Tweets to a Young 1L

A series of eleven tweets ruminating about the author\u27s law school experience received a positive and enthusiastic response from many lawyers, law professors, and law students, and ultimately caught the eye of one of the Green Bag’s editors. This short piece unpacks and contextualizes those tweets. The original tweets appear below, numbered as they first appeared on Twitter

The tropical shadow-vertex algorithm solves mean payoff games in polynomial time on average

We introduce an algorithm which solves mean payoff games in polynomial time on average, assuming the distribution of the games satisfies a flip invariance property on the set of actions associated with every state. The algorithm is a tropical analogue of the shadow-vertex simplex algorithm, which solves mean payoff games via linear feasibility problems over the tropical semiring $(\mathbb{R} \cup \{-\infty\}, \max, +)$. The key ingredient in our approach is that the shadow-vertex pivoting rule can be transferred to tropical polyhedra, and that its computation reduces to optimal assignment problems through Pl\"ucker relations.Comment: 17 pages, 7 figures, appears in 41st International Colloquium, ICALP 2014, Copenhagen, Denmark, July 8-11, 2014, Proceedings, Part

Generation of small-scale structures in the developed turbulence

The Navier-Stokes equation for incompressible liquid is considered in the limit of infinitely large Reynolds number. It is assumed that the flow instability leads to generation of steady-state large-scale pulsations. The excitation and evolution of the small-scale turbulence is investigated. It is shown that the developed small-scale pulsations are intermittent. The maximal amplitude of the vorticity fluctuations is reached along the vortex filaments. Basing on the obtained solution, the pair correlation function in the limit $r\to 0$ is calculated. It is shown that the function obeys the Kolmogorov law $r^{2/3}$.Comment: 18 page

On the Rational Type 0f Moment Angle Complexes

In this note it is shown that the moment angle complexes Z(K;(D^2,,S^1)) which are rationally elliptic are a product of odd spheres and a diskComment: This version avoids the use of an incorrect result from the literature in the proof of Theorem 1.3. There is some text overlap with arXiv:1410.645

A non-linear optimal estimation inverse method for radio occultation measurements of temperature, humidity and surface pressure

An optimal estimation inverse method is presented which can be used to retrieve simultaneously vertical profiles of temperature and specific humidity, in addition to surface pressure, from satellite-to-satellite radio occultation observations of the Earth's atmosphere. The method is a non-linear, maximum {\it a posteriori} technique which can accommodate most aspects of the real radio occultation problem and is found to be stable and to converge rapidly in most cases. The optimal estimation inverse method has two distinct advantages over the analytic inverse method in that it accounts for some of the effects of horizontal gradients and is able to retrieve optimally temperature and humidity simultaneously from the observations. It is also able to account for observation noise and other sources of error. Combined, these advantages ensure a realistic retrieval of atmospheric quantities. A complete error analysis emerges naturally from the optimal estimation theory, allowing a full characterisation of the solution. Using this analysis a quality control scheme is implemented which allows anomalous retrieval conditions to be recognised and removed, thus preventing gross retrieval errors. The inverse method presented in this paper has been implemented for bending angle measurements derived from GPS/MET radio occultation observations of the Earth. Preliminary results from simulated data suggest that these observations have the potential to improve NWP model analyses significantly throughout their vertical range.Comment: 18 (jgr journal) pages, 7 figure

Manifestation of systemic toxicity in rats after a short-time inhalation of lead oxide nanoparticles

Outbred female rats were exposed to inhalation of lead oxide nanoparticle aerosol produced right then and there at a concentration of 1.30 ± 0.10 mg/m3 during 5 days for 4 h a day in a nose-only setup. A control group of rats were sham-exposed in parallel under similar conditions. Even this short-time exposure of a relatively low level was associated with nanoparticles retention demonstrable by transmission electron microscopy in the lungs and the olfactory brain. Some impairments were found in the organism’s status in the exposed group, some of which might be considered lead-specific toxicological outcomes (in particular, increase in reticulocytes proportion, in δ-aminolevulinic acid (δ-ALA) urine excretion, and the arterial hypertension’s development). © 2020 by the authors. Licensee MDPI, Basel, Switzerland.Funding: This work was funded by the budget of the Ekaterinburg Medical Research Center for Prophylaxis and Health Protection in Industrial Workers

Thermodynamic aspects of materials' hardness: prediction of novel superhard high-pressure phases

In the present work we have proposed the method that allows one to easily estimate hardness and bulk modulus of known or hypothetical solid phases from the data on Gibbs energy of atomization of the elements and corresponding covalent radii. It has been shown that hardness and bulk moduli of compounds strongly correlate with their thermodynamic and structural properties. The proposed method may be used for a large number of compounds with various types of chemical bonding and structures; moreover, the temperature dependence of hardness may be calculated, that has been performed for diamond and cubic boron nitride. The correctness of this approach has been shown for the recently synthesized superhard diamond-like BC5. It has been predicted that the hypothetical forms of B2O3, diamond-like boron, BCx and COx, which could be synthesized at high pressures and temperatures, should have extreme hardness