In this paper, we show that for any dimension d ≥ 3 there exists a body of constant breadth C, such that its projection onto any 2-plane is non-spherical. We call such a body totally non-spherical. The circumradius of the projection of any totally non-spherical body C of constant breadth onto any 2-plane is bigger than the half diameter of C. Showing the existence of such a body extends results...

Three aspects of texture are considered by the fractal geometry: Fractal Dimension (FD), Lacunarity and Succolarity. Fractal Dimension has been well studied; a great number of approaches have been presented to extract it from images. It can be computed from black-white to multi-band image. There are many approaches also, from the simple Box-Dimension to the most complex Hausdorff Dimension. The...

In this paper we present some new properties of the metric dimension defined by Bouligand in 1928 and prove the following new projection theorem: Let dimb(A − A) denote the Bouligand dimension of the set A − A of differences between elements of A. Given any compact set A ⊆ R such that dimb(A−A) < m, then almost every orthogonal projection P of A of rank m is injective on A and P |A has Lipschit...

The paper deals with an algorithm for Hausdorff dimension estimation based on box-counting dimension calculation. The main goal of the paper is to propose a new approach to box-counting dimension calculation with less computational demands. Streszczenie. W artykule opisano algorytm estymacji wymiaru Hausdorffa oparty o wyznaczanie wymiaru pudełkowego. Głównym celem pracy jest zaproponowanie now...

We prove that among all constant width bodies of revolution, the minimum of the ratio of the volume to the cubed width is attained by the constant width body obtained by rotation of the Reuleaux triangle about an axis of symmetry. 2000 MSC: 52A15 Introduction The width of a convex body B in n-dimensional Euclidean space in the direction ~u is the distance between the two supporting planes of B ...

There seems to be no dimension of bodily awareness that cannot be disrupted. To account for such variety, there is a growing consensus that there are at least two distinct types of body representation that can be impaired, the body schema and the body image. However, the definition of these notions is often unclear. The notion of body image has attracted most controversy because of its lack of ...

The Efimov effect can be induced by means of an external deformed one-body field that effectively reduces the allowed spatial dimensions to less than three. To understand this new mechanism, conceptually and practically, we employ a formulation using non-integer dimension, which is equivalent strength oscillator field. most clearly appears when crucial two-body systems are unbound in three, but...