CM points, class numbers, and the Mahler measures of x3+y3+1−kxyx^3+y^3+1-kxy

We study the Mahler measures of the polynomial family $Q_k(x,y) = x^3+y^3+1-kxy$ using the method previously developed by the authors. An algorithm is implemented to search for CM points with class numbers $\leqslant 3$, we employ these points to derive interesting formulas that link the Mahler measures of $Q_k(x,y)$ to $L$-values of modular forms. As a by-product, three conjectural identities of Samart are confirmed. For $k=\sqrt[3]{729\pm405\sqrt{3}}$, we also prove an equality that expresses a $2\times 2$ determinant with entries the Mahler measures of $Q_k(x,y)$ as some multiple of the $L$-value of two isogenous elliptic curves over $\mathbb{Q}(\sqrt{3})$.Comment: 17 pages, 2 tables. Comments are welcom

An Airfield Minimum Operating Strip Selection Method Based on the TOPSIS Method

With Multiple Attribute Decision Making (MADM) method, the selection of airfield Minimum Operating Strip (MOS) schemes is researched. The influencing factors of the selection decision making are analyzed. The weight values of these factors are determined. Then the decision making optimization method based on TOPSIS is presented. At last, the feasibility of the method is validated with a calculation example

Reliability Research of Power Distribution System For Important Units at the Airfield

Important power units at the airport are the direct units of aviation security, the reliability of power supply and distribution system directly affect the safety of it for aviation security. This paper analyzes the important units of electricity power supply system into the units of reliability. The basic reliability model and the mission reliability model are constructed respectively and the corresponding reliabilities are calculated. Then the paper studies on the relationship between two kinds of reliability as well as the influence on the reliability of power supply and distribution system, providing theoretical basis of planning, equipment selection, engineering design, reliable operation and maintenance management for important units of power supply system

Antibody Responses and the Effects of Clinical Drugs in COVID-19 Patients

The coronavirus disease 2019 (COVID-19) emerged around December 2019 and have become a global epidemic disease currently. Specific antibodies against SAS-COV-2 could be detected in COVID-19 patients’ serum or plasma, but the clinical values of these antibodies as well as the effects of clinical drugs on humoral responses have not been fully demonstrated. In this study, 112 plasma samples were collected from 36 patients diagnosed with laboratory-confirmed COVID-19 in the Fifth Affiliated Hospital of Sun Yat-sen University. The IgG and IgM antibodies against receptor binding domain (RBD) and spike protein subunit 1 (S1) of SAS-COV-2 were detected by ELISA. We found that COVID-19 patients generated specific antibodies against SARS-CoV-2 after infection, and the levels of anti-RBD IgG within 2 to 3 weeks from onset were negatively associated with the time of positive-to-negative conversion of SARS-CoV-2 nucleic acid. Patients with severe symptoms had higher levels of anti-RBD IgG in 2 to 3 weeks from onset. The use of chloroquine did not significantly influence the patients’ antibody titer but reduced C-reaction protein (CRP) level. Using anti-viral drugs (lopinavir/ritonavir or arbidol) reduced antibody titer and peripheral lymphocyte count. While glucocorticoid therapy developed lower levels of peripheral lymphocyte count and higher levels of CRP, lactate dehydrogenase (LDH), α-Hydroxybutyrate dehydrogenase(α-HBDH), total bilirubin (TBIL), direct bilirubin (DBIL). From these results, we suggested that the anti-RBD IgG may provide an early protection of host humoral responses against SAS-COV-2 infection within 2 to 3 weeks from onset, and clinical treatment with different drugs displayed distinct roles in humoral and inflammatory responses

Seismic Performance of CFRP-Retrofitted Large-Scale Square RC Columns with High Axial Compression Ratios

