Consider the space of two-dimensional vector functions whose components and curl are square integrable with respect to the degenerate weight given by the radial variable. This space arises naturally when modeling electromagnetic problems under axial symmetry and performing a dimension reduction via cylindrical coordinates. We prove that if the original three-dimensional domain is convex then th...

Traditional visualization techniques for multidimensional data sets, such as parallel coordinates, star glyphs, and scatterplot matrices, do not scale well to high dimensional data sets. A common approach to solve this problem is dimensionality reduction. Existing dimensionality reduction techniques, such as Principal Component Analysis, Multidimensional Scaling, and Self Organizing Maps, have ...

The one-dimensional shallow water equations in Eulerian coordinates are considered. Relations between symmetries and conservation laws for the potential form of equations, shown. An invariant difference scheme with arbitrary bottom topography is constructed. It possesses all finite-difference analogues laws. Some topographies require moving meshes coordinates, which stationary mass Lagrangian c...

When a detector sensitive to the target plume IR seeker is used for tracking airborne targets, the seeker tends to follow the target hot point which is a point farther away from the target exhaust and its fuselage. In order to increase the missile effectiveness, it is necessary to modify the guidance law by adding a lead bias command. The resulting guidance is known as target adaptive guidance ...

The metric to the two-dimensional dilaton gravity can be writen in an alternative form, similar to the two-dimensional Schwarzschild metric, and allow us the identification of some quantitiies with those equivalent in the Schwarzschild solution. This new form, howewer, presents a non-physical singularity at the horizon in the same way that in the realistic four dimensional case. We show a proce...