Let Fn be a free group of rank n and F n the quotient group of Fn by the subgroup [Γn(3),Γn(3)][[Γn(2),Γn(2)],Γn(2)] where Γn(k) denotes the k-th subgroup of the lower central series of the free group Fn. In this paper, we determine the group structure of the graded quotients of the lower central series of the group F n by using a generalized Chen’s integration in free groups. Then we apply it ...

abstract the aim of this paper is to investigate annual and seasonal precipitation trends of some selective meteorological stations of central region in iran using non-parametric methods. two non-parametric methods including mann-kendall and sen's estimator slope methods were used here to analyze the seasonal and annual trends of precipitation data. some 48 meteorological stations in centr...

Suppose that f = ∑ n≥1 an(f)q n is a cusp form of weight 2k (k ∈ N). We denote by L(f, s) the L-function of f . For Re(s) sufficiently large, the value of L(f, s) is given by L(f, s) = ∑ n≥1 an(f) ns , and one can show that L(f, s) has analytic continuation to the entire complex plane. The value of L(f, s) at s = k will be of particular interest to us, and we will refer to this value as the cen...

We prove that every term of the lower central series and Johnson filtrations Torelli subgroups mapping class group automorphism a free is finitely generated in linear stable range. This was originally proved for second terms by Ershov He.

We define the stability of a subgroup under a class of maps, and establish the basic properties of this notion. Loosely speaking, we will say that a normal subgroup, or more generally a normal series {An} of a group A, is stable under a class of homomorphisms H if whenever f : A → B lies in H, we have that f(a) ∈ Bn if and only if a ∈ An. This translates to saying that each element of H induces...