A function and its first two derivatives are estimated by convolutions with well-chosen non-differentiable kernels. The convolutions are in turn approximated by Newton–Cotes integration techniques with the aid of a polynomial interpolation based on an arbitrary finite set of points. Precise numerical results are obtained with far fewer points than that in classic SPH, and error bounds are deriv...

We investigate in detail the electromagnetic fields of a uniformly accelerated charge, order to ascertain whether such charge does ‘emit’ radiation, especially view Poynting flow computed at large distances and taken as an evidence radiation emitted by charge. In this context, certain important aspects need be into account. First foremost is fact that case one cannot ignore velocity fields. Thi...

The New Horizons spacecraft provided near-global observations of Pluto that far exceed the resolution Earth-based datasets. However, most previous analyses focused on encounter hemisphere (i.e., anti-Charon containing Sputnik Planitia). In this work, we summarize and interpret data Pluto's “far side” its non-encounter or alternatively, sub-Charon hemisphere), providing first integrated overview...

A major problem in solving multi-waves inverse problems is the presence of critical points where the collected data completely vanishes. The set of these critical points depend on the choice of the boundary conditions, and can be directly determined from the data itself. To our knowledge, in the most existing stability results, the boundary conditions are assumed to be close to a set of CGO sol...

So far, we discussed clustering algorithms that involve a hard assignment of each datapoint to a cluster, typically based on its proximity to other points in that cluster. However, simply assigning points to the nearest cluster is not always adequate to capture more complex structure. For example, the lecture slides show an example where one cluster is much larger and less dense than another. W...