A special addition theorem for theta-functions and nonlinear equations

1998 ◽  
Vol 39 (5) ◽  
pp. 973-976
Author(s):  
R. K. Romanovskiî ◽  
S. G. Sadovnichuk
Keyword(s):  
Nonlinear Equations ◽  
Theta Functions ◽  
Addition Theorem

scholarly journals To the theory of synchronization of interacting pendulums oscillating in the parallel planes

2020 ◽  
Vol 20 (1) ◽  
pp. 15-37
Author(s):  
S.O. Gladkov ◽  
◽  
S.B. Bogdanova ◽  
Keyword(s):  
Numerical Solution ◽  
Complex Plane ◽  
Nonlinear Dynamic ◽  
Functional Equations ◽  
Electromagnetic Interaction ◽  
Theta Functions ◽  
Addition Theorem ◽  
Physical Factors ◽  
Motion Equations ◽  
Dynamic Motion

The problem of interacting metal pendulums oscillating in parallel planes, the distance $b$ between the suspension points of which is fixed and equally, has been solved. The principle possibility of their synchronization is provided by taking into account two physical factors: 1. Effect of electromagnetic interaction between them and 2. Accounting for EM radiation of each pendulum, leading to non-linear attenuation. The system of nonlinear dynamic motion equations obtained by a strict mathematical path is analyzed, and their numerical solution is given. The article offers a new method for constructing the pairs of function which are holomorphic on the whole complex plane and satisfy functional equations such as the addition theorem for theta functions.

Recognition of Signals with Application of Nonlinear Equations of Dynamics

1999 ◽  
Vol 31 (12) ◽  
pp. 81-87
Author(s):  
Tatyana I. Aksenova ◽  
Igor V. Tetko
Keyword(s):  
Nonlinear Equations

Solving System of Nonlinear Equations using Genetic Algorithm

2019 ◽  
Vol 10 (4) ◽  
pp. 877-886 ◽  
Author(s):  
Chhavi Mangla ◽  
Musheer Ahmad ◽  
Moin Uddin
Keyword(s):  
Genetic Algorithm ◽  
Nonlinear Equations ◽  
System Of Nonlinear Equations
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