We study the decidability problem for metric and layered temporal logics. The logics we consider are suitable to model time granularity in various contexts, and they allow one to build granular temporal models by referring to thènatural scale' in any component of the model and by properly constraining the interactions between diierently-grained components. A monadic second-order language combin...

A remarkable example of a nonempty closed convex set in the Euclidean plane for which the directional derivative of the metric projection mapping fails to exist was constructed by A. Shapiro. In this paper, we revisit and modify that construction to obtain a convex set with C boundary which possesses the same property.

We show how to make precise the vague idea that for compact metric spaces that are close together for Gromov– Hausdorff distance, suitable vector bundles on one metric space will have counterpart vector bundles on the other. Our approach employs the Lipschitz constants of projection-valued functions that determine vector bundles. We develop some computational techniques, and we illustrate our i...

We give an account on Otto’s geometrical heuristics for realizing, on a compact Riemannian manifold M , the L Wasserstein distance restricted to smooth positive probability measures, as a Riemannian distance. The Hilbertian metric discovered by Otto is obtained as the base metric of a Riemannian submersion with total space, the group of diffeomorphisms of M equipped with the Arnol’d metric, and...

We study the decidability problem for metric and layered temporal logics. The logics we consider are suitable to model time granularity in various contexts, and they allow one to build granular temporal models by referring to thènatural scale' in any component of the model and by properly constraining the interactions between diierently-grained components. A monadic second-order language combin...

We produce new examples of harmonic maps, having as either source or target manifold the tangent bundle TM on a Riemannian manifold (M,g), equipped with a Riemannian g-natural metric G. In particular, we study the harmonicity of the canonical projection π : (TM,G)→ (M,g), and of the identity map (TM,G)→ (TM,gS) and conversely, gS being the Sasaki metric on TM. A corresponding study is made for ...

— In this paper, we propose a distributed algorithm to solve planar minimum time multi-vehicle rendezvous problem with non-identical velocity constraints on cyclic di-graph (topology). Motivated by the cyclic alternating projection method that can compute a point's projection on the intersection of some convex sets, we transform the minimum time rendezvous problem into finding the distance betw...

In this article, we present some results concerning the harmonicity on tangent bundle equipped with vertical rescaled metric. We establish necessary and sufficient conditions under which a vector field is harmonic respect to metric construct examples of fields. also study along map between Riemannian manifolds, target manifold its bundle. Next discuss composition projection from into another ma...

Tissot indicatrices have provided visual measures of local area and isotropy distortions. Here we show how large scale distortions of flexion (bending) and skewness (lopsidedness) can be measured. Area and isotropy distortions depend on the map projection metric, flexion and skewness, which manifest themselves on continental scales, depend on the first derivatives of the metric. We introduce ne...

In our earlier work [1, 2], we developed a robust detector for multipath constrained environments when the transmitted signal is known. In this paper, we extend these results to the case where the transmitted signal is a random process. The approach in [1, 2] is to replace the orthogonal projection on the multipath signal subspace S by the orthogonal projection on a representation subspace G, s...