On the distribution of sequences of the form (qny)(q_ny)

We study the distribution of sequences of the form $(q_ny)_{n=1}^\infty$, where $(q_n)_{n=1}^\infty$ is some increasing sequence of integers. In particular, we study the Lebesgue measure and find bounds on the Hausdorff dimension of the set of points $\gamma \in [0,1)$ which are well approximated by points in the sequence $(q_ny)_{n=1}^\infty$. The bounds on Hausdorff dimension are valid for almost every $y$ in the support of a measure of positive Fourier dimension. When the required rate of approximation is very good or if our sequence is sufficiently rapidly growing, our dimension bounds are sharp. If the measure of positive Fourier dimension is itself Lebesgue measure, our measure bounds are also sharp for a very large class of sequences. We also give an application to inhomogeneous Littlewood type problems.Comment: 15 pages. Niclas Technau pointed out to us that Theorems 1 and 2 in the original version were in fact consequences of arXiv:2307.14871 . In this revised version, we have strengthened both theorems to cover a wider class of sequence

Sensory quality of organic milk based on grazing and high ratio of legumes in the feeding ration

Organic milk forms an important segment of the fresh milk production in Denmark. However, studies are needed to substantiate the high quality and future development of new variations of organic milk for different consumers. Differences in the composition of organically and conventionally produced milk (free fatty acids and a higher content of antioxidants in organic milk) are suggested to be a result of differences in feeding regimes (maize components in conventional production vs. grass and legumes in organic production). Also, milk from dairy cows fed grass silage has a different flavour compared to milk from dairy cows fed maize silage. This study evaluated the sensory properties of organic milk from dairy cows from different feeding trials. The effect of four different legumes and herbs, lucerne (Medicargo sativa), red clover (Trifolium pratense), white clover (Trifolium repens) and chicory (Cichorium intybus), was studied following a schedule including 4*12 Holstein Frisian cows. Descriptive sensory analysis was performed on the fresh pasteurized unhomogenized full-fat milk (6 replicates in 2 sessions) with a trained panel of 10 assessors. The preliminary results from the descriptive analysis of summer feeding (grazing) and winter feeding (silage) show that feeding with legumes and grass affects the sensory quality of full-fat unhomogenized organic milk. The most distinct milk was obtained from feeding ration high in chicory. This milk was characterized by a bitter and metallic taste and an astringent aftertaste both from the summer grazing and winter silage feeding trials. Red clover was characterized by a boiled milk flavour (summer), lucerne by a fatty aftertaste (winter) and white clover by a sweet and creamy flavour (winter). The results of the first season, which will also include relations between the sensory quality and the milk composition, serve as important inputs for the extensive studies to be conducted during the next three seasons. These studies include farm studies and consumer studies (product information, preference and purchase motives)

Catch Crops in Organic Farming Systems without Livestock Husbandry - Model Simulations

During the last years, an increasing number of stockless farms in Europe converted to organic farming practice without re-establishing a livestock. Due to the lack of animal manure as a nutrient input, the relocation and the external input of nutrients is limited in those organic cropping systems. The introduction of a one-year green manure fallow in a 4-year crop rotation, including clover-grass mixtures as a green manure crop is the classical strategy to solve at least some of the problems related to the missing livestock. The development of new crop rotations, including an extended use of catch crops and annual green manure (legumes) may be another possibility avoiding the economical loss during the fallow year. Modelling of the C and N turnover in the soil-plant-atmosphere system using the soil-plant-atmosphere model DAISY is one of the tools used for the development of new organic crop rotations. In this paper, we will present simulations based on a field experiment with incorporation of different catch crops. An important factor for the development of new crop rotations for stockless organic farming systems is the expected N mineralisation and immobilisation after incorporation of the plant materials. Therefore, special emphasise will be put on the simulation of N-mineralisation/-immobilisation and of soil microbial biomass N. Furthermore, particulate organic matter C and N as an indicator of remaining plant material under decomposition will be investigated

