scholarly journals Rotation Equivariant Vector Field Networks

Author(s):  
Diego Marcos ◽  
Michele Volpi ◽  
Nikos Komodakis ◽  
Devis Tuia
2006 ◽  
Vol 16 (04) ◽  
pp. 925-943 ◽  
Author(s):  
JIBIN LI ◽  
MINGJI ZHANG ◽  
SHUMIN LI

By using the bifurcation theory of planar dynamical systems and the method of detection functions, the bifurcations of limit cycles in a Z2-equivariant planar perturbed Hamiltonian polynomial vector fields of degree 7 are studied. An example of a special Z2-equivariant vector field having 50 limit cycles with a configuration of compound eyes are given.


2001 ◽  
Vol 11 (08) ◽  
pp. 2287-2298 ◽  
Author(s):  
H. S. Y. CHAN ◽  
K. W. CHUNG ◽  
JIBIN LI

A concrete numerical example of Z3-equivariant planar perturbed Hamiltonian vector field of fifth degree having 23 limit cycles and a configuration of compound eyes are given, by using the bifurcation theory of planar dynamical systems and the method of detection functions. It gives rise to the conclusion: the Hilbert number H(5) ≥ 23 for the second part of Hilbert's 16th problem.


2017 ◽  
Vol 7 (4) ◽  
pp. 1463-1477
Author(s):  
Chaoxiong Du ◽  
◽  
Qinlong Wang ◽  
Yirong Liu ◽  
Qi Zhang ◽  
...  

1996 ◽  
Vol 29 (17) ◽  
pp. 5359-5373 ◽  
Author(s):  
C Letellier ◽  
P Dutertre ◽  
J Reizner ◽  
G Gouesbet

Author(s):  
I. I. Kravchenko

The paper considers the mathematical model development technique to build a vector field of the shape deviations when machining flat surfaces of shell parts on multi-operational machines under conditions of anisotropic rigidity in technological system (TS). The technological system has an anisotropic rigidity, as its elastic strains do not obey the accepted concepts, i.e. the rigidity towards the coordinate axes of the machine is the same, and they occur only towards the external force. The record shows that the diagrams of elastic strains of machine units are substantially different from the circumference. The issues to ensure the specified accuracy require that there should be mathematical models describing kinematic models and physical processes of mechanical machining under conditions of the specific TS. There are such models for external and internal surfaces of rotation [2,3], which are successfully implemented in practice. Flat surfaces (FS) of shell parts (SP) are both assembly and processing datum surfaces. Therefore, on them special stipulations are made regarding deviations of shape and mutual arrangement. The axes of the main bearing holes are coordinated with respect to them. The joints that ensure leak tightness and distributed load on the product part are closed on these surfaces. The paper deals with the analytical construction of the vector field F, which describes with appropriate approximation the real surface obtained as a result of modeling the process of machining flat surfaces (MFS) through face milling under conditions of anisotropic properties.


2019 ◽  
Vol 2019 (2) ◽  
pp. 62-67
Author(s):  
R.A. Ilyasova

2017 ◽  
Vol 5 (2) ◽  
pp. 73-78
Author(s):  
Jay Prakash Singh ◽  

In this paper author present an investigation of some differential geometric properties of Para-Sasakian manifolds. Condition for a vector field to be Killing vector field in Para-Sasakian manifold is obtained. Mathematics Subject Classification (2010). 53B20, 53C15.


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