In this study, we examine some important subspaces by showing that the set of n-dimensional interval vectors is a quasilinear space. By defining concept dimensions in these spaces, show $n$-dimensional actually $(n_{r},n_{s})$-dimensional space and any $\left( n_{r},0_{s}\right) $-dimensional if only it linear We also give examples $(2_{r},0_{s})$ $(0_{r},2_{s})$-dimensional subspaces. define d...

Casimir forces of massive ferrnionic Dirac fields are calculated for parallel plates geometry in spatial space with dimension d and imposing bag model boundary conditions. It is shown that in the range of ma>>l where m is mass of fields quanta and a is the separation distance of the plates, it is equal to massive bosonic fields Casimir force for each degree of freedom. We argue this equalit...

We show that if the Banach-Mazur distance between an n-dimensional normed space X and l∞ is at most 3/2, then there exist n+ 1 equidistant points in X. By a well-known result of Alon and Milman, this implies that an arbitrary n-dimensional normed space admits at least e √ log n equidistant points, where c > 0 is an absolute constant. We also show that there exist n equidistant points in spaces ...

A norm ‖ · ‖ on R is said to be absolute if ‖(x, y)‖ = ‖(|x|, |y|)‖ for all (x, y) ∈R, and normalized if ‖(, )‖ = ‖(, )‖ = . The set of all absolute normalized norms onR is denoted by AN. Bonsall and Duncan [] showed the following characterization of absolute normalized norms on R. Namely, the set AN of all absolute normalized norms on R is in a one-to-one correspondence with the s...

A variational inequality for the images of k-dimensional hyper-planes under quasiconformal maps of the n-dimensional Euclidean space is proved when 1 ≤ k ≤ n − 2 .

In this paper we evaluate the performance of two reduced resolution filter approaches to data assimilation. The main distinction between these approaches is in the manner they propagate error covariances. Both account for error covariances is a space with dimension m smaller than the model's state vector dimension n. In the first approach the m-dimensional error covariance matrix is interpolate...