Cotton leaf curl virus disease (CLCuD) is caused by a suite of whitefly-transmitted begomovirus species and strains, resulting in extensive losses annually in India and Pakistan. RNA-interference (RNAi) is a proven technology used for knockdown of gene expression in higher organisms and viruses. In this study, a small interfering RNA (siRNA) construct was designed to target the AC1 gene of Cott...

We consider domain decomposition preconditioners for the linear algebraic equations which result from finite element discretization of problems involving the bilinear form α(·, ·) + (curl ·, curl ·) defined on a polyhedral domain Ω. Here (·, ·) denotes the inner product in (L(Ω)) and α is a positive number. We use Nedelec’s curl-conforming finite elements to discretize the problem. Both additiv...

Inflationary gravitational waves (GW) contribute to the curl component in the polarization of the cosmic microwave background (CMB). Cosmic shear--gravitational lensing of the CMB--converts a fraction of the dominant gradient polarization to the curl component. Higher-order correlations can be used to map the cosmic shear and subtract this contribution to the curl. Arcminute resolution will be ...

Abstract. We define discrete differential operators such as grad, div and curl, on general two-dimensional non-orthogonal meshes. These discrete operators verify discrete analogues of usual continuous theorems: discrete Green formulae, discrete Hodge decomposition of vector fields, vector curls have a vanishing divergence and gradients have a vanishing curl. We apply these ideas to discretize d...

Averaging diffeomorphisms is a challenging problem, and it has great applications in areas like medical image atlases. The simple Euclidean average can neither guarantee the averaged transformation is a diffeomorphism, nor get reasonable result when there is a local rotation. The goal of this paper is to propose a new approach to averaging diffeomorphisms based on the Jacobian determinant and t...

The common way to define a curl operator considers Stoke’s Theorem and the concept of circulation. Common numerical discretizations for this operator also use this approach. In this work, we revisit the construction of the curl operator using an extended form of Gauss’ Divergence Theorem instead. This new approach allows us to present a discretization framework that naturally inherits all the d...

1. SOBOLEV SPACES AND WEAK FORMULATIONS Let Ω be a bounded Lipschitz domain in R. We introduce the Sobolev spaces H(curl ; Ω) = {v ∈ L(Ω), curlv ∈ L(Ω)}, H(div; Ω) = {v ∈ L(Ω),div v ∈ L(Ω)} The vector fields (E,H) belong to H(curl ; Ω) while the flux (D,B) in H(div; Ω). We shall use the unified notation H(d; Ω) with d = grad , curl , or div. Note that H(grad ; Ω) is the familiar H(Ω) space. The...

The Web has transformed how we access information and applications, but Web application platforms have lagged behind the vision: Highly usable Web applications are too hard to build using established Web technology platforms. Web content needs to span the spectrum from simple formatted text, through graphics, animations, and scripting, to enterprise-scale applications that use client-side compu...

Abstract Consider the differential equation curl for a 3dimensional differentiable vector field We prove that is analytic and then prove an existence and uniqueness theorem for the differential equation with a prescribed boundary data. We also outline with a few variations Professor J. Ericksen’s work on a unit vector field that equals its own curl. AMS Subject Classification 2000 15A72, 35A10,...

Abstract A Lagrange finite element method is proposed for Maxwell’s equations in Lipschitz domains. The suitable the approximation of singular solutions lying outside $(H^1(\varOmega ))^3$, with nonhomogeneous boundary data tangential trace space $H({\mathbf{curl}}; \varOmega )$ and a right-hand-side source term $(H_0({\mathbf{curl}}; ))^{\prime}$ (the dual $H_0({\mathbf{curl}}; ))$. Numerical ...