Funktionen mit Stammfunktion

The aim of this note is to analyze the class \(St[a,b]\) of all real functions on \([a,b]\) with primitive with respect to its size and its relations to other function classes. Apart from recalling previously known results and discussing new results we put a particular emphasis on examples and counterexamples.     

Comparing predator–prey models with hidden and explicit resources

In this paper two mathematical models are proposed and analyzed to elucidate the influence on a generalist predator of its hidden and explicit resources. Boundedness of the system’s trajectories, feasibility, local and global stability of the equilibria for both models are established, as well as possible local bifurcations. The findings indicate that the relevant behaviour of the system, including switching of stability, extinction and persistence of the involved populations, depends mainly on the reproduction rate of the favorite prey. To achieve full ecosystem survival some balance between the respective grazing pressures exerted by the predator on the prey populations needs to be maintained, while higher grazing pressure just on one species always leads to its extinction.     

The Elekes–Szabó Theorem in four dimensions

Let F ∈ C[x, y, s, t] be an irreducible constant-degree polynomial, and let A,B,C,D ? C be finite sets of size n. We show that F vanishes on at most O(n^8/3) points of the Cartesian product A × B × C × D, unless F has a special group-related form. A similar statement holds for A,B,C,D of unequal sizes, with a suitably modified bound on the number of zeros. This is a four-dimensional extension of our recent improved analysis of the original Elekes–Szabó theorem in three dimensions. We give three applications: an expansion bound for three-variable real polynomials that do not have a special form, a bound on the number of coplanar quadruples on a space curve that is neither planar nor quartic, and a bound on the number of four-point circles on a plane curve that has degree at least five.     

Exponential stability of simultaneously triangularizable switched systems with explicit calculation of a common Lyapunov function

In this note, a common quadratic Lyapunov function is explicitly calculated for a linear hybrid system described by a family of simultaneously triangularizable matrices. The explicit construction of such a function allows not only obtaining an estimate of the convergence rate of the exponential stability of the switched system under arbitrary switching but also calculating an upper bound for the output during its transient response. Furthermore, the presented result is then extended to the case where the system is affected by parametric uncertainty, providing the corresponding results in terms of the nominal matrices and uncertainty bounds.     

Formation of Si-nanoparticles in a microwave reactor: Comparison between experiments and modelling

The formation and growth of silicon-nanoparticles from silane in a microwave reactor was investigated. Experiments were performed for the following conditions: precursor concentration 380–2530 ppm, pressures of 20–30 mbar, microwave powers 120–300 W. The formed particles were examined in-situ with a particle mass spectrometer. Additionally, particles were collected on grids and analyzed by transmission electron microscopy, X-ray diffraction, and by determining the specific surface area by BET. The particle size was found to be in the range of 5–8 nm in diameter. A simple model was used to simulate the particle formation processes taking place inside the reactor. The microwave energy coupled into the reactor flow was treated as a spatially distributed energy source resulting in a local temperature increase. The particles were assumed to have a monodisperse size distribution. To allow an approximation of their shape they were characterized by their volume and surface area. The model takes nucleation, convection, coagulation, and coalescence into account. The fluid flow inside the microwave reactor was simulated with the commercial CFD-code Fluent.     

Suppressing decoherence of quantum algorithms by jump codes

The stabilizing properties of one-error correcting jump codes are explored under the realistic non-ideal condition of finite recovery times. For this purpose the quantum algorithm of the tent-map is decomposed into a universal set of Hamiltonian quantum gates which ensure perfect correction of spontaneous decay processes under ideal circumstances even if they occur during a gate operation. An entanglement gate is presented which is capable of entangling any two logical qubits of different one-error correcting code spaces. With the help of this gate simultaneous spontaneous decay processes affecting physical qubits of different code spaces can be corrected and decoherence can be suppressed significantly.     

Receiving beam patterns in the horizontal plane of a harbor porpoise (Phocoena phocoena)

Receiving beam patterns of a harbor porpoise were measured in the horizontal plane, using narrow-band frequency modulated signals with center frequencies of 16, 64, and 100 kHz. Total signal duration was 1000 ms, including a 200 ms rise time and 300 ms fall time. The harbor porpoise was trained to participate in a psychophysical test and stationed itself horizontally in a specific direction in the center of a 16-m-diameter circle consisting of 16 equally-spaced underwater transducers. The animal's head and the transducers were in the same horizontal plane, 1.5 m below the water surface. The go/no-go response paradigm was used; the animal left the listening station when it heard a sound signal. The method of constants was applied. For each transducer the 50% detection threshold amplitude was determined in 16 trials per amplitude, for each of the three frequencies. The beam patterns were not symmetrical with respect to the midline of the animal's body, but had a deflection of 3-7 degrees to the right. The receiving beam pattern narrowed with increasing frequency. Assuming that the pattern is rotation-symmetrical according to an average of the horizontal beam pattern halves, the receiving directivity indices are 4.3 at 16 kHz, 6.0 at 64 kHz, and 11.7 dB at 100 kHz. The receiving directivity indices of the porpoise were lower than those measured for bottlenose dolphins. This means that harbor porpoises have wider receiving beam patterns than bottlenose dolphins for the same frequencies. Directivity of hearing improves the signal-to-noise ratio and thus is a tool for a better detection of certain signals in a given ambient noise condition.     

Effect of spermine and DNase on DNA release from bacteriophage T5

Bacterial viruses (bacteriophages) consist of nucleic acid protected by a protein envelope called capsid. At the start of infection, the phage genome is translocated into the bacterial cytoplasm. In vitro (and also in vivo), this DNA release can be triggered by binding a specific receptor protein to the phage tail. The force responsible for the release arises from energy stored in the capsid due to strong confinement of the DNA. We show that this force can be modified by adding molecules like spermine that affect DNA conformation. The tetravalent cation spermine can reduce the pressure inside the capsid and induce condensation of the released DNA. We examine the effect of spermine on DNA ejection from phage T5 by using light scattering and gel electrophoresis to measure the amount of DNA remaining in the capsid at the end of ejection. We discuss the results in terms of free energy minimization and we demonstrate that the presence of a DNA condensate outside the phage generates an additional force pulling passively on the DNA remaining inside the capsid.     

Impedance spectroscopy study of the sintering of yttria-stabilized zirconia/magnesia composites

In the present study, the sintering of (ZrO₂:8 mol%Y₂O₃)_1 ? m–(MgO)_m, YSZ–mMg composites, with m in the 0–30 mol% range, has been investigated by impedance spectroscopy (IS), dilatometry, and X-ray diffraction. Impedance diagrams were collected at 400 °C after heating the green compacts up to a selected sintering temperature, which was increased stepwise from 800 to 1400 °C. The combined experimental results revealed that the samples can be separated in two categories: below and above the solubility limit of MgO in the YSZ (m ~ 10). Moreover, important microstructural features associated with both the sintering process and solid solution formation of YSZ–mMgO samples were correlated to the electrical properties inferred by IS.