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...

To a large extent the present work is far from being conclusive, instead, new directions of research in combinatorial extremal theory are started. Also questions concerning generalizations are immediately noticeable. The incentive came from problems in several fields such as Algebra, Geometry, Probability, Information and Complexity Theory. Like several basic combinatorial problems they may pla...

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Using ε-bias spaces over F2, we show that the Remote Point Problem (RPP), introduced by Alon et al [APY09], has an NC algorithm (achieving the same parameters as [APY09]). We study a generalization of the Remote Point Problem to groups: we replace F2 by G n for an arbitrary fixed group G. When G is Abelian we give an NC algorithm for RPP, again using ε-bias spaces. For nonabelian G, we give a d...

At the beginning of every course, it can be expected that several students have some syllabus knowledge. For efficiency in learning systems, and to combat student frustration and boredom, it is important to quickly uncover this latent knowledge. This enables students to begin new learning immediately. In this paper we compare two algorithms used to achieve this goal, both based on the theory of...

We discuss a membrane-based calculus for the combination of conceptual spaces during runtime. Since our goal is to support emergent properties of behavior (and due to the fact that it is not possible to define a complete calculus for all situations) we introduce the notion of self-modification. Terms from situational description can evolve according to simple rules thus providing various possib...