Application of strip domain and parabolic region on univalent holomorphic functions

In this paper, by using univalent functions connected with the strip domain,parabolic starlike and parabolic uniformly convex functions are introduced.Some relations between these classes are proved.

Stability for the 2D MHD equations with horizontal dissipation

In this paper we consider the following 2D MHD system with horizontal dissipation in a strip domain T × R. ∂ t u + u · ∇ u + ∂ 11 u + ∇ p = b · ∇ b , ∂ t b + u · ∇ b + ∂ 11 b = b · ∇ u , ∇ · u = ∇ · b = 0 , u ( 0 ) = u 0 ( x ) , b ( 0 ) = b 0 ( x ) . A bootstrapping argument together with a more accurate energy functional is employed in order to get the stability for the above system. Moreover, using a suitable transform, we also investigate the 2D MHD system with vertical dissipation in a strip domain R × T.

Overexpression of OsCASP1 Improves Calcium Tolerance in Rice

The Casparian strip domain protein 1 (OsCASP1) is necessary for the formation of the Casparian strip (CS) in the rice endodermis. It also controls Ca2+ transport to the stele. Here, we demonstrated that OsCASP1 overexpression enhanced Ca tolerance in rice. Under normal conditions, OsCASP1-overexpressed lines showed similar concentrations of essential metals in the roots and shoots compared to the wild type, while under high Ca conditions, Ca in the roots, shoots, and xylem sap of the OsCASP1-overexpressed lines was significantly decreased. This did not apply to other essential metals. Ca-inhibited growth was significantly alleviated in the OsCASP1-overexpressed lines. Furthermore, OsCASP1 overexpression resulted in earlier formation of both the CS and functional apoplastic barrier in the endodermis but did not induce ectopic CS formation in non-endodermal cell layers and affect suberin accumulation in the endodermis. These results indicate that the overexpression of OsCASP1 promotes CS formation in endodermal cells and inhibits Ca2+ transport by the apoplastic pathway, restricting Ca accumulation in the roots and shoots under high Ca conditions. Taken together, the results suggest that OsCASP1 overexpression is an effective way to improve rice adaptation to high Ca environments.

Global well-posedness of the Navier-Stokes equations with Navier-slip boundary conditions in a strip domain

<p style='text-indent:20px;'>This paper is concerned with the existence and uniqueness of the strong solution to the incompressible Navier-Stokes equations with Navier-slip boundary conditions in a two-dimensional strip domain where the slip coefficients may not have defined sign. In the meantime, we also establish a number of Gagliardo-Nirenberg inequalities in the corresponding Sobolev spaces which will be applicable to other similar situations.</p>

Fourier Truncation Regularization Method for a Time-Fractional Backward Diffusion Problem with a Nonlinear Source

In present paper, we deal with a backward diffusion problem for a time-fractional diffusion problem with a nonlinear source in a strip domain. We all know this nonlinear problem is severely ill-posed, i.e., the solution does not depend continuously on the measurable data. Therefore, we use the Fourier truncation regularization method to solve this problem. Under an a priori hypothesis and an a priori regularization parameter selection rule, we obtain the convergence error estimates between the regular solution and the exact solution at 0 ≤ x < 1 .

A mollification method with Dirichlet kernel to solve Cauchy problem for two-dimensional Helmholtz equation

In this paper, the ill-posed Cauchy problem for the Helmholtz equation is investigated in a strip domain. To obtain stable numerical solution, a mollification regularization method with Dirichlet kernel is proposed. Error estimate between the exact solution and its approximation is given. A numerical experiment of interest shows that our procedure is effective and stable with respect to perturbations of noise in the data.