Erratum: Massless electrodynamics on the 5-dimensional unit hypersphere: An amplitude-integral formulation

1977 ◽  
Vol 15 (6) ◽  
pp. 1803-1803 ◽  
Author(s):  
Stephen L. Adler
2021 ◽  
Author(s):  
Johannes Kalliauer ◽  
Michał Malendowski ◽  
Herbert A. Mang

AbstractThe vertices of two specific eigenvectors, obtained from a novel linear eigenvalue problem, describe two curves on the surface of an N-dimensional unit hypersphere. N denotes the number of degrees of freedom in the framework of structural analysis by the Finite Element Method. The radii of curvature of these two curves are 0 and 1. They correlate with pure stretching and pure bending, respectively, of structures. The two coefficient matrices of the eigenvalue problem are the tangent stiffness matrix at the load level considered and the one at the onset of loading. The goals of this paper are to report on the numerical verification of the aforesaid geometric-mechanical synergism and to summarize current attempts of its extension to combinations of stretching and bending of structures.


2001 ◽  
Vol 115 (10) ◽  
pp. 4484-4495 ◽  
Author(s):  
Nicholas V. Blinov ◽  
Pierre-Nicholas Roy ◽  
Gregory A. Voth

Sensors ◽  
2021 ◽  
Vol 21 (9) ◽  
pp. 2939
Author(s):  
Yong Hong ◽  
Jin Liu ◽  
Zahid Jahangir ◽  
Sheng He ◽  
Qing Zhang

This paper provides an efficient way of addressing the problem of detecting or estimating the 6-Dimensional (6D) pose of objects from an RGB image. A quaternion is used to define an object′s three-dimensional pose, but the pose represented by q and the pose represented by -q are equivalent, and the L2 loss between them is very large. Therefore, we define a new quaternion pose loss function to solve this problem. Based on this, we designed a new convolutional neural network named Q-Net to estimate an object’s pose. Considering that the quaternion′s output is a unit vector, a normalization layer is added in Q-Net to hold the output of pose on a four-dimensional unit sphere. We propose a new algorithm, called the Bounding Box Equation, to obtain 3D translation quickly and effectively from 2D bounding boxes. The algorithm uses an entirely new way of assessing the 3D rotation (R) and 3D translation rotation (t) in only one RGB image. This method can upgrade any traditional 2D-box prediction algorithm to a 3D prediction model. We evaluated our model using the LineMod dataset, and experiments have shown that our methodology is more acceptable and efficient in terms of L2 loss and computational time.


Sign in / Sign up

Export Citation Format

Share Document