Ground state for Choquard equation with doubly critical growth nonlinearity

In this paper we consider nonlinear Choquard equation −∆u + V(x)u = (Iα ∗ F(u))f(u) in R N, where V ∈ C(RN), Iα denotes the Riesz potential, f(t) = |t| p−2 t + |t| q−2 t for all t ∈ R, N > 5 and α ∈ (0, N − 4). Under suitable conditions on V, we obtain that the Choquard equation with doubly critical growth nonlinearity, i.e., p = (N + α)/N, q = (N + α)/(N − 2), has a nonnegative ground state solution by variational methods

Ground state for Choquard equation with doubly critical growth nonlinearity

In this paper we consider nonlinear Choquard equation \begin{equation*} -\Delta u+V(x)u=(I_\alpha*F(u))f(u)\quad {\rm in}\ \mathbb{R}^{N}, \end{equation*} where $V\in C(\mathbb{R}^N)$, $I_\alpha$ denotes the Riesz potential, $f(t)=|t|^{p-2}t+|t|^{q-2}t$ for all $t\in\mathbb{R}$, $N\geqslant5$ and $\alpha\in(0,N-4)$. Under suitable conditions on $V$, we obtain that the Choquard equation with doubly critical growth nonlinearity, i.e., $p=(N+\alpha)/N,q=(N+\alpha)/(N-2)$, has a nonnegative ground state solution by variational methods

Improving the Efficacy of Conventional Therapy by Adding Andrographolide Sulfonate in the Treatment of Severe Hand, Foot, and Mouth Disease: A Randomized Controlled Trial

Background. Herb-derived compound andrographolide sulfonate (called Xiyanping injection) recommended control measure for severe hand, foot, and mouth disease (HFMD) by the Ministry of Health (China) during the 2010 epidemic. However, there is a lack of good quality evidence directly comparing the efficacy of Andrographolide Sulfonate combination therapy with conventional therapy. Methods. 230 patients were randomly assigned to 7–10 days of Andrographolide Sulfonate 5–10 mg/Kg/day and conventional therapy, or conventional therapy alone. Results. The major complications occurred less often after Andrographolide Sulfonate (2.6% versus 12.1%; risk difference [RD], 0.94; 95% CI, 0.28–1.61; P=0.006). Median fever clearance times were 96 hours (CI, 80 to 126) for conventional therapy recipients and 48 hours (CI, 36 to 54) for Andrographolide Sulfonate combination-treated patients (χ2=16.57, P<0.001). The two groups did not differ in terms of HFMD-cause mortality (P=1.00) and duration of hospitalization (P=0.70). There was one death in conventional therapy group. No important adverse event was found in Andrographolide Sulfonate combination therapy group. Conclusions. The addition of Andrographolide Sulfonate to conventional therapy reduced the occurrence of major complications, fever clearance time, and the healing time of typical skin or oral mucosa lesions in children with severe HFMD

Robust estimation of bacterial cell count from optical density

Optical density (OD) is widely used to estimate the density of cells in liquid culture, but cannot be compared between instruments without a standardized calibration protocol and is challenging to relate to actual cell count. We address this with an interlaboratory study comparing three simple, low-cost, and highly accessible OD calibration protocols across 244 laboratories, applied to eight strains of constitutive GFP-expressing E. coli. Based on our results, we recommend calibrating OD to estimated cell count using serial dilution of silica microspheres, which produces highly precise calibration (95.5% of residuals &lt;1.2-fold), is easily assessed for quality control, also assesses instrument effective linear range, and can be combined with fluorescence calibration to obtain units of Molecules of Equivalent Fluorescein (MEFL) per cell, allowing direct comparison and data fusion with flow cytometry measurements: in our study, fluorescence per cell measurements showed only a 1.07-fold mean difference between plate reader and flow cytometry data

Ground state for Choquard equation with doubly critical growth nonlinearity

In this paper we consider nonlinear Choquard equation \begin{equation*} -\Delta u+V(x)u=(I_\alpha*F(u))f(u)\quad {\rm in}\ \mathbb{R}^{N}, \end{equation*} where $V\in C(\mathbb{R}^N)$, $I_\alpha$ denotes the Riesz potential, $f(t)=|t|^{p-2}t+|t|^{q-2}t$ for all $t\in\mathbb{R}$, $N\geqslant5$ and $\alpha\in(0,N-4)$. Under suitable conditions on $V$, we obtain that the Choquard equation with doubly critical growth nonlinearity, i.e., $p=(N+\alpha)/N,q=(N+\alpha)/(N-2)$, has a nonnegative ground state solution by variational methods

Effects of Chloride Ions and Nitrate Ions on the Anodic Dissolution of Iron in Sulfuric Acid Solution

