scholarly journals Rotation Equivariant Vector Field Networks

2017 ◽  
Author(s):  
Diego Marcos ◽  
Michele Volpi ◽  
Nikos Komodakis ◽  
Devis Tuia
Keyword(s):  
Vector Field ◽  
Equivariant Vector Field

BIFURCATIONS OF LIMIT CYCLES IN A Z2-EQUIVARIANT PLANAR POLYNOMIAL VECTOR FIELD OF DEGREE 7

2006 ◽  
Vol 16 (04) ◽  
pp. 925-943 ◽  
Author(s):  
JIBIN LI ◽  
MINGJI ZHANG ◽  
SHUMIN LI
Keyword(s):  
Vector Field ◽  
Dynamical Systems ◽  
Limit Cycles ◽  
Bifurcation Theory ◽  
Vector Fields ◽  
Compound Eyes ◽  
Polynomial Vector ◽  
Polynomial Vector Fields ◽  
Planar Dynamical Systems ◽  
Equivariant Vector Field

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.

BIFURCATIONS OF LIMIT CYCLES IN A Z3-EQUIVARIANT VECTOR FIELD OF DEGREE 5

2001 ◽  
Vol 11 (08) ◽  
pp. 2287-2298 ◽  
Author(s):  
H. S. Y. CHAN ◽  
K. W. CHUNG ◽  
JIBIN LI
Keyword(s):  
Vector Field ◽  
Dynamical Systems ◽  
Limit Cycles ◽  
Bifurcation Theory ◽  
Compound Eyes ◽  
Hamiltonian Vector Field ◽  
Numerical Example ◽  
Hilbert Number ◽  
Planar Dynamical Systems ◽  
Equivariant Vector Field

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.

scholarly journals LIMIT CYCLE BIFURCATION FOR A NILPOTENT SYSTEM IN Z3-EQUIVARIANT VECTOR FIELD

2017 ◽  
Vol 7 (4) ◽  
pp. 1463-1477
Author(s):  
Chaoxiong Du ◽  
◽  
Qinlong Wang ◽  
Yirong Liu ◽  
Qi Zhang ◽  
...  
Keyword(s):  
Vector Field ◽  
Limit Cycle ◽  
Limit Cycle Bifurcation ◽  
Equivariant Vector Field

Evolution of a multimodal map induced by an equivariant vector field

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

Mathematical Model of Flat Surface Machining Inaccuracies due to Elastic Strains of Technological System

2018 ◽  
pp. 1-14 ◽  
Author(s):  
I. I. Kravchenko
Keyword(s):  
Mathematical Model ◽  
Vector Field ◽  
Model Development ◽  
Technological System ◽  
Mutual Arrangement ◽  
Real Surface ◽  
Main Bearing ◽  
Flat Surfaces ◽  
Internal Surfaces ◽  
Elastic Strains

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.

On the geometry of Killing vector field

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

Some Properties of Para-Sasakian Manifolds

2017 ◽  
Vol 5 (2) ◽  
pp. 73-78
Author(s):  
Jay Prakash Singh ◽  
Keyword(s):  
Vector Field ◽  
Killing Vector ◽  
Sasakian Manifold ◽  
Subject Classification ◽  
Killing Vector Field ◽  
Sasakian Manifolds ◽  
Geometric Properties ◽  
Paper Author

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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