Convergence of an extragradient-type method for variational inequality with applications to optimal control problems

Numerical Algorithms - Our aim in this paper is to introduce an extragradient-type method for solving variational inequality with uniformly continuous pseudomonotone operator. The strong...     

一类非线性奇异积分方程及其数值方法研究

探讨了一类非线性奇异积分方程的数理性质以及在颗粒雷诺数Rep＜1时此类方程解的存在条件，然后详细研究了该方程的数值计算方法并构造称之为P（EC）^k多步法的差分格式，分析了该格式的收敛性和代数精度，得到时域离散步长的约束关系。运用该格式计算了静止流场和均匀振荡流中球形小颗粒的非恒定运动，将计算结果与其解析解及有关实验数据的比较表明，上述数值方法具有良好的计算精度。     

Current Status of Endoplasmic Reticulum Stress in Type II Diabetes

The endoplasmic reticulum (ER) plays a multifunctional role in lipid biosynthesis, calcium storage, protein folding, and processing. Thus, maintaining ER homeostasis is essential for cellular functions. Several pathophysiological conditions and pharmacological agents are known to disrupt ER homeostasis, thereby, causing ER stress. The cells react to ER stress by initiating an adaptive signaling process called the unfolded protein response (UPR). However, the ER initiates death signaling pathways when ER stress persists. ER stress is linked to several diseases, such as cancer, obesity, and diabetes. Thus, its regulation can provide possible therapeutic targets for these. Current evidence suggests that chronic hyperglycemia and hyperlipidemia linked to type II diabetes disrupt ER homeostasis, thereby, resulting in irreversible UPR activation and cell death. Despite progress in understanding the pathophysiology of the UPR and ER stress, to date, the mechanisms of ER stress in relation to type II diabetes remain unclear. This review provides up-to-date information regarding the UPR, ER stress mechanisms, insulin dysfunction, oxidative stress, and the therapeutic potential of targeting specific ER stress pathways.     

Strong convergence theorems for a Mann-type iterative scheme for a family of Lipschitzian mappings

In the paper, we obtain the existence of triple positive solutions for the following second order three-point boundary value problem, $$\left\{\begin{array}{l}(\phi_p(u'))'(t)+q(t)f(u(t),u'(t),(Tu)(t),(Su)(t))=0,\quad 0\leq t\leq1,\\[4pt]u'(0)=\beta u'(\eta),\qquad u(1)=g(u'(1)),\end{array}\right.$$ where $\phi_{p}(s)=|s|^{p-2}s,p>1,\beta\in[0,1),\eta\in(0,\frac{1}{2}]$ , T and S are all linear operators, g(t) is continuous.     

Strong Convergence Theorem for Multiple Sets Split Feasibility Problems in Banach Spaces

The purpose of this article is to study the iterative approximation of solution to multiple sets split feasibility problems in p-uniformly convex real Banach spaces that are also uniformly smooth. We propose an iterative algorithm for solving multiple sets split feasibility problems and prove a strong convergence theorem of the sequence generated by our algorithm under some appropriate conditions in p-uniformly convex real Banach spaces that are also uniformly smooth.