We show that the loop spaces on real projective spaces are topologically approximated by the spaces of rational maps RP → RP. As a byproduct of our constructions we obtain an interpretation of the Kronecker characteristic (degree) of an ornament via particle spaces.

Online social platforms are beset with hateful speech content that expresses hatred for a person or group of people. Such content can frighten, intimidate, or silence platform users, and some of it can inspire other users to commit violence. Despite widespread recognition of the problems posed by such content, reliable solutions even for detecting hateful speech are lacking. In the present work...

We define a general notion of single-peaked preferences based on abstract betweenness relations. Special cases are the classical example of single-peaked preferences on a line, the separable preferences on the hypercube, the “multi-dimensionally singlepeaked” preferences on the product of lines, but also the unrestricted preference domain. Generalizing and unifying the existing literature, we s...

Good governance is based on recognition of the interests of all stakeholders and inclusion of their interests where possible. Interests can be expressed in a variety of ways, for example: sovereignty, jurisdiction, administration, ownership (title), lease, license, permit, quota, customary rights, aboriginal rights, collective rights, community rights, littoral rights, public rights, rights of ...

We introduce potential spaces on fractal metric spaces, investigate their embedding theorems, and derive various Besov spaces. Our starting point is that there exists a local, stochastically complete heat kernel satisfying a two-sided estimate on the fractal considered. The results of this paper are among the marvelous consequences of the heat kernel on the fractal.

in this paper, we obtain the general solution and the generalized  hyers--ulam--rassias stability in random normed spaces, in non-archimedean spacesand also in $p$-banach spaces and finally the stability viafixed point method for a functional equationbegin{align*}&d_f(x_{1},.., x_{m}):= sum^{m}_{k=2}(sum^{k}_{i_{1}=2}sum^{k+1}_{i_{2}=i_{1}+1}... sum^{m}_{i_{m-k+1}=i_{m-k}+1}) f(sum^{m}_{i=1...

The main purpose with this paper is to describe how a psychologically motivated conceptual space can be obtained with MDS (multidimensional scaling) and how it can be expressed in terms of a more primitive “physical” (or mathematical) one. The idea is demonstrated practically with the aid of two experimental pilot studies. The paper is concluded by a critical discussion of the method used.

THISARTICLE FOCUSES ON THE RELATIONSHIP between people and the spaces that they inhabit on a college campus. A folkloristic approach to the study of space examines the way people shape space through their practices and the way space shapes people's practices. People shape space through the way they organize physical objects in their environment, the way they talk in spaces they inhabit, and the...