Search

Summary: This paper is concerned with the optimal control problem governed by linear parabolic equation with box constraints on control variables. We employ the Fenchel duality scheme to derive an unconstrained dual problem. Compared with the primal problem, the objective functional of the dual problem includes a projection onto the box constraints. We prove the existence and uniqueness of solutions to the dual problem and derive the first‐order optimality conditions. Furthermore, we investigate the saddle point property between the solutions of the primal problem and the solutions of the dual problem. To solve the dual problem, we design two implementable methods: the conjugate gradient method and the semi‐smooth Newton method. The solutions of the primal problem can be easily obtained through the solutions of the dual problem. We demonstrate the effectiveness and accuracy of the proposed methods by solving three example problems. [ABSTRACT FROM AUTHOR]

Inactivation of the p53 pathway is linked to a variety of human cancers. As a critical component of the p53 pathway, ubiquitin‐specific protease 7 (USP7) acts as a deubiquitinase for both p53 and its ubiquitin E3 ligase mouse double minute 2 homolog. Here, myeloid leukemia factor 2 (MLF2) is reported as a new negative regulator of p53. MLF2 interacts with both p53 and USP7. Via these interactions, MLF2 inhibits the binding of USP7 to p53 and antagonizes USP7‐mediated deubiquitination of p53, thereby leading to p53 destabilization. Functionally, MLF2 plays an oncogenic role in colorectal cancer, at least partially, via the negative regulation of p53. Clinically, MLF2 is elevated in colorectal cancer and its high expression is associated with poor prognosis in patients with colorectal cancer. In wild‐type‐p53‐containing colorectal cancer, MLF2 and p53 expressions are inversely correlated. These findings establish MLF2 as an important suppressor of p53 function. The study also reveals a critical role for the MLF2–p53 axis in promoting colorectal carcinogenesis. [ABSTRACT FROM AUTHOR]

Aiming to utilize CO2 and solid waste form coal chemical industry synchronously, we proposed a novel process which integrated CO2 mineral carbonation and utilization of gasification slags based on chemical looping. With NH4Cl as the loop chemical, which generated HCl and NH3 through pyrolysis, the aluminum, calcium, and so forth were extracted by HCl from the coal slag, and CO2 was mineralized by calcium and NH3. NH4Cl was recovered after mineralization, and chemical looping was closed. A pilot setup with a capacity of 1‐kg CO2/h was conducted to demonstrate the feasibility of the chemical looping process. An airlift reactor was employed for mineral carbonation reaction, and conditions for extraction and mineral carbonation were optimized. The process presented the CO2 conversion of more than 90% with a calcium overall utilization ratio of 74.8%. The CO2 sequestration potential of the gasification slag is 121‐g CO2/kg slag, which is higher than that of steel slag and red mud. Calcium carbonate with the particle size of 1–10 μm can be obtained during the mineral carbonation. Simultaneously, the process extracted and enriched 62.3% of aluminum in the slag and enabled the deep utilization of the slag. [ABSTRACT FROM AUTHOR]