Busemann Functions for the N-Body Problem

the algorithm for solving the inverse numerical range problem

برد عددی ماتریس مربعی a را با w(a) نشان داده و به این صورت تعریف می کنیم w(a)={x8ax:x ?s1} ، که در آن s1 گوی واحد است. در سال 2009، راسل کاردن مساله برد عددی معکوس را به این صورت مطرح کرده است : برای نقطه z?w(a)، بردار x?s1 را به گونه ای می یابیم که z=x*ax، در این پایان نامه ، الگوریتمی برای حل مساله برد عددی معکوس ارانه می دهیم.

The N-body Problem

2 1 Ju n 20 04 THE BUSEMANN - PETTY PROBLEM FOR ARBITRARY MEASURES

Abstract. The aim of this paper is to study properties of sections of convex bodies with respect to different types of measures. We present a formula connecting the Minkowski functional of a convex symmetric body K with the measure of its sections. We apply this formula to study properties of general measures most of which were known before only in the case of the standard Lebesgue measure. We ...

The Generalized Busemann-petty Problem with Weights

This question is known as the generalized Busemann-Petty problem. For i = n − 1, the problem was posed by Busemann and Petty [2] in 1956. It has a long history, and the answer is affirmative if and only if n ≤ 4; see [3], [8], [11]. For the generalized Busemann-Petty problem the following statements are known. If i = 2, n = 4, an affirmative answer follows from that in the case i = n − 1. If 3 ...

New orbits for the n-body problem.

In this paper, we consider minimizing the action functional as a method for numerically discovering periodic solutions to the n-body problem. With this method, we can find a large number of choreographies and other more general solutions. We show that most of the solutions found, including all but one of the choreographies, are unstable. It appears to be much easier to find unstable solutions t...