We consider definably compact groups in an o-minimal expansion of a real closed field. It is known that to each such group G is associated a natural exact sequence 1→ G00 → G → G/G00 → 1 where G00 is the “infinitesimal subgroup” of G and G/G00 is a compact real Lie group. We show that given a connected open subset U of G/G00 there is a canonical isomorphism between the fundamental group of U an...

Covering behavior refers to the propensity of echinoids (Echinoidea) to lift materials from the surrounding environment onto their aboral surfaces using their tube feet and spines. This behavior has been widely documented in regular echinoids from a variety of well-lit, shallowmarine habitats. Covering behavior in the deep sea, however, is rarely observed, and the functional significance of cov...

This study investigated effects of mature compost on gaseous emissions during composting using pig manure amended with corn stalks. Apart from a control treatment, three treatments were conducted with the addition of 5% (wet weight of raw materials) of mature compost: (a) mixing raw materials with mature compost at the beginning of composting; (b) covering raw materials with mature compost thro...

Given a vector space V and a non-singular quadratic form Q on V , the orthogonal group O(Q) is the subgroup of GL(V ) that preserves Q. The special orthogonal group SO(Q) is given by O(Q) ∩ SL(V ). If Q is the standard inner product on R then SO(Q) is denoted SO(n). This is a connected, compact Lie group. For n > 2, the group is semi-simple. In the case that n is odd, SO(n) corresponds to the D...

In this article, we introduce the concept of co-covering which is the dual of covering concept. Then, we prove several theorems being similar to the theorems that have been de-veloped for the covering concept. For example, we provide the lifting criterion for co-coverings of a topological space X, which helps us to classify them by subgroups of the group of all homeomorphisms of X.

Geometric covering problems are found in application domains such as sensor coverage and repairing of materials. This paper considers covering problems in which a target shape to be covered is specified and a set of covering shapes is supplied. The goal is to find translational positions of the covering shapes that allow them to collectively cover the target. All the shapes are orthotopes (conv...