Existence of solutions to a higher dimensional mean-field equation on manifolds

For $m\geq 1$ we prove an existence result for the equation $$(-\Delta_g)^m u+\lambda=\lambda\frac{e^{2mu}}{\int_M e^{2mu}d\mu_g}$$ on a closed Riemannian manifold $(M,g)$ of dimension $2m$ for certain values of $\lambda$.Comment: 15 Page

Rolling-Tooth Core Breakoff and Retention Mechanism

Sampling cores requires the controlled breakoff of the core at a known location with respect to the drill end. An additional problem is designing a mechanism that can be implemented at a small scale that is robust and versatile enough to be used for a variety of core samples. This design consists of a set of tubes (a drill tube and an inner tube) and a rolling element (rolling tooth). An additional tube can be used as a sample tube. The drill tube and the inner tube have longitudinal holes with the axes offset from the axis of each tube. The two eccentricities are equal. The inner tube fits inside the drill tube, and the sample tube fits inside the inner tube. While drilling, the two tubes are positioned relative to each other such that the sample tube is aligned with the drill tube axis and core. The drill tube includes teeth and flutes for cuttings removal. The inner tube includes, at the base, the rolling element implemented as a wheel on a shaft in an eccentric slot. An additional slot in the inner tube and a pin in the drill tube limit the relative motion of the two tubes. While drilling, the drill assembly rotates relative to the core and forces the rolling tooth to stay hidden in the slot along the inner tube wall. When the drilling depth has been reached, the drill bit assembly is rotated in the opposite direction, and the rolling tooth is engaged and penetrates into the core. Depending on the strength of the created core, the rolling tooth can score, lock the inner tube relative to the core, start the eccentric motion of the inner tube, and break the core. The tooth and the relative position of the two tubes can act as a core catcher or core-retention mechanism as well. The design was made to fit the core and hole parameters produced by an existing bit; the parts were fabricated and a series of demonstration tests were performed. This invention is potentially applicable to sample return and in situ missions to planets such as Mars and Venus, to moons such as Titan and Europa, and to comets. It is also applicable to terrestrial applications like forensic sampling and geological sampling in the field

ESVM Guideline on peripheral arterial disease

International audienc

Properties of rf-sputtered indium-tin-oxynitride thin films

Indium-tin-oxide (ITO) and indium-tin-oxynitride (ITON) thin films have been fabricated by rf-sputtering in plasma containing Ar or a mixture of Ar and N-2, respectively. The structural, electrical and optical properties of ITON films were examined and compared with those of ITO films. The microstructure of ITON films was found to be dependent on the nitrogen concentration in the plasma. Increasing the amount of nitrogen in the plasma increased the resistivity and reduced the carrier concentration and mobility of the films. The electrical properties of the ITON films improved after annealing. The absorption edge of the ITON films deposited in pure N-2 plasma was shifted towards higher energies and showed reduced infrared reflectance compared to the respective properties of ITO films. The potential of indium-tin-oxynitride films for use as a transparent conductive material for optoelectronic devices is addressed

Existence theorems in the geometrically non-linear 6-parametric theory of elastic plates

In this paper we show the existence of global minimizers for the geometrically exact, non-linear equations of elastic plates, in the framework of the general 6-parametric shell theory. A characteristic feature of this model for shells is the appearance of two independent kinematic fields: the translation vector field and the rotation tensor field (representing in total 6 independent scalar kinematic variables). For isotropic plates, we prove the existence theorem by applying the direct methods of the calculus of variations. Then, we generalize our existence result to the case of anisotropic plates. We also present a detailed comparison with a previously established Cosserat plate model.Comment: 19 pages, 1 figur

Pan-cancer Alterations of the MYC Oncogene and Its Proximal Network across the Cancer Genome Atlas

Although theMYConcogene has been implicated incancer, a systematic assessment of alterations ofMYC, related transcription factors, and co-regulatoryproteins, forming the proximal MYC network (PMN),across human cancers is lacking. Using computa-tional approaches, we define genomic and proteo-mic features associated with MYC and the PMNacross the 33 cancers of The Cancer Genome Atlas.Pan-cancer, 28% of all samples had at least one ofthe MYC paralogs amplified. In contrast, the MYCantagonists MGA and MNT were the most frequentlymutated or deleted members, proposing a roleas tumor suppressors.MYCalterations were mutu-ally exclusive withPIK3CA,PTEN,APC,orBRAFalterations, suggesting that MYC is a distinct onco-genic driver. Expression analysis revealed MYC-associated pathways in tumor subtypes, such asimmune response and growth factor signaling; chro-matin, translation, and DNA replication/repair wereconserved pan-cancer. This analysis reveals insightsinto MYC biology and is a reference for biomarkersand therapeutics for cancers with alterations ofMYC or the PMN