On a P\'olya functional for rhombi, isosceles triangles, and thinning convex sets

Let $\Omega$ be an open convex set in ${\mathbb R}^m$ with finite width, and let $v_{\Omega}$ be the torsion function for $\Omega$, i.e. the solution of $-\Delta v=1, v\in H_0^1(\Omega)$. An upper bound is obtained for the product of $\Vert v_{\Omega}\Vert_{L^{\infty}(\Omega)}\lambda(\Omega)$, where $\lambda(\Omega)$ is the bottom of the spectrum of the Dirichlet Laplacian acting in $L^2(\Omega)$. The upper bound is sharp in the limit of a thinning sequence of convex sets. For planar rhombi and isosceles triangles with area $1$, it is shown that $\Vert v_{\Omega}\Vert_{L^{1}(\Omega)}\lambda(\Omega)\ge \frac{\pi^2}{24}$, and that this bound is sharp.Comment: 12 pages, 4 figure

Car-to-cyclist accidents from the car driver's point of view

A promising approach to prevent road traffic accidents between passenger cars and cyclists is the development of driver assistance systems. To develop such systems with maximum ef-fectiveness in road traffic, car-to-cyclist accidents have to be analysed from the car driver’s point of view to gain insight into the situations with which the drivers were faced and espe-cially why they failed to manage these crash situations. The EU funded project PROSPECT (Proactive Safety for Pedestrians and Cyclists) considered this approach and made the pre-sented research possible. This paper reports findings from a case-by-case analysis of 3,550 car-to-cyclist accidents in Germany. The results of the accident analysis confirm findings of previous studies showing that crossing scenarios play a predominant role in car-to-cyclist ac-cidents. Moreover, the results show that both the orientation of the cyclist and the driver’s task (in terms of the driver’s maneuver intention, road layout, traffic regulations) have an in-fluence on the distribution of those scenarios in so far as certain combinations lead to a higher or lower distribution. The results contribute towards a better understanding of possi-ble reasons why the driver failed to manage certain situations. Regarding PROSPECT, the most relevant use cases will be used to specify and develop advanced measures that will be implemented in the next generation of active safety systems

Axial Torsion-Dirac spin Effect in Rotating Frame with Relativistic Factor

In the framework of spacetime with torsion and without curvature, the Dirac particle spin precession in the rotational system is studied. We write out the equivalent tetrad of rotating frame, in the polar coordinate system, through considering the relativistic factor, and the resultant equivalent metric is a flat Minkowski one. The obtained rotation-spin coupling formula can be applied to the high speed rotating case, which is consistent with the expectation.Comment: 6 page

Multi-transmission-line-beam interactive system

We construct here a Lagrangian field formulation for a system consisting of an electron beam interacting with a slow-wave structure modeled by a possibly non-uniform multiple transmission line (MTL). In the case of a single line we recover the linear model of a traveling wave tube (TWT) due to J.R. Pierce. Since a properly chosen MTL can approximate a real waveguide structure with any desired accuracy, the proposed model can be used in particular for design optimization. Furthermore, the Lagrangian formulation provides for: (i) a clear identification of the mathematical source of amplification, (ii) exact expressions for the conserved energy and its flux distributions obtained from the Noether theorem. In the case of uniform MTLs we carry out an exhaustive analysis of eigenmodes and find sharp conditions on the parameters of the system to provide for amplifying regimes

Torsion Gravity: a Reappraisal

The role played by torsion in gravitation is critically reviewed. After a description of the problems and controversies involving the physics of torsion, a comprehensive presentation of the teleparallel equivalent of general relativity is made. According to this theory, curvature and torsion are alternative ways of describing the gravitational field, and consequently related to the same degrees of freedom of gravity. However, more general gravity theories, like for example Einstein-Cartan and gauge theories for the Poincare and the affine groups, consider curvature and torsion as representing independent degrees of freedom. By using an active version of the strong equivalence principle, a possible solution to this conceptual question is reviewed. This solution favors ultimately the teleparallel point of view, and consequently the completeness of general relativity. A discussion of the consequences for gravitation is presented.Comment: RevTeX, 34 pages. Review article to be published by Int. J. Mod. Phys.

An Innovative Therapeutic Option for the Treatment of Skeletal Sarcomas: Elimination of Osteo- and Ewing’s Sarcoma Cells Using Physical Gas Plasma

Osteosarcoma and Ewing’s sarcoma are the most common malignant bone tumors. Conventional therapies such as polychemotherapy, local surgery, and radiotherapy improve the clinical outcome for patients. However, they are accompanied by acute and chronic side effects that affect the quality of life of patients, motivating novel research lines on therapeutic options for the treatment of sarcomas. Previous experimental work with physical plasma operated at body temperature (cold atmospheric plasma, CAP) demonstrated anti-oncogenic effects on different cancer cell types. This study investigated the anti-cancer effect of CAP on two bone sarcoma entities, osteosarcoma and Ewing’s sarcoma, which were represented by four cell lines (U2-OS, MNNG/HOS, A673, and RD-ES). A time-dependent anti-proliferative effect of CAP on all cell lines was observed. CAP-induced alterations in cell membrane functionality were detected by performing a fluorescein diacetate (FDA) release assay and an ATP release assay. Additionally, modifications of the cell membrane and modifications in the actin cytoskeleton composition were examined using fluorescence microscopy monitoring dextran-uptake assay and G-/F-actin distribution. Furthermore, the CAP-induced induction of apoptosis was determined by TUNEL and active caspases assays. The observations suggest that a single CAP treatment of bone sarcoma cells may have significant anti-oncogenic effects and thus may be a promising extension to existing applications. © 2020 by the authors. Licensee MDPI, Basel, Switzerland