In this paper, an analysis is carried out for the similarity solution of the steady boundary layer flow and heat transfer of a Casson nanofluid flowing over a vertical cylinder which is stretching exponentially along its radial direction. Using boundary layer approach and suitable similarity transformation the governing partial differential equations with the boundary conditions are reduced to a system of nonlinear ordinary differential equations. The resulting system is solved with the help of numerical technique, the Runge-Kutta Fehlberg method. The effects of important parameters such as Reynolds number, Prandtl number, Lewis number and the natural convection parameter are described through graphs.

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Both plant receptor‐like protein kinases (RLKs) and ubiquitin‐mediated proteolysis play crucial roles in plant responses to drought stress. However, the mechanism by which E3 ubiquitin ligases modulate RLKs is poorly understood. In this study, we showed that Arabidopsis PLANT U‐BOX PROTEIN 11 (PUB11), an E3 ubiquitin ligase, negatively regulates abscisic acid (ABA)‐mediated drought responses. PUB11 interacts with and ubiquitinates two receptor‐like protein kinases, LEUCINE RICH REPEAT PROTEIN 1 (LRR1) and KINASE 7 (KIN7), and mediates their degradation during plant responses to drought stress in vitro and in vivo. pub11 mutants were more tolerant, whereas lrr1 and kin7 mutants were more sensitive, to drought stress than the wild type. Genetic analyses show that the pub11 lrr1 kin7 triple mutant exhibited similar drought sensitivity as the lrr1 kin7 double mutant, placing PUB11 upstream of the two RLKs. Abscisic acid and drought treatment promoted the accumulation of PUB11, which likely accelerates LRR1 and KIN7 degradation. Together, our results reveal that PUB11 negatively regulates plant responses to drought stress by destabilizing the LRR1 and KIN7 RLKs.

The phytohormone abscisic acid (ABA) and the Polycomb group proteins have key roles in regulating plant growth and development; however, their interplay and underlying mechanisms are not fully understood. Here, we identified an Arabidopsis (Arabidopsis thaliana) nodulin homeobox (AtNDX) protein as a negative regulator in the ABA signaling pathway. AtNDX mutants are hypersensitive to ABA, as measured by inhibition of seed germination and root growth, and the expression of AtNDX is downregulated by ABA. AtNDX interacts with the Polycomb Repressive Complex1 (PRC1) core components AtRING1A and AtRING1B in vitro and in vivo, and together, they negatively regulate the expression levels of some ABA-responsive genes. We identified ABA-INSENSITIVE (ABI4) as a direct target of AtNDX. AtNDX directly binds the downstream region of ABI4 and deleting this region increases the ABA sensitivity of primary root growth. Furthermore, ABI4 mutations rescue the ABAhypersensitive phenotypes of ndx mutants and ABI4-overexpressing plants are hypersensitive to ABA in primary root growth. Thus, our work reveals the critical functions of AtNDX and PRC1 in some ABA-mediated processes and their regulation of ABI4.

An analysis is carried out for axisymmetric stagnation flow of a micropolar nanofluid in a moving cylinder with finite radius. The coupled nonlinear partial differential equations of the problem are simplified with the help of similarity transformations and the resulting coupled nonlinear differential equations are solved analytically by homotopy analysis method (HAM). The features of the flow phenomena, inertia, heat transfer, and nanoparticles are analyzed and discussed.