hyper-tubes consisting of hyper-cubes of n-dimensions were designed and formulas for substructures of vary dimensions established.

It is shown that every fuzzy n-normed space naturally induces a locally convex topology, and that every finite dimensional fuzzy n-normed space is complete.

Linear discriminant analysis (LDA) finds an orientation that projects high dimensional feature vectors to reduced dimensional feature space in such a way that the overlapping between the classes in this feature space is minimum. This overlapping is usually finite and produces finite classification error which is further minimized by rotational LDA technique. This rotational LDA technique rotate...

We consider metric measure spaces satisfing a doubling condition and a Poincaré inequality in the upper gradient sense. We show that the results of [Che99] on differentiability of real valued Lipschitz functions and the resulting bi-Lipschitz nonembedding theorems for finite dimensional vector space targets extend to Banach space targets having what we term a good finite dimensional approximati...

We discuss correspondence between the predictions of quantum theories for rotation angle formulated in infinite and finite dimensional Hilbert spaces, taking as example, the calculation of matrix elements of phaseangular momentum commutator. A new derivation of the matrix elements is presented in infinite space, making use of a unitary transformation that maps from the state space of periodic f...

For a given d-dimensional Minkowski space (finite dimensional Banach space) with unit ball B, one can define the concept of surface area in different ways when d ≥ 3. There exist two well-known definitions of surface area: the Busemann definition and HolmesThompson definition of surface area. The purpose of this paper is to establish lower bounds for the surface area of the unit ball in a d-dim...