Using a bilinear method that is inspired by the of efficient congruencing Wooley [Adv. Math. 294 (2016), pp. 532–561], we prove sharp decoupling inequality for moment curve in $\mathbb {R}^3$.

We construct a Galacto-Local Group rotation curve, combining the Galactic rotation curve with a diagram, where galacto-centric radial velocities of outer globular clusters and member galaxies of the Local Group are plotted against their galacto-centric distances. The high-velocity ends of this pseudo rotation curve within a radius R ∼ 150 kpc are well traced by a rotation curve calculated for t...

Rotation of the plane of polarization of reflected light (Kerr effect) is a direct manifestation of broken time-reversal symmetry and is generally associated with the appearance of a ferromagnetic moment. Here I identify magnetic structures that may arise within the unit cell of cuprate superconductors that generate polarization rotation despite the absence of a net moment. For these magnetic s...

The environmental dependencies of the characteristics of spiral galaxy rotation curves are studied in this work. We use our large, homogeneously collected sample of 510 cluster spiral galaxy rotation curves to test the claim that the shape of a galaxy’s rotation curve strongly depends on its location within the cluster, and thus presumably on the strength of the local intracluster medium and on...

most of the contour detection methods suffers from some drawbacks such as noise, occlusion of objects, shifting, scaling and rotation of objects in image which they suppress the recognition accuracy. to solve the problem, this paper utilizes zernike moment (zm) and pseudo zernike moment (pzm) to extract object contour features in all situations such as rotation, scaling and shifting of object i...

Moment invariants have been frequently used as features for shape recognition. They are computed based on the information provided by both the shape boundary and its interior region. Although several fast algorithms for computing traditional moment invariants have been proposed, none has ever shown the theoretical results of moment invariants computed based on the shape boundary only. This pape...