The current work aims to develop an approximation of the slice of Minkowski sum of finite number of ellipsoids, sliced up by an arbitrarily oriented plane in Euclidean space $\mathbb{R}^3$ that, to the best of the author's knowledge, has not been addressed yet. This approximation of the actual slice is in a closed form of an explicit parametric equation in the case that the slice is not passing through those zones of the Minkowski surface with high curvatures, namely the "corners". At corners with high curvatures an alternative computational algorithm is introduced in which a family of ellipsoidal inner and outer bounds of the Minkowski's sum are used to construct a "narrow strip" for the actual slice of Minkowski sum. This strip can narrow persistently for a few more number of constructing bounds to precisely coincide on the actual slice of Minkowski sum. This algorithm is also applicable to the cases of slice of Minkowski sum of ellipsoids with high aspect ratio. In line with the main goal, some ellipsoidal inner and outer bounds of the Minkowski sum are reviewed, including the so called "Kurzhanski's" bounds. Also some ellipsoidal approximations are suggested for the Minkowski sum, which they can be used, as well as the inner and outer bounds, in calculation of the suggested parametric approximation of the slice of Minkowski sum.

Recently the number of studies investigating triterpenoid saponins has drastically increased due to their diverse and potentially attractive biological activities. Currently the literature contains chemical structures of few hundreds of triterpenoid saponins of plant and animal origin. Triterpenoid saponins consist of a triterpene aglycone with one or more sugar moieties attached to it. However, due to similar physico-chemical properties, isolation and identification of a large diversity of triterpenoid saponins remain challenging. This study demonstrates a methodology to screen saponins using hyphenated analytical platforms, GC-MS, LC-MS/MS, and LC-SPE-NMR/MS, in the example of two different phenotypes of the model plant Barbarea vulgaris (winter cress), glabrous (G) and pubescent (P) type that are known to differ by their insect resistance. The proposed methodology allows for detailed comparison of saponin profiles from intact plant extracts as well as saponin aglycone profiles from hydrolysed samples. Continuously measured 1D proton NMR data during LC separation along with mass spectrometry data revealed significant differences, including contents of saponins, types of aglycones and numbers of sugar moieties attached to the aglycone. A total of 49 peaks were tentatively identified as saponins from both plants; they are derived from eight types of aglycones and with 2–5 sugar moieties. Identification of two previously known insect-deterrent saponins, hederagenin cellobioside and oleanolic acid cellobioside, demonstrated the applicability of the methodology for relatively rapid screening of bioactive compounds.

Clinical and pre-clinical studies of neuropsychiatric (NP) disorders show altered astrocyte properties and synaptic networks. These are refined during early postnatal developmental (PND) stages. Thus, investigating early brain maturational trajectories is essential to understand NP disorders. However, animal experiments are highly time-/resource-consuming, thereby calling for alternative methodological approaches. The function of MEGF10 in astrocyte-mediated synapse elimination (pruning) is crucial to refine neuronal networks during development and adulthood. To investigate the impact of MEGF10 during PND in the rat prefrontal cortex (PFC) and its putative role in brain disorders, we established and validated an Organotypic Brain Slice Culture (OBSC) system.Using Western blot, we characterized the expression of MEGF10 and the synaptic markers synaptophysin and PSD95 in the cortex of developing pups. We then combined immunofluorescent-immunohistochemistry with Imaris-supported 3D-analysis to compare age- and sex-dependent astrocyte-mediated pruning within the PFC in pups and OBSCs. We thereby validated this system to investigate age-dependent astrocyte-mediated changes in pruning during PND. However, further optimizations are required to use OBSCs for revealing sex-dependent differences. In conclusion, OBSCs offer a valid alternative to study physiological astrocyte-mediated synaptic remodelling during PND and might be exploited to investigate pathomechanisms of brain disorders with aberrant synaptic development.

In metal continuous casting process is important to estimate the temperature evolution of casted section along machine from meniscus (point in which liquid metal is poured) to cutting machine where product is cut at commercial length. Particularly in the case of large sections, a convenient approximated model to achieve this goal with a feasible computational effort, is the so called travelling slice: the transversal section of casted product is subjected to different thermal boundary conditions (e.g. thermal flux, radiation, convection) that are found during the movement at constant speed from meniscus to the end of machine. In the case of an axisymmetric section, a comparison with the exact solution can be easily achieved. The article will show pros and cons of both, namely the far lower computational cost of travelling slice model without losing precision. Results confirm the validity of the travelling slice approach also at low casting speed and huge dimensions.

The load on the top of a slope is an important cause of slope failure, and it is of great significance to study the relationship between the load and the stability of the slope. This paper uses elastic theory and Moore Coulomb's theory as transformation conditions to obtain the slope stability coefficient expression under slope top load based on the Swedish slice method. In view of the actual engineering, the corresponding slope model structure was established, and 5 sliding surfaces were set with the crack on the top of the slope as the shear outlet. According to the slope stability coefficient expression, the stability coefficient of the set sliding surface is solved. The result shows that the slope is unstable under the load. The judgment result is consistent with the GEO-STUDIO check calculation result. This method can provide reference for theory and engineering practice.

Let b∈Cn∖{0} be a fixed direction. We consider slice holomorphic functions of several complex variables in the unit ball, i.e. we study functions which are analytic in intersection of every slice {z0+tb:t∈C} with the unit ball Bn={z∈C:|z|:=|z|12+…+|zn|2<1} for any z0∈Bn. For this class of functions there is introduced a concept of boundedness of L-index in the direction b where L:Bn→R+ is a positive continuous function such that L(z)>β|b|1−|z|, where β>1 is some constant. For functions from this class we describe local behavior of modulus of directional derivatives on every ’circle’ {z+tb:|t|=r/L(z)} with r∈(0;β],t∈C,z∈Cn. It is estimated by value of the function at center of the circle. Other propositions concern a connection between boundedness of L-index in the direction b of the slice holomorphic function F and boundedness of lz-index of the slice function gz(t)=F(z+tb) with lz(t)=L(z+tb). Also we show that every slice holomorphic and joint continuous function in the unit ball has bounded L-index in direction in any domain compactly embedded in the unit ball and for any continuous function L:Bn→R+.