Characteristic equation of a matrix

1970 ◽  
Vol 5 (3) ◽  
pp. 31-31
Author(s):  
T. A. Bickart
Keyword(s):  
Characteristic Equation

The inverse problem of recovering the coefficients of a differential equations on a graph

2020 ◽  
Vol 28 (5) ◽  
pp. 727-738
Author(s):  
Victor Sadovnichii ◽  
Yaudat Talgatovich Sultanaev ◽  
Azamat Akhtyamov
Keyword(s):  
Inverse Problem ◽  
Inverse Problems ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Finite Number ◽  
Characteristic Equation ◽  
Arbitrary Number ◽  
New Class ◽  
Finite Set

AbstractWe consider a new class of inverse problems on the recovery of the coefficients of differential equations from a finite set of eigenvalues of a boundary value problem with unseparated boundary conditions. A finite number of eigenvalues is possible only for problems in which the roots of the characteristic equation are multiple. The article describes solutions to such a problem for equations of the second, third, and fourth orders on a graph with three, four, and five edges. The inverse problem with an arbitrary number of edges is solved similarly.

scholarly journals Testing Stability of Digital Filters Using Optimization Methods with Phase Analysis

Energies ◽  
2021 ◽  
Vol 14 (5) ◽  
pp. 1488
Author(s):  
Damian Trofimowicz ◽  
Tomasz P. Stefański
Keyword(s):  
Unit Circle ◽  
Phase Analysis ◽  
Characteristic Equation ◽  
Digital Filter ◽  
Digital Filters ◽  
Computing Time ◽  
Complex Function ◽  
Stochastic Methods ◽  
Final Population ◽  
Candidate Regions

In this paper, novel methods for the evaluation of digital-filter stability are investigated. The methods are based on phase analysis of a complex function in the characteristic equation of a digital filter. It allows for evaluating stability when a characteristic equation is not based on a polynomial. The operation of these methods relies on sampling the unit circle on the complex plane and extracting the phase quadrant of a function value for each sample. By calculating function-phase quadrants, regions in the immediate vicinity of unstable roots (i.e., zeros), called candidate regions, are determined. In these regions, both real and imaginary parts of complex-function values change signs. Then, the candidate regions are explored. When the sizes of the candidate regions are reduced below an assumed accuracy, then filter instability is verified with the use of discrete Cauchy’s argument principle. Three different algorithms of the unit-circle sampling are benchmarked, i.e., global complex roots and poles finding (GRPF) algorithm, multimodal genetic algorithm with phase analysis (MGA-WPA), and multimodal particle swarm optimization with phase analysis (MPSO-WPA). The algorithms are compared in four benchmarks for integer- and fractional-order digital filters and systems. Each algorithm demonstrates slightly different properties. GRPF is very fast and efficient; however, it requires an initial number of nodes large enough to detect all the roots. MPSO-WPA prevents missing roots due to the usage of stochastic space exploration by subsequent swarms. MGA-WPA converges very effectively by generating a small number of individuals and by limiting the final population size. The conducted research leads to the conclusion that stochastic methods such as MGA-WPA and MPSO-WPA are more likely to detect system instability, especially when they are run multiple times. If the computing time is not vitally important for a user, MPSO-WPA is the right choice, because it significantly prevents missing roots.

scholarly journals CARACTERIZAÇÃO HIDRÁULICA DO MICROASPERSOR DAN SPRINKLERS GRUPO MODULAR

Irriga ◽  
2001 ◽  
Vol 6 (1) ◽  
pp. 13-18 ◽  
Author(s):  
Marcio Antonio Vilas Boas ◽  
Eurides Kuster Macedo Júnior ◽  
Silvio Cesar Sampaio ◽  
Melânia Inês Valiati
Keyword(s):  
Production Process ◽  
Power Function ◽  
Characteristic Equation ◽  
State University ◽  
The West ◽  
Potential Equation ◽  
Group 2 ◽  
The Relationship

