Primitive harmonic maps of finite type from a Riemann surface M into a k-symmetric space G/H are obtained by integrating a pair of commuting Hamiltonian vector fields on certain finite-dimensional subspaces of loop algebras. We will clarify and generalize Ohnita and Udagawa’s results concerning homogeneous projections p : G/H →G/K , with H ⊂ K , preserving finite-type property for primitive har...

The following conjecture generalizing the Contraction Mapping Theorem was made by Stein in [9]: Let (X, ρ) be a complete metric space and let F = {T1, . . . , Tn} be a finite family of self-maps of X. Suppose there is a constant γ ∈ (0, 1) such that for any x, y ∈ X there exists T ∈ F with ρ(T (x), T (y)) ≤ γρ(x, y). Then some composition of members of F has a fixed point. In this paper we disp...

This paper presents a common fixed point theorem for a family of R-weakly commuting mappings satisfying nonlinear type contractive conditions. This result improves and unifies previous results due to O’Regan and Saadati [D. O’Regan, R. Saadati, Nonlinear contraction theorems in probabilistic spaces, Appl. Math. Comput. 195 (2008) 86–93]. Also, the following results will be probabilistic version...

"This paper analyses whether the basic monocentric model of urban structure and commuting explains actual commuting in Europe, i.e. The Netherlands. As in the USA much wasteful commuting is established. The basic model has a low degree of explanatory power. In order to get more in line with actual commuting, the paper elaborates two alternatives to the basic model. Besides a deconcentrated mode...

We study integration over functions on superspaces. These functions are invariant under a transformation which maps the whole superspace onto the part of the superspace which only comprises purely commuting variables. We get a compact expression for the differential operator with respect to the commuting variables which results from Berezin integration over all Grassmann variables. Also, we der...