Some discussions on equipartition theorem

Some Results on Baer's Theorem

Baer has shown that, for a group G, finiteness of G=Zi(G) implies finiteness of ɣi+1(G). In this paper we will show that the converse is true provided that G=Zi(G) is finitely generated. In particular, when G is a finite nilpotent group we show that |G=Zi(G)| divides |ɣi+1(G)|d′ i(G), where d′i(G) =(d( G /Zi(G)))i.

Some discussions on uncertain measure

This paper will discuss some structural characteristics of uncertain measure. Some new convergence concepts of uncertain sequence are then introduced and the relationships among these convergence concepts are investigated. Finally, several inequalities of uncertain variables are obtained and their applications are discussed.

Some discussions on strong interaction

[Abstract] Using the gauge field model with massive gauge bosons, we could construct a new model to describe the strong interaction. In this new quantum chromodynamics(QCD) model, we will introduce two sets of gluon fields, one set is massive and another set is massless. Correspondingly, there may exists three sets of glueballs which have the same spin-parity but have different masses. A possib...

Generalized equipartition theorem and confining walls

A note on equipartition

The problem of the existence of an equi-partition of a curve in R has recently been raised in the context of computational geometry (see [2] and [3]). The problem is to show that for a (continuous) curve Γ : [0, 1] → R and for any positive integer N , there exist points t0 = 0 < t1 < . . . < tN−1 < 1 = tN , such that d(Γ(ti−1),Γ(ti)) = d(Γ(ti),Γ(ti+1)) for all i = 1, . . . , N , where d is a me...