(2.10) This integral formula proves by induction that (mathit{Li}_{n} z,q)) has an analytic continuation on (mathbb {C}-[1, infty)). Moreover, for (|z|<1), we have mathit{Li}_{n} z,q =sum_{k=1}^{infty}frac{z^{k}}{k^{n} 1-q^{k})} 1-q^{k}onverges absolutely for (|z| < 1) and defines a germ of a holomorphic function in the neighborhood of the origin.
We employ the terms "soma" and "germ" to represent the functions of within-group growth and dispersal leading to the founding of new groups, respectively.
For example, the algebra of germs of holomorphic functions at the origin in is a complex local algebra whose maximal ideal consists of all germs vanishing at 0. Clearly, every element of is the sum of the germ of a constant function and a germ vanishing at the origin.
Finally we present three examples, one is the algebra of germs of holomorphic functions in zero, the second related to Dirichlet series and the third in the setting of non-commutative stochastic distributions.
Uniqueness theorems allow us to choose (mathcal {F}) as the sheaf of germs of holomorphic functions with values in the Grassmann algebra (Lambda := wedge mathfrak {g}_1^*).
To gain a general picture of the functions of the 157 genes with the highest expression in the germ line, as well as the functions of all 4699 genes with SAGE tags in the germline library, genes were annotated with KOG (eu karyotic orthologous groups) descriptions and classified into KOG categories and sub-categories (Additional file 2; Figure 3a) [ 28, 29].
Despite the fundamental commonality of germ cell function in animals, the molecular mechanisms underlying germ cell specification are remarkably diverse across different taxa (Extavour and Akam, 2003; Extavour, 2007; Ewen-Campen et al., 2010; Juliano et al., 2010).
In particular, this holds if E is isomorphic to the space of tempered distributions S′ or to the space of germs of holomorphic functions over a one-point set H {0}).
