"Properties of the Triangle" in the Argand Diagram

1948 ◽  
Vol 32 (299) ◽  
pp. 59
Author(s):  
T. W. Chaundy
Keyword(s):  
Argand Diagram

On Graeffe's Method for Complex Roots of Algebraic Equations

1924 ◽  
Vol 22 (2) ◽  
pp. 83-87 ◽  
Author(s):  
S. Brodetsky ◽  
G. Smeal
Keyword(s):  
Nineteenth Century ◽  
Real Axis ◽  
Practical Method ◽  
Algebraic Equations ◽  
Argand Diagram ◽  
Considerable Difficulty ◽  
The Real ◽  
Real Roots ◽  
Bipolar Coordinates ◽  
Complex Roots

The only really useful practical method for solving numerical algebraic equations of higher orders, possessing complex roots, is that devised by C. H. Graeffe early in the nineteenth century. When an equation with real coefficients has only one or two pairs of complex roots, the Graeffe process leads to the evaluation of these roots without great labour. If, however, the equation has a number of pairs of complex roots there is considerable difficulty in completing the solution: the moduli of the roots are found easily, but the evaluation of the arguments often leads to long and wearisome calculations. The best method that has yet been suggested for overcoming this difficulty is that by C. Runge (Praxis der Gleichungen, Sammlung Schubert). It consists in making a change in the origin of the Argand diagram by shifting it to some other point on the real axis of the original Argand plane. The new moduli and the old moduli of the complex roots can then be used as bipolar coordinates for deducing the complex roots completely: this also checks the real roots.

Argand-diagram representation of transition amplitudes for resonant reactive scattering: e+HCl and e+H2

1989 ◽  
Vol 39 (1) ◽  
pp. 391-394 ◽  
Author(s):  
C. K. Lutrus ◽  
S. H. Suck Salk
Keyword(s):  
Reactive Scattering ◽  
Argand Diagram ◽  
Transition Amplitudes ◽  
Diagram Representation

THE ARGAND DIAGRAM

1966 ◽  
pp. 179-197
Author(s):  
K.S. SNELL ◽  
J.B. MORGAN
Keyword(s):  
Argand Diagram

41. Convergence on the Argand diagram

1959 ◽  
Vol 43 (345) ◽  
pp. 205-207
Author(s):  
L. W. H. Hull
Keyword(s):  
Argand Diagram

New experimental characterization of a resonance: Identification of the mode number using the Argand diagram and the GTD approach

1998 ◽  
Vol 103 (5) ◽  
pp. 2902-2902
Author(s):  
Serge Derible ◽  
Jean‐Marc Conoir ◽  
Jean‐Louis Izbicki ◽  
Pascal Rembert
Keyword(s):  
Mode Number ◽  
Experimental Characterization ◽  
Argand Diagram

Strophoidal Argand diagram and the distribution of relaxation times inK1−xLixTaO3

1993 ◽  
Vol 70 (1) ◽  
pp. 96-99 ◽  
Author(s):  
P. Doussineau ◽  
Y. Farssi ◽  
C. Frénois ◽  
A. Levelut ◽  
K. McEnaney ◽  
...  
Keyword(s):  
Relaxation Times ◽  
Argand Diagram

Applications of Complex Numbers to Geometry

1932 ◽  
Vol 25 (4) ◽  
pp. 215-226
Author(s):  
Allen A. Shaw
Keyword(s):  
Complex Variable ◽  
Geometric Reasoning ◽  
Present Writer ◽  
Complex Numbers ◽  
Two Dimensional ◽  
Single Variable ◽  
Argand Diagram

Introduction. It was with a real pleasure that the present writer read the two excellent articles by Professors L. L. Smail and A. A. Schelkunoff on geometric applications of the complex variable.1 Both papers are important for the doctrine they expound and for the good training they give the reader in rigorous geometric reasoning on the Argand diagram. While Smail prefers the use of the complex variable in the two-dimensional form, x+iy, Schelkunoff employs and recommends the usage of the single variable z to prove the same theorems and obtains very simple and elegant demonstrations.

Argand-diagram analysis of the pomeron coupling to theN and $$\bar K\mathcal{N}$$ systemsystem

1971 ◽  
Vol 1 (10) ◽  
pp. 409-415 ◽  
Author(s):  
W. Hogan ◽  
Y. Srivastava ◽  
M. Restignoli ◽  
G. Violini
Keyword(s):  
Argand Diagram ◽  
Pomeron Coupling ◽  
Diagram Analysis

Argand Diagram

2005 ◽  
Keyword(s):  
Argand Diagram

Axial Leakage Flow-Induced Vibration of the Elastic Rod as the Axisymmetric Continuous Flexible Beam

2001 ◽  
Vol 123 (4) ◽  
pp. 421-428 ◽  
Author(s):  
Katsuhisa Fujita ◽  
Atsuhiko Shintani
Keyword(s):  
Rigid Bodies ◽  
Flexible Body ◽  
Flexible Beam ◽  
Leakage Flow ◽  
Root Locus ◽  
Argand Diagram ◽  
Elastic Rod ◽  
Flow Induced Vibration ◽  
Critical Flow Velocity ◽  
Evaluation Methodologies

The evaluation methodologies for the flow-induced vibration instability of a long flexible rod due to axial leakage-flow are reported. In the previous papers, the axisymmetric rods are regarded as rigid bodies, not as continuous bodies. In this paper, we deal with the rod as a continuous flexible body. The equations for the fluid and the structure are coupled analytically and the added mass, added damping, and added stiffness are derived by considering unsteady pressure acting on the rod. The relation between the axial velocity and the unstable phenomena is clarified. Concerning the critical flow velocity, the root locus (Argand diagram) is shown. We compared our results with the experimental results which one of the authors reported before.

Sign in / Sign up

Export Citation Format

Share Document