A naive introduction of a dependency of the mass of a black hole on the Schwarzschild time coordinate results in singular behavior of curvature invariants at the horizon, violating expectations from complementarity. If instead a temporal dependence is introduced in terms of a coordinate akin to the river time representation, the Ricci scalar is nowhere singular away from the origin. It is found...

The importance of geometric moment (GM) invariants first received research attention when Hu [1] introduced them in his study. As they capture global features have been widely used in applications such as object classification, image and shape analysis and edge detection [2-8]. However, since GMs are non-orthogonal, a set of continuous orthogonal moments including Zernike and Legendre moments w...

For the iterative solution of large sparse linear systems we develop a theory for a family of augmented and deflated Krylov space solvers that are coordinate based in the sense that the given problem is transformed into one that is formulated in terms of the coordinates with respect to the augmented bases of the Krylov subspaces. Except for the augmentation, the basis is as usual generated by a...

The accuracy of stereotaxic coordinates determined using the Leksell apparatus with CT and MRI was investigated using an Agar filled head phantom. Both imaging techniques were found to produce an accuracy of better than 2 mm with the exception of the Z coordinate as measured by CT (2.3 mm). This latter error is greater because of the 3 mm slice width used. Direct coronal views were used to dete...

The holonomy group of a metric g at a point p of a manifold M is the group of all linear transformations in the tangent space of p defined by parallel translation along all possible loops starting at p 1 . It is obvious that a connection can only be the Levi-Civita connection of a metric g if the holonomy group is a subgroup of the generalized orthogonal group corresponding to the signature of ...

We study new separable orthogonally transitive abelian G2 on S2 models with two mutually orthogonal integrable Killing vector fields. For this purpose we consider separability of the metric functions in a coordinate system in which the velocity vector field of the perfect fluid does not take its canonical form, providing thereby solutions which are non-separable in comoving coordinates in gener...

[1] A thermomechanical ice flow model is formulated using the finite volume method. Separate submodels solve the full, two-dimensional momentum equations, the advective-diffusive heat equation, and evolution of the free surface. A unique aspect of the method is the use of a boundary-fitted, orthogonal, curvilinear coordinate system, which simplifies the implementation of boundary conditions, le...

This paper considers the asymptotic distribution of the longest edge of the minimal spanning tree and nearest neighbor graph on X1, . . . ,XNn where X1,X2, . . . are i.i.d. in R 2 with distribution F and Nn is independent of the Xi and satisfies Nn/n→p 1. A new approach based on spatial blocking and a locally orthogonal coordinate system is developed to treat cases for which F has unbounded sup...