CARACTERIZAÇÃO HIDRÁULICA DO MICROASPERSOR DAN SPRINKLERS GRUPO MODULAR                                     Márcio Antônio Vilas BoasEurides Kuster Macedo JuniorSilvio César SampaioMelânia Inês ValiatiUNIOESTE - Universidade Estadual do Oeste do ParanáCEP: 85814-110 - Cascavel – PR - Brasil - Cx. Postal   711Fone: (045) 225 -2100  (R-249) - Fax : (045) [email protected]  1 RESUMO  Este  trabalho  teve  como  objetivo  avaliar as características hidráulicas  do  microaspersor DAN SPRINKLERS do grupo modular de fabricação da DAN SPRINKLERS - ISRAEL, de uso recente no Oeste do Paraná. Os ensaios foram realizados no Laboratório de Hidráulica do Departamento de Engenharia da Universidade Estadual do Oeste do Paraná – UNIOESTE. Na  avaliação dos microaspersores  estudou-se, a variação decorrente do processo de fabricação e a determinação da equação característica da relação vazão–pressão. Os microaspersores do Grupo modular com diâmetros de bocais 0,94; 1,16;1,41;1,92 e 2,34 mm,  foram submetidos às pressões de 100, 150, 200, 250, 300 e 350 kPa. As equações características determinadas indicaram que o microaspersor testado não é auto-compensante , tolerante a sensibilidade de variações de pressões e que a equação potencial se ajusta bem aos dados. Os coeficientes de variação de fabricação obtidos foram menores que 5%, classificando-se, de acordo com a Norma ISO, como de categoria A. UNITERMOS: Microaspersão, coeficiente de variação, modelo potencial.  VILAS BÔAS, M. A., MACEDO JUNIOR, E. K. HYDRAULIC CHARACTERIZATION OF MICROSPRINKLER DAN SPRINKLER - MODULATE GROUP   2 ABSTRACT This work had as objective to evaluate the characteristics hydraulic of the microsprinklers of the group to modulate of production of DAN SPRINKLERS - ISRAEL, of recent use in the West of Paraná. The tests was accomplished in the Laboratory of Hydraulics of the Department of Engineering of the State University of the West of Paraná - UNIOESTE. In the evaluation of the microasprinklers it was studied such characteristics as, the variation due to the production process and the determination of the characteristic equation of the relationship vazão-pressure. The microsprinklers of the Group to modulate with diameters of nozzle 0,94; 1,16;1,41;1,92 and 2,34 mm, the pressures were submitted 100, 150, 200, 250, 300 and 350 kPa. The certain characteristic equations showed that the tested microsprinklers is not solemnity-compensante and that the potential equation was fit well to the data. The obtained coefficients of production variation were everybody below 5% being able to not this way to classify them in agreement with for ISO  category as A. KEYWORDS: Microsprinkler, coefficient variation, power function.

scholarly journals On the Stability of Collinear Points of the RTBP with Triaxial and Oblate Primaries and Relativistic Effects

2021 ◽  
pp. 56-73
Author(s):  
S. E. Abd El-Bar
Keyword(s):  
Characteristic Equation ◽  
Body Problem ◽  
Equilibrium Points ◽  
Equations Of Motion ◽  
Relativistic Effects ◽  
Three Body Problem ◽  
Total Potential ◽  
The Mean ◽  
The Stability ◽  
Three Body

Under the influence of some different perturbations, we study the stability of collinear equilibrium points of the Restricted Three Body Problem. More precisely, the perturbations due to the triaxiality of the bigger primary and the oblateness of the smaller primary, in addition to the relativistic effects, are considered. Moreover, the total potential and the mean motion of the problem are obtained. The equations of motion are derived and linearized around the collinear points. For studying the stability of these points, the characteristic equation and its partial derivatives are derived. Two real and two imaginary roots of the characteristic equation are deduced from the plotted figures throughout the manuscript. In addition, the instability of the collinear points is stressed. Finally, we compute some selected roots corresponding to the eigenvalues which are based on some selected values of the perturbing parameters in the Tables 1, 2.

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