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A natural extension of SLD-resolution is introduced as a goal directed proof procedure
for the full first order implicational fragment of intuitionistic logic. Its intuitionistic semantic fits a procedural interpretation of logic programming. By allowing arbitrary nested implications it can be used for implementing modularity in logic programs. With adequate negation axioms it gives an alternative to negation as failure and leads to a proof procedure for full first order predicate logic.

The Monte Carlo complexity of computing integrals depending on a parameter is analyzed for smooth integrands. An optimal algorithm is developed on the basis of a multigrid variance reduction technique. The complexity analysis implies that our algorithm attains a higher convergence rate than any deterministic algorithm. Moreover, because of savings due to computation on multiple grids, this rate is also higher than that of previously developed Monte Carlo algorithms for parametric integration.

The World Wide Web is a medium through which a manufacturer may allow Internet visitors to customize or compose his products. Due to missing or rapidly changing standards these applications are often restricted to relatively simple CGI or JAVA based scripts. Usually, results like images or movies are stored in a database and are transferred on demand to the web-user. Viper (Visualisierung parametrisch editierbarer Raumkomponenten) is a Toolkit [VIP96] written in C++ and JAVA which provides 3D-modeling and visualization methodsfor developing complex web-based applications. The Toolkit has been designed to built a prototype, which can be used to construct and visualize prefabricated homes on the Internet. Alternative applications are outlined in this paper. Within Viper, all objects are stored in a scene graph (VSSG ), which is the basic data structure of the Toolkit. To show the concept and structure of the Toolkit, functionality, and implementation of the prototype are described.

The flow of a liquid into an empty channel is simulated. The simulation is based on a recently published model for general fluid/liquid/solid systems which eliminates the shear stress singularity at the moving contact line between the liquid/fluid interface and the solid. This model is carefully analyzed for low Reynolds and Capillary numbers, adapted to the channel inflow problem, and implemented. Very convincing numerical results are presented.

Abstract: Random Matrix Theory (RMT) is a powerful statistical tool to model spectral fluctuations. This approach has also found fruitful application in Quantum Chromodynamics (QCD). Importantly, RMT provides very efficient means to separate different scales in the spectral fluctuations. We try to identify the equivalent of a Thouless energy in complete spectra of the QCD Dirac operator for staggered fermions from SU(2) lattice gauge theory for different lattice size and gauge couplings. We focus on the bulk of the spectrum. In disordered systems, the Thouless energy sets the universal scale for which RMT applies. This relates to recent theoretical studies which suggest a strong analogy between QCD and disordered systems. The wealth of data allows us to analyze several statistical measures in the bulk of the spectrum with high quality. We find deviations which allows us to give an estimate for this universal scale. Other deviations than these are seen whose possible origin is discussed. Moreover, we work out higher order correlators as well, in particular three-point correlation functions.

Abstract: We investigate the quantum properties of fields generated by resonantly enhanced wave mixing based on atomic coherence in Raman systems. We show that such a process can be used for generation of pairs of Stokes and anti-Stokes fields with nearly perfect quantum correlations, yielding almost complete (i.e. 100%) squeezing without the use of a cavity. We discuss the extension of the wave mixing interactions into the domain of a few interacting light quanta.

Abstract: Resonant optical pumping in dense atomic media is discussed, where the absorption length is less than the smallest characteristic dimension of the sample. It is shown that reabsorption and multiple scattering of spontaneous photons (radiation trapping) can substantially slow down the rate of optical pumping. A very slow relaxation out of the target state of the pump process is then sufficient to make optical pumping impossible. As model systems an inhomogeneously and a radiatively broadened 3-level system resonantly driven with a strong broad-band pump field are considered.

Abstract: We show that the physical mechanism of population transfer in a 3-level system with a closed loop of coherent couplings (loop-STIRAP) is not equivalent to an adiabatic rotation of the dark-state of the Hamiltonian but coresponds to a rotation of a higher-order trapping state in a generalized adiabatic basis. The concept of generalized adiabatic basis sets is used as a constructive toolto design pulse sequences for stimulated Raman adiabatic passage (STIRAP) which give maximum population transfer also under conditions when the usual condition of adiabaticty is only poorly fulfilled. Under certain conditions for the pulses (generalized matched pulses) there exists a higher-order trapping state, which is an exact constant of motion and analytic solutions for the atomic dynamics can be derived.

Abstract: We analyze the long-time quantum dynamics of degenerate parametric down-conversion from an initial sub-harmonic vacuum (spontaenous down-conversion). Standard linearization of the Heisenberg equations of motions fails in this case, since it is based on an expansion around an unstable classical solution and neglects pump depletion. Introducing a mean-field approximation we find a periodic exchange of energy between the pump and subharmonic mode goverened by an anharmonic pendulum equation. From this equation the optimum interaction time or crystal length for maximum conversion can be determined. A numerical integration of the 2-mode Schrödinger equation using a dynamically optimized basis of displaced and squeezed number states verifies the characteristic times predicted by the mean-field approximation. In contrast to semiclassical and mean-field predictions it is found that quantum uctuations of the pump mode lead to a substantial limitation of the efficiency of parametric down-conversion.