In this paper we will show that any complete manifold of nonnegative curvature has a flat soul provided it has curvature going to zero at infinity. We also show some similar results about manifolds with bounded curvature at infinity. To establish these theorems we will prove some rigidity results for Riemannian submersions, eg., any Riemannian submersion with complete flat total space and compa...

Rigidity theory enables us to specify the conditions of unique localizability in the cooperative localization problem of wireless sensor networks. This paper presents a combinatorial rigidity approach to measure (i) generic rigidity and (ii) generalized redundant rigidity properties of graph structures through graph invariants for the localization problem in wireless sensor networks. We define ...

We study the non-rigidity of Euclidean t-designs, namely we study when Euclidean designs (in particular certain tight Euclidean designs) can be deformed keeping the property of being Euclidean t-designs. We show that certain tight Euclidean t-designs are non-rigid, and in fact satisfy a stronger form of non-rigidity which we call strong non-rigidity. This shows that there are plenty of non-isom...

The present paper deals with the generation of Love waves in a layer of finite thickness over an initially stressed heterogeneous semi-infinite media. The rigidity and density of the layer are functions of temperature, i.e. they are temperature dependent.  The lower substratum is an initially stressed medium and its rigidity and density vary linearly with the depth. The frequency relation of Lo...