Lösung des absoluten Konvergenzproblems einer allgemeinen Klasse Dirichletscher Reihen

Ohne Zusammenfassung     

On the counting function of the lattice profile of periodic sequences

The lattice profile analyzes the intrinsic structure of pseudorandom number sequences with applications in Monte Carlo methods and cryptology. In this paper, using the discrete Fourier transform for periodic sequences and the relation between the lattice profile and the linear complexity, we give general formulas for the expected value, variance, and counting function of the lattice profile of periodic sequences with fixed period. Moreover, we determine in a more explicit form the expected value, variance, and counting function of the lattice profile of periodic sequences for special values of the period.     

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.     

Stochastic control problems with delay

We consider optimal control problems for systems described by stochastic differential equations with delay. We state conditions for certain classes of such systems under which the stochastic control problems become finite-dimensional. These conditions are illustrated with three applications. First, we solve some linear quadratic problems with delay. Then we find the optimal consumption rate in a financial market with delay. Finally, we solve explicitly a deterministic fluid problem with delay which arises from admission control in ATM communication networks.     

Effects of the switching time in OPS/OBS networks

In this paper we present an analytical model, which considers the effects of the switching time on the network performance in service differentiated optical packet/burst switching (OPS/OBS) networks. Our results indicate that the switching time must be less than 10 % of the packet/burst duration in order to avoid any significant reductions in the network performance. Furthermore, regarding a network with full wavelength conversion, we show that the benefits of statistical resource sharing are almost non-existent for low priority traffic when the switching time is large.     

Existence of many ergodic absolutely continuous invariant measures for piecewise-expandingC 2 chaotic transformations in ℝ2 on a fixed number of partitions

Let Ω be a region in ℝⁿ and letp = P_i ) _i ^1m , be a partition ofΩ into a finite number of closed subsets having piecewise C² boundaries of finite(n - 1 )dimensional measure. Let τ:Ω→Ω be piecewise C² onP where, τ_i = τ|p_i is aC ² diffeomorphism onto its image, and expanding in the sense that there exists α > 1 such that for anyi = 1, 2,...,m ‖Dτ_i ^-1 ‖ < α^-1, where Dτ_i ^-1 is the derivative matrixτ _i ^- 1 and |‖·‖ is the Euclidean matrix norm. By means of an example, we will show that the simple bound of one-dimensional dynamics cannot be generalized to higher dimensions. In fact, we will construct a piecewise expanding C² transformation on a fixed partition with a finite number of elements in ℝ², but which has an arbitrarily large number of ergodic, absolutely continuous invariant measures     

Algebraic composition operators

The focus of this paper is on the following problem. Given a linear space F of complex-valued functions on a set X and a polynomial p(z), is there an algebraic composition operator on F whose characteristic polynomial equals p(z)? We show that the supply of all the polynomials p(z) for which the answer to this question is affirmative depends heavily on the structure of the space F.     

Catalytic partial oxidation of methane using RhSr- and Ni-substituted hexaaluminates

This paper reports the results of experimental and modeling efforts to characterize partial oxidation of methane to produce synthesis gas (H₂ and CO) using metal-substituted hexaaluminate catalysts in short-contact-time reactors. Hexaaluminate catalysts offer excellent high-temperature stability compared to the equivalent metal-based catalysts. The hexaaluminates are synthesized by a metal-exchange process using alumoxane precursors that enable a wide range of metal substitutions. Of all the combinations tested, RhSr-substituted hexaaluminates yielded the best performance. The catalysts are supported on alumina porous-foam structures, which are positioned within a tube furnace to control the operating temperature. Two-stage combinations of RhSr- and Ni-substituted hexaaluminates are shown to improve conversion activity and selectivity compared to a single-catalyst system.