A priori and a posteriori error estimates for the quad-curl eigenvalue problem

In this paper, we consider a priori and a posteriori error estimates of the H(curl2)-conforming finite element when solving the quad-curl eigenvalue problem. An a priori estimate of eigenvalues with convergence order 2(s − 1) is obtained if the corresponding eigenvector u ∈ Hs − 1(Ω) and ∇ × u ∈ Hs(Ω). For the a posteriori estimate, by analyzing the associated source problem, we obtain lower and upper bounds for the errors of eigenvectors in the energy norm and upper bounds for the errors of eigenvalues. Numerical examples are presented for validation

Detection of Rutin in Flower Buds of Sophora japonica by Using Chitosan-Based Carbon Dot Paper Chip

Based on the selective quenching effect of the flavonoid rutin on the fluorescence of carbon dots prepared by asparagine pyrolysis, a method for rapid detection of rutin content in the flower buds of Sophora japonica by using chitosan-based carbon dot paper chip was developed. A filter paper was immersed in the casting solution of carbon dots and chitosan. After drying, a carbon dot chitosan film was formed on the surface of the filter paper, so that the chitosan-based carbon dot paper chip was obtained. After samples were dripped on the chip, chromogenic reaction occurred uniformly within a limited region, and pictures were taken under an ultraviolet (UV) lamp at 365 nm for analysis of the red (R), green (G), and blue (B) values of the colored spots in order to optimize the preparation conditions and detection conditions. The results showed that the optimal conditions were as follows: chitosan concentration of 20 mg/mL, carbon spot concentration of 1.0 mg/mL, 50% ethanol as sample solvent, and reaction time of 20 min. Under these conditions, the difference (ΔG) in G-value between sample and solvent spots had a linear relationship with rutin concentration (C) in the range of 4 to 120 mg/mL. Using this method, the average contents of rutin in the flower buds of S. japonica from three batches were determined to be 23.85%, 22.83% and 20.30%, the average relative standard deviations (RSDs) were 6.1%, 5.6% and 6.7%, and the recoveries were 91.27% to 107.5%, which were close to the results of high performance liquid chromatography (HPLC). The proposed method is simple and rapid, and can be used for rapid on-site determination of rutin content in the flower buds of S. japonica

Pharmacokinetics and bioequivalence of sunitinib and Sutent® in Chinese healthy subjects: an open-label, randomized, crossover study

Purpose: The purpose of this study was to examine the pharmacokinetics (PK), bioequivalence and safety of generic sunitinib and its original product Sutent® in healthy Chinese subjects through a phase-I clinical trial.Methods: The study selected two groups of 24 healthy Chinese subjects in a 1:1 ratio through random allocation. Each participant received either 12.5 mg of sunitinib or Sutent® per cycle. A total of 15 different time points were employed for blood sample collection during each cycle. Furthermore, a comprehensive assessment of the drugs’ safety was consistently maintained throughout the trial.Results: The average adjusted geometric mean ratios (GMR) (90% CI) for the primary PK parameters Cmax, AUC0-t and AUC0-∞ were 97.04% (93.06%–101.19%), 98.45% (93.27%–103.91%) and 98.22% (93.15%–103.56%), respectively. The adjusted GMRs for essential pharmacokinetic (PK) parameters all met the requirements for bioequivalence, with values within the acceptable range of 80%–125%. In addition, the two drugs showed comparable results for the other PK parameters. These results indicate that the two drugs were bioequivalent. Furthermore, both drugs showed well safety.Conclusion: The research results proved that the PK and safety profiles of sunitinib in healthy Chinese subjects were comparable to those of Sutent®. These results advocate the clinical application of generic sunitinib as a potential alternative to original product Sutent® in the treatment of certain medical conditions

Superconvergence Analysis of Curlcurl-Conforming Elements on Rectangular Meshes

In our recent work (Hu et al. in SIAM J Sci Comput 42(6):A3859–A3877, 2020), we observed numerically some superconvergence phenomena of the curlcurl-conforming finite elements on rectangular domains. In this paper, we provide a theoretical justification for our numerical observation and establish a superconvergence theory for the curlcurl-conforming elements on rectangular meshes. For the elements with parameters r (r= k- 1 , k, k+ 1) and k (k≥ 2), we show that the first (second) component of the numerical solution uh converges with rate r+ 1 at r vertical (horizontal) Gaussian lines in each element when r= k- 1 , k with k≥ 3 , ∇ × uh converges with rate k+ 1 at k2 Lobatto points in each element when k≥ 3 , and the first (second) component of ∇ × ∇ × uh converges with rate k at (k- 1) horizontal (vertical) Gaussian lines when k≥ 2. They are all one-order higher than the related optimal rates. More numerical experiments are provided to confirm our theoretical results

A priori and a posteriori error estimates for the quad-curl eigenvalue problem

In this paper, we consider a priori and a posteriori error estimates of the H(curl2)-conforming finite element when solving the quad-curl eigenvalue problem. An a priori estimate of eigenvalues with convergence order 2(s 1) is obtained if the corresponding eigenvector u a Hs 1(Ω) and-u a Hs(Ω). For the a posteriori estimate, by analyzing the associated source problem, we obtain lower and upper bounds for the errors of eigenvectors in the energy norm and upper bounds for the errors of eigenvalues. Numerical examples are presented for validation