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Ferroptosis is closely related to myocardial ischemia/reperfusion (I/R) damage. Kruppel‐like factor 6 (Klf6) can aggravate renal I/R injury. We aimed to elucidate the role of Klf6 in myocardial I/R damage as well as its potential mechanism. Myocardial I/R mice model and hypoxia/reoxygenation (H/R)‐treated HL‐1 cells were established. The levels of Fe 2+ , MDA, lipid ROS, and ferroptosis‐related proteins were measured for assessing ferroptosis. Infarct area, H&E staining, cardiac function, and cell viability were detected for evaluating myocardial injury. Immunohistochemistry, immunofluorescence, western blot, and RT‐qPCR were applied for detecting the levels of related genes. The m6A modification of Klf6, as well as the relationships between Klf6 and Mettl3, Igf2bp2, or Acsl4 promoter, was evaluated using MeRIP, RNA immunoprecipitation, RNA pull‐down, chromatin immunoprecipitation, and luciferase reporter assay accordingly.Klf6 protein and mRNA levels, as well as Klf6 m6A modification, were elevated in HL‐1 cells subjected to H/R and in the heart tissues from I/R mice. In H/R‐challenged HL‐1 cells, the binding relationships between Klf6 mRNA and Igf2bp2 or Mettl3 were confirmed; moreover, Igf2bp2 or Mettl3 knockdown decreased the Klf6 level and inhibited Klf6 mRNA stability. Klf6 knockdown restrained H/R‐triggered cell viability loss, improved I/R‐induced myocardial injury, and inhibited ferroptosis in myocardial I/R damage models. Klf6 directly bound to the Acsl4 promoter and positively regulated its expression. Acsl4 overexpression compromised the Klf6 knockdown‐generated protective effect in HL‐1 cells.m6A modification‐regulated Klf6 aggravated myocardial I/R damage through activating Acsl4‐mediated ferroptosis, thereby providing one potential target for the treatment of myocardial I/R.

We study numerical methods for solving a coupled Stokes-Darcy problem in porous media flow applications. A two-grid method is proposed for decoupling the mixed model by a coarse grid approximation to the interface coupling conditions. Error estimates are derived for the proposed method. Both theoretical analysis and numerical experiments show the efficiency and effectiveness of the two-grid approach for solving multimodeling problems. Potential extensions and future directions are discussed.

We study numerical methods for a coupled Navier—Stokes/Darcy model which describes a fluid flow filtrating through porous media. A decoupled and linearized two-grid algorithm is proposed. Numerical analysis and experiments are presented to show the efficiency and effectiveness of the decoupled and linearized algorithm.

Introduction Chronic prostatitis (CP) is a frequent prostate-related complaint, impacts negatively on quality of life and is mostly of unclear etiology. Increasing attention has been paid to the prevalence of sexual dysfunctions in CP patients; however, the impact of specific types of CP and the correlation of sexual dysfunctions with psychological disorders associated with CP are not well understood. Type IIIa CP is characterized by chronic pelvic pain, urination symptoms and white blood cells in expressed prostatic secretion, but free of bacterial infection. Methods A population of 600 type IIIa CP patients were randomly selected and 40 normal man were included as the control group. Queries were conducted by urologists. The National Institute of Health Chronic Prostatitis Symptom Index (NIH-CPSI), the International Index of Erectile Function (IIEF-5) and the Symptom Checklist 90-R were used to evaluate the symptoms and severity of prostatitis, erectile dysfunctions and psychological problems, respectively. Scores of ejaculatory pain and premature ejaculation were also collected. Results Our study revealed that sexual dysfunctions are frequently associated with this specific type of CP. The prevalence of erectile dysfunction, premature ejaculation and ejaculatory pain was 19, 30 and 30 %, respectively. A variety of psychological problems exist among type IIIa CP patients, including depression, anxiety, somatization, obsessive–compulsive and interpersonal sensitivity. In particular, the severity of erectile dysfunctions, but not premature ejaculation and ejaculatory pain, correlated significantly with depression and anxiety. Conclusion Our data indicate that a moderate level of sexual dysfunctions exists among the type IIIa CP patients, and highlight the association of depression and anxiety with erectile dysfunction in CP patients, suggestting that special attention should be paid to these psychological issues in clinical treatments of the prostatitis symptoms and the associated erectile dysfunctions.

