in this paper we introduce the concept of topological number for locally convex topological spaces and prove some of its properties. it gives some criterions to study locally convex topological spaces in a discrete approach.

A subset of a metric space is a k-distance set if there are exactly k non-zero distances occuring between points. We conjecture that a k-distance set in a d-dimensional Banach space (or Minkowski space), contains at most (k+1) points, with equality iff the unit ball is a parallelotope. We solve this conjecture in the affirmative for all 2-dimensional spaces and for spaces where the unit ball is...

The objective of this paper is to develop a set of reliable methods to build confidence sets for the Aumann mean of a random closed set estimated through the Minkowski empirical mean. In order to do so, we introduce a procedure to build a confidence set based on Weil’s result for the Hausdorff distance between the empirical and the Aumann means; then, we introduce another procedure based on the...

Let K be a totally real cyclic number field of degree n that is the product of two distinct primes and such that the class number of the n-th cyclotomic field equals 1. We derive certain necessary and sufficient conditions for the existence of a Minkowski unit for K.

bstract. A comprehensive survey of 48 filters for impulsive noise emoval from color images is presented. The filters are formulated sing a uniform notation and categorized into 8 families. The perforance of these filters is compared on a large set of images that over a variety of domains using three effectiveness and one effiiency criteria. In order to ensure a fair efficiency comparison, a fas...

We introduce a notion of the Euclidean and the Minkowski rank for arbitrary metric spaces and we study their behaviour with respect to products. We show that the Minkowski rank is additive with respect to metric products, while additivity of the Euclidean rank does not hold in general.

In this paper we study properties of sections of convex bodies with respect to the Gaussian measure. We develop a formula connecting the Minkowski functional of a convex symmetric body K with the Gaussian measure of its sections. Using this formula we solve an analog of the Busemann-Petty problem for Gaussian measures.

In this paper we study the impact of Minkowski metric matrix on a projection in the Minkowski Space M along with their basic algebraic and geometric properties.The relation between the m-projections and the Minkowski inverse of a matrix A in the minkowski space M is derived. In the remaining portion commutativity of Minkowski inverse in Minkowski Space M is analyzed in terms of m-projections as...

The spatial structure of the axonal and dendritic arborizations is closely related to the functionality of specific neurons or neuronal subsystems. The present work describes how multiscale Minkowski functionals can be used in order to characterize and compare the spatial organization of these two types of arborizations. The discrimination potential of the method is illustrated with respect to ...

If K is a 0-symmetric, bounded, convex body in the Euclidean n-space R (with a fixed origin O) then it defines a norm whose unit ball is K itself (see [12]). Such a space is called Minkowski normed space. The main results in this topic collected in the survey [16] and [17]. In fact, the norm is a continuous function which is considered (in the geometric terminology as in [12]) as a gauge functi...