scholarly journals Interpolation parameter and expansion for a three-dimensional nontrivial scalar infrared fixed point

1997 ◽  
Vol 89 (3-4) ◽  
pp. 817-845
Author(s):  
C. Wieczerkowski ◽  
J. Rolf
Keyword(s):  
Fixed Point ◽  
Three Dimensional ◽  
Interpolation Parameter

scholarly journals UV fixed-point structure of the three-dimensional Thirring model

2010 ◽  
Vol 82 (8) ◽  
Author(s):  
Holger Gies ◽  
Lukas Janssen
Keyword(s):  
Fixed Point ◽  
Three Dimensional ◽  
Thirring Model

Calibration Method of Microscopic Three-Dimensional Digital Image Correlation System Based on Fixed-Point Rotation

2018 ◽  
Vol 38 (12) ◽  
pp. 1215010
Author(s):  
吴敏杨 Wu Minyang ◽  
郭建军 Guo Jianjun ◽  
蒋明 Jiang Ming
Keyword(s):  
Fixed Point ◽  
Digital Image Correlation ◽  
Digital Image ◽  
Three Dimensional ◽  
Calibration Method ◽  
Image Correlation ◽  
Correlation System

scholarly journals On the Measure-Preserving Mappings with Three-Dimensions

1993 ◽  
Vol 132 ◽  
pp. 73-89
Author(s):  
Yi-Sui Sun
Keyword(s):  
Fixed Point ◽  
Invariant Manifolds ◽  
Three Dimensional ◽  
Invariant Curve ◽  
Three Dimensions ◽  
Two Dimensional ◽  
Kolmogorov Entropy ◽  
Numerical Exploration ◽  
Area Preserving ◽  
Dimensional Mapping

AbstractWe have systematically made the numerical exploration about the perturbation extension of area-preserving mappings to three-dimensional ones, in which the fixed points of area preserving are elliptic, parabolic or hyperbolic respectively. It has been observed that: (i) the invariant manifolds in the vicinity of the fixed point generally don’t exist (ii) when the invariant curve of original two-dimensional mapping exists the invariant tubes do also in the neighbourhood of the invariant curve (iii) for the perturbation extension of area-preserving mapping the invariant manifolds can only be generated in the subset of the invariant manifolds of original two-dimensional mapping, (iv) for the perturbation extension of area preserving mappings with hyperbolic or parabolic fixed point the ordered region near and far from the invariant curve will be destroyed by perturbation more easily than the other one, This is a result different from the case with the elliptic fixed point. In the latter the ordered region near invariant curve is solid. Some of the results have been demonstrated exactly.Finally we have discussed the Kolmogorov Entropy of the mappings and studied some applications.

Transmission Performance of the Mechanical Control System in the Aircraft

2014 ◽  
Vol 484-485 ◽  
pp. 368-372 ◽  
Author(s):  
Wei Na Huang ◽  
Jian Ming Zhang ◽  
Xiao Bo Liu
Keyword(s):  
Fixed Point ◽  
Control System ◽  
Mechanical System ◽  
Three Dimensional ◽  
System Optimization ◽  
Computational Method ◽  
Transmission Parameter ◽  
Mapping Software ◽  
Three Dimensional Mapping ◽  
Limit Position

This article introduces two ways of calculating the transmission parameter of the mechanical system in the aircraft based on the traditional computational method. One is the method of fixed point coordinate which is based on spatial Analytic Geometry and spatial coordinate transformation can calculate the motion parameter of various links, the effective radius of the limit position rocker as well as the transmission ratio by fixed point coordinate. The other method can establish the model of control system by using the MDT module of the three-dimensional mapping software CATLA. It also can realize analog computation and system optimization which points at the transmission parameter of the mechanical system by using DMU module.

NESTED INVARIANT 3-TORI EMBEDDED IN A SEA OF CHAOS IN A QUASIPERIODIC FLUID FLOW

2009 ◽  
Vol 19 (07) ◽  
pp. 2181-2191 ◽  
Author(s):  
HOPE L. WEISS ◽  
ANDREW J. SZERI
Keyword(s):  
Fixed Point ◽  
Fluid Flow ◽  
Cross Sections ◽  
Coherent Structures ◽  
Three Dimensional ◽  
Elliptic Type ◽  
Two Phase ◽  
Dimensional Phase Space ◽  
Hyperbolic Fixed Point ◽  
Stream Functions

Nested invariant 3-tori surrounding a torus braid of elliptic type are found to exist in a model of a fluid flow with quasiperiodic forcing. The Hamiltonian describing the system is given by the superposition of two steady stream functions, one with an elliptic fixed point and the other with a coincident hyperbolic fixed point. The superposition, modulated by two incommensurate frequencies, yields an elliptic torus braid at the location of the fixed point. The system is suspended in a four-dimensional phase space (two space and two phase directions). To analyze this system we define two three-dimensional, global, Poincaré sections of the flow. The coherent structures (cross-sections of nested 2 tori) are found each to have a fractal dimensional of two, in each Poincaré cross-section. This framework has applications to tidal and other mixing problems of geophysical interest.

