scholarly journals The Problem of the Existence of a Tree with a Characteristic Vector of Node Vertices

2021 ◽  
Vol 24 (3) ◽  
pp. 474-484
Author(s):  
Ivan Nikolaevich Popov
Keyword(s):  
Inverse Problem ◽  
Characteristic Vector ◽  
Natural Numbers

The paper presents the problem of the existence of a tree with certain numerical characteristics. It is clear that if a tree is given, it is possible to determine the number of node vertices of the tree and leaves, as well as to determine their degrees. Thus, for a tree, you can define a set of pairs whose coordinates are numbers corresponding to the number of node vertices and their degrees. We can form the inverse problem: we give pairs of natural numbers whose second coordinates are greater than 1, and we should determine whether there is at least one tree that the numbers of its node vertices and their degrees coincide with these pairs. The solution to this problem is presented in this paper.

scholarly journals Solution of the Rodriguez Equation in Modeling Volumetric Geometric Accuracy of Multi-Coordinate Systems

2021 ◽  
Vol 248 ◽  
pp. 04004
Author(s):  
M.M. Stebulyanin ◽  
Ya.I. Pimushkin
Keyword(s):  
Inverse Problem ◽  
Numerical Solutions ◽  
Type System ◽  
Coupled System ◽  
Characteristic Vector ◽  
Controlled Systems ◽  
Nonlinear Coupled System ◽  
Volumetric Accuracy ◽  
Mechanical Movement ◽  
Second Order Equations

The article describes the solution to the Rodrigues equation for determining the volumetric accuracy of multi-axis CNC-controlled systems. An algorithm for calculating the position of the axis of a rotary kinematic pair in problems of volumetric accuracy of mechanical motion of a portal-type system with an additional pair of rotation. The algorithm is based on the analytical solution of the Rodrigues equation in the inverse problem of finding the vector of the final rotation of the known modulus from the known initial and final values of the characteristic vector of the rotated rigid body. In contrast to the well-known direct problem, where based on a finite rotation vector known in direction and magnitude, and the initial value of the characteristic vector of a body, its final value is found, the inverse problem of the Rodrigues equation is not that common due to the nonlinearity and need to solve a nonlinear coupled system of second order equations. The results of this work make it possible to expand the dimension of the space of generalized coordinates of the system analyzed for the volumetric accuracy from three to four. This is expected contribute to the development of ultra-precise systems of controlled mechanical movement. The analytical results of this study were verified by comparing with numerical solutions of the inverse problem in Maple.

AN INVERSE PROBLEM IN THE DYNAMICAL REATOR THEORY

1982 ◽  
Vol 2 (1) ◽  
pp. 9-16 ◽  
Author(s):  
Dexing Feng ◽  
Guangtian Zhu
Keyword(s):  
Inverse Problem

REDUCED MODEL OF PLASMA DISCHARGE CONTROL IN TOKAMAK WITH IRON CORE

2020 ◽  
Vol 7 (3) ◽  
pp. 11-22
Author(s):  
VALERY ANDREEV ◽  
◽  
ALEXANDER POPOV
Keyword(s):  
Optimal Control ◽  
Inverse Problem ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Nonlinear Behavior ◽  
Plasma Discharge ◽  
Reduced Model ◽  
Iron Core ◽  
Power Sources ◽  
Real Power

A reduced model has been developed to describe the time evolution of a discharge in an iron core tokamak, taking into account the nonlinear behavior of the ferromagnetic during the discharge. The calculation of the discharge scenario and program regime in the tokamak is formulated as an inverse problem - the optimal control problem. The methods for solving the problem are compared and the analysis of the correctness and stability of the control problem is carried out. A model of “quasi-optimal” control is proposed, which allows one to take into account real power sources. The discharge scenarios are calculated for the T-15 tokamak with an iron core.

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