Weyl covariance, and proposals for superconformal prepotentials in 10D superspaces

Proposals are made to describe the Weyl scaling transformation laws of supercovariant derivatives ∇A, the torsion supertensors TABC, and curvature supertensors RABcd in 10D superspaces. Starting from the proposal that an unconstrained supergravity prepotential for the 11D, $$ \mathcal{N} $$ N = 1 theory is described by a scalar superfield, considerations for supergravity prepotentials in the 10D theories are enumerated. We derive infinitesimal 10D superspace Weyl transformation laws and discover ten possible 10D, $$ \mathcal{N} $$ N = 1 superfield supergravity prepotentials. The first identification of all off-shell ten dimensional supergeometrical Weyl field strength tensors, constructed from respective torsions, is presented.

Research on Sugarcane Seed-Bud Location Based on Anisotropic Scaling Transformation

Highlights A method of locating sugarcane seed bud based on anisotropy transformation is proposed.Using computer binocular vision technology, the location of the sugarcane seed bud was determined by edge feature matching of the sugarcane seed bud.There are few methods to study the automatic location of sugarcane seed buds, and our research provides a new research idea.Abstract. Sugarcane is a major economic crop in China, but the degree of mechanization in sugarcane cultivation is low. To improve the economic benefit of sugarcane planting, promoting the use of mechanization in sugarcane planting is necessary. Currently, the sugarcane planted using mechanization has a low survival rate and the mechanization efficiency is low because the existing sugarcane precutting machine fails to address the problem of damaging seed buds. This study proposed a sugarcane bud localization method based on computer binocular vision technology. The sugarcane stem segment positions can be determined by the grayscale horizontal projection after preprocessing the sugarcane image based on color and grayscale features. Then, the bud area can be intercepted according to the positional relationship between the seed bud and the stem node, and the planar position of the seed bud will be determined by using the color space conversion and the gray vertical projection. Finally, the anisotropic scaling transformation is used to match the seed-bud area and restore the spatial coordinates of the seed bud, and the spatial position of the seed bud can be determined. The image pyramid acceleration matching process is adopted, which can make the method more suitable for real-time applications. The experimental results show that the accuracy of seed-bud matching based on the anisotropic scaling transformation is 98%, which provides a basis for research on the anti-injury germ system in the automatic planting process of sugarcane. Keywords: Anisotropic scaling, Binocular vision, Image pyramid, Mechanization planting of sugarcane, Seed bud location.

A scaling transformation method and exact solutions of nonlinear reaction–diffusion model

We find a very simple scaling transformation method by which a kind of rank non-homogenous second order nonlinear ODEs is reduced to an integral form. Comparing with the canonical-like transformation method and the first integral method, our method provides a simple mechanism of reduction of such equations. As an application, a reaction–diffusion equation with variable coefficients is integrated, and its exact cnoidal wave solution is obtained. Furthermore, by using the complete discrimination system for polynomial method, more exact solutions are obtained.