Add to ORKGConsider the potential generated by finitely many positive charges in 3-space: u(x) = n∑ k=1 ak |x − xk|, ak> 0. A point x is an equilibrium point if grad u(x) = 0. Question 1. Is the set of equilibrium points always finite? (It can be infinite if we allow charges ak of different signs). Question 2. If the set of equilibrium points is finite, how many points can it contain? The answer to question 2 is unknown even if there are three points and all ak = 1. J. C. Maxwell stated without proof that the number of equilibrium points is at most (n − 1)2. This gives 4 for n = 3 which would be bes
Includes bibliographical references (pages 38-39).This thesis studies optimal distribution of N poin...
This talk has two parts. Initially, I will present a survey of various minimal energy problems in po...
SummaryThe paper deals with equilibrium distributions of n electrons (point charges −1) on plane con...
We discuss the problem of finding an upper bound for the number of equilibrium points of a potential...
To Vladimir Igorevich Arnold who taught us to study classics Abstract. We discuss the problem of fin...
This paper deals with approximating an upper bound for the number of equilibrium points of a potenti...
For an infinite discrete set of point masses in space, is it always true that the force created by t...
In this work, we study the properties of electric (or electrostatic) potentials and fields generated...
We study equilibrium configurations of infinitely many identical particles on the real line or finit...
In this paper, we consider the electrostatic Born-Infeld model [Figure presented] where ρ is a charg...
Abstract. In dynamical system theory the determination of the equilibrium points often requires the ...
We study the critical points of Coulomb energy considered as a function on configuration spaces asso...
The existence of equilibriu:m points in finite ga:me s, as formulated by von Neu:mann and Morgenster...
The electrostatic properties of uniformly charged regular bodies are prominently discussed on colleg...
A collection of point charges cannot be maintained in a stable stationary equilibrium configuration ...
Includes bibliographical references (pages 38-39).This thesis studies optimal distribution of N poin...
This talk has two parts. Initially, I will present a survey of various minimal energy problems in po...
SummaryThe paper deals with equilibrium distributions of n electrons (point charges −1) on plane con...
We discuss the problem of finding an upper bound for the number of equilibrium points of a potential...
To Vladimir Igorevich Arnold who taught us to study classics Abstract. We discuss the problem of fin...
This paper deals with approximating an upper bound for the number of equilibrium points of a potenti...
For an infinite discrete set of point masses in space, is it always true that the force created by t...
In this work, we study the properties of electric (or electrostatic) potentials and fields generated...
We study equilibrium configurations of infinitely many identical particles on the real line or finit...
In this paper, we consider the electrostatic Born-Infeld model [Figure presented] where ρ is a charg...
Abstract. In dynamical system theory the determination of the equilibrium points often requires the ...
We study the critical points of Coulomb energy considered as a function on configuration spaces asso...
The existence of equilibriu:m points in finite ga:me s, as formulated by von Neu:mann and Morgenster...
The electrostatic properties of uniformly charged regular bodies are prominently discussed on colleg...
A collection of point charges cannot be maintained in a stable stationary equilibrium configuration ...
Includes bibliographical references (pages 38-39).This thesis studies optimal distribution of N poin...
This talk has two parts. Initially, I will present a survey of various minimal energy problems in po...
SummaryThe paper deals with equilibrium distributions of n electrons (point charges −1) on plane con...