We study numerical algorithms for solving Biot’s model. Based on a three-field reformulation, we present some algorithms that are inspired by the work of Chaabane et al. (Comput Math Appl 75(7):2328–2337) and Lee (Unconditionally stable second order convergent partitioned methods for multiple-network poroelasticity arXiv:1901.06078 , 2019) for decoupling the computation of Biot’s model. A new theoretical framework is developed to analyze the algorithms. Considering a uniform temporal discretization, these algorithms solve the coupled model on the first time level. On the remaining time levels, one algorithm solves a reaction-diffusion subproblem first and then solves a generalized Stokes subproblem. Another algorithm reverses the order of solving the two subproblems. Our algorithms manage to decouple the numerical computation of the coupled system while retaining the convergence properties of the original coupled algorithm. Theoretical analysis is conducted to show that these algorithms are unconditionally stable and optimally convergent. Numerical experiments are also carried out to validate the theoretical analysis and demonstrate the advantages of the proposed algorithms.

We study numerical methods for solving a non-stationary mixed Stokes-Darcy problem that models coupled fluid flow and porous media flow. A decoupling approach based on interface approximation via temporal extrapolation is proposed for devising decoupled marching algorithms for the mixed model. Error estimates are derived and numerical experiments are conducted to demonstrate the computational effectiveness of the decoupling approach.

The time-dependent Ginzburg-Landau model of superconductors consists of coupled nonlinear partial differential equations, which presents difficulties in the numerical solution. We present an alternating Crank-Nicolson method for this model that leads to two decoupled algebraic subsystems; one is linear and the other is semilinear. Both have nice numerical properties and can be solved by efficient matrix solvers. We show the stability and convergence and derive error estimates for this scheme. Numerical results are also reported.

The time-dependent Ginzburg-Landau model is used extensively in studying the nonequilibrium state of superconductivity. The computer simulation of this model requires high-performance computing power and reliable and efficient numerical methods to solve the Ginzburg-Landau equtions. In this paper, a linearized Crank-Nicolson-Galerkin method is proposed for solving these nonlinear and coupled partial differential equations. The method uses the Galerkin finite element approximation in spatial discretization and the Crank-Nicolson implicit scheme in time discretization, together with certain techniques which linearize and decouple the Ginzburg-Landau equations. While retaining the stabillity and accuracy of the Crank-Nicolson scheme, the proposed approach results in symmetric and positive definite matrix problems, thus substantially improving the computational efficiency. Furthermore, and even more important, the proposed approach is suitable for large-scale parallel computation. Numerical results from simulating the vortex dynamics of superconductivity by using the linearized Crank-Nicolson-Galerkin method are presented.

This paper deals with a solution approach suitable for composite partial differential equations (PDEs) with interface conditions. We present a general framework based on interface relaxation which provides a uniform platform for building problem solving environments through efficient software integration and for implementing various relaxation schemes. Mathematically, this framework contains many existing domain decomposition methods and also allows the extension to a variety of new relaxers. In particular, we describe a class of relaxers which are suitable for general and complicated interface conditions. Interface relaxation is more general than the traditional domain decomposition methods in that it allows unrelated PDE problems on different subdomains. Convergence analysis, error estimates, and preconditioning strategies are presented which show that these relaxers are competitive with existing domain decomposition methods for model problems involving a single PDE. We present experimental results whichdemonstrate the wide applicability of this approach. Differences between this approach and other domain decomposition methods are also discussed.

Stabilizer-free \\(P_k\\) virtual elements are constructed on polygonal and polyhedral meshes. Here the interpolating space is the space of continuous \\(P_k\\) polynomials on a triangular-subdivision of each polygon, or a tetrahedral-subdivision of each polyhedron. With such an accurate and proper interpolation, the stabilizer of the virtual elements is eliminated while the system is kept positive-definite. We show that the stabilizer-free virtual elements converge at the optimal order in 2D and 3D. Numerical examples are computed, validating the theory.