Weakly harmonic maps from a domain Ω⊂Rd, d≥2 (the upper half-space R+d or bounded C1,α domain, α∈(0,1]) into smooth closed manifold are studied. Prescribing small Dirichlet data in either of the classes L∞(∂Ω) BMO(∂Ω), we establish solvability resulting boundary value problems by means nonvariational method. As by-product, solutions shown to be locally smooth, Cloc∞. Moreover, show that can cho...

The set of periodic points of self-maps of intervals has been studied for different reasons. The functions with smaller sets of periodic points are more likely not to share a periodic point. Of course, one has to decide what “big” or “small” means and how to describe this notion. In this direction one would be interested in studying the size of the sets of periodic points of self-maps of an int...

We study unfrustrated spin Hamiltonians that consist of commuting tensor products of Pauli matrices. Assuming translation-invariance, we observe that the Hamiltonian is described by a map between modules over the translation group algebra, so homological methods are applicable. We show universal properties of topologically ordered phases in low spatial dimensions. Particularly, we prove that in...

Let S be a subset of a normed space X = (X ,‖ · ‖) and T and I self-mappings of X . Then T is called (1) nonexpansive on S if ‖Tx− Ty‖ ≤ ‖x− y‖ for all x, y ∈ S; (2) Inonexpansive on S if ‖Tx − Ty‖ ≤ ‖Ix − I y‖ for all x, y ∈ S; (3) I-contraction on S if there exists k ∈ [0,1) such that ‖Tx − Ty‖ ≤ k‖Ix − I y‖ for all x, y ∈ S. The set of fixed points of T (resp., I) is denoted by F(T) (resp., ...

In this paper, we prove common fixed point theorems for a pair of weakly compatible maps under E.A .property. A major benefit of property (E.A.) is that it ensures convergence of desired sequences without completeness. At the end we rectify the main result of the paper, entitled “Common fixed points for weakly compatible maps, Proc. Indian Acad. Sci. (Math. Sci.) Vol. 111(2001), No. 2, pp 241-247.

Active commuting between home and place of work or study is often cited as an interesting source of physical activity in a public health perspective. However, knowledge about these behaviors is meager. This was therefore studied in adult active commuters (n = 1872) in Greater Stockholm, Sweden, a Nordic metropolitan setting. They received questionnaires and individually adjusted maps to draw th...