The eg-orbital states with complex coefficients of the linear combination of x2 − y2 and 3z2 − r2 are studied for the ferromagnetic state in doped manganites. Especially the focus is put on the competition among uniform complex, staggered complex, and real orbital states. As the hole-doping x increases, the real, the canted complex, and the staggered complex orbital states appears successively....

Despite the promise of low-dimensional manifold models for image processing, computer vision, and machine learning tasks, their utility has been hamstrung in practice by two fundamental challenges. First, practical image manifolds are non-isometric to their underlying parameter space, while the state-of-the-art manifold modeling and learning frameworks assume isometry. Second, practical image m...

In this paper, we use Riemann geometry to develop a general framework for the characterization of and mapping between color spaces. Within this framework we show how to construct maps, so-called isometries, between two color spaces that preserve color differences. We illustrate applications of this framework by constructing a uniform color space and developing algorithms for color reproduction ...

Let T be a measure-preserving transformation acting on a probability space (a, Sr, P). This T induces a linear isometry V on &(a, F, P) defined by V(f) = f o T. The analysis of T by using properties of V is referred to as spectral analysis. It is often profitable to consider the action of V on certain closed linear invariant subspaces 9 of L,(O, ST, P). In this note we make the following assump...