Algorithm for locating complex zeros and poles with the use of border tracking on complex plane, and its application in dispersion characteristics calculation

2018 ◽  
Author(s):  
Jerzy Julian Michalski
Keyword(s):  
Complex Plane ◽  
Dispersion Characteristics ◽  
Complex Zeros ◽  
Zeros And Poles

Innovative Genetic Algorithmic Approach to Select Potential Patches Enclosing Real and Complex Zeros of Nonlinear Equation

2017 ◽  
Vol 6 (2) ◽  
pp. 18-37 ◽  
Author(s):  
Vijaya Lakshmi V. Nadimpalli ◽  
Rajeev Wankar ◽  
Raghavendra Rao Chillarige
Keyword(s):  
Genetic Algorithm ◽  
Nonlinear Equation ◽  
Complex Plane ◽  
Search Space ◽  
Regions Of Interest ◽  
Real Numbers ◽  
Algorithmic Approach ◽  
Space Reduction ◽  
Complex Zeros ◽  
The Given

In this article, an innovative Genetic Algorithm is proposed to find potential patches enclosing roots of real valued function f:R→R. As roots of f can be real as well as complex, the function is reframed on to complex plane by writing it as f(z). Thus, the problem now is transformed to finding potential patches (rectangles in C) enclosing z such that f(z)=0, which is resolved into two components as real and imaginary parts. The proposed GA generates two random populations of real numbers for the real and imaginary parts in the given regions of interest and no other initial guesses are needed. This is the prominent advantage of the method in contrast to various other methods. Additionally, the proposed ‘Refinement technique' aids in the exhaustive coverage of potential patches enclosing roots and reinforces the selected potential rectangles to be narrow, resulting in significant search space reduction. The method works efficiently even when the roots are closely packed. A set of benchmark functions are presented and the results show the effectiveness and robustness of the new method.

SURVEY AND ADJUSTMENT OF CONTROLLER OF A GRAPH-ANALYTICAL METHOD TO A SECOND ORDER OBJECT

2020 ◽  
Vol 70 (2) ◽  
Author(s):  
Boris Grasiani
Keyword(s):  
Control System ◽  
Automatic Control ◽  
Control Systems ◽  
Quality Indicators ◽  
Automatic Control System ◽  
Complex Plane ◽  
Analytical Method ◽  
Second Order ◽  
Location Of Zeros ◽  
Zeros And Poles

This paper proposes to adjust the controller using a graph-analytical method in the complex plane. The various configurations regarding the location of zeros and poles to those of the object are also considered. Adjusted controllers are surveyed, such as they are integrated into control systems, and some of the quality indicators of an automatic control system are analyzed.

scholarly journals On the complex zeros of Airy and Bessel functions and those of their derivatives

2014 ◽  
Vol 12 (05) ◽  
pp. 537-561 ◽  
Author(s):  
Amparo Gil ◽  
Javier Segura
Keyword(s):  
Complex Plane ◽  
Bessel Functions ◽  
Distribution Of Zeros ◽  
General Solutions ◽  
Complex Zeros

We study the distribution of zeros of general solutions of the Airy and Bessel equations in the complex plane. Our results characterize the patterns followed by the zeros for any solution, in such a way that if one zero is known it is possible to determine the location of the rest of zeros.

Monte Carlo Algorithms for Moments of Transition Arrays

1988 ◽  
Vol 102 ◽  
pp. 79-81
Author(s):  
A. Goldberg ◽  
S.D. Bloom
Keyword(s):  
Monte Carlo ◽  
State Vector ◽  
Basis Vector ◽  
Collective State ◽  
Dispersion Characteristics ◽  
Dipole Strength ◽  
The Third ◽  
Monte Carlo Algorithms ◽  
Third Moment ◽  
Very High

AbstractClosed expressions for the first, second, and (in some cases) the third moment of atomic transition arrays now exist. Recently a method has been developed for getting to very high moments (up to the 12th and beyond) in cases where a “collective” state-vector (i.e. a state-vector containing the entire electric dipole strength) can be created from each eigenstate in the parent configuration. Both of these approaches give exact results. Herein we describe astatistical(or Monte Carlo) approach which requires onlyonerepresentative state-vector |RV> for the entire parent manifold to get estimates of transition moments of high order. The representation is achieved through the random amplitudes associated with each basis vector making up |RV>. This also gives rise to the dispersion characterizing the method, which has been applied to a system (in the M shell) with≈250,000 lines where we have calculated up to the 5th moment. It turns out that the dispersion in the moments decreases with the size of the manifold, making its application to very big systems statistically advantageous. A discussion of the method and these dispersion characteristics will be presented.

Dispersion Characteristics of Multi-Step Open Slow-Wave Systems of Finite Width: Analysis

1997 ◽  
Vol 51 (8) ◽  
pp. 77-84
Author(s):  
L. M. Buzik ◽  
O. F. Pishko ◽  
S.A. Churilova ◽  
O. I. Sheremet
Keyword(s):  
Slow Wave ◽  
Finite Width ◽  
Dispersion Characteristics
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