooling of ion beams. This revised version was published online in August 2006 with corrections to the Cover Date.