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.     

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.     

Investigation of the photothermally modulated ferromagnetic resonance signal from magnetostatic modes in yttrium iron garnet films

The conventional and photothermally modulated (PM) ferromagnetic resonance (FMR) of magnetostatic modes (MSM) in yttrium iron garnet (YIG) films have been investigated as a function of temperature. Approaching the ferrimagnetic transition at T _c=560 K a strong enhancement of the PM-FMR signal amplitude is observed which is accompanied by a change of the signal shape. The observations are discussed in the framework of a model that takes into account the temperature derivatives of those quantities that contribute to the high-frequency susceptibility. At temperatures still below T _c a paramagnetic line emerges. The MSM disappear in a state of finite magnetization which is explained on the basis of damping of the MSM being important in the vicinity of the magnetic phase transition. Additionally, frequency and power dependent measurements are presented and the imaging ability of PM-FMR is demonstrated.     

On the Causes and Effects of Contaminations during rf Diode Deposition of Cr-Si Alloys

Investigations to the causes and effects of contaminants at the rf diode deposition of CrSi films in a non-heated high vacuum apparatus were carried out comparing an oxygen-free fusion target with an oxygen-containing cermet target. The films of the fusion target contained considerable amounts of oxygen; analogously the oxygen concentration in the films was increased in the case of the cermet target. Moreover, hydrogen was found. The concentration of the contaminants decreased with the sputtering power, however the rate of incorporation increased. For high sputtering rates the contamination process was reproducible and independent of the plant conditioning; the deposited films were depth-homogeneous. The reasons for this behaviour lie in water sources which are activated first of all by the discharge itself. The electrical properties found are explained by the contaminants and the deposition conditions.     

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.