In this paper, the flow injection (FI) technique combined with a partially-closed electrode (PCE) was used to manipulate the physicochemical microenvironment at the electrode/electrolyte interface so as to study the effects of chloride ions (Cl&minus; ions) and nitrate ions (NO3&minus; ions) on the anodic dissolution of the Fe/0.5 mol dm&minus;3 H2SO4 system. The anodic dissolution is modified by injecting various composition-containing solutions into the vicinity of the PCE, and then, the electrodissolution processes are analyzed by comparing the j&ndash;t curves before and after the injections. At the initial stage of the passive region, it is found that NO3&minus; ions promote the anodic dissolution of iron by creating more active sites on the surface of the electrode when CNO3&minus;/CCl&minus; = 1:1; however, they inhibit the anodic dissolution by making the film more compact for the strong oxidized characteristics of NO3&minus; ions when CNO3&minus;/CCl&minus; = 10:1

Feeding Postures and Substrate Use of François’ Langurs (<i>Trachypithecus francoisi</i>) in the Limestone Forest of Southwest China

The feeding posture of a group of François’ langurs in Fusui County, Guangxi, was studied using instantaneous scan sampling from January to December 2016 to explore how the species adapts to karst limestone forests by collecting data on feeding posture, forest strata height, and substrate use. The results showed that leaves were the main food type of the François’ langurs, with young leaves accounting for 64.97% ± 19.08% of the food composition, mature leaves accounting for 11.88% ± 12.09%, fruits accounting for 12.96% ± 12.89%, flowers accounting for 4.16% ± 4.06%, and other food types, including stems, petioles, and other unknown parts of the tree, accounting for a total of 6.03% ± 9.09%. The François’ langurs had four main postures during feeding, of which sitting and bipedal standing feeding accounted for the largest proportions, at 85.99% ± 5.97% and 12.33% ± 6.08% of the total records, respectively. Quadrupedal standing and suspending were rarely observed and only appeared occasionally during feeding activities at the peak resting period, the two postures together accounting for 1.39% ± 1.59% of the total records. The feeding postures of the langurs had marked seasonal variation, as evidenced by the fact that seated feeding accounted for a significantly higher proportion of the total behavioral records in the rainy season than in the dry season, whereas feeding while standing bipedally was significantly more frequent during the dry season. Correlation analyses showed that feeding posture was correlated with food composition, showing a positive correlation between the proportion of bipedal standing feeding and mature leaf consumption. François’ langurs preferred to forage in the lower and middle forest layers, with the lower forest layer accounting for 55.93% ± 16.50% of the total number of recordings and the middle forest layer accounting for 33.63% ± 18.33%. Langurs were less likely to forage on the ground (rocks), accounting for only 6.79% ± 4.78% of the records. The frequency of langurs feeding in the upper part of the forest layer was the lowest at 3.65% ± 2.73%. Additionally, in the dry season, langurs utilized the lower forest layer more but used the middle forest layer less than in the rainy season. This study demonstrates that the spatial distribution of foods in the limestone forest has an important effect on the feeding posture of François’ langurs and their forest layer utilization

Chemical Constituents of Supercritical Extracts from Alpinia officinarum and the Feeding Deterrent Activity against Tribolium castaneum

Alpinia officinarum has been confirmed to possess bioactivities against some pests. In this work, a sample was obtained from A. officinarum rhizomes by supercritical fluid CO2 extraction (SFE). According to GC-MS analysis, the main chemical components for SFE-sample included benzylacetone (26.77%), 1,7-diphenyl-5-hydroxy-3-heptanone (17.78%), guaiacylacetone (10.03%) and benzenepropanal (7.42%). The essential oil of A. officinarum rhizomes (LD50 = 20.71 μg/adult) exhibited more contact toxicity than SFE extract (LD50 = 82.72 μg/adult) against Tribolium castaneum. From SFE extracts, one new compound, 1-phenyl-4-(16,17-dimethyl-9,13-octadiene)-5-isopentenyl-7-(4”-methoxyl-3”-hydroxyl-phenyl)-3-heptanone (3), together with five known compounds identified as 5-hydroxy-1,7-diphenyl-3-heptanone (1), 1,7-diphenyl-4-hepten-3-one (2), galangin (4), galangin-3-methyl ether (5) and pinocembrin (6), were isolated and their feeding deterrent activities against T. castaneum adults were assessed. It was found that compounds 1–6 had feeding deterrent activities against T. castaneum with feeding deterrent indices of 18.21%, 18.94%, 19.79%, 26.99%, 20.34%, and 35.81%, respectively, at the concentration of 1500 ppm. Hence, the essential oil and SFE extracts/compounds of A. officinarum rhizomes represent promising alternatives in the control of T. castaneum adults