Numerous reinforced concrete frames have collapsed in major earthquakes because of severe local damage at the ends of columns. Many of these frames were designed and built according to out-of-date codes in which earthquake loads were either not taken into account or not sufficiently considered. To date, there are still a large number of such nonductile RC frames serving in the potential earthquake regions across the world. Thus, there is an urgent need for preearthquake retrofitting and strengthening of these RC frames to achieve desirable seismic performance. In this paper, a total of 11 large-scale cantilever square RC columns were constructed and nine of them were retrofitted with carbon fiber-reinforced polymers (CFRP) wraps at the column ends. These columns were then tested under combined constant axial compression and cyclic lateral displacement excursions. The variables in the tests included the axial compression ratio, the thickness of CFRP wraps, and the column size. The failure modes, hysteretic responses, energy dissipation, stiffness degradation, and equivalent viscous damping ratio of the tested columns were presented and interpreted. The test results showed that the ductility and energy dissipation capacities of nonductile RC columns can be significantly improved with the potential plastic hinge regions of the columns being retrofitted. The retrofitted columns were found to exhibit satisfactory seismic performance even when tested under an ultrahigh axial compression level (i.e., 0.75). Based on the test results, the degradation of the effective stiffness and the unloading stiffness of the columns was discussed and empirical equations were proposed through nonlinear regression analysis

Spermatophyte Flora Distribution in Hubei Daqi Mountain Nature Reserve

A basic ingredient analysis of flora and geographic elements of plant genera and families in Daqi Mountain Nature Reserve was conducted through the field survey and specimen collection, based on the system investigation of plant flora, and an R/T ratio comparison between the flora in Daqi Mountain and adjacent mountain floras was made. Plant taxonomy identification indicates that spermatophytes in the nature reserve comprises 1035 species of 534 genera, falling in 140families, of which 10 gymnosperm species of 8 genera fall in 5 families, while 1025 angiosperm species of 526 genera in 135 families. The analysis of flora demonstrates that the region harbors 15 flora distribution types, with high complexity, paleo-flora origin, distinct trait of temperate zone, abundant ingredient of tropical zone, and close connection with the flora of East China

Recent Advances in Cyanotoxin Synthesis and Applications: A Comprehensive Review

Over the past few decades, nearly 300 known cyanotoxins and more than 2000 cyanobacterial secondary metabolites have been reported from the environment. Traditional studies have focused on the toxic cyanotoxins produced by harmful cyanobacteria, which pose a risk to both human beings and wildlife, causing acute and chronic poisoning, resulting in diarrhea, nerve paralysis, and proliferation of cancer cells. Actually, the biotechnological potential of cyanotoxins is underestimated, as increasing studies have demonstrated their roles as valuable products, including allelopathic agents, insecticides and biomedicines. To promote a comprehensive understanding of cyanotoxins, a critical review is in demand. This review aims to discuss the classifications; biosynthetic pathways, especially heterogenous production; and potential applications of cyanotoxins. In detail, we first discuss the representative cyanotoxins and their toxic effects, followed by an exploration of three representative biosynthetic pathways (non-ribosomal peptide synthetases, polyketide synthetases, and their combinations). In particular, advances toward the heterologous biosynthesis of cyanotoxins in vitro and in vivo are summarized and compared. Finally, we indicate the potential applications and solutions to bottlenecks for cyanotoxins. We believe that this review will promote a comprehensive understanding, synthetic biology studies, and potential applications of cyanotoxins in the future

Characterization of different substituted carboxymethyl starch microgels and their interactions with lysozyme.

A carboxymethyl starch (CMS) microgel system was prepared for the control of uptaking and releasing proteins (lysozyme). The physicochemical properties of microgels in various degrees of substitution (DS) were determined by thermal gravimetric analysis (TGA), swelling degree, and rheological analysis. The microgel particle size mostly ranged from 25 µm to 45 µm. The result obtained from the TGA studies indicated that carboxymethylation decreased the thermal stability of starch, but crosslinking increased the thermal stability of CMS. The CMS microgels showed typical pH sensitivity, and the swelling degree of microgel increased with the increasing of DS and pH, because of the large amounts of carboxyl group ionization. The samples (2.25%) could behave as viscoelastic solids since the storage modulus was larger than the loss modulus over the entire frequency range. The protein uptake increased with increasing pH and DS at low salt concentration. The optimal pH shifted to lower pH with increasing ionic strength. The saturated protein uptake decreased with increasing ionic strength at each pH. The protein was easily released from the microgel with high pH and high salt concentration