In this report, we give a brief survey of various results relating the Teaching Dimension and VC-Dimension. The concept of Teaching Dimension was first introduced by Goldman and Kearns, 1995 and Sinohara and Miyano, 1991. In this model, an algorithm tries to learn the hidden concept c from examples, called the teaching set, which uniquely identifies c from the rest of the concepts in the concep...

‎In this essay we introduce and study the notion of dimension for observers via Caratheodory structures and relative probability measures‎. ‎We show that the dimension as a three variables function is an increasing function on observers‎, ‎and decreasing function on the cuts of an observer‎. ‎We find observers with arbitrary non-negative dimensions‎. ‎We show that Caratheodory dimension for obs...

Using a system of axioms among with a modified definition of boundary on the basis of the intuitionistic fuzzy sets, we formulate an inductive structure for the dimension of fuzzy spaces which has been defined by Coker. This new definition of boundary allows to characterize an intuitionistic fuzzy clopen set as a set with zero boundary. Also, some critical properties and applications are establ...

We introduce a new measure for capital market efficiency. The measure takes into consideration the correlation structure of the returns (long-term memory), local herding behavior (information dimension) and uncertainty in the process (entropy). The efficiency measure is then taken as a distance from an ideal efficient market situation. Methodology is applied to a portfolio of 41 stock indices. ...

in this paper we investigate the algebraic properties of dimension of fuzzy hypervector spaces. also, we prove that two isomorphic fuzzy hypervector spaces have the same dimension.

we define and studyco-noetherian dimension of rings for which the injective envelopeof simple modules have finite krull-dimension. this  is a moritainvariant dimension that measures how far the ring is from beingco-noetherian. the co-noetherian dimension of certain rings,including commutative rings, are determined. it is shown that the class ${mathcal w}_n$ of rings with co-noetherian dimension...

In this study, two-dimensional finite element modeling was used to study the simultaneous effect of the cell shape and regular cell distribution on the anisotropy of the elastic properties of 316L stainless steel foam. In this way, the uniaxial compressive stress-strain curve was predicted using a geometric model and fully solid 316L stainless steel. The results showed that the elastic tangent ...