scholarly journals The Algorithm for Determining the Coordinates of a Point in Three-Dimensional Space by Using the Auxiliary Point

2013 ◽  
Vol 48 (4) ◽  
pp. 141-145 ◽  
Author(s):  
Bartlomiej Oszczak ◽  
Eliza Sitnik
Keyword(s):  
Fixed Point ◽  
Precise Measurement ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Satellite Navigation ◽  
Reference Points ◽  
Two Dimensional ◽  
Approximate Location ◽  
The Many ◽  
Three Dimensional Space

ABSTRACT During the process of satellite navigation, and also in the many tasks of classical positioning, we need to calculate the corrections to the initial (or approximate) location of the point using precise measurement of distances to the permanent points of reference (reference points). In this paper the authors have provided a way of developing Hausbrandt's equations, on the basis of which the exact coordinates of the point in two-dimensional space can be determined by using the computed correction to the coordinates of the auxiliary point. The authors developed generalised equations for threedimensional space introducing additional fixed point and have presented proof of derived formulas.

scholarly journals Positive Solutions and Mann Iterative Algorithms for a Nonlinear Three-Dimensional Difference System

2014 ◽  
Vol 2014 ◽  
pp. 1-23
Author(s):  
Zeqing Liu ◽  
Yan Lu ◽  
Shin Min Kang ◽  
Young Chel Kwun
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Positive Solutions ◽  
Point Theorem ◽  
Three Dimensional ◽  
Iterative Algorithms ◽  
Banach Fixed Point Theorem ◽  
Difference System

The existence of uncountably many positive solutions and Mann iterative approximations for a nonlinear three-dimensional difference system are proved by using the Banach fixed point theorem. Four illustrative examples are also provided.

Classical harmonic oscillator approach of a helical-wiggler free-electron laserwith axial guide field

2000 ◽  
Vol 78 (12) ◽  
pp. 1069-1085 ◽  
Author(s):  
M N Rhimi ◽  
R El-Bahi ◽  
A W Cheikhrouhou
Keyword(s):  
Fixed Point ◽  
Free Electron ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Basic Feature ◽  
Operating Conditions ◽  
The Other ◽  
Guide Field ◽  
Constants Of Motion ◽  
Definition Of

Electron beam dynamics in a helical-wiggler free-electron laser (FEL) with a uniform axial guide magnetic field are studied using a three-dimensional Hamiltonian approach. The basic feature of the analysis is the definition of a rotational variable, [Formula: see text], that plays the primordial role in lowering to the half the dimension of the quadratic Hamiltonian as a system of two uncoupled oscillators with definite frequencies and amplitudes. It is through applying this variable in the vicinity of a fixed point that the Heisenberg picture of the dynamics of the particles comes to light, leading thus to the association of the steady-state ideal helical trajectories with arbitrary trajectories. The approach recognized the usual two constants of motion, one being the total energy while the other is the canonical axial angular momentum, Pz'. If the value of the latter is such that a fixed point exists, the Hamiltonian is expanded about the fixed point up to second order. The so-obtained oscillator characteristic frequencies allowed one to study the different modes of propagation and to identify, and then avoid the problematic operating conditions of the FEL concerned. On the other hand, the amplitudes of the oscillations, which do depend on the frequencies, are fortunately found to be constants of motion and then controlled by the boundary conditions (initial conditions). PACS Nos.: 52.40-w, 52.60+h, 42.55.Tb, 52.75Ms

Julia Sets and Their Control in a Three-Dimensional Discrete Fractional-Order Financial Model

2021 ◽  
Vol 31 (16) ◽  
Author(s):  
Zhongyuan Zhao ◽  
Yongping Zhang
Keyword(s):  
Fixed Point ◽  
Fractional Order ◽  
Julia Set ◽  
Julia Sets ◽  
Three Dimensional ◽  
Financial System ◽  
Order Theory ◽  
System Model ◽  
Financial Model ◽  
Fractal Characteristics

It is of great significance to study the three-dimensional financial system model based on the discrete fractional-order theory. In this paper, the Julia set of the three-dimensional discrete fractional-order financial model is identified to show its fractal characteristics. The sizes of the Julia sets need to be changed in some situations, so it is necessary to achieve control of the Julia sets. In combination with the characteristics of the model, two different controllers based on the fixed point are designed, and the control of the three-dimensional Julia sets is realized by adding the controllers into the model in different ways. Finally, the simulation graphs show that the controllers can effectively control the fractal behaviors.

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