Consider the Schrödinger equation: $$\mathrm{i}\partial _tu=Hu$$ over $$\mathbb {R}^n$$ , where H is a self-adjoint operator on $$L^2(\mathbb {R}^n)$$ which sum of $$-\Delta $$ and some potential. This paper aims to study observability for above equation, including observable sets time. We mention that measurable subset $$E\subset \mathbb called an set at time $$T>0$$ if there constant $$C>0$$ ...

It is well-known that observability (and, by duality, controllability) of the elliptic wave equation, i.e., with a Riemannian Laplacian, in time $T_0$ almost equivalent to Geometric Control Condition (GCC), which stipulates any geodesic ray meets control set within $T_0$. We show subelliptic setting, GCC never verified, and equations are observable finite time. More precisely, given Laplacian $...

Abstract In this paper we introduce a new observable to measure cosmic shear. We show that if can with good accuracy both the orientation of galaxy and polarisation direction its radio emission, angle between them is sensitive foreground Even signal-to-noise ratio for single measurement expected be rather small, fact all galaxies in given pixel are subject same shear used overcome noise. An add...

In this paper, using the best proximity theorems for an extensionof Brosowski's theorem. We obtain other results on farthest points. Finally, wedene the concept of e- farthest points. We shall prove interesting relationshipbetween the -best approximation and the e-farthest points in normed linearspaces (X; ||.||). If z in W is a e-farthest point from an x in X, then z is also a-best approximati...