Comparative Toxicity of Oil Spill Response Agents and Crude Oils to Five Species of Aquatic Test Species

The majority of aquatic toxicity data for petroleum products has been limited to a few intensively studied crude oils and Corexit chemical dispersants, and toxicity testing in two standard estuarine test species: mysids (Americamysis bahia) and inland silversides (Menidia beryllina). This study compared the toxicity of three chemical dispersants (Corexit EC9500A®, Finasol®OSR 52, Accell Clean®DWD), two less studied agents (CytoSol® surface washing agent; Gelco200® solidifier), and three crude oils differing in hydrocarbon composition (Dorado, Endicott, Alaska North Slope). Consistent with listings on the U.S. National Contingency Plan Product Schedule, general rank order toxicity was greatest for dispersants and lowest for the solidifier. The results indicate that freshwater species can have similar sensitivity as the conventionally tested mysids and silversides, and that the sea urchin (Arbacia punctulata) appears to be a reasonable addition to increase taxa diversity in standardized oil agent testing.

Onto extensions of free groups

An extension of subgroups $H\leqslant K\leqslant F_A$ of the free group of rank $|A|=r\geqslant 2$ is called onto when, for every ambient free basis $A'$, the Stallings graph $\Gamma_{A'}(K)$ is a quotient of $\Gamma_{A'}(H)$. Algebraic extensions are onto and the converse implication was conjectured by Miasnikov-Ventura-Weil, and resolved in the negative, first by Parzanchevski-Puder for rank $r=2$, and recently by Kolodner for general rank. In this note we study properties of this new type of extension among free groups (as well as the fully onto variant), and investigate their corresponding closure operators. Interestingly, the natural attempt for a dual notion -- into extensions -- becomes trivial, making a Takahasi type theorem not possible in this setting.

Laboratory indicators of pathological changes in patients with chronic heart failure with metabolic syndrome

The presence of metabolic syndrome (MS) significantly increases the risk of developing cardiovascular diseases that lead to chronic heart failure (CHF). The values of NT-proBNP, ST-2, and CRP markers and their mutual correlations were studied in 37 patients with chronic heart failure (CHF) without metabolic syndrome (MS) (group 1) and 37 patients with CHF with MS (group 2). The aim of the study was to determine the features of their changes in patients with CHF complicated by MS, and to rank patients by assigning a rank value to the values of NTproBNP, ST2, and CRP concentrations. The average ST2 level was 51±24 ng/ml in group 1 and 62±27 ng/ml in group 2. The average values of CRP in group 1 were 23.1±5.3 mg/l, in group 2-33.0±4.4 mg/l (p<0.05). The NTproBNP level was 2413±1586 PG/ml and 2721±1635 PG/ml in groups 1 and 2, respectively. Correlations between the values of NTproBNP and ST2, NTproBNP and CRP were demonstrated. In the group of CHF with MS, compared with the group of CHF, there were significantly more patients with the most pronounced pathological levels of damage markers: the number of patients with a General rank of 6-9 in the group of CHF with MS was 59%, in the group of CHF without MS-38% (p<0.05). Of the 18 patients who died, 17 were among those who had an overall rank of 6 to 9, only 1 patient who died after hospitalization had an overall rank of 5. At the same time, among 22 patients who had improved CHF in the outcome of hospitalization, 18 patients had a total rank from 0 to 5, and in 4 patients of this category, the clinical manifestations of CHF remained virtually unchanged. The results of ranking the level of the studied laboratory markers indicate that they can be used as a predictor of various outcomes of CHF.

THE UNIFORM OF A MINING ENGINEER FROM THE BURIAL OF THE FORMER NAGORNY CEMETERY OF BARNAUL

The study of materials obtained during emergency work on the territory of the former Nagorny cemetery in Barnaul in 2015-2016 continues. This article attempts to determine the rank of the official whose burial was discovered in the autumn of 2015. The identification is carried out by the uniform of dark blue cloth preserved on the remains of the official with full gold embroidery on the collar and cuffs, indicating that he belongs to the Mining Department and general rank. The work is complicated by the incomplete preservation of the uniform and numerous changes in the uniform of the officials of the Mining Department throughout the 19th century. In the future, when determining the specific rank and time of existence of a uniform of this cut, it is possible to establish a fairly reliable identity. The number of employees of this rank in Barnaul was insignificant. The record of the official’s death was to be preserved in the metrical registers of one of the city’s most important churches. Keywords: Barnaul, Nagorny cemetery, emergency work, study of finds, uniform of the mining department, departmental gold embroidery, establishment of the rank of the buried engineer

Fermi gas approach to general rank theories and quantum curves

It is known that matrix models computing the partition functions of three-dimensional $$ \mathcal{N} $$ N = 4 superconformal Chern-Simons theories described by circular quiver diagrams can be written as the partition functions of ideal Fermi gases when all the nodes have equal ranks. We extend this approach to rank deformed theories. The resulting matrix models factorize into factors depending only on the relative ranks in addition to the Fermi gas factors. We find that this factorization plays a critical role in showing the equality of the partition functions of dual theories related by the Hanany-Witten transition. Furthermore, we show that the inverses of the density matrices of the ideal Fermi gases can be simplified and regarded as quantum curves as in the case without rank deformations. We also comment on four nodes theories using our results.

Phase retrieval of low-rank matrices by anchored regression

We study the low-rank phase retrieval problem, where our goal is to recover a $d_1\times d_2$ low-rank matrix from a series of phaseless linear measurements. This is a fourth-order inverse problem, as we are trying to recover factors of a matrix that have been observed, indirectly, through some quadratic measurements. We propose a solution to this problem using the recently introduced technique of anchored regression. This approach uses two different types of convex relaxations: we replace the quadratic equality constraints for the phaseless measurements by a search over a polytope and enforce the rank constraint through nuclear norm regularization. The result is a convex program in the space of $d_1 \times d_2$ matrices. We analyze two specific scenarios. In the first, the target matrix is rank-$1$, and the observations are structured to correspond to a phaseless blind deconvolution. In the second, the target matrix has general rank, and we observe the magnitudes of the inner products against a series of independent Gaussian random matrices. In each of these problems, we show that anchored regression returns an accurate estimate from a near-optimal number of measurements given that we have access to an anchor matrix of sufficient quality. We also show how to create such an anchor in the phaseless blind deconvolution problem from an optimal number of measurements and present a partial result in this direction for the general rank problem.

Rank-Engel conditions on linear groups

We study linear groups G for which for every g in G there exists a subgroup E of G satisfying some sort of rank condition and such that for every x in G there is a positive integer m such that for all n ≥ m the repeated commutator [x, ng] lies in E. If E can always be chosen to be a Chernikov group (resp. a polycyclic-by-finite group) such G can be completely described (Wehrfritz in Adv Group Theory Appl 7:143–157, 2019; Wehrfritz in Boll Unione Mat Ital, to appear). For more general rank conditions our analyses below are complete for positive characteristics but are less so for characteristic zero.