Motor Performance as Risk Factor for Lower Extremity Injuries in Children

Purpose: Physical activity related injuries in children constitute a costly public health matter. The influence of motor performance on injury risk is unclear. The purpose was to examine if motor performance was a risk factor of traumatic and overuse lower extremity injuries in a normal population of children. Methods: This study included 1244 participants from 8 to 14-years-old at baseline, all participating in "the Childhood Health, Activity and Motor Performance School Study Denmark". The follow-up period was up to 15 months. The motor performance tests were static balance, single leg hop for distance, core stability tests, vertical jump, shuttle run, and a cardiorespiratory fitness test. Lower extremity injuries were registered by clinicians by weekly questionnaires and classified according to the ICD-10 system. Results: Poor balance increased risk for traumatic injury in the foot region (IRR=1.09-1.15), and good performance in single leg hop for distance protected against traumatic knee injuries (IRR=0.66-0.68). Good performance in core stability tests and vertical jump increased the risk for traumatic injuries in the foot region (IRR=1.12-1.16). Poor balance increased the risk for overuse injuries in the foot region (IRR=1.65), as did good performance in core stability tests and shuttle run, especially for knee injuries (IRR=1.07-1.18). Conclusions: Poor balance (sway) performance was a consistent predictor of traumatic injuries, in particular for traumatic ankle injuries. Good motor performance (core stability, vertical jump, shuttle run) was positively associated with traumatic and overuse injuries, and negatively (single leg hop) associated with traumatic injuries, indicating different influence on injury risk. Previous injury was a confounder affecting the effect size and the significance. More studies are needed to consolidate the findings, to clarify the influence of different performance tests on different types of injuries and to examine the influence of behaviour in relation to injury ris

Rotational properties of dipolar Bose-Einstein condensates confined in anisotropic harmonic potentials

We study the rotational properties of a dipolar Bose-Einstein condensate confined in a quasi-two- dimensional anisotropic trap, for an arbitrary orientation of the dipoles with respect to their plane of motion. Within the mean-field approximation we find that the lowest-energy state of the system depends strongly on the relative strength between the dipolar and the contact interactions, as well as on the size and the orientation of the dipoles, and the size and the orientation of the deformation of the trapping potential.Comment: 6 pages, 5 figure

[OI]63micron jets in class 0 sources detected by Herschel

We present Herschel PACS mapping observations of the [OI]63 micron line towards protostellar outflows in the L1448, NGC1333-IRAS4, HH46, BHR71 and VLA1623 star forming regions. We detect emission spatially resolved along the outflow direction, which can be associated with a low excitation atomic jet. In the L1448-C, HH46 IRS and BHR71 IRS1 outflows this emission is kinematically resolved into blue- and red-shifted jet lobes, having radial velocities up to 200 km/s. In the L1448-C atomic jet the velocity increases with the distance from the protostar, similarly to what observed in the SiO jet associated with this source. This suggests that [OI] and molecular gas are kinematically connected and that this latter could represent the colder cocoon of a jet at higher excitation. Mass flux rates (\.M$_{jet}$(OI)) have been measured from the [OI]63micron luminosity adopting two independent methods. We find values in the range 1-4 10$^{-7}$ Mo/yr for all sources but HH46, for which an order of magnitude higher value is estimated. \.M$_{jet}$(OI) are compared with mass accretion rates (\.M$_{acc}$) onto the protostar and with \.M$_{jet}$ derived from ground-based CO observations. \.M$_{jet}$(OI)/\.M$_{acc}$ ratios are in the range 0.05-0.5, similar to the values for more evolved sources. \.M$_{jet}$(OI) in HH46 IRS and IRAS4A are comparable to \.M$_{jet}$(CO), while those of the remaining sources are significantly lower than the corresponding \.M$_{jet}$(CO). We speculate that for these three sources most of the mass flux is carried out by a molecular jet, while the warm atomic gas does not significantly contribute to the dynamics of the system.Comment: 37 pages and 12 figures, accepted for publication on Astrophysical Journa