This master’s thesis is concerned with the sequential and parallel implementations of a Discontinuous-Galerkin Solver for the shallow water equations in a newly developed framework using stacks. One of the other main aspects of the thesis is to keep a strong focus on memory efficiency using Sierpinski space-filling curves, which avoid redundant memory to keep the neighborhood information of the...

v. dannon showed that spherical curves in e4 can be given by frenet-like equations, and he thengave an integral characterization for spherical curves in e4 . in this paper, lorentzian spherical timelike andspacelike curves in the space time 41 r are shown to be given by frenet-like equations of timelike andspacelike curves in the euclidean space e3 and the minkowski 3-space 31 r . thus, finding...

We introduce a number of new tools for the study of relatively hyperbolic groups. First, given a relatively hyperbolic group G, we construct a nice combinatorial Gromov hyperbolic model space acted on properly by G, which reflects the relative hyperbolicity of G in many natural ways. Second, we construct two useful bicombings on this space. The first of these, preferred paths, is combinatorial ...

The interesting subsets of a Peano space which were later called the arc-sets or A -sets were defined independently and in a different manner by G. T. Whyburn and the author, and each studied the properties of these sets which have proved so useful in the later theory. The similarity of the properties led shortly to the conjecture that a relation existed between the two definitions, and investi...

We prove that many features of Thurston’s Dehn surgery theory for hyperbolic 3manifolds generalize to Einstein metrics in any dimension. In particular, this gives large, infinite families of new Einstein metrics on compact manifolds.

The symplectomorphism group of a 2-dimensional surface S is homotopy equivalent to the orbit of a filling system of curves on S. We give a generalization of this statement to dimension 4. The filling system of curves is replaced by a decomposition of M into a disjoint union of an isotropic 2-complex L and a disc bundle over a symplectic surface Σ Poincare dual to a multiple of the form. We show...

Efficiently accessing multidimensional data is a challenge for building modern database applications that involve many folds of data such as temporal, spatial, data warehousing, bio-informatics, etc. This problem stems from the fact that multidimensional data have no given order that preserves proximity. The majority of the existing solutions to this problem cannot be easily integrated into the...

Box-counting dimension is one of the most widely used fractal dimensions, because it is relatively easy for empirical estimation. Unfortunately, the task is simple only if one operates on oneor twodimensional data. Otherwise, the amount of computation grows exponentially with the number of space coordinates.A newmethod of estimation of the box-counting dimension of multivariate objects using sp...