Some of the proofs for results from the previous sections also work in higher dimensions. For example, if z lies in a Siegel domain of f (a domain where the action of f is holomorphically conjugate to a rotation) then f has a local time average near…

Consider the bimolecular mass action system (10), which we repeat here for convenience.

The purpose of this appendix is to illustrate the geometric origin of the transition behavior of the J-Bessel function, by recalling the derivation of the Petersson trace formula as a relative trace formula following [KL06]. Let G=PSL(2,R), and Γ=PS…

Let F be a p-adic field. Throughout this section we assume p≠2,3. Let R be the ring of integers of F, ϖ a uniformizer, k the residue field, and q its cardinality. Write v:F×→Z for the additive valuation such that v(ϖ)=1. Let G=GL3(F), K=GL3(R), and …

The simplest immigration process assumes that the space–time point process giving the arrival times and locations of the immigrants is a Poisson process. Assuming temporal homogeneity, immigration is introduced by adding the generator of a space–tim…

In this section, we complete the proofs of the results stated in the Introduction.

Let A⊂C(E)×C(E) with D(A) dense in C(E), and assume that there exist solutions of the martingale problem for A with sample paths in DE[0,∞) for all initial distributions ν∈P(E).

As we showed in Example 3.1 and Example 3.2, strong endotacticity is not a sufficient condition for positive recurrence of the associated Markov model introduced in section 2.4. Thus, in this section we provide additional network conditions for stro…

In this paper, we study the inverse problem of diffuse optical tomography to reconstruct the scattering coefficient. Partial and noisy data is assumed, and hence a Bayesian formulation of inversion is natural. Two forward models are described, one e…

It is well known that, for a fixed n, the rencontre numbers r(n,k) can be calculated using permanents. Specifically, let Jn be the all 1s matrix of order n, and let In be the identity matrix of order n. Then