Femtosecond holography in lithium niobate crystals

Spatial gratings are recorded holographically by two femtosecond pump pulses at 388 nm in lithium niobate (LiNbO3) crystals and read out by a Bragg-matched, temporally delayed probe pulse at 776 nm. We claim, to our knowledge, the first holographic pump-probe experiments with subpicosecond temporal resolution for LiNbO3. An instantaneous grating that is due mostly to the Kerr effect as well as a long-lasting grating that results mainly from the absorption caused by photoexcited carriers was observed. The Kerr coefficient of LiNbO3 for our experimental conditions, i.e., pumped and probed at different wavelengths, was approximately 1.0 x 10(-5) cm2/GW.     

Photochemical preparation of highly functionalized 1-indanones

A series of o-alkylphenyl alkyl ketones 1 were synthesized by different methods. The presence of a leaving group X adjacent to the carbonyl group is the special peculiarity of these ketones. Upon irradiation the keto carbonyl group of these compounds undergoes an n-pi* excitation followed by a 1,5-hydrogen migration from the o-alkyl substituent to the carbonyl oxygen atom. The thus formed 1,4-diradicals are subject to a very rapid elimination of acid HX, giving 1,5-diradicals. We called this process spin center shift. After intersystem crossing these diradicals cyclize to 1-indanones 20 in good yields. Depending on the solvent and on substituents, o-alkoxyalkyl ketones 22 or benzo[c]furanes 21 are obtained as byproducts. The mechanism of the cyclization was elucidated by quantum chemical calculations and kinetic measurements.     

Atomic resolution imaging of the (001) surface of UHV cleaved MgO by dynamic scanning force microscopy

The (001) surface of UHV cleaved single MgO crystals was imaged with dynamic mode scanning force microscopy. Large-scale images show various defects, like steps of mostly one atomic height, rectangular holes of nanometer size, and some complex adstructures. First time images with atomic resolution show one square ionic sublattice in its bulklike dimension with a corrugation of up to 40 pm along the <001> direction. Most images exhibit atomic point defects which appear as depressions including a few ionic lattice sites proving that point defects are stable on flat terraces.     

ChipCheck--a program predicting total hybridization equilibria for DNA binding to small oligonucleotide microarrays

Presented here is the program ChipCheck that allows the computation of total hybridization equilibria for hybridization experiments involving small oligonucleotide arrays. The calculation requires the free energies of binding for all pairs of probes and targets as well as total strand concentrations and probe molecule numbers. ChipCheck has been tested computationally on microarrays with up to 100 spots and 42 target strands (4200 binding equilibria). It arrives at solutions through iterations employing the multidimensional Newton method. While currently running in simulation mode only, an extension of the approach to the exhaustive analysis of chip results is being outlined and may be implemented in the future. The output displays the extent of correct and cross hybridization both graphically and numerically. In principle, calculating total hybridization equilibria allows for eliminating noise from DNA chip results and thus an improvement in sensitivity and accuracy.     

Axiomatic homotopy theory for operads

We give sufficient conditions for the existence of a model structure on operads in an arbitrary symmetric monoidal model category. General invariance properties for homotopy algebras over operads are deduced.     

Multiple right-hand side techniques for the numerical simulation of quasistatic electric and magnetic fields

The simulation of slowly varying transient electric high-voltage fields and magnetic fields requires the repeated and successive solution of high-dimensional linear algebraic systems of equations with identical or near-identical system matrices and different right-hand side vectors. For these solution processes which are required within implicit time integration schemes and nonlinear (quasi-)Newton–Raphson methods an iterative multiple right-hand side (mrhs) scheme is used which recycles vector subspaces resulting from previous preconditioned conjugate gradient iteration runs. The combination of this scheme with a subspace projection extrapolation start value generation scheme is discussed. Numerical results for three-dimensional electric and magnetic field simulations are presented and the efficiency of the new schemes re-using eigenvector information from previous iteration processes with different tolerance criteria are compared to those of standard conjugate gradient iterations.     

On quantitative aspects of the unit sum number problem

We investigate the function u _K,S (n; q) which counts the number of representations of algebraic integers α with |N_{K/\mathbb Q}(a)| ￡ q{|N_{K/{\mathbb Q}}(\alpha)| \leq q} for some real positive q that can be written as sums of exactly n S-units of the number field K.