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

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

Hybrid Prediction Model of the Temperature Field of a Motorized Spindle

The thermal characteristics of a motorized spindle are the main determinants of its performance, and influence the machining accuracy of computer numerical control machine tools. It is important to accurately predict the thermal field of a motorized spindle during its operation to improve its thermal characteristics. This paper proposes a model to predict the temperature field of a high-speed and high-precision motorized spindle under different working conditions using a finite element model and test data. The finite element model considers the influence of the parameters of the cooling system and the lubrication system, and that of environmental conditions on the coefficient of heat transfer based on test data for the surface temperature of the motorized spindle. A genetic algorithm is used to optimize the coefficient of heat transfer of the spindle, and its temperature field is predicted using a three-dimensional model that employs this optimal coefficient. A prediction model of the 170MD30 temperature field of the motorized spindle is created and simulation data for the temperature field are compared with the test data. The results show that when the speed of the spindle is 10,000 rpm, the relative mean prediction error is 1.5%, and when its speed is 15,000 rpm, the prediction error is 3.6%. Therefore, the proposed prediction model can predict the temperature field of the motorized spindle with high accuracy

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