Maximal inequalities for fractional L\'evy and related processes

In this paper we study processes which are constructed by a convolution of a deterministic kernel with a martingale. A special emphasis is put on the case where the driving martingale is a centred L\'evy process, which covers the popular class of fractional L\'evy processes. As a main result we show that, under appropriate assumptions on the kernel and the martingale, the maximum process of the corresponding `convoluted martingale' is $p$-integrable and we derive maximal inequalities in terms of the kernel and of the moments of the driving martingale

Tree Felling with a Drill Cone

Motor-manual timber felling is one of the most dangerous operations in the forest and cannot be completely replaced by fully mechanized timber harvesting by a harvester when dealing with large and deciduous trees. Shifting the center of gravity of tree ready to be felled beyond its tipping line using conventional felling wedges is dangerous because the forest worker is directly behind the stem and under the tree crown until just before the tree falls. The worker can be hit by the trunk itself, but also by falling parts of the crown. In a preliminary study for the development of a new type of felling head, felling with a drill cone that can open the felling cut with the help of an applied torque was investigated. A drill cone does not require any special cutting technique, no counter forces to the tree, works without impulses, it is self-retaining and can be unscrewed again. In order to determine the torque required for felling the tree as a function of the tree parameters, the mathematical equation framework was established and practical experiments were used to determine the friction parameters and verify the calculations. The torque of the drill cone is used to bend the intact fibers of the hinge, shift the center of gravity of the tree in the direction of fall, and to overcome the friction of the drill cone on the felling cut. The effects of forward or backward leaning trees on the required torque can also be quantified. It has been shown that the efficiency of a drill cone is low, but this is compensated for by the high internal torque to lift ratio. The maximum measured input torque for felling trees with a felling diameter up to 55 centimeter was 100 Nm

Assessment of 3D velocity vector fields and turbulent kinetic energy in a realistic aortic phantom using multi-point variable-density velocity encoding

ISSN:1097-6647ISSN:1532-429

Bragg diffraction of large organic molecules

We demonstrate Bragg diffraction of the antibiotic ciprofloxacin and the dye molecule phthalocyanine at a thick optical grating. The observed patterns show a single dominant diffraction order with the expected dependence on the incidence angle as well as oscillating population transfer between the undiffracted and diffracted beams. We achieve an equal-amplitude splitting of $14 \hbar k$ (photon momenta) and maximum momentum transfer of $18 \hbar k$. This paves the way for efficient, large-momentum beam splitters and mirrors for hot and complex molecules.Comment: 8 pages, 7 figures (including Supplemental Material). Corrected errors in bibliograph

Assessment of energy loss across aortic valves using accelerated CMR multi-point flow measurements

ISSN:1097-6647ISSN:1532-429

Single-, double-, and triple-slit diffraction of molecular matter waves

Even 100 years after its introduction by Louis de Broglie, the wave-nature of matter is often regarded as a mind-boggling phenomenon. To give an intuitive introduction to this field, we here discuss the diffraction of massive molecules through a single, a double, and a triple slit, as well as a nanomechanical grating. While the experiments are in good agreement with undergraduate textbook predictions, we also observe pronounced differences resulting from the molecules' mass and internal complexity. The molecules' polarizability causes an attractive van der Waals interaction with the slit walls, which can be modified by rotating the nanomechanical mask with respect to the molecular beam. The text is meant to introduce students and teachers to the concepts of molecule diffraction, supported by problems and solutions that can be discussed in class